Rajagopalan, Vidya; Scott, Julia; Habas, Piotr A; Kim, Kio; Rousseau, Francois; Glenn, Orit A; Barkovich, A James; Studholme, Colin
2012-11-01
Tensor based morphometry (TBM) is a powerful approach to analyze local structural changes in brain anatomy. However, conventional scalar TBM methods do not completely capture all direction specific volume changes required to model complex changes such as those during brain growth. In this paper, we describe novel TBM descriptors for studying direction-specific changes in a subject population which can be used in conjunction with scalar TBM to analyze local patterns in directionality of volume change during brain development. We also extend the methodology to provide a new approach to mapping directional asymmetry in deformation tensors associated with the emergence of structural asymmetry in the developing brain. We illustrate the use of these methods by studying developmental patterns in the human fetal brain, in vivo. Results show that fetal brain development exhibits a distinct spatial pattern of anisotropic growth. The most significant changes in the directionality of growth occur in the cortical plate at major sulci. Our analysis also detected directional growth asymmetry in the peri-Sylvian region and the medial frontal lobe of the fetal brain. Copyright © 2012 Elsevier Inc. All rights reserved.
Interactive Volume Rendering of Diffusion Tensor Data
Energy Technology Data Exchange (ETDEWEB)
Hlawitschka, Mario; Weber, Gunther; Anwander, Alfred; Carmichael, Owen; Hamann, Bernd; Scheuermann, Gerik
2007-03-30
As 3D volumetric images of the human body become an increasingly crucial source of information for the diagnosis and treatment of a broad variety of medical conditions, advanced techniques that allow clinicians to efficiently and clearly visualize volumetric images become increasingly important. Interaction has proven to be a key concept in analysis of medical images because static images of 3D data are prone to artifacts and misunderstanding of depth. Furthermore, fading out clinically irrelevant aspects of the image while preserving contextual anatomical landmarks helps medical doctors to focus on important parts of the images without becoming disoriented. Our goal was to develop a tool that unifies interactive manipulation and context preserving visualization of medical images with a special focus on diffusion tensor imaging (DTI) data. At each image voxel, DTI provides a 3 x 3 tensor whose entries represent the 3D statistical properties of water diffusion locally. Water motion that is preferential to specific spatial directions suggests structural organization of the underlying biological tissue; in particular, in the human brain, the naturally occuring diffusion of water in the axon portion of neurons is predominantly anisotropic along the longitudinal direction of the elongated, fiber-like axons [MMM+02]. This property has made DTI an emerging source of information about the structural integrity of axons and axonal connectivity between brain regions, both of which are thought to be disrupted in a broad range of medical disorders including multiple sclerosis, cerebrovascular disease, and autism [Mos02, FCI+01, JLH+99, BGKM+04, BJB+03].
Diffusion tensor imaging for target volume definition in glioblastoma multiforme
Energy Technology Data Exchange (ETDEWEB)
Berberat, Jatta; Remonda, Luca [Cantonal Hospital, Department of Neuro-radiology, Aarau (Switzerland); McNamara, Jane; Rogers, Susanne [Cantonal Hospital, Department of Radiation Oncology, Aarau (Switzerland); Bodis, Stephan [Cantonal Hospital, Department of Radiation Oncology, Aarau (Switzerland); University Hospital, Department of Radiation Oncology, Zurich (Switzerland)
2014-10-15
Diffusion tensor imaging (DTI) is an MR-based technique that may better detect the peritumoural region than MRI. Our aim was to explore the feasibility of using DTI for target volume delineation in glioblastoma patients. MR tensor tracts and maps of the isotropic (p) and anisotropic (q) components of water diffusion were coregistered with CT in 13 glioblastoma patients. An in-house image processing program was used to analyse water diffusion in each voxel of interest in the region of the tumour. Tumour infiltration was mapped according to validated criteria and contralateral normal brain was used as an internal control. A clinical target volume (CTV) was generated based on the T{sub 1}-weighted image obtained using contrast agent (T{sub 1Gd}), tractography and the infiltration map. This was compared to a conventional T{sub 2}-weighted CTV (T{sub 2}-w CTV). Definition of a diffusion-based CTV that included the adjacent white matter tracts proved highly feasible. A statistically significant difference was detected between the DTI-CTV and T{sub 2}-w CTV volumes (p < 0.005, t = 3.480). As the DTI-CTVs were smaller than the T{sub 2}-w CTVs (tumour plus peritumoural oedema), the pq maps were not simply detecting oedema. Compared to the clinical planning target volume (PTV), the DTI-PTV showed a trend towards volume reduction. These diffusion-based volumes were smaller than conventional volumes, yet still included sites of tumour recurrence. Extending the CTV along the abnormal tensor tracts in order to preserve coverage of the likely routes of dissemination, whilst sparing uninvolved brain, is a rational approach to individualising radiotherapy planning for glioblastoma patients. (orig.) [German] Die Diffusions-Tensor-Bildgebung (DTI) ist eine MR-Technik, die dank der Erfassung des peritumoralen Bereichs eine Verbesserung bezueglich MRI bringt. Unser Ziel war die Pruefung der Machbarkeit der Verwendung der DTI fuer die Zielvolumenabgrenzung fuer Patienten mit
Volume illustration of muscle from diffusion tensor images.
Chen, Wei; Yan, Zhicheng; Zhang, Song; Crow, John Allen; Ebert, David S; McLaughlin, Ronald M; Mullins, Katie B; Cooper, Robert; Ding, Zi'ang; Liao, Jun
2009-01-01
Medical illustration has demonstrated its effectiveness to depict salient anatomical features while hiding the irrelevant details. Current solutions are ineffective for visualizing fibrous structures such as muscle, because typical datasets (CT or MRI) do not contain directional details. In this paper, we introduce a new muscle illustration approach that leverages diffusion tensor imaging (DTI) data and example-based texture synthesis techniques. Beginning with a volumetric diffusion tensor image, we reformulate it into a scalar field and an auxiliary guidance vector field to represent the structure and orientation of a muscle bundle. A muscle mask derived from the input diffusion tensor image is used to classify the muscle structure. The guidance vector field is further refined to remove noise and clarify structure. To simulate the internal appearance of the muscle, we propose a new two-dimensional example based solid texture synthesis algorithm that builds a solid texture constrained by the guidance vector field. Illustrating the constructed scalar field and solid texture efficiently highlights the global appearance of the muscle as well as the local shape and structure of the muscle fibers in an illustrative fashion. We have applied the proposed approach to five example datasets (four pig hearts and a pig leg), demonstrating plausible illustration and expressiveness.
'Finite' non-Gaussianities and tensor-scalar ratio in large volume Swiss-cheese compactifications
International Nuclear Information System (INIS)
Misra, Aalok; Shukla, Pramod
2009-01-01
Developing on the ideas of (Section 4 of) [A. Misra, P. Shukla, Moduli stabilization, large-volume dS minimum without anti-D3-branes, (non-)supersymmetric black hole attractors and two-parameter Swiss cheese Calabi-Yau's, Nucl. Phys. B 799 (2008) 165-198, (arXiv: 0707.0105)] and [A. Misra, P. Shukla, Large volume axionic Swiss-cheese inflation, Nucl. Phys. B 800 (2008) 384-400, (arXiv: 0712.1260 [hep-th])] and using the formalisms of [S. Yokoyama, T. Suyama, T. Tanaka, Primordial non-Gaussianity in multi-scalar slow-roll inflation, (arXiv: 0705.3178 [astro-ph]); S. Yokoyama, T. Suyama, T. Tanaka, Primordial non-Gaussianity in multi-scalar inflation, Phys. Rev. D 77 (2008) 083511, (arXiv: 0711.2920 [astro-ph])], after inclusion of perturbative and non-perturbative α' corrections to the Kaehler potential and (D1- and D3-)instanton generated superpotential, we show the possibility of getting finite values for the non-linear parameter f NL while looking for non-Gaussianities in type IIB compactifications on orientifolds of the Swiss cheese Calabi-Yau WCP 4 [1,1,1,6,9] in the L(arge) V(olume) S(cenarios) limit. We show the same in two contexts. First is multi-field slow-roll inflation with D3-instanton contribution coming from a large number of multiple wrappings of a single (Euclidean) D3-brane around the 'small' divisor yielding f NL ∼O(1). The second is when the slow-roll conditions are violated and for the number of the aforementioned D3-instanton wrappings being of O(1) but more than one, yielding f NL ∼O(1). Based on general arguments not specific to our (string-theory) set-up, we argue that requiring curvature perturbations not to grow at horizon crossing and at super-horizon scales, automatically picks out hybrid inflationary scenarios which in our set up can yield f NL ∼O(1) and tensor-scalar ratio of O(10 -2 ). For all our calculations, the world-sheet instanton contributions to the Kaehler potential coming from the non-perturbative α ' corrections
Diffusion tensor imaging correlates with lesion volume in cerebral hemisphere infarctions
International Nuclear Information System (INIS)
Rossi, Maija E; Jason, Eeva; Marchesotti, Silvia; Dastidar, Prasun; Ollikainen, Jyrki; Soimakallio, Seppo
2010-01-01
Both a large lesion volume and abnormalities in diffusion tensor imaging are independently associated with a poor prognosis after cerebral infarctions. Therefore, we assume that they are associated. This study assessed the associations between lesion volumes and diffusion tensor imaging in patients with a right-sided cerebral infarction. The lesion volumes of 33 patients (age 65.9 ± 8.7, 26 males and 7 females) were imaged using computed tomography (CT) in the acute phase (within 3-4 hours) and magnetic resonance imaging (MRI) in the chronic phase (follow-up at 12 months, with a range of 8-27 months). The chronic-phase fractional anisotropy (FA) and mean diffusivity (MD) values were measured at the site of the infarct and selected white matter tracts. Neurological tests in both the acute and chronic phases, and DTI lateralization were assessed with the Wilcoxon signed-rank test. The effects of thrombolytic therapy (n = 10) were assessed with the Mann-Whitney U test. The correlations between the measured parameters were analysed with Spearman's rho correlation. Bonferroni post-hoc correction was used to compensate for the familywise error rate in multiple comparisons. Several MD values in the right hemisphere correlated positively and FA values negatively with the lesion volumes. These correlations included both lesion area and healthy tissue. The results of the mini-mental state examination and the National Institutes of Health Stroke Scale also correlated with the lesion volume. A larger infarct volume is associated with more pronounced tissue modifications in the chronic stage as observed with the MD and FA alterations
Energy Technology Data Exchange (ETDEWEB)
Sato, Kanako; Masutani, Yoshitaka; Watadani, Takeyuki; Nakata, Yasuhiro; Yoshida, Mariko; Abe, Osamu; Ohtomo, Kuni [University of Tokyo, Department of Radiology, Graduate School of Medicine, Bunkyo, Tokyo (Japan); Aoki, Shigeki [Juntendo University, Department of Radiology, Bunkyo, Tokyo (Japan); Iwata, Nobue K.; Terao, Yasuo; Tsuji, Shoji [University of Tokyo, Department of Neurology, Graduate School of Medicine, Bunkyo, Tokyo (Japan)
2010-08-15
The uncinate fasciculus (UF) consists of core fibers connecting the frontal and temporal lobes and is considered to be related to cognitive/behavioral function. Using diffusion tensor tractography, we quantitatively evaluated changes in fractional anisotropy (FA) and the apparent diffusion coefficient (ADC) of the UF by tract-specific analysis to evaluate the damage of the UF in patients with amyotrophic lateral sclerosis (ALS). We obtained diffusion tensor images of 15 patients with ALS and 9 age-matched volunteers. Patients with ALS showed significantly lower mean FA (P = 0.029) compared with controls. No significant difference was seen in mean ADC. The results suggest that damage of the UF in patients with ALS can be quantitatively evaluated with FA. (orig.)
Tensor rank is not multiplicative under the tensor product
Christandl, Matthias; Jensen, Asger Kjærulff; Zuiddam, Jeroen
2017-01-01
The tensor rank of a tensor t is the smallest number r such that t can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an l-tensor. The tensor product of s and t is a (k + l)-tensor. Tensor rank is sub-multiplicative under the tensor product. We revisit the connection between restrictions and degenerations. A result of our study is that tensor rank is not in general multiplicative under the tensor product. This answers a question of Draisma and Saptharishi. Specif...
Specification of volume and dose in radiotherapy
International Nuclear Information System (INIS)
Levernes, S.
1997-01-01
As a result of a questionnaire about dose and volume specifications in radiotherapy in the Nordic countries, a group has been set up to propose common recommendations for these countries. The proposal is partly based on ICRU 50, but with major extensions. These extensions fall into three areas: patient geometry, treatment geometry, and dose specifications. For patient geometry and set-up one need alignment markings and anatomical reference points, the latter can be divided into internal and external reference points. These points are necessary to get relationships between coordinate systems related to patient and to treatment unit. For treatment geometry the main volume will be an anatomical target volume which just encompass the clinical target volume with all its variations and movements. This anatomical volume are the most suitable volume for prescription, optimization and reporting dose. A set-up margin should be added to the beam periphery in beams-eye-view to get the minimum size and shape of the beam. For dose specification the most important parameter for homogeneous dose distributions is the arithmetic mean of dose to the anatomical target volume together with its standard deviation. In addition the dose to the ICRU reference point should be reported for intercomparison, together with minimum and maximum doses or dose volume histograms for the anatomical target volume. (author)
TensorLy: Tensor Learning in Python
Kossaifi, Jean; Panagakis, Yannis; Pantic, Maja
2016-01-01
Tensor methods are gaining increasing traction in machine learning. However, there are scant to no resources available to perform tensor learning and decomposition in Python. To answer this need we developed TensorLy. TensorLy is a state of the art general purpose library for tensor learning.
Yang, Yaling; Nuechterlein, Keith H; Phillips, Owen R; Gutman, Boris; Kurth, Florian; Dinov, Ivo; Thompson, Paul M; Asarnow, Robert F; Toga, Arthur W; Narr, Katherine L
2012-09-01
Structural brain deficits, especially frontotemporal volume reduction and ventricular enlargement, have been repeatedly reported in patients with schizophrenia. However, it remains unclear whether brain structural deformations may be attributable to disease-related or genetic factors. In this study, the structural magnetic resonance imaging data of 48 adult-onset schizophrenia patients, 65 first-degree nonpsychotic relatives of schizophrenia patients, 27 community comparison (CC) probands, and 73 CC relatives were examined using tensor-based morphometry (TBM) to isolate global and localized differences in tissue volume across the entire brain between groups. We found brain tissue contractions most prominently in frontal and temporal regions and expansions in the putamen/pallidum, and lateral and third ventricles in schizophrenia patients when compared with unrelated CC probands. Results were similar, though less prominent when patients were compared with their nonpsychotic relatives. Structural deformations observed in unaffected patient relatives compared to age-similar CC relatives were suggestive of schizophrenia-related genetic liability and were pronounced in the putamen/pallidum and medial temporal regions. Schizophrenia and genetic liability effects for the putamen/pallidum were confirmed by regions-of-interest analysis. In conclusion, TBM findings complement reports of frontal, temporal, and ventricular dysmorphology in schizophrenia and further indicate that putamen/pallidum enlargements, originally linked mainly with medication exposure in early studies, also reflect a genetic predisposition for schizophrenia. Thus, brain deformation profiles revealed in this study may help to clarify the role of specific genetic or environmental risk factors toward altered brain morphology in schizophrenia.
Shukla, Dinesh K.; Keehn, Brandon; Muller, Ralph-Axel
2011-01-01
Background: Previous diffusion tensor imaging (DTI) studies have shown white matter compromise in children and adults with autism spectrum disorder (ASD), which may relate to reduced connectivity and impaired function of distributed networks. However, tract-specific evidence remains limited in ASD. We applied tract-based spatial statistics (TBSS)…
International Nuclear Information System (INIS)
Trivedi, Richa; Gupta, Rakesh K.; Saksena, Sona; Husain, Nuzhat; Srivastava, Savita; Rathore, Ram K.S.; Sarma, Manoj K.; Malik, Gyanendra K.; Das, Vinita; Pradhan, Mandakini; Pandey, Chandra M.; Narayana, Ponnada A.
2009-01-01
In this study, diffusion tensor imaging (DTI) and glial fibrillary acidic protein (GFAP) immunohistochemical analysis in different cortical regions in fetal brains at different gestational age (GA) were performed. DTI was performed on 50 freshly aborted fetal brains with GA ranging from 12 to 42 weeks to compare age-related fractional anisotropy (FA) changes in different cerebral cortical regions that include frontal, parietal, occipital, and temporal lobes at the level of thalami. GFAP immunostaining was performed and the percentage of GFAP-positive areas was quantified. The cortical FA values in the frontal lobe peaked at around 26 weeks of GA, occipital and temporal lobes at around 20 weeks, and parietal lobe at around 23 weeks. A significant, but modest, positive correlation (r=0.31, p=0.02) was observed between cortical FA values and percentage area of GFAP expression in cortical region around the time period during which the migrational events are at its peak, i.e., GA ≤ 28 weeks for frontal cortical region and GA≤22 weeks for rest of the lobes. The DTI-derived FA quantification with its GFAP immunohistologic correlation in cortical regions of the various lobes of the cerebral hemispheres supports region-specific migrational and maturational events in human fetal brain. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Trivedi, Richa; Gupta, Rakesh K.; Saksena, Sona [Sanjay Gandhi Post Graduate Institute of Medical Sciences, Department of Radiodiagnosis, Lucknow, UP (India); Husain, Nuzhat; Srivastava, Savita [CSM Medical University, Department of Pathology, Lucknow (India); Rathore, Ram K.S.; Sarma, Manoj K. [Indian Institute of Technology, Department of Mathematics and Statistics, Kanpur (India); Malik, Gyanendra K. [CSM Medical University, Department of Pediatrics, Lucknow (India); Das, Vinita [CSM Medical University, Department of Obstetrics and Gynecology, Lucknow (India); Pradhan, Mandakini [Sanjay Gandhi Postgraduate Institute of Medical Sciences, Department of Medical Genetics, Lucknow (India); Pandey, Chandra M. [Sanjay Gandhi Postgraduate Institute of Medical Sciences, Department of Biostatistics, Lucknow (India); Narayana, Ponnada A. [University of Texas Medical School at Houston, Department of Diagnostic and Interventional Imaging, Houston, TX (United States)
2009-09-15
In this study, diffusion tensor imaging (DTI) and glial fibrillary acidic protein (GFAP) immunohistochemical analysis in different cortical regions in fetal brains at different gestational age (GA) were performed. DTI was performed on 50 freshly aborted fetal brains with GA ranging from 12 to 42 weeks to compare age-related fractional anisotropy (FA) changes in different cerebral cortical regions that include frontal, parietal, occipital, and temporal lobes at the level of thalami. GFAP immunostaining was performed and the percentage of GFAP-positive areas was quantified. The cortical FA values in the frontal lobe peaked at around 26 weeks of GA, occipital and temporal lobes at around 20 weeks, and parietal lobe at around 23 weeks. A significant, but modest, positive correlation (r=0.31, p=0.02) was observed between cortical FA values and percentage area of GFAP expression in cortical region around the time period during which the migrational events are at its peak, i.e., GA {<=} 28 weeks for frontal cortical region and GA{<=}22 weeks for rest of the lobes. The DTI-derived FA quantification with its GFAP immunohistologic correlation in cortical regions of the various lobes of the cerebral hemispheres supports region-specific migrational and maturational events in human fetal brain. (orig.)
Kamson, David O; Juhász, Csaba; Chugani, Harry T; Jeong, Jeong-Won
2015-04-01
Diffusion tensor imaging (DTI) has expanded our knowledge of corticospinal tract (CST) anatomy and development. However, previous developmental DTI studies assessed the CST as a whole, overlooking potential differences in development of its components related to control of the upper and lower extremities. The present cross-sectional study investigated age-related changes, side and gender differences in streamline volume of the leg- and hand-related segments of the CST in children. DTI data of 31 children (1-14 years; mean age: 6±4 years; 17 girls) with normal conventional MRI were analyzed. Leg- and hand-related CST streamline volumes were quantified separately, using a recently validated novel tractography approach. CST streamline volumes on both sides were compared between genders and correlated with age. Higher absolute streamline volumes were found in the left leg-related CST compared to the right (p=0.001) without a gender effect (p=0.4), whereas no differences were found in the absolute hand-related CST volumes (p>0.4). CST leg-related streamline volumes, normalized to hemispheric white matter volumes, declined with age in the right hemisphere only (R=-.51; p=0.004). Absolute leg-related CST streamline volumes showed similar, but slightly weaker correlations. Hand-related absolute or normalized CST streamline volumes showed no age-related variations on either side. These results suggest differential development of CST segments controlling hand vs. leg movements. Asymmetric volume changes in the lower limb motor pathway may be secondary to gradually strengthening left hemispheric dominance and is consistent with previous data suggesting that footedness is a better predictor of hemispheric lateralization than handedness. Copyright © 2014 The Japanese Society of Child Neurology. Published by Elsevier B.V. All rights reserved.
Schlaffke, Lara; Rehmann, Robert; Froeling, Martijn; Kley, Rudolf; Tegenthoff, Martin; Vorgerd, Matthias; Schmidt-Wilcke, Tobias
2017-10-01
To investigate to what extent inter- and intramuscular variations of diffusion parameters of human calf muscles can be explained by age, gender, muscle location, and body mass index (BMI) in a specific age group (20-35 years). Whole calf muscles of 18 healthy volunteers were evaluated. Magnetic resonance imaging (MRI) was performed using a 3T scanner and a 16-channel Torso XL coil. Diffusion-weighted images were acquired to perform fiber tractography and diffusion tensor imaging (DTI) analysis for each muscle of both legs. Fiber tractography was used to separate seven lower leg muscles. Associations between DTI parameters and confounds were evaluated. All muscles were additionally separated in seven identical segments along the z-axis to evaluate intramuscular differences in diffusion parameters. Fractional anisotropy (FA) and mean diffusivity (MD) were obtained for each muscle with low standard deviations (SDs) (SD FA : 0.01-0.02; SD MD : 0.07-0.14(10 -3 )). We found significant differences in FA values of the tibialis anterior muscle (AT) and extensor digitorum longus (EDL) muscles between men and women for whole muscle FA (two-sample t-tests; AT: P = 0.0014; EDL: P = 0.0004). We showed significant intramuscular differences in diffusion parameters between adjacent segments in most calf muscles (P < 0.001). Whereas muscle insertions showed higher (SD 0.03-0.06) than muscle bellies (SD 0.01-0.03), no relationships between FA or MD with age or BMI were found. Inter- and intramuscular variations in diffusion parameters of the calf were shown, which are not related to age or BMI in this age group. Differences between muscle belly and insertion should be considered when interpreting datasets not including whole muscles. 3 Technical Efficacy: Stage 1 J. Magn. Reson. Imaging 2017;46:1137-1148. © 2017 International Society for Magnetic Resonance in Medicine.
TensorLy: Tensor Learning in Python
Kossaifi, Jean; Panagakis, Yannis; Pantic, Maja
2016-01-01
Tensors are higher-order extensions of matrices. While matrix methods form the cornerstone of machine learning and data analysis, tensor methods have been gaining increasing traction. However, software support for tensor operations is not on the same footing. In order to bridge this gap, we have developed \\emph{TensorLy}, a high-level API for tensor methods and deep tensorized neural networks in Python. TensorLy aims to follow the same standards adopted by the main projects of the Python scie...
Energy Technology Data Exchange (ETDEWEB)
Li, Yi; Chen, Wei; Xu, Hongyi; Jin, Xuejun
2016-01-01
To provide a seamless integration of manufacturing processing simulation and fiber microstructure modeling, two new stochastic 3D microstructure reconstruction methods are proposed for two types of random fiber composites: random short fiber composites, and Sheet Molding Compounds (SMC) chopped fiber composites. A Random Sequential Adsorption (RSA) algorithm is first developed to embed statistical orientation information into 3D RVE reconstruction of random short fiber composites. For the SMC composites, an optimized Voronoi diagram based approach is developed for capturing the substructure features of SMC chopped fiber composites. The proposed methods are distinguished from other reconstruction works by providing a way of integrating statistical information (fiber orientation tensor) obtained from material processing simulation, as well as capturing the multiscale substructures of the SMC composites.
Breckinridge Project, initial effort. Report III, Volume 2. Specifications
Energy Technology Data Exchange (ETDEWEB)
None
1982-01-01
Report III, Volume 2 contains those specifications numbered K through Y, as follows: Specifications for Compressors (K); Specifications for Piping (L); Specifications for Structures (M); Specifications for Insulation (N); Specifications for Electrical (P); Specifications for Concrete (Q); Specifications for Civil (S); Specifications for Welding (W); Specifications for Painting (X); and Specifications for Special (Y). The standard specifications of Bechtel Petroleum Incorporated have been amended as necessary to reflect the specific requirements of the Breckinridge Project and the more stringent specifications of Ashland Synthetic Fuels, Inc. These standard specifications are available for the Initial Effort (Phase Zero) work performed by all contractors and subcontractors.
Baseline design of an OTEC pilot plantship. Volume C. Specifications
Energy Technology Data Exchange (ETDEWEB)
Glosten, L. R.; Bringloe, Thomas; Soracco, Dave; Fenstermacher, Earl; Magura, Donald; Sander, Olof; Richards, Dennis; Seward, Jerry
1979-05-01
Volume C is part of a three-volume report that presents a baseline engineering design of an Ocean Thermal Energy Conversion (OTEC) plantship. This volume provides the specifications for the hull, cold-water pipe, ship outfitting and machinery, OTEC power system, electrical system, and folded-tube heat exchangers.
Meintjes, E M; Narr, K L; van der Kouwe, A J W; Molteno, C D; Pirnia, T; Gutman, B; Woods, R P; Thompson, P M; Jacobson, J L; Jacobson, S W
2014-01-01
Reductions in brain volumes represent a neurobiological signature of fetal alcohol spectrum disorders (FASD). Less clear is how regional brain tissue reductions differ after normalizing for brain size differences linked with FASD and whether these profiles can predict the degree of prenatal exposure to alcohol. To examine associations of regional brain tissue excesses/deficits with degree of prenatal alcohol exposure and diagnosis with and without correction for overall brain volume, tensor-based morphometry (TBM) methods were applied to structural imaging data from a well-characterized, demographically homogeneous sample of children diagnosed with FASD (n = 39, 9.6-11.0 years) and controls (n = 16, 9.5-11.0 years). Degree of prenatal alcohol exposure was significantly associated with regionally pervasive brain tissue reductions in: (1) the thalamus, midbrain, and ventromedial frontal lobe, (2) the superior cerebellum and inferior occipital lobe, (3) the dorsolateral frontal cortex, and (4) the precuneus and superior parietal lobule. When overall brain size was factored out of the analysis on a subject-by-subject basis, no regions showed significant associations with alcohol exposure. FASD diagnosis was associated with a similar deformation pattern, but few of the regions survived FDR correction. In data-driven independent component analyses (ICA) regional brain tissue deformations successfully distinguished individuals based on extent of prenatal alcohol exposure and to a lesser degree, diagnosis. The greater sensitivity of the continuous measure of alcohol exposure compared with the categorical diagnosis across diverse brain regions underscores the dose dependence of these effects. The ICA results illustrate that profiles of brain tissue alterations may be a useful indicator of prenatal alcohol exposure when reliable historical data are not available and facial features are not apparent.
Directory of Open Access Journals (Sweden)
E.M. Meintjes
2014-01-01
Full Text Available Reductions in brain volumes represent a neurobiological signature of fetal alcohol spectrum disorders (FASD. Less clear is how regional brain tissue reductions differ after normalizing for brain size differences linked with FASD and whether these profiles can predict the degree of prenatal exposure to alcohol. To examine associations of regional brain tissue excesses/deficits with degree of prenatal alcohol exposure and diagnosis with and without correction for overall brain volume, tensor-based morphometry (TBM methods were applied to structural imaging data from a well-characterized, demographically homogeneous sample of children diagnosed with FASD (n = 39, 9.6–11.0 years and controls (n = 16, 9.5–11.0 years. Degree of prenatal alcohol exposure was significantly associated with regionally pervasive brain tissue reductions in: (1 the thalamus, midbrain, and ventromedial frontal lobe, (2 the superior cerebellum and inferior occipital lobe, (3 the dorsolateral frontal cortex, and (4 the precuneus and superior parietal lobule. When overall brain size was factored out of the analysis on a subject-by-subject basis, no regions showed significant associations with alcohol exposure. FASD diagnosis was associated with a similar deformation pattern, but few of the regions survived FDR correction. In data-driven independent component analyses (ICA regional brain tissue deformations successfully distinguished individuals based on extent of prenatal alcohol exposure and to a lesser degree, diagnosis. The greater sensitivity of the continuous measure of alcohol exposure compared with the categorical diagnosis across diverse brain regions underscores the dose dependence of these effects. The ICA results illustrate that profiles of brain tissue alterations may be a useful indicator of prenatal alcohol exposure when reliable historical data are not available and facial features are not apparent.
Categorical Tensor Network States
Directory of Open Access Journals (Sweden)
Jacob D. Biamonte
2011-12-01
Full Text Available We examine the use of string diagrams and the mathematics of category theory in the description of quantum states by tensor networks. This approach lead to a unification of several ideas, as well as several results and methods that have not previously appeared in either side of the literature. Our approach enabled the development of a tensor network framework allowing a solution to the quantum decomposition problem which has several appealing features. Specifically, given an n-body quantum state |ψ〉, we present a new and general method to factor |ψ〉 into a tensor network of clearly defined building blocks. We use the solution to expose a previously unknown and large class of quantum states which we prove can be sampled efficiently and exactly. This general framework of categorical tensor network states, where a combination of generic and algebraically defined tensors appear, enhances the theory of tensor network states.
Energy Technology Data Exchange (ETDEWEB)
Yasmin, Hasina; Abe, Osamu; Nakata, Yasuhiro; Hayashi, Naoto; Masutani, Yoshitaka; Goto, Masami; Ohtomo, Kuni [University of Tokyo, Department of Radiology, Bunkyo-ku, Tokyo (Japan); Aoki, Shigeki [Juntendo University, Department of Radiology, Bunkyo-ku, Tokyo (Japan)
2009-12-15
To date, very scant data is available regarding normal diffusion properties of white matter (WM) fibers. The present study aimed to initiate the establishment of a database of normal diffusion tensor metrics of cerebral WM fibers, including the uncinate fasciculus (UF), posterior cingulum (PC), fornix, and corticospinal tract (CST) for healthy adults using tract-specific analysis by diffusion tensor tractography (DTT). We also attempted to clarify whether age and laterality exerted any effects on this study group. DTT of WM fibers were generated for 100 healthy subjects, then mean diffusivity (MD) and fractional anisotropy (FA) of the tracts were measured. Pearson correlation analysis was used to evaluate age relationships. Paired t testing was used to compare hemispheric asymmetry. Interobserver correlation tests were also performed. Our results showed FA values for UF (right, 0.42 {+-} 0.03; left, 0.40{+-}0.03), PC (0.51 {+-} 0.06, 0.52 {+-} 0.06), fornix (0.37 {+-} 0.06, 0.38 {+-} 0.06), CST (0.70 {+-} 0.06, 0.69 {+-} 0.07), and MD values for UF (0.81 {+-} 0.03, 0.82 {+-} 0.04), PC (0.72 {+-} 0.03, 0.72 {+-} 0.04), fornix (1.86 {+-} 0.32, 1.94 {+-} 0.37), and CST (0.72 {+-} 0.03, 0.74 {+-} 0.04). We identified a significant positive correlation between age and MD in the right UF and bilateral fornices, and a negative correlation between age and FA in bilateral fornices. Hemispheric asymmetry was observed in FA of UF (right > left) and MD of CST (left > right). The results constitute a normative dataset for diffusion parameters of four WM tracts that can be used to identify, characterize, and establish the significance of changes in diseases affecting specific tracts. (orig.)
Tensor surgery and tensor rank
M. Christandl (Matthias); J. Zuiddam (Jeroen)
2018-01-01
textabstractWe introduce a method for transforming low-order tensors into higher-order tensors and apply it to tensors defined by graphs and hypergraphs. The transformation proceeds according to a surgery-like procedure that splits vertices, creates and absorbs virtual edges and inserts new vertices
Tensor surgery and tensor rank
M. Christandl (Matthias); J. Zuiddam (Jeroen)
2016-01-01
textabstractWe introduce a method for transforming low-order tensors into higher-order tensors and apply it to tensors defined by graphs and hypergraphs. The transformation proceeds according to a surgery-like procedure that splits vertices, creates and absorbs virtual edges and inserts new
Schlaffke, Lara; Rehmann, Robert; Froeling, Martijn; Kley, Rudolf; Tegenthoff, Martin; Vorgerd, Matthias; Schmidt-Wilcke, Tobias
2017-01-01
Purpose: To investigate to what extent inter- and intramuscular variations of diffusion parameters of human calf muscles can be explained by age, gender, muscle location, and body mass index (BMI) in a specific age group (20-35 years). Materials and Methods: Whole calf muscles of 18 healthy
Maki, Satoshi; Koda, Masao; Saito, Junya; Takahashi, Sho; Inada, Taigo; Kamiya, Koshiro; Ota, Mitsutoshi; Iijima, Yasushi; Masuda, Yoshitada; Matsumoto, Koji; Kojima, Masatoshi; Takahashi, Kazuhisa; Obata, Takayuki; Yamazaki, Masashi; Furuya, Takeo
2016-12-01
Patients with cervical compression myelopathy (CCM) generally present bilateral neurological symptoms in their extremities. However, a substantial portion of patients with CCM exhibit laterality of neurological symptoms. The aim of this study was to assess the correlation between intrinsic structural damage and laterality of symptoms using spinal cord diffusion tensor imaging (DTI) of the corticospinal tract. We enrolled 10 healthy volunteers and 40 patients with CCM in this study. We evaluated motor function using the American Spinal Injury Association (ASIA) motor score for left and right extremities. For DTI acquisitions, a 3.0-T magnetic resonance imaging system with diffusion-weighted spin-echo sequence was used. Regions-of-interest in the lateral column tracts were determined. We determined the correlations between fractional anisotropy (FA) and ASIA motor scores. An FA asymmetry index was calculated using left and right regions-of-interest. Four patients exhibited laterality of symptoms in their extremities, for which left and right ASIA scores correlated moderately with FA in the left and right lateral columns, respectively (left: ρ = 0.64, P laterality of symptoms. Using tract-specific DTI, we demonstrated that microstructural damages in the left and right corticospinal tracts correlated with corresponding neurological symptoms in the ipsilateral side and the FA asymmetry index could indicate laterality in neurological symptoms of patients with CCM. Copyright Â© 2016 Elsevier Inc. All rights reserved.
Visualizing Tensor Normal Distributions at Multiple Levels of Detail.
Abbasloo, Amin; Wiens, Vitalis; Hermann, Max; Schultz, Thomas
2016-01-01
Despite the widely recognized importance of symmetric second order tensor fields in medicine and engineering, the visualization of data uncertainty in tensor fields is still in its infancy. A recently proposed tensorial normal distribution, involving a fourth order covariance tensor, provides a mathematical description of how different aspects of the tensor field, such as trace, anisotropy, or orientation, vary and covary at each point. However, this wealth of information is far too rich for a human analyst to take in at a single glance, and no suitable visualization tools are available. We propose a novel approach that facilitates visual analysis of tensor covariance at multiple levels of detail. We start with a visual abstraction that uses slice views and direct volume rendering to indicate large-scale changes in the covariance structure, and locations with high overall variance. We then provide tools for interactive exploration, making it possible to drill down into different types of variability, such as in shape or orientation. Finally, we allow the analyst to focus on specific locations of the field, and provide tensor glyph animations and overlays that intuitively depict confidence intervals at those points. Our system is demonstrated by investigating the effects of measurement noise on diffusion tensor MRI, and by analyzing two ensembles of stress tensor fields from solid mechanics.
Dose and volume specification for reporting interstitial therapy
International Nuclear Information System (INIS)
1997-01-01
The ICRU has previously published reports dealing with Dose Specification for Reporting External Beam Therapy with Photons and Electrons (ICRU Report 29, ICRU, 1978), Dose Specification for Reporting External Beam Therapy (ICRU Report 50, ICRU, 1993) and Dose and Volume Specification for Reporting Intracavitary Therapy in Gynecology (ICRU Report 38, ICRU, 1985). The present report addresses the problem of absorbed dose specification for report interstitial therapy. Although specific to interstitial therapy, many of the concepts developed in this report are also applicable to certain other kinds of brachytherapy applications. In particular, special cases of intraluminal brachytherapy and plesio-brachytherapy via surface molds employing x or gamma emitters are addressed in this report
Directory of Open Access Journals (Sweden)
Regina Esterhammer
Full Text Available The purpose of the present study was to evaluate the potential of multimodal MR imaging including mean diffusivity (MD, fractional anisotropy (FA, relaxation rates R2 and R2* to detect disease specific alterations in Parkinson's Disease (PD. We enrolled 82 PD patients (PD-all with varying disease durations (≤5 years: PD≤5, n = 43; >5 years: PD>5, n = 39 and 38 matched healthy controls (HC, receiving diffusion tensor imaging as well as R2 and R2* relaxometry calculated from multi-echo T2*-weighted and dual-echo TSE imaging, respectively. ROIs were drawn to delineate caudate nucleus (CN, putamen (PU, globus pallidus (GP and substantia nigra (SN on the co-registered maps. The SN was divided in 3 descending levels (SL 1-3. The most significant parameters were used for a flexible discrimination analysis (FDA in a training collective consisting of 25 randomized subjects from each group in order to predict the classification of remaining subjects. PD-all showed significant increases in MD, R2 and R2* within SN and its subregions as well as in MD and R2* within different basal ganglia regions. Compared to the HC group, the PD≤5 and the PD>5 group showed significant MD increases within the SN and its lower two subregions, while the PD≤5 group exhibited significant increases in R2 and R2* within SN and its subregions, and tended to elevation within the basal ganglia. The PD>5 group had significantly increased MD in PU and GP, whereas the PD≤5 group presented normal MD within the basal ganglia. FDA achieved right classification in 84% of study participants. Micro-structural damage affects primarily the SN of PD patients and in later disease stages the basal ganglia. Iron contents of PU, GP and SN are increased at early disease stages of PD.
DEFF Research Database (Denmark)
Ziegel, Johanna; Nyengaard, Jens Randel; Jensen, Eva B. Vedel
In the present paper, statistical procedures for estimating shape and orientation of arbitrary three-dimensional particles are developed. The focus of this work is on the case where the particles cannot be observed directly, but only via sections. Volume tensors are used for describing particle s...
Traffic Speed Data Imputation Method Based on Tensor Completion
Directory of Open Access Journals (Sweden)
Bin Ran
2015-01-01
Full Text Available Traffic speed data plays a key role in Intelligent Transportation Systems (ITS; however, missing traffic data would affect the performance of ITS as well as Advanced Traveler Information Systems (ATIS. In this paper, we handle this issue by a novel tensor-based imputation approach. Specifically, tensor pattern is adopted for modeling traffic speed data and then High accurate Low Rank Tensor Completion (HaLRTC, an efficient tensor completion method, is employed to estimate the missing traffic speed data. This proposed method is able to recover missing entries from given entries, which may be noisy, considering severe fluctuation of traffic speed data compared with traffic volume. The proposed method is evaluated on Performance Measurement System (PeMS database, and the experimental results show the superiority of the proposed approach over state-of-the-art baseline approaches.
Traffic speed data imputation method based on tensor completion.
Ran, Bin; Tan, Huachun; Feng, Jianshuai; Liu, Ying; Wang, Wuhong
2015-01-01
Traffic speed data plays a key role in Intelligent Transportation Systems (ITS); however, missing traffic data would affect the performance of ITS as well as Advanced Traveler Information Systems (ATIS). In this paper, we handle this issue by a novel tensor-based imputation approach. Specifically, tensor pattern is adopted for modeling traffic speed data and then High accurate Low Rank Tensor Completion (HaLRTC), an efficient tensor completion method, is employed to estimate the missing traffic speed data. This proposed method is able to recover missing entries from given entries, which may be noisy, considering severe fluctuation of traffic speed data compared with traffic volume. The proposed method is evaluated on Performance Measurement System (PeMS) database, and the experimental results show the superiority of the proposed approach over state-of-the-art baseline approaches.
Chlorophyll-a specific volume scattering function of phytoplankton.
Tan, Hiroyuki; Oishi, Tomohiko; Tanaka, Akihiko; Doerffer, Roland; Tan, Yasuhiro
2017-06-12
Chlorophyll-a specific light volume scattering functions (VSFs) by cultured phytoplankton in visible spectrum range is presented. Chlorophyll-a specific VSFs were determined based on the linear least squares method using a measured VSFs with different chlorophyll-a concentrations. We found obvious variability of it in terms of spectral and angular shapes of VSF between cultures. It was also presented that chlorophyll-a specific scattering significantly affected on spectral variation of the remote sensing reflectance, depending on spectral shape of b. This result is useful for developing an advance algorithm of ocean color remote sensing and for deep understanding of light in the sea.
Tensors, relativity, and cosmology
Dalarsson, Mirjana
2015-01-01
Tensors, Relativity, and Cosmology, Second Edition, combines relativity, astrophysics, and cosmology in a single volume, providing a simplified introduction to each subject that is followed by detailed mathematical derivations. The book includes a section on general relativity that gives the case for a curved space-time, presents the mathematical background (tensor calculus, Riemannian geometry), discusses the Einstein equation and its solutions (including black holes and Penrose processes), and considers the energy-momentum tensor for various solutions. In addition, a section on relativistic astrophysics discusses stellar contraction and collapse, neutron stars and their equations of state, black holes, and accretion onto collapsed objects, with a final section on cosmology discussing cosmological models, observational tests, and scenarios for the early universe. This fully revised and updated second edition includes new material on relativistic effects, such as the behavior of clocks and measuring rods in m...
International Nuclear Information System (INIS)
Yasmin, Hasina; Nakata, Yasuhiro; Abe, Osamu; Masutani, Yoshitaka; Ohtomo, Kuni; Aoki, Shigeki; Sato, Noriko; Nemoto, Kiyotaka; Arima, Kunimasa; Furuta, Nobuo; Uno, Masatake; Hirai, Shigeo
2008-01-01
Our aim was to determine diffusion abnormalities in the uncinate fasciculus (UF) in Alzheimer's disease (AD) by diffusion tensor tractography (DTT) using a new method for measuring the core of the tract. We studied 19 patients with AD and 19 age-matched control subjects who underwent MRI using diffusion tensor imaging (DTI). DTT of the UF was generated. The mean diffusivity (MD) and fractional anisotropy (FA) of the core of the tract were measured after voxelized tract shape processing. Student's t-test was used to compare results between patients with AD and controls. Intraobserver correlation tests were also performed. FA was significantly lower (P 0.93 for measured FA and r > 0.92 for measured MD. Our results suggest that FA reflects progression of AD-related histopathological changes in the UF of the white matter and may represent a useful biological index in monitoring AD. Diffusion tensor tract-specific analysis with voxelized tract shape processing to measure the core of the tract may be a sensitive tool for evaluation of diffusion abnormalities of white matter tracts in AD. (orig.)
International Nuclear Information System (INIS)
1995-04-01
This report documents the results of the combined effort of the NRC and the industry to produce improved Standard Technical Specifications (STS), Revision 1 for General Electric BWR/4 Plants. The changes reflected in Revision 1 resulted from the experience gained from license amendment applications to convert to these improved STS or to adopt partial improvements to existing technical specifications. This NUREG is the result of extensive public technical meetings and discussions between the Nuclear Regulatory Commission (NRC) staff and various nuclear power plant licensees, Nuclear Steam Supply System (NSSS) Owners Groups, NSSS vendors, and the Nuclear Energy Institute (NEI). The improved STS were developed based on the criteria in the Final Commission Policy Statement on Technical Specifications Improvements for Nuclear Power Reactors, dated July 22, 1993. The improved STS will be used as the basis for individual nuclear power plant licensees to develop improved plant-specific technical specifications. This report contains three volumes. Volume 1 contains the Specifications for all chapters and sections of the improved STS. Volume 2 contains the Bases for Chapters 2.0 and 3.0, and Sections 3.1--3.3 of the improved STS. Volume 3 contains the Bases for Sections 3.4--3.10 of the improved STS
International Nuclear Information System (INIS)
1995-04-01
This report documents the results of the combined effort of the NRC and the industry to produce improved Standard Technical Specifications (STS), Revision 1 for Combustion Engineering Plants. The changes reflected in Revision 1 resulted from the experience gained from license amendment applications to convert to these improved STS or to adopt partial improvements to existing technical specifications. This NUREG is the result of extensive public technical meetings and discussions between the Nuclear Regulatory Commission (NRC) staff and various nuclear power plant licensees, Nuclear Steam Supply System (NSSS) Owners Groups, NSSS vendors, and the Nuclear Energy Institute (NEI). The improved STS were developed based on the criteria in the Final Commission Policy Statement on Technical Specifications Improvements for Nuclear Power Reactors, dated July 22, 1993. The improved STS will be used as the basis for individual nuclear power plant licensees to develop improved plant-specific technical specifications. This report contains three volumes. Volume 1 contains the Specifications for all chapters and sections of the improved STS. Volume 2 contains the Bases for Chapters 2.0 and 3.0, and Sections 3.1--3.3 of the improved STS. Volume 3 contains the Bases for Sections 3.4--3.9 of the improved STS
Dillon, Joshua V.; Langmore, Ian; Tran, Dustin; Brevdo, Eugene; Vasudevan, Srinivas; Moore, Dave; Patton, Brian; Alemi, Alex; Hoffman, Matt; Saurous, Rif A.
2017-01-01
The TensorFlow Distributions library implements a vision of probability theory adapted to the modern deep-learning paradigm of end-to-end differentiable computation. Building on two basic abstractions, it offers flexible building blocks for probabilistic computation. Distributions provide fast, numerically stable methods for generating samples and computing statistics, e.g., log density. Bijectors provide composable volume-tracking transformations with automatic caching. Together these enable...
“Finite” non-Gaussianities and tensor-scalar ratio in large volume Swiss-cheese compactifications
Misra, Aalok; Shukla, Pramod
2009-03-01
Developing on the ideas of (Section 4 of) [A. Misra, P. Shukla, Moduli stabilization, large-volume dS minimum without anti-D3-branes, (non-)supersymmetric black hole attractors and two-parameter Swiss cheese Calabi-Yau's, Nucl. Phys. B 799 (2008) 165-198, arXiv: 0707.0105] and [A. Misra, P. Shukla, Large volume axionic Swiss-cheese inflation, Nucl. Phys. B 800 (2008) 384-400, arXiv: 0712.1260 [hep-th
Liu, Wenyu; An, Dongmei; Tong, Xin; Niu, Running; Gong, Qiyong; Zhou, Dong
2017-10-01
Periventricular nodular heterotopia (PNH) is an important cause of chronic epilepsy. The purpose of this study was to evaluate region-specific connectivity in PNH patients with epilepsy and assess correlation between connectivity strength and clinical factors including duration and prognosis. Diffusion tensor imaging (DTI) and resting state functional MRI (fMRI) were performed in 28 subjects (mean age 27.4years; range 9-56years). The structural connectivity of fiber bundles passing through the manually-selected segmented nodules and other brain regions were analyzed by tractography. Cortical lobes showing functional correlations to nodules were also determined. For all heterotopic gray matter nodules, including at least one in each subject, the most frequent segments to which nodular heterotopia showed structural (132/151) and functional (146/151) connectivity were discrete regions of the ipsilateral overlying cortex. Agreement between diffusion tensor tractography and functional connectivity analyses was conserved in 81% of all nodules (122/151). In patients with longer duration or refractory epilepsy, the connectivity was significantly stronger, particularly to the frontal and temporal lobes (P<0.05). Nodules in PNH were structurally and functionally connected to the cortex. The extent is stronger in patients with longstanding or intractable epilepsy. These findings suggest the region-specific interactions may help better evaluate prognosis and seek medical or surgical interventions of PNH-related epilepsy. Copyright © 2017 Elsevier B.V. All rights reserved.
International Nuclear Information System (INIS)
Abe, Osamu; Yamasue, Hidenori; Kasai, Kiyoto
2008-01-01
Previous neuroimaging studies have revealed that frontolimbic dysfunction may contribute to the pathophysiology of major depressive disorder. We used voxel-based analysis to simultaneously elucidate regional changes in gray/white matter volume, mean diffusivity (MD), and fractional anisotropy (FA) in the central nervous system of patients with unipolar major depression. We studied 21 right-handed patients and 42 age- and gender-matched right-handed normal subjects without central nervous system disorders. All image processing and statistical analyses were performed using SPM5 software. Local areas showing significant gray matter volume reduction in depressive patients compared with normal controls were observed in the right parahippocampal gyrus, hippocampus, bilateral middle frontal gyri, bilateral anterior cingulate cortices, left parietal and occipital lobes, and right superior temporal gyrus. Local areas showing increased mean diffusivity in depressive patients were observed in the bilateral parahippocampal gyri, hippocampus, pons, cerebellum, left frontal and temporal lobes, and right frontal lobe. There was no significant difference between the 2 groups for fractional anisotropy and white matter volume in the entire brain. Although there was no local area in which FA and MD were significantly correlated with disease severity, FA tended to correlate negatively with depression days (total accumulated days in depressive state) in the right anterior cingulate and the left frontal white matter (FDR-corrected P=0.055 for both areas). These results suggest that the frontolimbic neural circuit may play an important role in the neuropathology of patients with major depression. (author)
Colored Tensor Models - a Review
Directory of Open Access Journals (Sweden)
Razvan Gurau
2012-04-01
Full Text Available Colored tensor models have recently burst onto the scene as a promising conceptual and computational tool in the investigation of problems of random geometry in dimension three and higher. We present a snapshot of the cutting edge in this rapidly expanding research field. Colored tensor models have been shown to share many of the properties of their direct ancestor, matrix models, which encode a theory of fluctuating two-dimensional surfaces. These features include the possession of Feynman graphs encoding topological spaces, a 1/N expansion of graph amplitudes, embedded matrix models inside the tensor structure, a resumable leading order with critical behavior and a continuum large volume limit, Schwinger-Dyson equations satisfying a Lie algebra (akin to the Virasoro algebra in two dimensions, non-trivial classical solutions and so on. In this review, we give a detailed introduction of colored tensor models and pointers to current and future research directions.
Tensor voting for robust color edge detection
Moreno, Rodrigo; García, Miguel Ángel; Puig, Domenec
2014-01-01
The final publication is available at Springer via http://dx.doi.org/10.1007/978-94-007-7584-8_9 This chapter proposes two robust color edge detection methods based on tensor voting. The first method is a direct adaptation of the classical tensor voting to color images where tensors are initialized with either the gradient or the local color structure tensor. The second method is based on an extension of tensor voting in which the encoding and voting processes are specifically tailored to ...
International Nuclear Information System (INIS)
Ito, Kenji; Masutani, Yoshitaka; Suzuki, Yuichi; Ino, Kenji; Kunimatsu, Akira; Ohtomo, Kuni; Kamagata, Koji; Yasmin, Hasina; Aoki, Shigeki
2013-01-01
Tract-specific analysis (TSA) measures diffusion parameters along a specific fiber that has been extracted by fiber tracking using manual regions of interest (ROIs), but TSA is limited by its requirement for manual operation, poor reproducibility, and high time consumption. We aimed to develop a fully automated extraction method for the cingulum bundle (CB) and to apply the method to TSA in neurobehavioral disorders such as Parkinson's disease (PD). We introduce the voxel classification (VC) and auto diffusion tensor fiber-tracking (AFT) methods of extraction. The VC method directly extracts the CB, skipping the fiber-tracking step, whereas the AFT method uses fiber tracking from automatically selected ROIs. We compared the results of VC and AFT to those obtained by manual diffusion tensor fiber tracking (MFT) performed by 3 operators. We quantified the Jaccard similarity index among the 3 methods in data from 20 subjects (10 normal controls [NC] and 10 patients with Parkinson's disease dementia [PDD]). We used all 3 extraction methods (VC, AFT, and MFT) to calculate the fractional anisotropy (FA) values of the anterior and posterior CB for 15 NC subjects, 15 with PD, and 15 with PDD. The Jaccard index between results of AFT and MFT, 0.72, was similar to the inter-operator Jaccard index of MFT. However, the Jaccard indices between VC and MFT and between VC and AFT were lower. Consequently, the VC method classified among 3 different groups (NC, PD, and PDD), whereas the others classified only 2 different groups (NC, PD or PDD). For TSA in Parkinson's disease, the VC method can be more useful than the AFT and MFT methods for extracting the CB. In addition, the results of patient data analysis suggest that a reduction of FA in the posterior CB may represent a useful biological index for monitoring PD and PDD. (author)
Tensor Transpose and Its Properties
Pan, Ran
2014-01-01
Tensor transpose is a higher order generalization of matrix transpose. In this paper, we use permutations and symmetry group to define? the tensor transpose. Then we discuss the classification and composition of tensor transposes. Properties of tensor transpose are studied in relation to tensor multiplication, tensor eigenvalues, tensor decompositions and tensor rank.
International Nuclear Information System (INIS)
Park, Chang-hyun; Seo, Cheong Hoon; Joo, So Young; Jung, Myung Hun; Jang, Soyeon; Lee, Ho Young; Ohn, Suk Hoon
2017-01-01
We utilized cerebral blood volume (CBV) magnetic resonance imaging and diffusion tensor imaging (DTI) to investigate changes in cognitive networks in patients experiencing cognitive dysfunction following electrical injury. Cognitive function was assessed across various domains, including attention, verbal memory, executive function, and language. Depressive symptoms were also evaluated. CBV maps and DTI measures were obtained from 24 patients (age, 41.8 ± 5.8 years; education, 13.3 ± 1.9 years) and 24 healthy controls (age, 42.3 ± 2.7 years; education, 14.3 ± 1.9 years). CBV maps and DTI measures were compared between patients and controls, and correlations between these measures and each cognitive assessment score were examined. Patients exhibited lower attention, verbal memory, and executive function scores than controls (all p < 0.01). Patients also exhibited higher depression scores than controls (p < 0.01), as well as a predominant increase in CBV in the cerebellar vermis relative to that of controls (height p < uncorrected 0.001, extent p < corrected 0.05). Correlation analyses revealed a strong association between executive function scores and CBV in the bilateral posterior cingulate cortex and left mammillary body in patients (height p < uncorrected 0.001, extent p < corrected 0.05). There were no significant differences in DTI measures between patients and controls. The CBV maps showed hypermetabolism in the cerebello-limbic system; DTI did not find any microstructural changes. Our results suggest that patients experiencing cognitive dysfunction following electrical injury may possess a cognitive reserve that protects against deteriorating conditions such as dementia. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Park, Chang-hyun [Catholic University of Korea, Department of Psychiatry, College of Medicine, Seoul (Korea, Republic of); Seo, Cheong Hoon; Joo, So Young [Hallym University College of Medicine, Department of Physical Medicine and Rehabilitation, Hangang Sacred Heart Hospital, Seoul (Korea, Republic of); Jung, Myung Hun [Hallym University Sacred Heart Hospital, Hallym University College of Medicine, Department of Psychiatry, Dongan-gu Anyang, Gyeonggi-do (Korea, Republic of); Jang, Soyeon; Lee, Ho Young; Ohn, Suk Hoon [Hallym University Sacred Heart Hospital, Hallym University College of Medicine, Department of Physical Medicine and Rehabilitation, Dongan-gu Anyang, Gyeonggi-do (Korea, Republic of)
2017-09-15
We utilized cerebral blood volume (CBV) magnetic resonance imaging and diffusion tensor imaging (DTI) to investigate changes in cognitive networks in patients experiencing cognitive dysfunction following electrical injury. Cognitive function was assessed across various domains, including attention, verbal memory, executive function, and language. Depressive symptoms were also evaluated. CBV maps and DTI measures were obtained from 24 patients (age, 41.8 ± 5.8 years; education, 13.3 ± 1.9 years) and 24 healthy controls (age, 42.3 ± 2.7 years; education, 14.3 ± 1.9 years). CBV maps and DTI measures were compared between patients and controls, and correlations between these measures and each cognitive assessment score were examined. Patients exhibited lower attention, verbal memory, and executive function scores than controls (all p < 0.01). Patients also exhibited higher depression scores than controls (p < 0.01), as well as a predominant increase in CBV in the cerebellar vermis relative to that of controls (height p < uncorrected 0.001, extent p < corrected 0.05). Correlation analyses revealed a strong association between executive function scores and CBV in the bilateral posterior cingulate cortex and left mammillary body in patients (height p < uncorrected 0.001, extent p < corrected 0.05). There were no significant differences in DTI measures between patients and controls. The CBV maps showed hypermetabolism in the cerebello-limbic system; DTI did not find any microstructural changes. Our results suggest that patients experiencing cognitive dysfunction following electrical injury may possess a cognitive reserve that protects against deteriorating conditions such as dementia. (orig.)
Smaller superior temporal gyrus volume specificity in schizotypal personality disorder
Goldstein, Kim E.; Hazlett, Erin A.; New, Antonia S.; Haznedar, M. Mehmet; Newmark, Randall E.; Zelmanova, Yuliya; Passarelli, Vincent; Weinstein, Shauna R.; Canfield, Emily L.; Meyerson, David A.; Tang, Cheuk Y.; Buchsbaum, Monte S.; Siever, Larry J.
2009-01-01
Background Superior temporal gyrus (STG/BA22) volume is reduced in schizophrenia and to a milder degree in schizotypal personality disorder (SPD), representing a less severe disorder in the schizophrenia-spectrum. SPD and Borderline personality disorder (BPD) are severe personality disorders characterized by social and cognitive dysfunction. However, while SPD is characterized by social withdrawal/anhedonia, BPD is marked by hyper-reactivity to interpersonal stimuli and hyper-emotionality. This is the first morphometric study to directly compare SPD and BPD patients in temporal volume. Methods We compared three age-gender- and education-matched groups: 27 unmedicated SPD individuals with no BPD traits, 52 unmedicated BPD individuals with no SPD traits, and 45 healthy controls. We examined gray matter volume of frontal and temporal lobe Brodmann areas (BAs), and dorsal/ventral amygdala from 3T magnetic resonance imaging. Results In the STG, an auditory association area reported to be dysfunctional in SPD and BPD, the SPD patients had significantly smaller volume than healthy controls and BPD patients. No group differences were found between BPD patients and controls. Smaller BA22 volume was associated with greater symptom severity in SPD patients. Reduced STG volume may be an important endophenotype for schizophrenia-spectrum disorders. SPD is distinct from BPD in terms of STG volume abnormalities which may reflect different underlying pathophysiological mechanisms and could help discriminate between them. PMID:19473820
Hess, Siegfried
2015-01-01
This book presents the science of tensors in a didactic way. The various types and ranks of tensors and the physical basis is presented. Cartesian Tensors are needed for the description of directional phenomena in many branches of physics and for the characterization the anisotropy of material properties. The first sections of the book provide an introduction to the vector and tensor algebra and analysis, with applications to physics, at undergraduate level. Second rank tensors, in particular their symmetries, are discussed in detail. Differentiation and integration of fields, including generalizations of the Stokes law and the Gauss theorem, are treated. The physics relevant for the applications in mechanics, quantum mechanics, electrodynamics and hydrodynamics is presented. The second part of the book is devoted to tensors of any rank, at graduate level. Special topics are irreducible, i.e. symmetric traceless tensors, isotropic tensors, multipole potential tensors, spin tensors, integration and spin-...
Gurau, Razvan
2017-01-01
Written by the creator of the modern theory of random tensors, this book is the first self-contained introductory text to this rapidly developing theory. Starting from notions familiar to the average researcher or PhD student in mathematical or theoretical physics, the book presents in detail the theory and its applications to physics. The recent detections of the Higgs boson at the LHC and gravitational waves at LIGO mark new milestones in Physics confirming long standing predictions of Quantum Field Theory and General Relativity. These two experimental results only reinforce today the need to find an underlying common framework of the two: the elusive theory of Quantum Gravity. Over the past thirty years, several alternatives have been proposed as theories of Quantum Gravity, chief among them String Theory. While these theories are yet to be tested experimentally, key lessons have already been learned. Whatever the theory of Quantum Gravity may be, it must incorporate random geometry in one form or another....
Tensor rank is not multiplicative under the tensor product
DEFF Research Database (Denmark)
Christandl, Matthias; Jensen, Asger Kjærulff; Zuiddam, Jeroen
2018-01-01
The tensor rank of a tensor t is the smallest number r such that t can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an ℓ-tensor. The tensor product of s and t is a (k+ℓ)-tensor. Tensor rank is sub-multiplicative under the tensor product. We revisit the connection b...
Tensor rank is not multiplicative under the tensor product
M. Christandl (Matthias); A. K. Jensen (Asger Kjærulff); J. Zuiddam (Jeroen)
2018-01-01
textabstractThe tensor rank of a tensor t is the smallest number r such that t can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an ℓ-tensor. The tensor product of s and t is a (k+ℓ)-tensor. Tensor rank is sub-multiplicative under the tensor product. We revisit the
Tensor rank is not multiplicative under the tensor product
M. Christandl (Matthias); A. K. Jensen (Asger Kjærulff); J. Zuiddam (Jeroen)
2017-01-01
textabstractThe tensor rank of a tensor is the smallest number r such that the tensor can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an l-tensor. The tensor product of s and t is a (k + l)-tensor (not to be confused with the "tensor Kronecker product" used in
Mod-5A wind turbine generator program design report. Volume 4: Drawings and specifications, book 5
1984-01-01
The design, development and analysis of the 7.3 MW MOD-5A wind turbine generator is documented. There are four volumes. This volume contains the drawings and specifications that were developed in preparation for building the MOD-5A wind turbine generator. Detail drawings of several assemblies and subassemblies are given. This is the fifth book of volume 4.
Prostate-specific antigen lowering effect of metabolic syndrome is influenced by prostate volume.
Choi, Woo Suk; Heo, Nam Ju; Paick, Jae-Seung; Son, Hwancheol
2016-04-01
To investigate the influence of metabolic syndrome on prostate-specific antigen levels by considering prostate volume and plasma volume. We retrospectively analyzed 4111 men who underwent routine check-ups including prostate-specific antigen and transrectal ultrasonography. The definition of metabolic syndrome was based on the modified Adult Treatment Panel III criteria. Prostate-specific antigen mass density (prostate-specific antigen × plasma volume / prostate volume) was calculated for adjusting plasma volume and prostate volume. We compared prostate-specific antigen and prostate-specific antigen mass density levels of participants with metabolic syndrome (metabolic syndrome group, n = 1242) and without metabolic syndrome (non-prostate-specific antigen metabolic syndrome group, n = 2869). To evaluate the impact of metabolic syndrome on prostate-specific antigen, linear regression analysis for the natural logarithm of prostate-specific antigen was used. Patients in the metabolic syndrome group had significantly older age (P prostate volume (P prostate-specific antigen (non-metabolic syndrome group vs metabolic syndrome group; 1.22 ± 0.91 vs 1.15 ± 0.76 ng/mL, P = 0.006). Prostate-specific antigen mass density in the metabolic syndrome group was still significantly lower than that in the metabolic syndrome group (0.124 ± 0.084 vs 0.115 ± 0.071 μg/mL, P = 0.001). After adjusting for age, prostate volume and plasma volume using linear regression model, the presence of metabolic syndrome was a significant independent factor for lower prostate-specific antigen (prostate-specific antigen decrease by 4.1%, P = 0.046). Prostate-specific antigen levels in patients with metabolic syndrome seem to be lower, and this finding might be affected by the prostate volume. © 2016 The Japanese Urological Association.
Optical Automatic Car Identification (OACI) : Volume 1. Advanced System Specification.
1978-12-01
A performance specification is provided in this report for an Optical Automatic Car Identification (OACI) scanner system which features 6% improved readability over existing industry scanner systems. It also includes the analysis and rationale which ...
Tensor gauge condition and tensor field decomposition
Zhu, Ben-Chao; Chen, Xiang-Song
2015-10-01
We discuss various proposals of separating a tensor field into pure-gauge and gauge-invariant components. Such tensor field decomposition is intimately related to the effort of identifying the real gravitational degrees of freedom out of the metric tensor in Einstein’s general relativity. We show that as for a vector field, the tensor field decomposition has exact correspondence to and can be derived from the gauge-fixing approach. The complication for the tensor field, however, is that there are infinitely many complete gauge conditions in contrast to the uniqueness of Coulomb gauge for a vector field. The cause of such complication, as we reveal, is the emergence of a peculiar gauge-invariant pure-gauge construction for any gauge field of spin ≥ 2. We make an extensive exploration of the complete tensor gauge conditions and their corresponding tensor field decompositions, regarding mathematical structures, equations of motion for the fields and nonlinear properties. Apparently, no single choice is superior in all aspects, due to an awkward fact that no gauge-fixing can reduce a tensor field to be purely dynamical (i.e. transverse and traceless), as can the Coulomb gauge in a vector case.
Tensor structure for Nori motives
Barbieri-Viale, Luca; Huber, Annette; Prest, Mike
2018-01-01
We construct a tensor product on Freyd's universal abelian category attached to an additive tensor category or a tensor quiver and establish a universal property. This is used to give an alternative construction for the tensor product on Nori motives.
Tensor eigenvalues and their applications
Qi, Liqun; Chen, Yannan
2018-01-01
This book offers an introduction to applications prompted by tensor analysis, especially by the spectral tensor theory developed in recent years. It covers applications of tensor eigenvalues in multilinear systems, exponential data fitting, tensor complementarity problems, and tensor eigenvalue complementarity problems. It also addresses higher-order diffusion tensor imaging, third-order symmetric and traceless tensors in liquid crystals, piezoelectric tensors, strong ellipticity for elasticity tensors, and higher-order tensors in quantum physics. This book is a valuable reference resource for researchers and graduate students who are interested in applications of tensor eigenvalues.
Reconstruction of convex bodies from surface tensors
DEFF Research Database (Denmark)
Kousholt, Astrid; Kiderlen, Markus
2016-01-01
We present two algorithms for reconstruction of the shape of convex bodies in the two-dimensional Euclidean space. The first reconstruction algorithm requires knowledge of the exact surface tensors of a convex body up to rank s for some natural number s. When only measurements subject to noise...... of surface tensors are available for reconstruction, we recommend to use certain values of the surface tensors, namely harmonic intrinsic volumes instead of the surface tensors evaluated at the standard basis. The second algorithm we present is based on harmonic intrinsic volumes and allows for noisy...... measurements. From a generalized version of Wirtinger's inequality, we derive stability results that are utilized to ensure consistency of both reconstruction procedures. Consistency of the reconstruction procedure based on measurements subject to noise is established under certain assumptions on the noise...
Energy Technology Data Exchange (ETDEWEB)
Hohmann, Manuel [Physikalisches Institut, Universitaet Tartu (Estonia)
2016-07-01
Tensor harmonics are a useful mathematical tool for finding solutions to differential equations which transform under a particular representation of the rotation group SO(3). In order to make use of this tool also in the setting of Finsler geometry, where the objects of relevance are d-tensors instead of tensors, we construct a set of d-tensor harmonics for both SO(3) and SO(4) symmetries and show how these can be used for calculations in Finsler geometry and gravity.
Sirlin, Samuel W.
1993-01-01
Eight-page report describes systems of notation used most commonly to represent tensors of various ranks, with emphasis on tensors in Cartesian coordinate systems. Serves as introductory or refresher text for scientists, engineers, and others familiar with basic concepts of coordinate systems, vectors, and partial derivatives. Indicial tensor, vector, dyadic, and matrix notations, and relationships among them described.
Norm of the Riemannian Curvature Tensor
Indian Academy of Sciences (India)
We consider the Riemannian functional R p ( g ) = ∫ M | R ( g ) | p d v g defined on the space of Riemannian metrics with unit volume on a closed smooth manifold where R ( g ) and d v g denote the corresponding Riemannian curvature tensor and volume form and p ∈ ( 0 , ∞ ) . First we prove that the Riemannian metrics ...
International Nuclear Information System (INIS)
Beig, Robert; Krammer, Werner
2004-01-01
For a conformally flat 3-space, we derive a family of linear second-order partial differential operators which sends vectors into trace-free, symmetric 2-tensors. These maps, which are parametrized by conformal Killing vectors on the 3-space, are such that the divergence of the resulting tensor field depends only on the divergence of the original vector field. In particular, these maps send source-free electric fields into TT tensors. Moreover, if the original vector field is the Coulomb field on R 3 {0}, the resulting tensor fields on R 3 {0} are nothing but the family of TT tensors originally written by Bowen and York
A Comparison of Regional and SiteSpecific Volume Estimation Equations
Joe P. McClure; Jana Anderson; Hans T. Schreuder
1987-01-01
Regression equations for volume by region and site class were examined for lobiolly pine. The regressions for the Coastal Plain and Piedmont regions had significantly different slopes. The results shared important practical differences in percentage of confidence intervals containing the true total volume and in percentage of estimates within a specific proportion of...
Conformal field theories and tensor categories. Proceedings
Energy Technology Data Exchange (ETDEWEB)
Bai, Chengming [Nankai Univ., Tianjin (China). Chern Institute of Mathematics; Fuchs, Juergen [Karlstad Univ. (Sweden). Theoretical Physics; Huang, Yi-Zhi [Rutgers Univ., Piscataway, NJ (United States). Dept. of Mathematics; Kong, Liang [Tsinghua Univ., Beijing (China). Inst. for Advanced Study; Runkel, Ingo; Schweigert, Christoph (eds.) [Hamburg Univ. (Germany). Dept. of Mathematics
2014-08-01
First book devoted completely to the mathematics of conformal field theories, tensor categories and their applications. Contributors include both mathematicians and physicists. Some long expository articles are especially suitable for beginners. The present volume is a collection of seven papers that are either based on the talks presented at the workshop ''Conformal field theories and tensor categories'' held June 13 to June 17, 2011 at the Beijing International Center for Mathematical Research, Peking University, or are extensions of the material presented in the talks at the workshop. These papers present new developments beyond rational conformal field theories and modular tensor categories and new applications in mathematics and physics. The topics covered include tensor categories from representation categories of Hopf algebras, applications of conformal field theories and tensor categories to topological phases and gapped systems, logarithmic conformal field theories and the corresponding non-semisimple tensor categories, and new developments in the representation theory of vertex operator algebras. Some of the papers contain detailed introductory material that is helpful for graduate students and researchers looking for an introduction to these research directions. The papers also discuss exciting recent developments in the area of conformal field theories, tensor categories and their applications and will be extremely useful for researchers working in these areas.
Conformal field theories and tensor categories. Proceedings
International Nuclear Information System (INIS)
Bai, Chengming; Fuchs, Juergen; Huang, Yi-Zhi; Kong, Liang; Runkel, Ingo; Schweigert, Christoph
2014-01-01
First book devoted completely to the mathematics of conformal field theories, tensor categories and their applications. Contributors include both mathematicians and physicists. Some long expository articles are especially suitable for beginners. The present volume is a collection of seven papers that are either based on the talks presented at the workshop ''Conformal field theories and tensor categories'' held June 13 to June 17, 2011 at the Beijing International Center for Mathematical Research, Peking University, or are extensions of the material presented in the talks at the workshop. These papers present new developments beyond rational conformal field theories and modular tensor categories and new applications in mathematics and physics. The topics covered include tensor categories from representation categories of Hopf algebras, applications of conformal field theories and tensor categories to topological phases and gapped systems, logarithmic conformal field theories and the corresponding non-semisimple tensor categories, and new developments in the representation theory of vertex operator algebras. Some of the papers contain detailed introductory material that is helpful for graduate students and researchers looking for an introduction to these research directions. The papers also discuss exciting recent developments in the area of conformal field theories, tensor categories and their applications and will be extremely useful for researchers working in these areas.
Energy Technology Data Exchange (ETDEWEB)
Yasmin, Hasina; Nakata, Yasuhiro; Abe, Osamu; Masutani, Yoshitaka; Ohtomo, Kuni [University of Tokyo, Department of Radiology, Tokyo (Japan); Aoki, Shigeki [University of Tokyo, Department of Radiology, Tokyo (Japan); Sato, Noriko [National Center of Neurology and Psychiatry, Department of Radiology, National Center Hospital for Mental, Nervous and Muscular Disorders, Tokyo (Japan); Nemoto, Kiyotaka [Ibaraki Prefectural Tomobe Hospital, Department of Psychiatry, Ibaraki (Japan); Arima, Kunimasa; Furuta, Nobuo [National Center of Neurology and Psychiatry, Department of Psychiatry, National Center Hospital for Mental, Nervous and Muscular Disorders, Tokyo (Japan); Uno, Masatake [Yoshioka Rehabilitation Clinic, Department of Psychiatry, Tokyo (Japan); Hirai, Shigeo [Iruma Hirai Clinic, Department of Psychiatry, Saitama (Japan)
2008-04-15
Our aim was to determine diffusion abnormalities in the uncinate fasciculus (UF) in Alzheimer's disease (AD) by diffusion tensor tractography (DTT) using a new method for measuring the core of the tract. We studied 19 patients with AD and 19 age-matched control subjects who underwent MRI using diffusion tensor imaging (DTI). DTT of the UF was generated. The mean diffusivity (MD) and fractional anisotropy (FA) of the core of the tract were measured after voxelized tract shape processing. Student's t-test was used to compare results between patients with AD and controls. Intraobserver correlation tests were also performed. FA was significantly lower (P < 0.0001) in the UF of patients with AD than of controls. There was no significant difference in MD along the UF between the two groups. Intraobserver reliability (intraclass correlation coefficient) for the first and second measurement was r > 0.93 for measured FA and r > 0.92 for measured MD. Our results suggest that FA reflects progression of AD-related histopathological changes in the UF of the white matter and may represent a useful biological index in monitoring AD. Diffusion tensor tract-specific analysis with voxelized tract shape processing to measure the core of the tract may be a sensitive tool for evaluation of diffusion abnormalities of white matter tracts in AD. (orig.)
Lepore, N; Brun, C; Chou, Y Y; Chiang, M C; Dutton, R A; Hayashi, K M; Luders, E; Lopez, O L; Aizenstein, H J; Toga, A W; Becker, J T; Thompson, P M
2008-01-01
This paper investigates the performance of a new multivariate method for tensor-based morphometry (TBM). Statistics on Riemannian manifolds are developed that exploit the full information in deformation tensor fields. In TBM, multiple brain images are warped to a common neuroanatomical template via 3-D nonlinear registration; the resulting deformation fields are analyzed statistically to identify group differences in anatomy. Rather than study the Jacobian determinant (volume expansion factor) of these deformations, as is common, we retain the full deformation tensors and apply a manifold version of Hotelling's $T(2) test to them, in a Log-Euclidean domain. In 2-D and 3-D magnetic resonance imaging (MRI) data from 26 HIV/AIDS patients and 14 matched healthy subjects, we compared multivariate tensor analysis versus univariate tests of simpler tensor-derived indices: the Jacobian determinant, the trace, geodesic anisotropy, and eigenvalues of the deformation tensor, and the angle of rotation of its eigenvectors. We detected consistent, but more extensive patterns of structural abnormalities, with multivariate tests on the full tensor manifold. Their improved power was established by analyzing cumulative p-value plots using false discovery rate (FDR) methods, appropriately controlling for false positives. This increased detection sensitivity may empower drug trials and large-scale studies of disease that use tensor-based morphometry.
Cartesian tensors an introduction
Temple, G
2004-01-01
This undergraduate text provides an introduction to the theory of Cartesian tensors, defining tensors as multilinear functions of direction, and simplifying many theorems in a manner that lends unity to the subject. The author notes the importance of the analysis of the structure of tensors in terms of spectral sets of projection operators as part of the very substance of quantum theory. He therefore provides an elementary discussion of the subject, in addition to a view of isotropic tensors and spinor analysis within the confines of Euclidean space. The text concludes with an examination of t
Linear Invariant Tensor Interpolation Applied to Cardiac Diffusion Tensor MRI
Gahm, Jin Kyu; Wisniewski, Nicholas; Kindlmann, Gordon; Kung, Geoffrey L.; Klug, William S.; Garfinkel, Alan; Ennis, Daniel B.
2015-01-01
Purpose Various methods exist for interpolating diffusion tensor fields, but none of them linearly interpolate tensor shape attributes. Linear interpolation is expected not to introduce spurious changes in tensor shape. Methods Herein we define a new linear invariant (LI) tensor interpolation method that linearly interpolates components of tensor shape (tensor invariants) and recapitulates the interpolated tensor from the linearly interpolated tensor invariants and the eigenvectors of a linearly interpolated tensor. The LI tensor interpolation method is compared to the Euclidean (EU), affine-invariant Riemannian (AI), log-Euclidean (LE) and geodesic-loxodrome (GL) interpolation methods using both a synthetic tensor field and three experimentally measured cardiac DT-MRI datasets. Results EU, AI, and LE introduce significant microstructural bias, which can be avoided through the use of GL or LI. Conclusion GL introduces the least microstructural bias, but LI tensor interpolation performs very similarly and at substantially reduced computational cost. PMID:23286085
Efficient MATLAB computations with sparse and factored tensors.
Energy Technology Data Exchange (ETDEWEB)
Bader, Brett William; Kolda, Tamara Gibson (Sandia National Lab, Livermore, CA)
2006-12-01
In this paper, the term tensor refers simply to a multidimensional or N-way array, and we consider how specially structured tensors allow for efficient storage and computation. First, we study sparse tensors, which have the property that the vast majority of the elements are zero. We propose storing sparse tensors using coordinate format and describe the computational efficiency of this scheme for various mathematical operations, including those typical to tensor decomposition algorithms. Second, we study factored tensors, which have the property that they can be assembled from more basic components. We consider two specific types: a Tucker tensor can be expressed as the product of a core tensor (which itself may be dense, sparse, or factored) and a matrix along each mode, and a Kruskal tensor can be expressed as the sum of rank-1 tensors. We are interested in the case where the storage of the components is less than the storage of the full tensor, and we demonstrate that many elementary operations can be computed using only the components. All of the efficiencies described in this paper are implemented in the Tensor Toolbox for MATLAB.
Lepore, Natasha; Brun, Caroline; Chou, Yi-Yu; Chiang, Ming-Chang; Dutton, Rebecca A.; Hayashi, Kiralee M.; Luders, Eileen; Lopez, Oscar L.; Aizenstein, Howard J.; Toga, Arthur W.; Becker, James T.; Thompson, Paul M.
2008-01-01
This paper investigates the performance of a new multivariate method for tensor-based morphometry (TBM). Statistics on Riemannian manifolds are developed that exploit the full information in deformation tensor fields. In TBM, multiple brain images are warped to a common neuroanatomical template via 3-D nonlinear registration; the resulting deformation fields are analyzed statistically to identify group differences in anatomy. Rather than study the Jacobian determinant (volume expansion factor...
Surface tensor estimation from linear sections
DEFF Research Database (Denmark)
Kousholt, Astrid; Kiderlen, Markus; Hug, Daniel
From Crofton's formula for Minkowski tensors we derive stereological estimators of translation invariant surface tensors of convex bodies in the n-dimensional Euclidean space. The estimators are based on one-dimensional linear sections. In a design based setting we suggest three types of estimators....... These are based on isotropic uniform random lines, vertical sections, and non-isotropic random lines, respectively. Further, we derive estimators of the specific surface tensors associated with a stationary process of convex particles in the model based setting....
Surface tensor estimation from linear sections
DEFF Research Database (Denmark)
Kousholt, Astrid; Kiderlen, Markus; Hug, Daniel
2015-01-01
From Crofton’s formula for Minkowski tensors we derive stereological estimators of translation invariant surface tensors of convex bodies in the n-dimensional Euclidean space. The estimators are based on one-dimensional linear sections. In a design based setting we suggest three types of estimators....... These are based on isotropic uniform random lines, vertical sections, and non-isotropic random lines, respectively. Further, we derive estimators of the specific surface tensors associated with a stationary process of convex particles in the model based setting....
Motion-specific internal target volumes for FDG-avid mediastinal and hilar lymph nodes
International Nuclear Information System (INIS)
Lamb, James M.; Robinson, Clifford G.; Bradley, Jeffrey D.; Low, Daniel A.
2013-01-01
Background and purpose: To quantify the benefit of motion-specific internal target volumes for FDG-avid mediastinal and hilar lymph nodes generated using 4D-PET, vs. conventional internal target volumes generated using non-respiratory gated PET and 4D-CT scans. Materials and methods: Five patients with FDG-avid tumors metastatic to 11 hilar or mediastinal lymph nodes were imaged with respiratory-correlated FDG-PET (4D-PET) and 4D-CT. FDG-avid nodes were contoured by a radiation oncologist in two ways. Standard-of-care volumes were contoured using conventional un-gated PET, 4D-CT, and breath-hold CT. A second, motion-specific, set of volumes were contoured using 4D-PET.Contours based on 4D-PET corresponded directly to an internal target volume (ITV 4D ), whereas contours based on un-gated PET were expanded by a series of exploratory isotropic margins (from 5 to 13 mm) based on literature recommendations on lymph node motion to form internal target volumes (ITV 3D ). Results: A 13 mm expansion of the un-gated PET nodal volume was needed to cover the ITV 4D for 10 of 11 nodes studied. The ITV 3D based on a 13 mm expansion included on average 45 cm 3 of tissue that was not included in the ITV 4D . Conclusions: Motion-specific lymph-node internal target volumes generated from 4D-PET imaging could be used to improve accuracy and/or reduce normal-tissue irradiation compared to the standard-of-care un-gated PET based internal target volumes
Mod-5A wind turbine generator program design report. Volume 4: Drawings and specifications, book 3
1984-01-01
The design, development and analysis of the 7.3 MW MOD-5A wind turbine generator is documented. This volume contains the drawings and specifications developed for the final design. This volume is divided into 5 books of which this is the third, containing drawings 47A380074 through 47A380126. A full breakdown parts listing is provided as well as a where used list.
Mod-5A wind turbine generator program design report. Volume 4: Drawings and specifications, book 4
1984-01-01
The design, development and analysis of the 7.3 MW MOD-5A wind turbine generator are documented. There are four volumes. This volume contains the drawings and specifications that were developed in preparation for building the MOD-5A wind turbine generator. This volume contains 5 books of which this is the fourth, providing drawings 47A380128 through 47A387125. In addition to the parts listing and where-used list, the logic design of the controller software and the code listing of the controller software are provided. Also given are the aerodynamic profile coordinates.
Mod-5A wind turbine generator program design report. Volume 4: Drawings and specifications, book 2
1984-01-01
The design, development and analysis of the 7.3 MW MOD-5A wind turbine generator is documented. There are four volumes. This volume contains the drawings and specifications that were developed in preparation for building the MOD-5A wind turbine generator. This is the second book of volume four. Some of the items it contains are specs for the emergency shutdown panel, specs for the simulator software, simulator hardware specs, site operator terminal requirements, control data system requirements, software project management plan, elastomeric teeter bearing requirement specs, specs for the controls electronic cabinet, and specs for bolt pretensioning.
International Nuclear Information System (INIS)
Wit, B. de; Rocek, M.
1982-01-01
We construct a conformally invariant theory of the N = 1 supersymmetric tensor gauge multiplet and discuss the situation in N = 2. We show that our results give rise to the recently proposed variant of Poincare supergravity, and provide the complete tensor calculus for the theory. Finally, we argue that this theory cannot be quantized sensibly. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Price, R. E.
1983-12-31
The specifications and design criteria for all plant systems and subsystems used in developing the preliminary design of Carrisa Plains 30-MWe Solar Plant are contained in this volume. The specifications have been organized according to plant systems and levels. The levels are arranged in tiers. Starting at the top tier and proceeding down, the specification levels are the plant, system, subsystem, components, and fabrication. A tab number, listed in the index, has been assigned each document to facilitate document location.
Time integration of tensor trains
Lubich, Christian; Oseledets, Ivan; Vandereycken, Bart
2014-01-01
A robust and efficient time integrator for dynamical tensor approximation in the tensor train or matrix product state format is presented. The method is based on splitting the projector onto the tangent space of the tensor manifold. The algorithm can be used for updating time-dependent tensors in the given data-sparse tensor train / matrix product state format and for computing an approximate solution to high-dimensional tensor differential equations within this data-sparse format. The formul...
Standard technical specifications General Electric plants, BWR/6. Volume 1, Revision 1
International Nuclear Information System (INIS)
1995-04-01
This report documents the results of the combined effort of the NRC and the industry to produce improved Standard Technical Specifications (STS), Revision 1 for General Electric BWR/6 Plants. The changes reflected in Revision 1 resulted from the experience gained from license amendment applications to convert to these improved STS or to adopt partial improvements to existing technical specifications. This NUREG is the result of extensive public technical meetings and discussions between the Nuclear Regulatory Commission (NRC) staff and various nuclear power plant licensees, Nuclear Steam Supply System (NSSS) Owners Groups, NSSS vendors, and the Nuclear Energy Institute (NEI). The improved STS were developed based on the criteria in the Final Commission Policy Statement on Technical Specifications Improvements for Nuclear Power Reactors, dated July 22, 1993. The improved STS will be used as the basis for individual nuclear power plant licensees to develop improved plant-specific technical specifications. This report contains three volumes. Volume 1 contains the Specifications for all chapters and sections of the improved STS. Volume 2 contains the Bases for Chapters 2.0 and 3.0, and Sections 3.1--3.3 of the improved STS. Volume 3 contains the Bases for Sections 3.4--3.10 of the improved STS
Bregant, Tina; Rados, Milan; Vasung, Lana; Derganc, Metka; Evans, Alan C; Neubauer, David; Kostovic, Ivica
2013-11-01
A severe form of perinatal hypoxic-ischaemic encephalopathy (HIE) carries a high risk of perinatal death and severe neurological sequelae while in mild HIE only discrete cognitive disorders may occur. To compare total brain volumes and region-specific cortical measurements between young adults with mild-moderate perinatal HIE and a healthy control group of the same age. MR imaging was performed in a cohort of 14 young adults (9 males, 5 females) with a history of mild or moderate perinatal HIE. The control group consisted of healthy participants, matched with HIE group by age and gender. Volumetric analysis was done after the processing of MR images using a fully automated CIVET pipeline. We measured gyrification indexes, total brain volume, volume of grey and white matter, and of cerebrospinal fluid. We also measured volume, thickness and area of the cerebral cortex in the parietal, occipital, frontal, and temporal lobe, and of the isthmus cinguli, parahippocampal and cingulated gyrus, and insula. The HIE patient group showed smaller absolute volumetric data. Statistically significant (p right hemisphere, of cortical areas in the right temporal lobe and parahippocampal gyrus, of cortical volumes in the right temporal lobe and of cortical thickness in the right isthmus of the cingulate gyrus were found. Comparison between the healthy group and the HIE group of the same gender showed statistically significant changes in the male HIE patients, where a significant reduction was found in whole brain volume; left parietal, bilateral temporal, and right parahippocampal gyrus cortical areas; and bilateral temporal lobe cortical volume. Our analysis of total brain volumes and region-specific corticometric parameters suggests that mild-moderate forms of perinatal HIE lead to reductions in whole brain volumes. In the study reductions were most pronounced in temporal lobe and parahippocampal gyrus. Copyright © 2013 European Paediatric Neurology Society. All rights reserved.
Grey matter volume loss is associated with specific clinical motor signs in Huntington's disease.
Coppen, Emma M; Jacobs, Milou; van den Berg-Huysmans, Annette A; van der Grond, Jeroen; Roos, Raymund A C
2018-01-01
Motor disturbances are clinical hallmarks of Huntington's disease (HD) and involve chorea, dystonia, hypokinesia and visuomotor dysfunction. Investigating the association between specific motor signs and different regional volumes is important to understand the heterogeneity of HD. To investigate the motor phenotype of HD and associations with subcortical and cortical grey matter volume loss. Structural T1-weighted MRI scans of 79 HD patients and 30 healthy controls were used to calculate volumes of seven subcortical structures including the nucleus accumbens, hippocampus, thalamus, caudate nucleus, putamen, pallidum and amygdala. Multiple linear regression analyses, corrected for age, gender, CAG, MRI scan protocol and normalized brain volume, were performed to assess the relationship between subcortical volumes and different motor subdomains (i.e. eye movements, chorea, dystonia, hypokinesia/rigidity and gait/balance). Voxel-based morphometry analysis was used to investigate the relationship between cortical volume changes and motor signs. Subcortical volume loss of the accumbens nucleus, caudate nucleus, putamen, and pallidum were associated with higher chorea scores. No other subcortical region was significantly associated with motor symptoms after correction for multiple comparisons. Voxel-based cortical grey matter volume reductions in occipital regions were related with an increase in eye movement scores. In HD, chorea is mainly associated with subcortical volume loss, while eye movements are more related to cortical volume loss. Both subcortical and cortical degeneration has an impact on motor impairment in HD. This implies that there is a widespread contribution of different brain regions resulting in the clinical motor presentation seen in HD patients. Copyright © 2017 Elsevier Ltd. All rights reserved.
Introduction to vector and tensor analysis
Wrede, Robert C
1972-01-01
A broad introductory treatment, this volume examines general Cartesian coordinates, the cross product, Einstein's special theory of relativity, bases in general coordinate systems, maxima and minima of functions of two variables, line integrals, integral theorems, fundamental notions in n-space, Riemannian geometry, algebraic properties of the curvature tensor, and more. 1963 edition.
Tensor spherical harmonics and tensor multipoles. II. Minkowski space
International Nuclear Information System (INIS)
Daumens, M.; Minnaert, P.
1976-01-01
The bases of tensor spherical harmonics and of tensor multipoles discussed in the preceding paper are generalized in the Hilbert space of Minkowski tensor fields. The transformation properties of the tensor multipoles under Lorentz transformation lead to the notion of irreducible tensor multipoles. We show that the usual 4-vector multipoles are themselves irreducible, and we build the irreducible tensor multipoles of the second order. We also give their relations with the symmetric tensor multipoles defined by Zerilli for application to the gravitational radiation
van der Beek, M.H.E.; Peters, G.W.M.; Meijer, H.E.H.
2006-01-01
The influence of shear flow on the temperature evolution of the specific volume and the crystalline morphology of two iPP's, differing in weight-averaged molar mass w, was investigated at nonisothermal conditions and elevated pressures, using a custom-designed dilatometer. These conditions are
A dilatometer to measure the influence of cooling rate and melt shearing on specific volume
van der Beek, M.H.E.; Peters, G.W.M.; Meijer, H.E.H.
2005-01-01
We developed a dilatometer to investigate the specific volume of polymers as a function of pressure (to 100 MPa), temperature (to 260 oC), cooling rate (to 80 C/s), and shear rate (to 77 1/s). The dilatometeris based on the principle of con¯ned compression and comprises of a pressure cell used in
Weisburd, Melvin I.
The Field Operations and Enforcement Manual for Air Pollution Control, Volume III, explains in detail the following: inspection procedures for specific sources, kraft pulp mills, animal rendering, steel mill furnaces, coking operations, petroleum refineries, chemical plants, non-ferrous smelting and refining, foundries, cement plants, aluminum…
Reconstruction of convex bodies from surface tensors
DEFF Research Database (Denmark)
Kousholt, Astrid; Kiderlen, Markus
We present two algorithms for reconstruction of the shape of convex bodies in the two-dimensional Euclidean space. The first reconstruction algorithm requires knowledge of the exact surface tensors of a convex body up to rank s for some natural number s. The second algorithm uses harmonic intrinsic...... volumes which are certain values of the surface tensors and allows for noisy measurements. From a generalized version of Wirtinger's inequality, we derive stability results that are utilized to ensure consistency of both reconstruction procedures. Consistency of the reconstruction procedure based...
Park, Tae Yong; Chae, Ji Yun; Kim, Jong Wook; Kim, Jin Wook; Oh, Mi Mi; Yoon, Cheol Yong; Moon, Du Geon
2013-01-01
Purpose It has been reported that prostate-specific antigen (PSA) correlates with prostate volume. Recently, some studies have reported that PSA mass (PSA adjusted for plasma volume) is more accurate than PSA at predicting prostate volume. In this study, we analyzed the accuracy of PSA and the related parameters of PSA mass, free PSA (fPSA), and fPSA mass in predicting prostate volume. Materials and Methods We retrospectively investigated 658 patients who underwent prostate biopsy from 2006 t...
Tensors and their applications
Islam, Nazrul
2006-01-01
About the Book: The book is written is in easy-to-read style with corresponding examples. The main aim of this book is to precisely explain the fundamentals of Tensors and their applications to Mechanics, Elasticity, Theory of Relativity, Electromagnetic, Riemannian Geometry and many other disciplines of science and engineering, in a lucid manner. The text has been explained section wise, every concept has been narrated in the form of definition, examples and questions related to the concept taught. The overall package of the book is highly useful and interesting for the people associated with the field. Contents: Preliminaries Tensor Algebra Metric Tensor and Riemannian Metric Christoffel`s Symbols and Covariant Differentiation Riemann-Christoffel Tensor The e-Systems and the Generalized Krönecker Deltas Geometry Analytical Mechanics Curvature of a Curve, Geodesic Parallelism of Vectors Ricci`s Coefficients of Rotation and Congruence Hyper Surfaces
Symmetric Tensor Decomposition
DEFF Research Database (Denmark)
Brachat, Jerome; Comon, Pierre; Mourrain, Bernard
2010-01-01
We present an algorithm for decomposing a symmetric tensor, of dimension n and order d, as a sum of rank-1 symmetric tensors, extending the algorithm of Sylvester devised in 1886 for binary forms. We recall the correspondence between the decomposition of a homogeneous polynomial in n variables...... of polynomial equations of small degree in non-generic cases. We propose a new algorithm for symmetric tensor decomposition, based on this characterization and on linear algebra computations with Hankel matrices. The impact of this contribution is two-fold. First it permits an efficient computation...... of the decomposition of any tensor of sub-generic rank, as opposed to widely used iterative algorithms with unproved global convergence (e.g. Alternate Least Squares or gradient descents). Second, it gives tools for understanding uniqueness conditions and for detecting the rank....
International Nuclear Information System (INIS)
Scheunert, M.
1982-10-01
We develop a graded tensor calculus corresponding to arbitrary Abelian groups of degrees and arbitrary commutation factors. The standard basic constructions and definitions like tensor products, spaces of multilinear mappings, contractions, symmetrization, symmetric algebra, as well as the transpose, adjoint, and trace of a linear mapping, are generalized to the graded case and a multitude of canonical isomorphisms is presented. Moreover, the graded versions of the classical Lie algebras are introduced and some of their basic properties are described. (orig.)
Mod-5A Wind Turbine Generator Program Design Report. Volume 4: Drawings and Specifications, Book 1
1984-01-01
The design, development and analysis of the 7.3 MW MOD-5A wind turbine generator is documented. Volume 4 contains the drawings and specifications that were developed in preparation for building the MOD-5A wind turbine generator. This is the first of five books of volume four. It contains structural design criteria, generator step-up transformer specs, specs for design, fabrication and testing of the system, specs for the ground control enclosure, systems specs, slip ring specs, and control system specs.
Lazzeretti, Paolo
2018-04-01
It is shown that nonsymmetric second-rank current density tensors, related to the current densities induced by magnetic fields and nuclear magnetic dipole moments, are fundamental properties of a molecule. Together with magnetizability, nuclear magnetic shielding, and nuclear spin-spin coupling, they completely characterize its response to magnetic perturbations. Gauge invariance, resolution into isotropic, deviatoric, and antisymmetric parts, and contributions of current density tensors to magnetic properties are discussed. The components of the second-rank tensor properties are rationalized via relationships explicitly connecting them to the direction of the induced current density vectors and to the components of the current density tensors. The contribution of the deviatoric part to the average value of magnetizability, nuclear shielding, and nuclear spin-spin coupling, uniquely determined by the antisymmetric part of current density tensors, vanishes identically. The physical meaning of isotropic and anisotropic invariants of current density tensors has been investigated, and the connection between anisotropy magnitude and electron delocalization has been discussed.
Properties of the tensor correlation in He isotopes
International Nuclear Information System (INIS)
Myo, Takayuki; Sugimoto, Satoru; Kato, Kiyoshi; Toki, Hiroshi; Ikeda, Kiyomi
2006-01-01
We investigate the roles of the tensor correlation on the structures of 4,5 He. For 4 He, we take the high angular momentum states as much as possible with the 2p2h excitations of the shell model type method to describe the tensor correlation. Three specific configurations are found to be favored for the tensor correlation. This correlation is also important to describe the scattering phenomena of the 4 He+nsystem including the higher partial waves consistently
Depping, Malte S; Wolf, Nadine D; Vasic, Nenad; Sambataro, Fabio; Thomann, Philipp A; Christian Wolf, R
2015-03-15
Abnormal brain volume has been frequently demonstrated in major depressive disorder (MDD). It is unclear if these findings are specific for MDD since aberrant brain structure is also present in disorders with depressive comorbidity and affective dysregulation, such as borderline personality disorder (BPD). In this transdiagnostic study, we aimed to investigate if regional brain volume loss differentiates between MDD and BPD. Further, we tested for associations between brain volume and clinical variables within and between diagnostic groups. 22 Females with a DSM-IV diagnosis of MDD, 17 females with a DSM-IV diagnosis of BPD and without comorbid posttraumatic stress disorder, and 22 age-matched female healthy controls (HC) were investigated using magnetic resonance imaging. High-resolution structural data were analyzed using voxel-based morphometry. A significant (pdisorders. Copyright © 2014 Elsevier B.V. All rights reserved.
A Review of Tensors and Tensor Signal Processing
Cammoun, L.; Castaño-Moraga, C. A.; Muñoz-Moreno, E.; Sosa-Cabrera, D.; Acar, B.; Rodriguez-Florido, M. A.; Brun, A.; Knutsson, H.; Thiran, J. P.
Tensors have been broadly used in mathematics and physics, since they are a generalization of scalars or vectors and allow to represent more complex properties. In this chapter we present an overview of some tensor applications, especially those focused on the image processing field. From a mathematical point of view, a lot of work has been developed about tensor calculus, which obviously is more complex than scalar or vectorial calculus. Moreover, tensors can represent the metric of a vector space, which is very useful in the field of differential geometry. In physics, tensors have been used to describe several magnitudes, such as the strain or stress of materials. In solid mechanics, tensors are used to define the generalized Hooke’s law, where a fourth order tensor relates the strain and stress tensors. In fluid dynamics, the velocity gradient tensor provides information about the vorticity and the strain of the fluids. Also an electromagnetic tensor is defined, that simplifies the notation of the Maxwell equations. But tensors are not constrained to physics and mathematics. They have been used, for instance, in medical imaging, where we can highlight two applications: the diffusion tensor image, which represents how molecules diffuse inside the tissues and is broadly used for brain imaging; and the tensorial elastography, which computes the strain and vorticity tensor to analyze the tissues properties. Tensors have also been used in computer vision to provide information about the local structure or to define anisotropic image filters.
Tensor network decompositions in the presence of a global symmetry
International Nuclear Information System (INIS)
Singh, Sukhwinder; Pfeifer, Robert N. C.; Vidal, Guifre
2010-01-01
Tensor network decompositions offer an efficient description of certain many-body states of a lattice system and are the basis of a wealth of numerical simulation algorithms. We discuss how to incorporate a global symmetry, given by a compact, completely reducible group G, in tensor network decompositions and algorithms. This is achieved by considering tensors that are invariant under the action of the group G. Each symmetric tensor decomposes into two types of tensors: degeneracy tensors, containing all the degrees of freedom, and structural tensors, which only depend on the symmetry group. In numerical calculations, the use of symmetric tensors ensures the preservation of the symmetry, allows selection of a specific symmetry sector, and significantly reduces computational costs. On the other hand, the resulting tensor network can be interpreted as a superposition of exponentially many spin networks. Spin networks are used extensively in loop quantum gravity, where they represent states of quantum geometry. Our work highlights their importance in the context of tensor network algorithms as well, thus setting the stage for cross-fertilization between these two areas of research.
Aarnink, R. G.; de la Rosette, J. J.; Huynen, A. L.; Giesen, R. J.; Debruyne, F. M.; Wijkstra, H.
1996-01-01
Standardized estimations of prostate volumes are used for interpretation of prostate specific antigen (PSA) levels. In 243 patients with clinically benign diagnosis, automated and reference prostate volumes and transition zone volumes are correlated to PSA levels. Besides, growth curves of PSA level
Tensor spaces and exterior algebra
Yokonuma, Takeo
1992-01-01
This book explains, as clearly as possible, tensors and such related topics as tensor products of vector spaces, tensor algebras, and exterior algebras. You will appreciate Yokonuma's lucid and methodical treatment of the subject. This book is useful in undergraduate and graduate courses in multilinear algebra. Tensor Spaces and Exterior Algebra begins with basic notions associated with tensors. To facilitate understanding of the definitions, Yokonuma often presents two or more different ways of describing one object. Next, the properties and applications of tensors are developed, including the classical definition of tensors and the description of relative tensors. Also discussed are the algebraic foundations of tensor calculus and applications of exterior algebra to determinants and to geometry. This book closes with an examination of algebraic systems with bilinear multiplication. In particular, Yokonuma discusses the theory of replicas of Chevalley and several properties of Lie algebras deduced from them.
Tensor analysis for physicists
Schouten, J A
1989-01-01
This brilliant study by a famed mathematical scholar and former professor of mathematics at the University of Amsterdam integrates a concise exposition of the mathematical basis of tensor analysis with admirably chosen physical examples of the theory. The first five chapters incisively set out the mathematical theory underlying the use of tensors. The tensor algebra in EN and RN is developed in Chapters I and II. Chapter II introduces a sub-group of the affine group, then deals with the identification of quantities in EN. The tensor analysis in XN is developed in Chapter IV. In chapters VI through IX, Professor Schouten presents applications of the theory that are both intrinsically interesting and good examples of the use and advantages of the calculus. Chapter VI, intimately connected with Chapter III, shows that the dimensions of physical quantities depend upon the choice of the underlying group, and that tensor calculus is the best instrument for dealing with the properties of anisotropic media. In Chapte...
Generalized dielectric permittivity tensor
International Nuclear Information System (INIS)
Borzdov, G.N.; Barkovskii, L.M.; Fedorov, F.I.
1986-01-01
The authors deal with the question of what is to be done with the formalism of the electrodynamics of dispersive media based on the introduction of dielectric-permittivity tensors for purely harmonic fields when Voigt waves and waves of more general form exist. An attempt is made to broaden and generalize the formalism to take into account dispersion of waves of the given type. In dispersive media, the polarization, magnetization, and conduction current-density vectors of point and time are determined by the values of the electromagnetic field vectors in the vicinity of this point (spatial dispersion) in the preceding instants of time (time dispersion). The dielectric-permittivity tensor and other tensors of electrodynamic parameters of the medium are introduced in terms of a set of evolution operators and not the set of harmonic function. It is noted that a magnetic-permeability tensor and an elastic-modulus tensor may be introduced for an acoustic field in dispersive anisotropic media with coupling equations of general form
Killing tensors and conformal Killing tensors from conformal Killing vectors
International Nuclear Information System (INIS)
Rani, Raffaele; Edgar, S Brian; Barnes, Alan
2003-01-01
Koutras has proposed some methods to construct reducible proper conformal Killing tensors and Killing tensors (which are, in general, irreducible) when a pair of orthogonal conformal Killing vectors exist in a given space. We give the completely general result demonstrating that this severe restriction of orthogonality is unnecessary. In addition, we correct and extend some results concerning Killing tensors constructed from a single conformal Killing vector. A number of examples demonstrate that it is possible to construct a much larger class of reducible proper conformal Killing tensors and Killing tensors than permitted by the Koutras algorithms. In particular, by showing that all conformal Killing tensors are reducible in conformally flat spaces, we have a method of constructing all conformal Killing tensors, and hence all the Killing tensors (which will in general be irreducible) of conformally flat spaces using their conformal Killing vectors
Energy Technology Data Exchange (ETDEWEB)
Chatzistavrakidis, Athanasios [Van Swinderen Institute for Particle Physics and Gravity, University of Groningen,Nijenborgh 4, 9747 AG Groningen (Netherlands); Khoo, Fech Scen [Department of Physics and Earth Sciences, Jacobs University Bremen,Campus Ring 1, 28759 Bremen (Germany); Roest, Diederik [Van Swinderen Institute for Particle Physics and Gravity, University of Groningen,Nijenborgh 4, 9747 AG Groningen (Netherlands); Schupp, Peter [Department of Physics and Earth Sciences, Jacobs University Bremen,Campus Ring 1, 28759 Bremen (Germany)
2017-03-13
The particular structure of Galileon interactions allows for higher-derivative terms while retaining second order field equations for scalar fields and Abelian p-forms. In this work we introduce an index-free formulation of these interactions in terms of two sets of Grassmannian variables. We employ this to construct Galileon interactions for mixed-symmetry tensor fields and coupled systems thereof. We argue that these tensors are the natural generalization of scalars with Galileon symmetry, similar to p-forms and scalars with a shift-symmetry. The simplest case corresponds to linearised gravity with Lovelock invariants, relating the Galileon symmetry to diffeomorphisms. Finally, we examine the coupling of a mixed-symmetry tensor to gravity, and demonstrate in an explicit example that the inclusion of appropriate counterterms retains second order field equations.
Tziatzios, C.; Precup, A.A.; Weidl, C.H.; Schubert, U.S.; Schuck, P.; Durchschlag, H.; Mächtle, W.; Broek, van den J.A.; Schubert, D.
2002-01-01
The specific volume of charged supramolecular compounds dissolved in organic solvents varies considerably with the solvent system applied; in addition, it is influenced by the presence of salt. In this study we determined the specific volume of an uncharged molecule from the same molar mass range in
Tensor Basis Neural Network v. 1.0 (beta)
Energy Technology Data Exchange (ETDEWEB)
2017-03-28
This software package can be used to build, train, and test a neural network machine learning model. The neural network architecture is specifically designed to embed tensor invariance properties by enforcing that the model predictions sit on an invariant tensor basis. This neural network architecture can be used in developing constitutive models for applications such as turbulence modeling, materials science, and electromagnetism.
Tensor valuations and their applications in stochastic geometry and imaging
Kiderlen, Markus
2017-01-01
The purpose of this volume is to give an up-to-date introduction to tensor valuations and their applications. Starting with classical results concerning scalar-valued valuations on the families of convex bodies and convex polytopes, it proceeds to the modern theory of tensor valuations. Product and Fourier-type transforms are introduced and various integral formulae are derived. New and well-known results are presented, together with generalizations in several directions, including extensions to the non-Euclidean setting and to non-convex sets. A variety of applications of tensor valuations to models in stochastic geometry, to local stereology and to imaging are also discussed.
International Nuclear Information System (INIS)
Alsing, Paul M; McDonald, Jonathan R; Miller, Warner A
2011-01-01
The Ricci tensor (Ric) is fundamental to Einstein's geometric theory of gravitation. The three-dimensional Ric of a spacelike surface vanishes at the moment of time symmetry for vacuum spacetimes. The four-dimensional Ric is the Einstein tensor for such spacetimes. More recently, the Ric was used by Hamilton to define a nonlinear, diffusive Ricci flow (RF) that was fundamental to Perelman's proof of the Poincare conjecture. Analytic applications of RF can be found in many fields including general relativity and mathematics. Numerically it has been applied broadly to communication networks, medical physics, computer design and more. In this paper, we use Regge calculus (RC) to provide the first geometric discretization of the Ric. This result is fundamental for higher dimensional generalizations of discrete RF. We construct this tensor on both the simplicial lattice and its dual and prove their equivalence. We show that the Ric is an edge-based weighted average of deficit divided by an edge-based weighted average of dual area-an expression similar to the vertex-based weighted average of the scalar curvature reported recently. We use this Ric in a third and independent geometric derivation of the RC Einstein tensor in arbitrary dimensions.
Alsing, Paul M.; McDonald, Jonathan R.; Miller, Warner A.
2011-08-01
The Ricci tensor (Ric) is fundamental to Einstein's geometric theory of gravitation. The three-dimensional Ric of a spacelike surface vanishes at the moment of time symmetry for vacuum spacetimes. The four-dimensional Ric is the Einstein tensor for such spacetimes. More recently, the Ric was used by Hamilton to define a nonlinear, diffusive Ricci flow (RF) that was fundamental to Perelman's proof of the Poincarè conjecture. Analytic applications of RF can be found in many fields including general relativity and mathematics. Numerically it has been applied broadly to communication networks, medical physics, computer design and more. In this paper, we use Regge calculus (RC) to provide the first geometric discretization of the Ric. This result is fundamental for higher dimensional generalizations of discrete RF. We construct this tensor on both the simplicial lattice and its dual and prove their equivalence. We show that the Ric is an edge-based weighted average of deficit divided by an edge-based weighted average of dual area—an expression similar to the vertex-based weighted average of the scalar curvature reported recently. We use this Ric in a third and independent geometric derivation of the RC Einstein tensor in arbitrary dimensions.
The evolution of tensor polarization
International Nuclear Information System (INIS)
Huang, H.; Lee, S.Y.; Ratner, L.
1993-01-01
By using the equation of motion for the vector polarization, the spin transfer matrix for spin tensor polarization, the spin transfer matrix for spin tensor polarization is derived. The evolution equation for the tensor polarization is studied in the presence of an isolate spin resonance and in the presence of a spin rotor, or snake
Tensor Calculus: Unlearning Vector Calculus
Lee, Wha-Suck; Engelbrecht, Johann; Moller, Rita
2018-01-01
Tensor calculus is critical in the study of the vector calculus of the surface of a body. Indeed, tensor calculus is a natural step-up for vector calculus. This paper presents some pitfalls of a traditional course in vector calculus in transitioning to tensor calculus. We show how a deeper emphasis on traditional topics such as the Jacobian can…
Time-optimized high-resolution readout-segmented diffusion tensor imaging.
Directory of Open Access Journals (Sweden)
Gernot Reishofer
Full Text Available Readout-segmented echo planar imaging with 2D navigator-based reacquisition is an uprising technique enabling the sampling of high-resolution diffusion images with reduced susceptibility artifacts. However, low signal from the small voxels and long scan times hamper the clinical applicability. Therefore, we introduce a regularization algorithm based on total variation that is applied directly on the entire diffusion tensor. The spatially varying regularization parameter is determined automatically dependent on spatial variations in signal-to-noise ratio thus, avoiding over- or under-regularization. Information about the noise distribution in the diffusion tensor is extracted from the diffusion weighted images by means of complex independent component analysis. Moreover, the combination of those features enables processing of the diffusion data absolutely user independent. Tractography from in vivo data and from a software phantom demonstrate the advantage of the spatially varying regularization compared to un-regularized data with respect to parameters relevant for fiber-tracking such as Mean Fiber Length, Track Count, Volume and Voxel Count. Specifically, for in vivo data findings suggest that tractography results from the regularized diffusion tensor based on one measurement (16 min generates results comparable to the un-regularized data with three averages (48 min. This significant reduction in scan time renders high resolution (1 × 1 × 2.5 mm(3 diffusion tensor imaging of the entire brain applicable in a clinical context.
Solid Waste Operations Complex W-113, Detail Design Report (Title II). Volume 3: Specifications
International Nuclear Information System (INIS)
1995-09-01
The Solid Waste Retrieval Facility--Phase 1 (Project W113) will provide the infrastructure and the facility required to retrieve from Trench 04, Burial ground 4C, contact handled (CH) drums and boxes at a rate that supports all retrieved TRU waste batching, treatment, storage, and disposal plans. This includes (1) operations related equipment and facilities, viz., a weather enclosure for the trench, retrieval equipment, weighing, venting, obtaining gas samples, overpacking, NDE, NDA, shipment of waste and (2) operations support related facilities, viz., a general office building, a retrieval staff change facility, and infrastructure upgrades such as supply and routing of water, sewer, electrical power, fire protection, roads, and telecommunication. Title I design for the operations related equipment and facilities was performed by Raytheon/BNFL, and that for the operations support related facilities including infrastructure upgrade was performed by KEH. These two scopes were combined into an integrated W113 Title II scope that was performed by Raytheon/BNFL. Volume 3 is a compilation of the construction specifications that will constitute the Title II materials and performance specifications. This volume contains CSI specifications for non-equipment related construction material type items, performance type items, and facility mechanical equipment items. Data sheets are provided, as necessary, which specify the equipment overall design parameters
Solid Waste Operations Complex W-113, Detail Design Report (Title II). Volume 3: Specifications
Energy Technology Data Exchange (ETDEWEB)
NONE
1995-09-01
The Solid Waste Retrieval Facility--Phase 1 (Project W113) will provide the infrastructure and the facility required to retrieve from Trench 04, Burial ground 4C, contact handled (CH) drums and boxes at a rate that supports all retrieved TRU waste batching, treatment, storage, and disposal plans. This includes (1) operations related equipment and facilities, viz., a weather enclosure for the trench, retrieval equipment, weighing, venting, obtaining gas samples, overpacking, NDE, NDA, shipment of waste and (2) operations support related facilities, viz., a general office building, a retrieval staff change facility, and infrastructure upgrades such as supply and routing of water, sewer, electrical power, fire protection, roads, and telecommunication. Title I design for the operations related equipment and facilities was performed by Raytheon/BNFL, and that for the operations support related facilities including infrastructure upgrade was performed by KEH. These two scopes were combined into an integrated W113 Title II scope that was performed by Raytheon/BNFL. Volume 3 is a compilation of the construction specifications that will constitute the Title II materials and performance specifications. This volume contains CSI specifications for non-equipment related construction material type items, performance type items, and facility mechanical equipment items. Data sheets are provided, as necessary, which specify the equipment overall design parameters.
Structural connectivity via the tensor-based morphometry
Kim, S.; Chung, M.; Hanson, J.; Avants, B.; Gee, J.; Davidson, R.; Pollak, S.
2011-01-01
The tensor-based morphometry (TBM) has been widely used in characterizing tissue volume difference between populations at voxel level. We present a novel computational framework for investigating the white matter connectivity using TBM. Unlike other diffusion tensor imaging (DTI) based white matter connectivity studies, we do not use DTI but only T1-weighted magnetic resonance imaging (MRI). To construct brain network graphs, we have developed a new data-driven approach called the ε-neighbor ...
Diffusion tensor image registration using hybrid connectivity and tensor features.
Wang, Qian; Yap, Pew-Thian; Wu, Guorong; Shen, Dinggang
2014-07-01
Most existing diffusion tensor imaging (DTI) registration methods estimate structural correspondences based on voxelwise matching of tensors. The rich connectivity information that is given by DTI, however, is often neglected. In this article, we propose to integrate complementary information given by connectivity features and tensor features for improved registration accuracy. To utilize connectivity information, we place multiple anchors representing different brain anatomies in the image space, and define the connectivity features for each voxel as the geodesic distances from all anchors to the voxel under consideration. The geodesic distance, which is computed in relation to the tensor field, encapsulates information of brain connectivity. We also extract tensor features for every voxel to reflect the local statistics of tensors in its neighborhood. We then combine both connectivity features and tensor features for registration of tensor images. From the images, landmarks are selected automatically and their correspondences are determined based on their connectivity and tensor feature vectors. The deformation field that deforms one tensor image to the other is iteratively estimated and optimized according to the landmarks and their associated correspondences. Experimental results show that, by using connectivity features and tensor features simultaneously, registration accuracy is increased substantially compared with the cases using either type of features alone. Copyright © 2013 Wiley Periodicals, Inc.
Technical specifications manual for the MARK-1 pulsed ionizing radiation detection system. Volume 1
Energy Technology Data Exchange (ETDEWEB)
Lawrence, R.S.; Harker, Y.D.; Jones, J.L.; Hoggan, J.M.
1993-03-01
The MARK-1 detection system was developed by the Idaho National Engineering Laboratory for the US Department of Energy Office of Arms Control and Nonproliferation. The completely portable system was designed for the detection and analysis of intense photon emissions from pulsed ionizing radiation sources. This manual presents the technical design specifications for the MARK-1 detection system and was written primarily to assist the support or service technician in the service, calibration, and repair of the system. The manual presents the general detection system theory, the MARK-1 component design specifications, the acquisition and control software, the data processing sequence, and the system calibration procedure. A second manual entitled: Volume 2: Operations Manual for the MARK-1 Pulsed Ionizing Radiation Detection System (USDOE Report WINCO-1108, September 1992) provides a general operational description of the MARK-1 detection system. The Operations Manual was written primarily to assist the field operator in system operations and analysis of the data.
Roquet, F.; Madec, G.; McDougall, Trevor J.; Barker, Paul M.
2015-06-01
A new set of approximations to the standard TEOS-10 equation of state are presented. These follow a polynomial form, making it computationally efficient for use in numerical ocean models. Two versions are provided, the first being a fit of density for Boussinesq ocean models, and the second fitting specific volume which is more suitable for compressible models. Both versions are given as the sum of a vertical reference profile (6th-order polynomial) and an anomaly (52-term polynomial, cubic in pressure), with relative errors of ∼0.1% on the thermal expansion coefficients. A 75-term polynomial expression is also presented for computing specific volume, with a better accuracy than the existing TEOS-10 48-term rational approximation, especially regarding the sound speed, and it is suggested that this expression represents a valuable approximation of the TEOS-10 equation of state for hydrographic data analysis. In the last section, practical aspects about the implementation of TEOS-10 in ocean models are discussed.
Gogny interactions with tensor terms
Energy Technology Data Exchange (ETDEWEB)
Anguiano, M.; Lallena, A.M.; Bernard, R.N. [Universidad de Granada, Departamento de Fisica Atomica, Molecular y Nuclear, Granada (Spain); Co' , G. [INFN, Lecce (Italy); De Donno, V. [Universita del Salento, Dipartimento di Matematica e Fisica ' ' E. De Giorgi' ' , Lecce (Italy); Grasso, M. [Universite Paris-Sud, Institut de Physique Nucleaire, IN2P3-CNRS, Orsay (France)
2016-07-15
We present a perturbative approach to include tensor terms in the Gogny interaction. We do not change the values of the usual parameterisations, with the only exception of the spin-orbit term, and we add tensor terms whose only free parameters are the strengths of the interactions. We identify observables sensitive to the presence of the tensor force in Hartree-Fock, Hartree-Fock-Bogoliubov and random phase approximation calculations. We show the need of including two tensor contributions, at least: a pure tensor term and a tensor-isospin term. We show results relevant for the inclusion of the tensor term for single-particle energies, charge-conserving magnetic excitations and Gamow-Teller excitations. (orig.)
The geomagnetic field gradient tensor
DEFF Research Database (Denmark)
Kotsiaros, Stavros; Olsen, Nils
2012-01-01
We develop the general mathematical basis for space magnetic gradiometry in spherical coordinates. The magnetic gradient tensor is a second rank tensor consisting of 3 × 3 = 9 spatial derivatives. Since the geomagnetic field vector B is always solenoidal (∇ · B = 0) there are only eight independent...... tensor elements. Furthermore, in current free regions the magnetic gradient tensor becomes symmetric, further reducing the number of independent elements to five. In that case B is a Laplacian potential field and the gradient tensor can be expressed in series of spherical harmonics. We present properties...... of the magnetic gradient tensor and provide explicit expressions of its elements in terms of spherical harmonics. Finally we discuss the benefit of using gradient measurements for exploring the Earth’s magnetic field from space, in particular the advantage of the various tensor elements for a better determination...
International Nuclear Information System (INIS)
Davis, E.; Rasmussen, B.
2004-01-01
This report is a guide for a technical specification change submittal and subsequent implementation of on-line monitoring for safety-related applications. This report is the third in a three-volume set. Volume 1, ''Guidelines for Model Development and Implementation'', presents the various tasks that must be completed to prepare models for and to implement an on-line monitoring system
International Nuclear Information System (INIS)
Littlejohn, R.G.
1982-01-01
The Hamiltonian structures discovered by Morrison and Greene for various fluid equations were obtained by guessing a Hamiltonian and a suitable Poisson bracket formula, expressed in terms of noncanonical (but physical) coordinates. In general, such a procedure for obtaining a Hamiltonian system does not produce a Hamiltonian phase space in the usual sense (a symplectic manifold), but rather a family of symplectic manifolds. To state the matter in terms of a system with a finite number of degrees of freedom, the family of symplectic manifolds is parametrized by a set of Casimir functions, which are characterized by having vanishing Poisson brackets with all other functions. The number of independent Casimir functions is the corank of the Poisson tensor J/sup ij/, the components of which are the Poisson brackets of the coordinates among themselves. Thus, these Casimir functions exist only when the Poisson tensor is singular
The tensor distribution function.
Leow, A D; Zhu, S; Zhan, L; McMahon, K; de Zubicaray, G I; Meredith, M; Wright, M J; Toga, A W; Thompson, P M
2009-01-01
Diffusion weighted magnetic resonance imaging is a powerful tool that can be employed to study white matter microstructure by examining the 3D displacement profile of water molecules in brain tissue. By applying diffusion-sensitized gradients along a minimum of six directions, second-order tensors (represented by three-by-three positive definite matrices) can be computed to model dominant diffusion processes. However, conventional DTI is not sufficient to resolve more complicated white matter configurations, e.g., crossing fiber tracts. Recently, a number of high-angular resolution schemes with more than six gradient directions have been employed to address this issue. In this article, we introduce the tensor distribution function (TDF), a probability function defined on the space of symmetric positive definite matrices. Using the calculus of variations, we solve the TDF that optimally describes the observed data. Here, fiber crossing is modeled as an ensemble of Gaussian diffusion processes with weights specified by the TDF. Once this optimal TDF is determined, the orientation distribution function (ODF) can easily be computed by analytic integration of the resulting displacement probability function. Moreover, a tensor orientation distribution function (TOD) may also be derived from the TDF, allowing for the estimation of principal fiber directions and their corresponding eigenvalues.
Tensor-Based Dictionary Learning for Spectral CT Reconstruction.
Zhang, Yanbo; Mou, Xuanqin; Wang, Ge; Yu, Hengyong
2017-01-01
Spectral computed tomography (CT) produces an energy-discriminative attenuation map of an object, extending a conventional image volume with a spectral dimension. In spectral CT, an image can be sparsely represented in each of multiple energy channels, and are highly correlated among energy channels. According to this characteristics, we propose a tensor-based dictionary learning method for spectral CT reconstruction. In our method, tensor patches are extracted from an image tensor, which is reconstructed using the filtered backprojection (FBP), to form a training dataset. With the Candecomp/Parafac decomposition, a tensor-based dictionary is trained, in which each atom is a rank-one tensor. Then, the trained dictionary is used to sparsely represent image tensor patches during an iterative reconstruction process, and the alternating minimization scheme is adapted for optimization. The effectiveness of our proposed method is validated with both numerically simulated and real preclinical mouse datasets. The results demonstrate that the proposed tensor-based method generally produces superior image quality, and leads to more accurate material decomposition than the currently popular popular methods.
Tensor-based Dictionary Learning for Spectral CT Reconstruction
Zhang, Yanbo; Wang, Ge
2016-01-01
Spectral computed tomography (CT) produces an energy-discriminative attenuation map of an object, extending a conventional image volume with a spectral dimension. In spectral CT, an image can be sparsely represented in each of multiple energy channels, and are highly correlated among energy channels. According to this characteristics, we propose a tensor-based dictionary learning method for spectral CT reconstruction. In our method, tensor patches are extracted from an image tensor, which is reconstructed using the filtered backprojection (FBP), to form a training dataset. With the Candecomp/Parafac decomposition, a tensor-based dictionary is trained, in which each atom is a rank-one tensor. Then, the trained dictionary is used to sparsely represent image tensor patches during an iterative reconstruction process, and the alternating minimization scheme is adapted for optimization. The effectiveness of our proposed method is validated with both numerically simulated and real preclinical mouse datasets. The results demonstrate that the proposed tensor-based method generally produces superior image quality, and leads to more accurate material decomposition than the currently popular popular methods. PMID:27541628
Tensor Permutation Matrices in Finite Dimensions
Christian, Rakotonirina
2005-01-01
We have generalised the properties with the tensor product, of one 4x4 matrix which is a permutation matrix, and we call a tensor commutation matrix. Tensor commutation matrices can be constructed with or without calculus. A formula allows us to construct a tensor permutation matrix, which is a generalisation of tensor commutation matrix, has been established. The expression of an element of a tensor commutation matrix has been generalised in the case of any element of a tensor permutation ma...
Relativistic interpretation of the nature of the nuclear tensor force
Zong, Yao-Yao; Sun, Bao-Yuan
2018-02-01
The spin-dependent nature of the nuclear tensor force is studied in detail within the relativistic Hartree-Fock approach. The relativistic formalism for the tensor force is supplemented with an additional Lorentz-invariant tensor formalism in the σ-scalar channel, so as to take into account almost fully the nature of the tensor force brought about by the Fock diagrams in realistic nuclei. Specifically, the tensor sum rules are tested for the spin and pseudo-spin partners with and without nodes, to further understand the nature of the tensor force within the relativistic model. It is shown that the interference between the two components of nucleon spinors causes distinct violations of the tensor sum rules in realistic nuclei, mainly due to the opposite signs on the κ quantities of the upper and lower components, as well as the nodal difference. However, the sum rules can be precisely reproduced if the same radial wave functions are taken for the spin/pseudo-spin partners in addition to neglecting the lower/upper components, revealing clearly the nature of the tensor force. Supported by National Natural Science Foundation of China (11375076, 11675065) and the Fundamental Research Funds for the Central Universities (lzujbky-2016-30)
OPERATOR NORM INEQUALITIES BETWEEN TENSOR UNFOLDINGS ON THE PARTITION LATTICE.
Wang, Miaoyan; Duc, Khanh Dao; Fischer, Jonathan; Song, Yun S
2017-05-01
Interest in higher-order tensors has recently surged in data-intensive fields, with a wide range of applications including image processing, blind source separation, community detection, and feature extraction. A common paradigm in tensor-related algorithms advocates unfolding (or flattening) the tensor into a matrix and applying classical methods developed for matrices. Despite the popularity of such techniques, how the functional properties of a tensor changes upon unfolding is currently not well understood. In contrast to the body of existing work which has focused almost exclusively on matricizations, we here consider all possible unfoldings of an order- k tensor, which are in one-to-one correspondence with the set of partitions of {1, …, k }. We derive general inequalities between the l p -norms of arbitrary unfoldings defined on the partition lattice. In particular, we demonstrate how the spectral norm ( p = 2) of a tensor is bounded by that of its unfoldings, and obtain an improved upper bound on the ratio of the Frobenius norm to the spectral norm of an arbitrary tensor. For specially-structured tensors satisfying a generalized definition of orthogonal decomposability, we prove that the spectral norm remains invariant under specific subsets of unfolding operations.
Dark energy in scalar-tensor theories
Energy Technology Data Exchange (ETDEWEB)
Moeller, J.
2007-12-15
We investigate several aspects of dynamical dark energy in the framework of scalar-tensor theories of gravity. We provide a classification of scalar-tensor coupling functions admitting cosmological scaling solutions. In particular, we recover that Brans-Dicke theory with inverse power-law potential allows for a sequence of background dominated scaling regime and scalar field dominated, accelerated expansion. Furthermore, we compare minimally and non-minimally coupled models, with respect to the small redshift evolution of the dark energy equation of state. We discuss the possibility to discriminate between different models by a reconstruction of the equation-of-state parameter from available observational data. The non-minimal coupling characterizing scalar-tensor models can - in specific cases - alleviate fine tuning problems, which appear if (minimally coupled) quintessence is required to mimic a cosmological constant. Finally, we perform a phase-space analysis of a family of biscalar-tensor models characterized by a specific type of {sigma}-model metric, including two examples from recent literature. In particular, we generalize an axion-dilaton model of Sonner and Townsend, incorporating a perfect fluid background consisting of (dark) matter and radiation. (orig.)
Dark energy in scalar-tensor theories
International Nuclear Information System (INIS)
Moeller, J.
2007-12-01
We investigate several aspects of dynamical dark energy in the framework of scalar-tensor theories of gravity. We provide a classification of scalar-tensor coupling functions admitting cosmological scaling solutions. In particular, we recover that Brans-Dicke theory with inverse power-law potential allows for a sequence of background dominated scaling regime and scalar field dominated, accelerated expansion. Furthermore, we compare minimally and non-minimally coupled models, with respect to the small redshift evolution of the dark energy equation of state. We discuss the possibility to discriminate between different models by a reconstruction of the equation-of-state parameter from available observational data. The non-minimal coupling characterizing scalar-tensor models can - in specific cases - alleviate fine tuning problems, which appear if (minimally coupled) quintessence is required to mimic a cosmological constant. Finally, we perform a phase-space analysis of a family of biscalar-tensor models characterized by a specific type of σ-model metric, including two examples from recent literature. In particular, we generalize an axion-dilaton model of Sonner and Townsend, incorporating a perfect fluid background consisting of (dark) matter and radiation. (orig.)
Choi, Hyungsuk; Choi, Woohyuk; Quan, Tran Minh; Hildebrand, David G C; Pfister, Hanspeter; Jeong, Won-Ki
2014-12-01
As the size of image data from microscopes and telescopes increases, the need for high-throughput processing and visualization of large volumetric data has become more pressing. At the same time, many-core processors and GPU accelerators are commonplace, making high-performance distributed heterogeneous computing systems affordable. However, effectively utilizing GPU clusters is difficult for novice programmers, and even experienced programmers often fail to fully leverage the computing power of new parallel architectures due to their steep learning curve and programming complexity. In this paper, we propose Vivaldi, a new domain-specific language for volume processing and visualization on distributed heterogeneous computing systems. Vivaldi's Python-like grammar and parallel processing abstractions provide flexible programming tools for non-experts to easily write high-performance parallel computing code. Vivaldi provides commonly used functions and numerical operators for customized visualization and high-throughput image processing applications. We demonstrate the performance and usability of Vivaldi on several examples ranging from volume rendering to image segmentation.
Role of cerebral blood volume changes in brain specific-gravity measurements
International Nuclear Information System (INIS)
Picozzi, P.; Todd, N.V.; Crockard, A.H.
1985-01-01
Cerebral blood volume (CBV) was calculated in gerbils from specific-gravity (SG) changes between normal and saline-perfused brains. Furthermore, changes in CBV were investigated during ischemia using carbon-14-labeled dextran (MW 70,000) as an intravascular marker. Both data were used to evaluate the possible error due to a change in CBV on the measurement of ischemic brain edema by the SG method. The methodological error found was 0.0004 for a 100% CBV change. This error is insignificant, being less than the standard deviation in the SG measured for the gerbil cortex. Thus, CBV changes are not responsible for the SG variations observed during the first phase of ischemia. These variations are better explained as an increase of brain water content during ischemia
Tensor Factorization for Low-Rank Tensor Completion.
Zhou, Pan; Lu, Canyi; Lin, Zhouchen; Zhang, Chao
2018-03-01
Recently, a tensor nuclear norm (TNN) based method was proposed to solve the tensor completion problem, which has achieved state-of-the-art performance on image and video inpainting tasks. However, it requires computing tensor singular value decomposition (t-SVD), which costs much computation and thus cannot efficiently handle tensor data, due to its natural large scale. Motivated by TNN, we propose a novel low-rank tensor factorization method for efficiently solving the 3-way tensor completion problem. Our method preserves the low-rank structure of a tensor by factorizing it into the product of two tensors of smaller sizes. In the optimization process, our method only needs to update two smaller tensors, which can be more efficiently conducted than computing t-SVD. Furthermore, we prove that the proposed alternating minimization algorithm can converge to a Karush-Kuhn-Tucker point. Experimental results on the synthetic data recovery, image and video inpainting tasks clearly demonstrate the superior performance and efficiency of our developed method over state-of-the-arts including the TNN and matricization methods.
Tensor Train Neighborhood Preserving Embedding
Wang, Wenqi; Aggarwal, Vaneet; Aeron, Shuchin
2018-05-01
In this paper, we propose a Tensor Train Neighborhood Preserving Embedding (TTNPE) to embed multi-dimensional tensor data into low dimensional tensor subspace. Novel approaches to solve the optimization problem in TTNPE are proposed. For this embedding, we evaluate novel trade-off gain among classification, computation, and dimensionality reduction (storage) for supervised learning. It is shown that compared to the state-of-the-arts tensor embedding methods, TTNPE achieves superior trade-off in classification, computation, and dimensionality reduction in MNIST handwritten digits and Weizmann face datasets.
Notes on super Killing tensors
Energy Technology Data Exchange (ETDEWEB)
Howe, P.S. [Department of Mathematics, King’s College London,The Strand, London WC2R 2LS (United Kingdom); Lindström, University [Department of Physics and Astronomy, Theoretical Physics, Uppsala University,SE-751 20 Uppsala (Sweden); Theoretical Physics, Imperial College London,Prince Consort Road, London SW7 2AZ (United Kingdom)
2016-03-14
The notion of a Killing tensor is generalised to a superspace setting. Conserved quantities associated with these are defined for superparticles and Poisson brackets are used to define a supersymmetric version of the even Schouten-Nijenhuis bracket. Superconformal Killing tensors in flat superspaces are studied for spacetime dimensions 3,4,5,6 and 10. These tensors are also presented in analytic superspaces and super-twistor spaces for 3,4 and 6 dimensions. Algebraic structures associated with superconformal Killing tensors are also briefly discussed.
Tensor norms and operator ideals
Defant, A; Floret, K
1992-01-01
The three chapters of this book are entitled Basic Concepts, Tensor Norms, and Special Topics. The first may serve as part of an introductory course in Functional Analysis since it shows the powerful use of the projective and injective tensor norms, as well as the basics of the theory of operator ideals. The second chapter is the main part of the book: it presents the theory of tensor norms as designed by Grothendieck in the Resumé and deals with the relation between tensor norms and operator ideals. The last chapter deals with special questions. Each section is accompanied by a series of exer
Reliable nanomaterial classification of powders using the volume-specific surface area method
Energy Technology Data Exchange (ETDEWEB)
Wohlleben, Wendel, E-mail: wendel.wohlleben@basf.com [Department of Material Physics, BASF SE (Germany); Mielke, Johannes [BAM–Federal Institute for Materials Research and Testing (Germany); Bianchin, Alvise [MBN Nanomaterialia s.p.a (Italy); Ghanem, Antoine [R& I Centre Brussels, Solvay (Belgium); Freiberger, Harald [Department of Material Physics, BASF SE (Germany); Rauscher, Hubert [European Commission, Nanobiosciences Unit, Joint Research Centre (Italy); Gemeinert, Marion; Hodoroaba, Vasile-Dan, E-mail: dan.hodoroaba@bam.de [BAM–Federal Institute for Materials Research and Testing (Germany)
2017-02-15
The volume-specific surface area (VSSA) of a particulate material is one of two apparently very different metrics recommended by the European Commission for a definition of “nanomaterial” for regulatory purposes: specifically, the VSSA metric may classify nanomaterials and non-nanomaterials differently than the median size in number metrics, depending on the chemical composition, size, polydispersity, shape, porosity, and aggregation of the particles in the powder. Here we evaluate the extent of agreement between classification by electron microscopy (EM) and classification by VSSA on a large set of diverse particulate substances that represent all the anticipated challenges except mixtures of different substances. EM and VSSA are determined in multiple labs to assess also the level of reproducibility. Based on the results obtained on highly characterized benchmark materials from the NanoDefine EU FP7 project, we derive a tiered screening strategy for the purpose of implementing the definition of nanomaterials. We finally apply the screening strategy to further industrial materials, which were classified correctly and left only borderline cases for EM. On platelet-shaped nanomaterials, VSSA is essential to prevent false-negative classification by EM. On porous materials, approaches involving extended adsorption isotherms prevent false positive classification by VSSA. We find no false negatives by VSSA, neither in Tier 1 nor in Tier 2, despite real-world industrial polydispersity and diverse composition, shape, and coatings. The VSSA screening strategy is recommended for inclusion in a technical guidance for the implementation of the definition.
Reliable nanomaterial classification of powders using the volume-specific surface area method
International Nuclear Information System (INIS)
Wohlleben, Wendel; Mielke, Johannes; Bianchin, Alvise; Ghanem, Antoine; Freiberger, Harald; Rauscher, Hubert; Gemeinert, Marion; Hodoroaba, Vasile-Dan
2017-01-01
The volume-specific surface area (VSSA) of a particulate material is one of two apparently very different metrics recommended by the European Commission for a definition of “nanomaterial” for regulatory purposes: specifically, the VSSA metric may classify nanomaterials and non-nanomaterials differently than the median size in number metrics, depending on the chemical composition, size, polydispersity, shape, porosity, and aggregation of the particles in the powder. Here we evaluate the extent of agreement between classification by electron microscopy (EM) and classification by VSSA on a large set of diverse particulate substances that represent all the anticipated challenges except mixtures of different substances. EM and VSSA are determined in multiple labs to assess also the level of reproducibility. Based on the results obtained on highly characterized benchmark materials from the NanoDefine EU FP7 project, we derive a tiered screening strategy for the purpose of implementing the definition of nanomaterials. We finally apply the screening strategy to further industrial materials, which were classified correctly and left only borderline cases for EM. On platelet-shaped nanomaterials, VSSA is essential to prevent false-negative classification by EM. On porous materials, approaches involving extended adsorption isotherms prevent false positive classification by VSSA. We find no false negatives by VSSA, neither in Tier 1 nor in Tier 2, despite real-world industrial polydispersity and diverse composition, shape, and coatings. The VSSA screening strategy is recommended for inclusion in a technical guidance for the implementation of the definition.
Fermionic topological quantum states as tensor networks
Wille, C.; Buerschaper, O.; Eisert, J.
2017-06-01
Tensor network states, and in particular projected entangled pair states, play an important role in the description of strongly correlated quantum lattice systems. They do not only serve as variational states in numerical simulation methods, but also provide a framework for classifying phases of quantum matter and capture notions of topological order in a stringent and rigorous language. The rapid development in this field for spin models and bosonic systems has not yet been mirrored by an analogous development for fermionic models. In this work, we introduce a tensor network formalism capable of capturing notions of topological order for quantum systems with fermionic components. At the heart of the formalism are axioms of fermionic matrix-product operator injectivity, stable under concatenation. Building upon that, we formulate a Grassmann number tensor network ansatz for the ground state of fermionic twisted quantum double models. A specific focus is put on the paradigmatic example of the fermionic toric code. This work shows that the program of describing topologically ordered systems using tensor networks carries over to fermionic models.
Mckee, James W.
1990-01-01
This volume (3 of 4) contains the specification for the command language for the AMPS system. The volume contains a requirements specification for the operating system and commands and a design specification for the operating system and command. The operating system and commands sits on top of the protocol. The commands are an extension of the present set of AMPS commands in that the commands are more compact, allow multiple sub-commands to be bundled into one command, and have provisions for identifying the sender and the intended receiver. The commands make no change to the actual software that implement the commands.
Energy Technology Data Exchange (ETDEWEB)
E Davis, B Rasmussen
2004-12-31
This report is a guide for a technical specification change submittal and subsequent implementation of on-line monitoring for safety-related applications. This report is the third in a three-volume set. Volume 1, ''Guidelines for Model Development and Implementation'', presents the various tasks that must be completed to prepare models for and to implement an on-line monitoring system.
Typesafe Abstractions for Tensor Operations
Chen, Tongfei
2017-01-01
We propose a typesafe abstraction to tensors (i.e. multidimensional arrays) exploiting the type-level programming capabilities of Scala through heterogeneous lists (HList), and showcase typesafe abstractions of common tensor operations and various neural layers such as convolution or recurrent neural networks. This abstraction could lay the foundation of future typesafe deep learning frameworks that runs on Scala/JVM.
Indicial tensor manipulation on MACSYMA
International Nuclear Information System (INIS)
Bogen, R.A.; Pavelle, R.
1977-01-01
A new computational tool for physical calculations is described. It is the first computer system capable of performing indicial tensor calculus (as opposed to component tensor calculus). It is now operational on the symbolic manipulation system MACSYMA. The authors outline the capabilities of the system and describe some of the physical problems considered as well as others being examined at this time. (Auth.)
Stanescu, T; Jaffray, D
2018-05-25
Magnetic resonance imaging is expected to play a more important role in radiation therapy given the recent developments in MR-guided technologies. MR images need to consistently show high spatial accuracy to facilitate RT specific tasks such as treatment planning and in-room guidance. The present study investigates a new harmonic analysis method for the characterization of complex 3D fields derived from MR images affected by system-related distortions. An interior Dirichlet problem based on solving the Laplace equation with boundary conditions (BCs) was formulated for the case of a 3D distortion field. The second-order boundary value problem (BVP) was solved using a finite elements method (FEM) for several quadratic geometries - i.e., sphere, cylinder, cuboid, D-shaped, and ellipsoid. To stress-test the method and generalize it, the BVP was also solved for more complex surfaces such as a Reuleaux 9-gon and the MR imaging volume of a scanner featuring a high degree of surface irregularities. The BCs were formatted from reference experimental data collected with a linearity phantom featuring a volumetric grid structure. The method was validated by comparing the harmonic analysis results with the corresponding experimental reference fields. The harmonic fields were found to be in good agreement with the baseline experimental data for all geometries investigated. In the case of quadratic domains, the percentage of sampling points with residual values larger than 1 mm were 0.5% and 0.2% for the axial components and vector magnitude, respectively. For the general case of a domain defined by the available MR imaging field of view, the reference data showed a peak distortion of about 12 mm and 79% of the sampling points carried a distortion magnitude larger than 1 mm (tolerance intrinsic to the experimental data). The upper limits of the residual values after comparison with the harmonic fields showed max and mean of 1.4 mm and 0.25 mm, respectively, with only 1.5% of
Fundamental study on REV based on crack tensor at the Mizunami Underground Research Laboratory
International Nuclear Information System (INIS)
Tanno, Takeo; Sato, Toshinori; Sanada, Hiroyuki; Hikima, Ryoichi; Kumasaka, Hiroo; Tada, Hiroyuki
2013-01-01
The crack tensor model which is a kind of equivalent continuum model has been studied in rock mechanical investigation in the MIU. The fractured rock mass is modeled as the elastic continuum model with this crack tensor. In this study, this crack tensor based on the geological observation in the MIU project was calculated, and Representative Elementary Volume (REV) in the ventilation shaft and -300 m access/research gallery was studied based on the relative error of this crack tensor. As a result, the convergence of the relative error was faster in the -300 m access/research gallery than in the ventilation shaft. (author)
Anisotropic diffusion tensor applied to temporal mammograms
DEFF Research Database (Denmark)
Karemore, Gopal; Brandt, Sami; Sporring, Jon
2010-01-01
changes related to specific effects like Hormonal Replacement Therapy (HRT) and aging. Given effect-grouped patient data, we demonstrated how anisotropic diffusion tensor and its coherence features computed in an anatomically oriented breast coordinate system followed by statistical learning...
Reduction schemes for one-loop tensor integrals
International Nuclear Information System (INIS)
Denner, A.; Dittmaier, S.
2006-01-01
We present new methods for the evaluation of one-loop tensor integrals which have been used in the calculation of the complete electroweak one-loop corrections to e + e - ->4 fermions. The described methods for 3-point and 4-point integrals are, in particular, applicable in the case where the conventional Passarino-Veltman reduction breaks down owing to the appearance of Gram determinants in the denominator. One method consists of different variants for expanding tensor coefficients about limits of vanishing Gram determinants or other kinematical determinants, thereby reducing all tensor coefficients to the usual scalar integrals. In a second method a specific tensor coefficient with a logarithmic integrand is evaluated numerically, and the remaining coefficients as well as the standard scalar integral are algebraically derived from this coefficient. For 5-point tensor integrals, we give explicit formulas that reduce the corresponding tensor coefficients to coefficients of 4-point integrals with tensor rank reduced by one. Similar formulas are provided for 6-point functions, and the generalization to functions with more internal propagators is straightforward. All the presented methods are also applicable if infrared (soft or collinear) divergences are treated in dimensional regularization or if mass parameters (for unstable particles) become complex
International Nuclear Information System (INIS)
1995-04-01
This report documents the results of the combined effort of the NRC and the industry to produce improved Standard Technical Specifications (STS), Revision 1 for General Electric BWR/4 Plants. The changes reflected in Revision 1 resulted from the experience gained from license amendment applications to convert to these improved STS or to adopt partial improvements to existing technical specifications. This NUREG is the result of extensive public technical meetings and discussions between the Nuclear Regulatory Commission (NRC) staff and various nuclear power plant licensees, Nuclear Steam Supply System (NSSS) Owners Groups, NSSS vendors, and the Nuclear Energy Institute (NEI). The improved STS were developed based on the criteria in the Final Commission Policy Statement on Technical Specifications Improvements for Nuclear Power Reactors, dated July 22, 1993. The improved STS will be used as the basis for individual nuclear power plant licensees to develop improved plant-specific technical specifications. This report contains three volumes. Volume 1 contains the specifications for all chapters and sections of the improved STS. Volume 2 contains he Bases for Chapters 2.0 and 3.0, and Sections 3.1-3.3 of the improved STS. This document, Volume 3, contains the Bases for Sections 3.4-3.10 of the improved STS
International Nuclear Information System (INIS)
1995-04-01
This report documents the results of the combined effort of the NRC and the industry to produce improved Standard Technical Specifications (STS), Revision 1 for Combustion Engineering Plants. The changes reflected in Revision 1 resulted from the experience gained from license amendment applications to convert to these improved STS or to adopt partial improvements to existing technical specifications. This NUREG is the result of extensive public technical meetings and discussions between the Nuclear Regulatory Commission (NRC) staff and various nuclear power plant licensees, Nuclear Steam Supply System (NSSS) Owners Groups, NSSS vendors, and the Nuclear Energy Institute (NEI). The improved STS were developed based on the criteria in the Final Commission Policy Statement on Technical Specifications Improvements for Nuclear Power Reactors, dated July 22, 1993. The improved STS will be used as the basis for individual nuclear power plant licensees to develop improved plant-specific technical specifications. This report contains three volumes. Volume 1 contains the Specifications for all chapters and sections of the improved STS. Volume 2 contains the Bases for Chapters 2.0 and 3.0, and Sections 3.1--3.3 of the improved STS Volume 3 contains the Bases for Sections 3.4--3.9 of the improved STS
International Nuclear Information System (INIS)
1995-04-01
This report documents the results of the combined effort of the NRC and the industry to produce improved Standard Technical Specifications (STS), Revision 1 for Babcock and Wilcox Plants. The changes reflected in Revision 1 resulted from the experience gained from license amendment applications to convert to these improved STS or to adopt partial improvements to existing technical specifications. This NUREG is the result of extensive public technical meetings and discussions between the Nuclear Regulatory Commission (NRC) staff and various nuclear power plant licensees, Nuclear Steam Supply System (NSSS) Owners Groups, NSSS vendors, and the Nuclear Energy Institute (NEI). The improved STS were developed based on the criteria in the Final Commission Policy Statement on Technical Specifications Improvements for Nuclear Power Reactors, dated July 22, 1993. The improved STS will be used as the basis for individual nuclear power plant licensees to develop improved plant-specific technical specifications. This report contains three volumes. Volume 1 contains the Specifications for all chapters and sections of the improved STS. Volume 2 contains the Bases for Chapters 2.0 and 3.0, and Sections 3.1--3.3 of the improved STS. Volume 3 contains the Bases for Sections 3.4--3.9 of the improved STS
International Nuclear Information System (INIS)
1995-04-01
This report documents the results of the combined effort of the NRC and the industry produce improved Standard Technical Specifications (STS), Revision 1 for General Electric BWR/4 Plants. The changes reflected in Revision 1 resulted from the experience gained from license amendment applications to convert to these improved ST or to adopt partial improvements to existing technical specifications. This NUREG is the result of extensive public technical meetings and discussions between the Nuclear Regulatory Commission (NRC) staff and various nuclear power plant licensees, Nuclear Steam Supply System (NSSS) Owners Groups, NSSS vendors, and the Nuclear Energy Institute (NEI). The improved STS were developed based on the criteria in the Final Commission Policy Statement on Technical Specifications Improvements for Nuclear Power Reactors, dated July 22, 1993. The improved STS will be used as the basis for individual nuclear power plant licensees to develop improved plant-specific technical specifications. This report contains three volumes. Volume I contains the Specifications for all chapters and sections of the improved STS. This document, Volume 2, contains the Bases for Chapters 2.0 and 3.0, and Sections 3.1-3.3 of the improved STS. Volume 3 contains the Bases for Sections 3.4-3.10 of the improved STS
Killing-Yano tensors and Nambu mechanics
International Nuclear Information System (INIS)
Baleanu, D.
1998-01-01
Killing-Yano tensors were introduced in 1952 by Kentaro-Yano from mathematical point of view. The physical interpretation of Killing-Yano tensors of rank higher than two was unclear. We found that all Killing-Yano tensors η i 1 i 2 . .. i n with covariant derivative zero are Nambu tensors. We found that in the case of flat space case all Killing-Yano tensors are Nambu tensors. In the case of Taub-NUT and Kerr-Newmann metric Killing-Yano tensors of order two generate Nambu tensors of rank 3
DEFF Research Database (Denmark)
Ramskov, Daniel; Rasmussen, Sten; Sørensen, Henrik
2018-01-01
-training. Participants were randomized to one of two running schedules: Schedule Intensity(Sch-I) or Schedule Volume(Sch-V). Sch-I progressed the amount of high intensity running (≥88% VO2max) each week. Sch-V progressed total weekly running volume. Global positioning system watch or smartphone collected data on running...
MATLAB tensor classes for fast algorithm prototyping.
Energy Technology Data Exchange (ETDEWEB)
Bader, Brett William; Kolda, Tamara Gibson (Sandia National Laboratories, Livermore, CA)
2004-10-01
Tensors (also known as mutidimensional arrays or N-way arrays) are used in a variety of applications ranging from chemometrics to psychometrics. We describe four MATLAB classes for tensor manipulations that can be used for fast algorithm prototyping. The tensor class extends the functionality of MATLAB's multidimensional arrays by supporting additional operations such as tensor multiplication. The tensor as matrix class supports the 'matricization' of a tensor, i.e., the conversion of a tensor to a matrix (and vice versa), a commonly used operation in many algorithms. Two additional classes represent tensors stored in decomposed formats: cp tensor and tucker tensor. We descibe all of these classes and then demonstrate their use by showing how to implement several tensor algorithms that have appeared in the literature.
Efficient tensor completion for color image and video recovery: Low-rank tensor train
Bengua, Johann A.; Phien, Ho N.; Tuan, Hoang D.; Do, Minh N.
2016-01-01
This paper proposes a novel approach to tensor completion, which recovers missing entries of data represented by tensors. The approach is based on the tensor train (TT) rank, which is able to capture hidden information from tensors thanks to its definition from a well-balanced matricization scheme. Accordingly, new optimization formulations for tensor completion are proposed as well as two new algorithms for their solution. The first one called simple low-rank tensor completion via tensor tra...
Random SU(2) invariant tensors
Li, Youning; Han, Muxin; Ruan, Dong; Zeng, Bei
2018-04-01
SU(2) invariant tensors are states in the (local) SU(2) tensor product representation but invariant under the global group action. They are of importance in the study of loop quantum gravity. A random tensor is an ensemble of tensor states. An average over the ensemble is carried out when computing any physical quantities. The random tensor exhibits a phenomenon known as ‘concentration of measure’, which states that for any bipartition the average value of entanglement entropy of its reduced density matrix is asymptotically the maximal possible as the local dimensions go to infinity. We show that this phenomenon is also true when the average is over the SU(2) invariant subspace instead of the entire space for rank-n tensors in general. It is shown in our earlier work Li et al (2017 New J. Phys. 19 063029) that the subleading correction of the entanglement entropy has a mild logarithmic divergence when n = 4. In this paper, we show that for n > 4 the subleading correction is not divergent but a finite number. In some special situation, the number could be even smaller than 1/2, which is the subleading correction of random state over the entire Hilbert space of tensors.
Sex-specific Gray Matter Volume Differences in Females with Developmental Dyslexia
Evans, Tanya M.; Flowers, D. Lynn; Napoliello, Eileen M.; Eden, Guinevere F.
2013-01-01
Developmental dyslexia, characterized by unexpected reading difficulty, is associated with anomalous brain anatomy and function. Previous structural neuroimaging studies have converged in reports of less gray matter volume (GMV) in dyslexics within left hemisphere regions known to subserve language. Due to the higher prevalence of dyslexia in males, these studies are heavily weighted towards males, raising the question whether studies of dyslexia in females only and using the same techniques, would generate the same findings. In a replication study of men we obtained the same findings of less GMV in dyslexics in left middle/inferior temporal gyri and right postcentral/supramarginal gyri as reported in the literature. However, comparisons in women with and without dyslexia did not yield left hemisphere differences and instead we found less GMV in right precuneus and paracentral lobule/medial frontal gyrus. In boys, we found less GMV in left inferior parietal cortex (supramarginal/angular gyri), again consistent with previous work, while in girls differences were within right central sulcus, spanning adjacent gyri, and left primary visual cortex. Our investigation into anatomical variants in dyslexia replicates existing studies in males, but at the same time shows that dyslexia in females is not characterized by involvement of left hemisphere language regions but rather early sensory and motor cortices (i.e. motor and premotor cortex, primary visual cortex). Our findings suggest that models on the brain basis of dyslexia, primarily developed through the study of males, may not be appropriate for females and suggest a need for more sex-specific investigations into dyslexia. PMID:23625146
Bohnen, A.M.; Groeneveld, F.P.; Bosch, J.L.H.R.
2007-01-01
OBJECTIVES: Serum prostate-specific antigen (PSA) is considered a proxy for prostate volume (PV). This study investigates which range of PSA values has the best utility in the determination of PV (4. Low PSA ranges (0-2 and 2.1-4.0) discriminate better for a PV of 30 cc (eg, in men with a PSA range
Mochtar, CA; Kiemeney, LALM; van Riemsdijk, MM; Barnett, GS; Laguna, MP; Debruyne, FMJ; de la Rosette, JJMCH
2003-01-01
Objectives: To assess the ability of serum prostate specific antigen (PSA) to estimate prostate volume (PV) to aid in the management of patients with benign prostatic hyperplasia (BPH). Methods: From 1989 to 2002, data were collected from 2264 patients complaining of lower urinary tract symptoms
Dose and volume specification for reporting NCT. An ICRU-IAEA initiative
International Nuclear Information System (INIS)
Wambersie, A.; Gahbauer, R.A.; Whitmore, G.; Levin, C.V.
2000-01-01
The present recommendations result from of an ICRU-IAEA initiative for harmonization of reporting NCT (Neutron Capture Therapy). As stated by the ISNCT, harmonization of reporting is required to understand what has actually been done and interpret the clinical results on the basis of reliable information. Prescription of a treatment remains the responsibility of the radiation oncologist in charge of the patient. Complete oncological data should be reported, including Gross Tumor Volume (GTV) and Clinical Target Volume (CTV) as well as Planning Target Volume (PTV), Treated Volume and Organs/Structures at Risk. A reference point for reporting dose should be selected in the central part of the PTV/CTV. At each point of interest, the four components contributing to the absorbed dose and the weighting factors applied to take account of the RBE (Relative Biological Effectiveness) differences should be specified. (author)
Thermodynamical inequivalence of quantum stress-energy and spin tensors
International Nuclear Information System (INIS)
Becattini, F.; Tinti, L.
2011-01-01
It is shown that different couples of stress-energy and spin tensors of quantum-relativistic fields, which would be otherwise equivalent, are in fact inequivalent if the second law of thermodynamics is taken into account. The proof of the inequivalence is based on the analysis of a macroscopic system at full thermodynamical equilibrium with a macroscopic total angular momentum and a specific instance is given for the free Dirac field, for which we show that the canonical and Belinfante stress-energy tensors are not equivalent. For this particular case, we show that the difference between the predicted angular momentum densities for a rotating system at full thermodynamical equilibrium is a quantum effect, persisting in the nonrelativistic limit, corresponding to a polarization of particles of the order of (ℎ/2π)ω/KT (ω being the angular velocity) and could in principle be measured experimentally. This result implies that specific stress-energy and spin tensors are physically meaningful even in the absence of gravitational coupling and raises the issue of finding the thermodynamically right (or the right class of) tensors. We argue that the maximization of the thermodynamic potential theoretically allows us to discriminate between two different couples, yet for the present we are unable to provide a theoretical method to single out the best couple of tensors in a given quantum field theory. The existence of a nonvanishing spin tensor would have major consequences in hydrodynamics, gravity and cosmology.
Tensor Product of Polygonal Cell Complexes
Chien, Yu-Yen
2017-01-01
We introduce the tensor product of polygonal cell complexes, which interacts nicely with the tensor product of link graphs of complexes. We also develop the unique factorization property of polygonal cell complexes with respect to the tensor product, and study the symmetries of tensor products of polygonal cell complexes.
The Einstein tensor characterizing some Riemann spaces
International Nuclear Information System (INIS)
Rahman, M.S.
1993-07-01
A formal definition of the Einstein tensor is given. Mention is made of how this tensor plays a role of expressing certain conditions in a precise form. The cases of reducing the Einstein tensor to a zero tensor are studied on its merit. A lucid account of results, formulated as theorems, on Einstein symmetric and Einstein recurrent spaces is then presented. (author). 5 refs
Tensor calculus, relativity, and cosmology a first course
Dalarsson, M
2005-01-01
This book combines relativity, astrophysics, and cosmology in a single volume, providing an introduction to each subject that enables students to understand more detailed treatises as well as the current literature. The section on general relativity gives the case for a curved space-time, presents the mathematical background (tensor calculus, Riemannian geometry), discusses the Einstein equation and its solutions (including black holes, Penrose processes, and similar topics), and considers the energy-momentum tensor for various solutions. The next section on relativistic astrophysics discusses
STRUCTURAL CONNECTIVITY VIA THE TENSOR-BASED MORPHOMETRY.
Kim, Seung-Goo; Chung, Moo K; Hanson, Jamie L; Avants, Brian B; Gee, James C; Davidson, Richard J; Pollak, Seth D
2011-01-01
The tensor-based morphometry (TBM) has been widely used in characterizing tissue volume difference between populations at voxel level. We present a novel computational framework for investigating the white matter connectivity using TBM. Unlike other diffusion tensor imaging (DTI) based white matter connectivity studies, we do not use DTI but only T1-weighted magnetic resonance imaging (MRI). To construct brain network graphs, we have developed a new data-driven approach called the ε -neighbor method that does not need any predetermined parcellation. The proposed pipeline is applied in detecting the topological alteration of the white matter connectivity in maltreated children.
Girbau-Massana, Dolors; Garcia-Marti, Gracian; Marti-Bonmati, Luis; Schwartz, Richard G
2014-04-01
We studied gray-white matter and cerebrospinal fluid (CSF) alterations that may be critical for language, through an optimized voxel-based morphometry evaluation in children with Specific Language Impairment (SLI), compared to Typical Language Development (TLD). Ten children with SLI (8;5-10;9) and 14 children with TLD (8;2-11;8) participated. They received a comprehensive language and reading test battery. We also analyzed a subgroup of six children with SLI+RD (Reading Disability). Brain images from 3-Tesla MRIs were analyzed with intelligence, age, gender, and total intracranial volume as covariates. Children with SLI or SLI+RD exhibited a significant lower overall gray matter volume than children with TLD. Particularly, children with SLI showed a significantly lower volume of gray matter compared to children with TLD in the right postcentral parietal gyrus (BA4), and left and right medial occipital gyri (BA19). The group with SLI also exhibited a significantly greater volume of gray matter in the right superior occipital gyrus (BA19), which may reflect a brain reorganization to compensate for their lower volumes at medial occipital gyri. Children with SLI+RD, compared to children with TLD, showed a significantly lower volume of: (a) gray matter in the right postcentral parietal gyrus; and (b) white matter in the right inferior longitudinal fasciculus (RILF), which interconnects the temporal and occipital lobes. Children with TLD exhibited a significantly lower CSF volume than children with SLI and children with SLI+RD respectively, who had somewhat smaller volumes of gray matter allowing for more CSF volume. The significant lower gray matter volume at the right postcentral parietal gyrus and greater cerebrospinal fluid volume may prove to be unique markers for SLI. We discuss the association of poor knowledge/visual representations and language input to brain development. Our comorbid study showed that a significant lower volume of white matter in the right
Virtual Library Effluent Volume to Soil Disposal Sites Module Specification; TOPICAL
International Nuclear Information System (INIS)
M. A. deLamare
2001-01-01
This document provides the design specifications for each of the modules identified in the Virtual Library. The design specifications include design logic, input and output specifications, validation, and error handling
He, Lifang; Kong, Xiangnan; Yu, Philip S.; Ragin, Ann B.; Hao, Zhifeng; Yang, Xiaowei
2015-01-01
With advances in data collection technologies, tensor data is assuming increasing prominence in many applications and the problem of supervised tensor learning has emerged as a topic of critical significance in the data mining and machine learning community. Conventional methods for supervised tensor learning mainly focus on learning kernels by flattening the tensor into vectors or matrices, however structural information within the tensors will be lost. In this paper, we introduce a new scheme to design structure-preserving kernels for supervised tensor learning. Specifically, we demonstrate how to leverage the naturally available structure within the tensorial representation to encode prior knowledge in the kernel. We proposed a tensor kernel that can preserve tensor structures based upon dual-tensorial mapping. The dual-tensorial mapping function can map each tensor instance in the input space to another tensor in the feature space while preserving the tensorial structure. Theoretically, our approach is an extension of the conventional kernels in the vector space to tensor space. We applied our novel kernel in conjunction with SVM to real-world tensor classification problems including brain fMRI classification for three different diseases (i.e., Alzheimer's disease, ADHD and brain damage by HIV). Extensive empirical studies demonstrate that our proposed approach can effectively boost tensor classification performances, particularly with small sample sizes. PMID:25927014
He, Lifang; Kong, Xiangnan; Yu, Philip S; Ragin, Ann B; Hao, Zhifeng; Yang, Xiaowei
With advances in data collection technologies, tensor data is assuming increasing prominence in many applications and the problem of supervised tensor learning has emerged as a topic of critical significance in the data mining and machine learning community. Conventional methods for supervised tensor learning mainly focus on learning kernels by flattening the tensor into vectors or matrices, however structural information within the tensors will be lost. In this paper, we introduce a new scheme to design structure-preserving kernels for supervised tensor learning. Specifically, we demonstrate how to leverage the naturally available structure within the tensorial representation to encode prior knowledge in the kernel. We proposed a tensor kernel that can preserve tensor structures based upon dual-tensorial mapping. The dual-tensorial mapping function can map each tensor instance in the input space to another tensor in the feature space while preserving the tensorial structure. Theoretically, our approach is an extension of the conventional kernels in the vector space to tensor space. We applied our novel kernel in conjunction with SVM to real-world tensor classification problems including brain fMRI classification for three different diseases ( i.e ., Alzheimer's disease, ADHD and brain damage by HIV). Extensive empirical studies demonstrate that our proposed approach can effectively boost tensor classification performances, particularly with small sample sizes.
Zaitchik, Deborah; Solomon, Gregg E A
2009-09-01
Two studies investigated whether patients with Alzheimer's disease (AD) suffer high-level and category-specific impairment in the conceptual domain of living things. In Experiment 1, AD patients and healthy young and healthy elderly controls took part in three tasks: the conservation of species, volume, and belief. All 3 tasks required tracking an object's identity in the face of irrelevant but salient transformations. Healthy young and elderly controls performed at or near ceiling on all tasks. AD patients were at or near ceiling on the volume and belief tasks, but only about half succeeded on the species task. Experiment 2 demonstrated that the results were not due to simple task demands. AD patients' failure to conserve species indicates that they are impaired in their theoretical understanding of living things, and their success on the volume and belief tasks suggests that the impairment is domain-specific. Two hypotheses are put forward to explain the phenomenon: The first, a category-specific account, holds that the intuitive theory of biology undergoes pervasive degradation; the second, a hybrid domain-general/domain-specific account, holds that impairment to domain-general processes such as executive function interacts with core cognition, the primitive elements that are the foundation of domain-specific knowledge.
Tensor Completion Algorithms in Big Data Analytics
Song, Qingquan; Ge, Hancheng; Caverlee, James; Hu, Xia
2017-01-01
Tensor completion is a problem of filling the missing or unobserved entries of partially observed tensors. Due to the multidimensional character of tensors in describing complex datasets, tensor completion algorithms and their applications have received wide attention and achievement in areas like data mining, computer vision, signal processing, and neuroscience. In this survey, we provide a modern overview of recent advances in tensor completion algorithms from the perspective of big data an...
Diffusion tensor MRI: clinical applications
International Nuclear Information System (INIS)
Meli, Francisco; Romero, Carlos; Carpintiero, Silvina; Salvatico, Rosana; Lambre, Hector; Vila, Jose
2005-01-01
Purpose: To evaluate the usefulness of diffusion-tensor imaging (DTI) on different neurological diseases, and to know if this technique shows additional information than conventional Magnetic Resonance Imaging (MRI). Materials and method: Eight patients, with neurological diseases (five patients with brain tumors, one with multiple sclerosis (MS), one with variant Creutzfeldt-Jakob disease (vCJD) and the other with delayed CO intoxication were evaluated. A MR scanner of 1.5 T was used and conventional sequences and DTI with twenty-five directions were done. Quantitative maps were gotten, where the fractional anisotropy (FA) through regions of interest (ROIs) in specific anatomic area were quantified (i.e.: internal and external capsules, frontal and temporal bundles, corpus fibers). Results: In the patients with brain tumors, there was a decrease of FA on intra and peritumoral fibers. Some of them had a disruption in their pattern. In patients with MS and CO intoxication, partial interruption along white matter bundles was demonstrated. However, a 'mismatch' between the findings of FLAIR, Diffusion-weighted images (DWI) and DTI, in the case of CO intoxication, was seen. Conclusions: DTI gave more information compared to conventional sequences about ultrastructural brain tissue in almost all the diseases above mentioned. Therefore, there is a work in progress about DTI acquisition, to evaluate a new technique, called tractography. (author)
International Nuclear Information System (INIS)
Leont'ev, K.L.
1981-01-01
Known theoretical and empirical formulae are considered for the difference in specific heats at constant pressure and volume. On the basis of the Grunaiser law on the ratio of specific heat to thermal expansion and on the basis of the correlation proposed by the author, between this ratio and average velocity of elastic waves obtained in a new expression for the difference in specific heats and determined are conditions at which empiric Nernst-Lindeman equation can be considered to be strict. Results of calculations for metals with fcc lattice are presented
2010-04-01
... respective volumes of alcohol and water and the specific gravity in both air and vacuum of spirituous liquor... volumes of alcohol and water and the specific gravity in both air and vacuum of spirituous liquor. This... gallon of water in air by the specific gravity in air of the spirits—8.32823 by 0.88862—the product (7...
Development of the Tensoral Computer Language
Ferziger, Joel; Dresselhaus, Eliot
1996-01-01
The research scientist or engineer wishing to perform large scale simulations or to extract useful information from existing databases is required to have expertise in the details of the particular database, the numerical methods and the computer architecture to be used. This poses a significant practical barrier to the use of simulation data. The goal of this research was to develop a high-level computer language called Tensoral, designed to remove this barrier. The Tensoral language provides a framework in which efficient generic data manipulations can be easily coded and implemented. First of all, Tensoral is general. The fundamental objects in Tensoral represent tensor fields and the operators that act on them. The numerical implementation of these tensors and operators is completely and flexibly programmable. New mathematical constructs and operators can be easily added to the Tensoral system. Tensoral is compatible with existing languages. Tensoral tensor operations co-exist in a natural way with a host language, which may be any sufficiently powerful computer language such as Fortran, C, or Vectoral. Tensoral is very-high-level. Tensor operations in Tensoral typically act on entire databases (i.e., arrays) at one time and may, therefore, correspond to many lines of code in a conventional language. Tensoral is efficient. Tensoral is a compiled language. Database manipulations are simplified optimized and scheduled by the compiler eventually resulting in efficient machine code to implement them.
DEFF Research Database (Denmark)
Goussanou, Cédric A.; Guendehou, Sabin; Assogbadjo, Achille E.
2016-01-01
The quantification of the contribution of tropical forests to global carbon stocks and climate change mitigation requires availability of data and tools such as allometric equations. This study made available volume and biomass models for eighteen tree species in a semi-deciduous tropical forest...... in West Africa. Generic models were also developed for the forest ecosystem, and basic wood density determined for the tree species. Non-destructive sampling approach was carried out on five hundred and one sample trees to analyse stem volume and biomass. From the modelling of volume and biomass...... enabled to conclude that the non-destructive sampling was a good approach to determining reliable basic wood density. The comparative analysis of species-specific models in this study with selected generic models for tropical forests indicated low probability to identify effective generic models with good...
Sex Differences in Brain Volume Are Related to Specific Skills, Not to General Intelligence
Burgaleta, Miguel; Head, Kevin; Alvarez-Linera, Juan; Martinez, Kenia; Escorial, Sergio; Haier, Richard; Colom, Roberto
2012-01-01
It has been proposed that males would show higher mean scores than females in general intelligence ("g") because (1) men have, on average, larger brains than women, and (2) brain volume correlates with "g." Here we report a failure to support the conclusion derived from these premises. High resolution MRIs were acquired in a sample of one hundred…
Physical and Geometric Interpretations of the Riemann Tensor, Ricci Tensor, and Scalar Curvature
Loveridge, Lee C.
2004-01-01
Various interpretations of the Riemann Curvature Tensor, Ricci Tensor, and Scalar Curvature are described. Also, the physical meanings of the Einstein Tensor and Einstein's Equations are discussed. Finally a derivation of Newtonian Gravity from Einstein's Equations is given.
Glass Transition Temperature- and Specific Volume- Composition Models for Tellurite Glasses
Energy Technology Data Exchange (ETDEWEB)
Riley, Brian J. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Vienna, John D. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
2017-09-01
This report provides models for predicting composition-properties for tellurite glasses, namely specific gravity and glass transition temperature. Included are the partial specific coefficients for each model, the component validity ranges, and model fit parameters.
International Nuclear Information System (INIS)
1995-04-01
This report documents the results of the combined effort of the NRC and the industry to produce improved Standard Technical Specifications (STS), Revision 1 for General Electric BWR/6 Plants. The changes reflected in Revision 1 resulted from the experience gained from license amendment applications to convert to these improved STS or to adopt partial improvements to existing technical specifications. This NUREG is the result of extensive public technical meetings and discussions between the Nuclear Regulatory Commission (NRC) staff and various nuclear power plant licensees, Nuclear Steam Supply System (NSSS) Owners Groups, NSSS vendors, and the Nuclear Energy Institute (NEI). The improved STS were developed based on the criteria in the Final Commission Policy Statement on Technical Specifications Improvements for Nuclear Power Reactors, dated July 22, 1993. The improved STS will be used as the basis for individual nuclear power plant licensees to develop improved plant-specific technical specifications. This report contains three volumes
The tensor rank of tensor product of two three-qubit W states is eight
Chen, Lin; Friedland, Shmuel
2017-01-01
We show that the tensor rank of tensor product of two three-qubit W states is not less than eight. Combining this result with the recent result of M. Christandl, A. K. Jensen, and J. Zuiddam that the tensor rank of tensor product of two three-qubit W states is at most eight, we deduce that the tensor rank of tensor product of two three-qubit W states is eight. We also construct the upper bound of the tensor rank of tensor product of many three-qubit W states.
Longitudinal volumetric changes following traumatic brain injury: a tensor-based morphometry study.
Farbota, Kimberly D M; Sodhi, Aparna; Bendlin, Barbara B; McLaren, Donald G; Xu, Guofan; Rowley, Howard A; Johnson, Sterling C
2012-11-01
After traumatic injury, the brain undergoes a prolonged period of degenerative change that is paradoxically accompanied by cognitive recovery. The spatiotemporal pattern of atrophy and the specific relationships of atrophy to cognitive changes are ill understood. The present study used tensor-based morphometry and neuropsychological testing to examine brain volume loss in 17 traumatic brain injury (TBI) patients and 13 controls over a 4-year period. Patients were scanned at 2 months, 1 year, and 4 years post-injury. High-dimensional warping procedures were used to create change maps of each subject's brain for each of the two intervals. TBI patients experienced volume loss in both cortical areas and white matter regions during the first interval. We also observed continuing volume loss in extensive regions of white matter during the second interval. Neuropsychological correlations indicated that cognitive tasks were associated with subsequent volume loss in task-relevant regions. The extensive volume loss in brain white matter observed well beyond the first year post-injury suggests that the injured brain remains malleable for an extended period, and the neuropsychological relationships suggest that this volume loss may be associated with subtle cognitive improvements.
Link prediction via generalized coupled tensor factorisation
DEFF Research Database (Denmark)
Ermiş, Beyza; Evrim, Acar Ataman; Taylan Cemgil, A.
2012-01-01
and higher-order tensors. We propose to use an approach based on probabilistic interpretation of tensor factorisation models, i.e., Generalised Coupled Tensor Factorisation, which can simultaneously fit a large class of tensor models to higher-order tensors/matrices with com- mon latent factors using...... different loss functions. Numerical experiments demonstrate that joint analysis of data from multiple sources via coupled factorisation improves the link prediction performance and the selection of right loss function and tensor model is crucial for accurately predicting missing links....
NASIS data base management system: IBM 360 TSS implementation. Volume 3: Data set specifications
1973-01-01
The data set specifications for the NASA Aerospace Safety Information System (NASIS) are presented. The data set specifications describe the content, format, and medium of communication of every data set required by the system. All relevant information pertinent to a particular data set is prepared in a standard form and centralized in a single document. The format for the data set is provided.
Spectral Tensor-Train Decomposition
DEFF Research Database (Denmark)
Bigoni, Daniele; Engsig-Karup, Allan Peter; Marzouk, Youssef M.
2016-01-01
The accurate approximation of high-dimensional functions is an essential task in uncertainty quantification and many other fields. We propose a new function approximation scheme based on a spectral extension of the tensor-train (TT) decomposition. We first define a functional version of the TT...... adaptive Smolyak approach. The method is also used to approximate the solution of an elliptic PDE with random input data. The open source software and examples presented in this work are available online (http://pypi.python.org/pypi/TensorToolbox/)....
Confinement through tensor gauge fields
International Nuclear Information System (INIS)
Salam, A.; Strathdee, J.
1977-12-01
Using the 0(3,2)-symmetric de Sitter solution of Einstein's equation describing a strongly interacting tensor field it is shown that hadronic bags confining quarks can be represented as de Sitter ''micro-universes'' with radii given 1/R 2 =lambdak 2 /6. Here k 2 and lambda are the strong coupling and the ''cosmological'' constant which apear in the Einstein equation used. Surprisingly the energy spectrum for the two-body hadronic states is the same as that for a harmonic oscillator potential, though the wave functions are completely different. The Einstein equation can be extended to include colour for the tensor fields
Tensor product of quantum logics
Pulmannová, Sylvia
1985-01-01
A quantum logic is the couple (L,M) where L is an orthomodular σ-lattice and M is a strong set of states on L. The Jauch-Piron property in the σ-form is also supposed for any state of M. A ``tensor product'' of quantum logics is defined. This definition is compared with the definition of a free orthodistributive product of orthomodular σ-lattices. The existence and uniqueness of the tensor product in special cases of Hilbert space quantum logics and one quantum and one classical logic are studied.
Gloger, Oliver; Tönnies, Klaus; Bülow, Robin; Völzke, Henry
2017-07-01
To develop the first fully automated 3D spleen segmentation framework derived from T1-weighted magnetic resonance (MR) imaging data and to verify its performance for spleen delineation and volumetry. This approach considers the issue of low contrast between spleen and adjacent tissue in non-contrast-enhanced MR images. Native T1-weighted MR volume data was performed on a 1.5 T MR system in an epidemiological study. We analyzed random subsamples of MR examinations without pathologies to develop and verify the spleen segmentation framework. The framework is modularized to include different kinds of prior knowledge into the segmentation pipeline. Classification by support vector machines differentiates between five different shape types in computed foreground probability maps and recognizes characteristic spleen regions in axial slices of MR volume data. A spleen-shape space generated by training produces subject-specific prior shape knowledge that is then incorporated into a final 3D level set segmentation method. Individually adapted shape-driven forces as well as image-driven forces resulting from refined foreground probability maps steer the level set successfully to the segment the spleen. The framework achieves promising segmentation results with mean Dice coefficients of nearly 0.91 and low volumetric mean errors of 6.3%. The presented spleen segmentation approach can delineate spleen tissue in native MR volume data. Several kinds of prior shape knowledge including subject-specific 3D prior shape knowledge can be used to guide segmentation processes achieving promising results.
International Nuclear Information System (INIS)
1992-03-01
This report presents specifications related to the buildings and equipment of the wrap facility. The facility will retrieve, process, and certify transuranic, mixed, and low-level radioactive wastes for disposal
International Nuclear Information System (INIS)
1995-04-01
This NUREG contains the improved Standard Technical Specifications (STS) for Westinghouse plants. Revision 1 incorporates the cumulative changes to Revision 0, which was published in September 1992. The changes reflected in Revision 1 resulted from the experience gained from license amendment applications to convert to these improved STS or to adopt partial improvements to existing technical specifications. This NUREG is the result of extensive public technical meetings and discussions between the Nuclear Regulatory Commission (NRC) staff and various nuclear power plant licensees, Nuclear Steam Supply System (NSSS) Owners Groups, specifically the Westinghouse Owners Group (WOG), NSSS vendors, and the Nuclear Energy Institute (NEI). The improved STS were developed based on the criteria in the Final Commission Policy Statement on Technical Specifications Improvements for Nuclear Power Reactors, dated July 22, 1993 (58 FR 39132). Licensees are encouraged to upgrade their technical specifications consistent with those criteria and conforming, to the extent practical and consistent with the licensing basis for the facility, to Revision 1 to the improved STS. The Commission continues to place the highest priority on requests for complete conversions to the improved STS. Licensees adopting portions of the improved STS to existing technical specifications should adopt all related requirements, as applicable, to achieve a high degree of standardization and consistency
International Nuclear Information System (INIS)
1995-04-01
This NUREG contains the improved Standard Technical Specifications (STS) for Westinghouse plants. Revision 1 incorporates the cumulative changes to Revision 0, which was published in September 1992. The changes reflected in Revision 1 resulted from the experience gained from license amendment applications to convert to these improved STS or to adopt partial improvements to existing technical specifications. This NUREG is the result of extensive public technical meetings and discussions between the Nuclear Regulatory Commission (NRC) staff and various nuclear power plant licensees, Nuclear Steam Supply System (NSSS) Owners Groups, specifically the Westinghouse Owners Group (WOG), NSSS vendors, and the Nuclear Energy Institute (NEI). The improved STS were developed based on the criteria in the Final Commission Policy Statement on Technical Specifications Improvements for Nuclear Power Reactors, dated July 22, 1993 (58 FR 39132). Licensees are encouraged to upgrade their technical specifications consistent with those criteria and conforming, to the extent practical and consistent with the licensing basis for the facility, to Revision 1 to the improved STS. The Commission continues to place the highest priority on requests for complete conversions to the improved STS. Licensees adopting portions of the improved STS to existing technical specifications should adopt all related requirements, as applicable, to achieve a high degree of standardization and consistency
Retinal Vessel Segmentation via Structure Tensor Coloring and Anisotropy Enhancement
Directory of Open Access Journals (Sweden)
Mehmet Nergiz
2017-11-01
Full Text Available Retinal vessel segmentation is one of the preliminary tasks for developing diagnosis software systems related to various retinal diseases. In this study, a fully automated vessel segmentation system is proposed. Firstly, the vessels are enhanced using a Frangi Filter. Afterwards, Structure Tensor is applied to the response of the Frangi Filter and a 4-D tensor field is obtained. After decomposing the Eigenvalues of the tensor field, the anisotropy between the principal Eigenvalues are enhanced exponentially. Furthermore, this 4-D tensor field is converted to the 3-D space which is composed of energy, anisotropy and orientation and then a Contrast Limited Adaptive Histogram Equalization algorithm is applied to the energy space. Later, the obtained energy space is multiplied by the enhanced mean surface curvature of itself and the modified 3-D space is converted back to the 4-D tensor field. Lastly, the vessel segmentation is performed by using Otsu algorithm and tensor coloring method which is inspired by the ellipsoid tensor visualization technique. Finally, some post-processing techniques are applied to the segmentation result. In this study, the proposed method achieved mean sensitivity of 0.8123, 0.8126, 0.7246 and mean specificity of 0.9342, 0.9442, 0.9453 as well as mean accuracy of 0.9183, 0.9442, 0.9236 for DRIVE, STARE and CHASE_DB1 datasets, respectively. The mean execution time of this study is 6.104, 6.4525 and 18.8370 s for the aforementioned three datasets respectively.
The 'gravitating' tensor in the dualistic theory
International Nuclear Information System (INIS)
Mahanta, M.N.
1989-01-01
The exact microscopic system of Einstein-type field equations of the dualistic gravitation theory is investigated as well as an analysis of the modified energy-momentum tensor or so called 'gravitating' tensor is presented
Tensor calculus for physics a concise guide
Neuenschwander, Dwight E
2015-01-01
Understanding tensors is essential for any physics student dealing with phenomena where causes and effects have different directions. A horizontal electric field producing vertical polarization in dielectrics; an unbalanced car wheel wobbling in the vertical plane while spinning about a horizontal axis; an electrostatic field on Earth observed to be a magnetic field by orbiting astronauts—these are some situations where physicists employ tensors. But the true beauty of tensors lies in this fact: When coordinates are transformed from one system to another, tensors change according to the same rules as the coordinates. Tensors, therefore, allow for the convenience of coordinates while also transcending them. This makes tensors the gold standard for expressing physical relationships in physics and geometry. Undergraduate physics majors are typically introduced to tensors in special-case applications. For example, in a classical mechanics course, they meet the "inertia tensor," and in electricity and magnetism...
Mean template for tensor-based morphometry using deformation tensors.
Leporé, Natasha; Brun, Caroline; Pennec, Xavier; Chou, Yi-Yu; Lopez, Oscar L; Aizenstein, Howard J; Becker, James T; Toga, Arthur W; Thompson, Paul M
2007-01-01
Tensor-based morphometry (TBM) studies anatomical differences between brain images statistically, to identify regions that differ between groups, over time, or correlate with cognitive or clinical measures. Using a nonlinear registration algorithm, all images are mapped to a common space, and statistics are most commonly performed on the Jacobian determinant (local expansion factor) of the deformation fields. In, it was shown that the detection sensitivity of the standard TBM approach could be increased by using the full deformation tensors in a multivariate statistical analysis. Here we set out to improve the common space itself, by choosing the shape that minimizes a natural metric on the deformation tensors from that space to the population of control subjects. This method avoids statistical bias and should ease nonlinear registration of new subjects data to a template that is 'closest' to all subjects' anatomies. As deformation tensors are symmetric positive-definite matrices and do not form a vector space, all computations are performed in the log-Euclidean framework. The control brain B that is already the closest to 'average' is found. A gradient descent algorithm is then used to perform the minimization that iteratively deforms this template and obtains the mean shape. We apply our method to map the profile of anatomical differences in a dataset of 26 HIV/AIDS patients and 14 controls, via a log-Euclidean Hotelling's T2 test on the deformation tensors. These results are compared to the ones found using the 'best' control, B. Statistics on both shapes are evaluated using cumulative distribution functions of the p-values in maps of inter-group differences.
Reciprocal mass tensor : a general form
International Nuclear Information System (INIS)
Roy, C.L.
1978-01-01
Using the results of earlier treatment of wave packets, a general form of reciprocal mass tensor has been obtained. The elements of this tensor are seen to be dependent on momentum as well as space coordinates of the particle under consideration. The conditions under which the tensor would reduce to the usual space-independent form, are discussed and the impact of the space-dependence of this tensor on the motion of Bloch electrons, is examined. (author)
A new deteriorated energy-momentum tensor
International Nuclear Information System (INIS)
Duff, M.J.
1982-01-01
The stress-tensor of a scalar field theory is not unique because of the possibility of adding an 'improvement term'. In supersymmetric field theories the stress-tensor will appear in a super-current multiplet along with the sypersymmetry current. The general question of the supercurrent multiplet for arbitrary deteriorated stress tensors and their relationship to supercurrent multiplets for models with gauge antisymmetric tensors is answered for various models of N = 1, 2 and 4 supersymmetry. (U.K.)
Tensor-based spatiotemporal saliency detection
Dou, Hao; Li, Bin; Deng, Qianqian; Zhang, LiRui; Pan, Zhihong; Tian, Jinwen
2018-03-01
This paper proposes an effective tensor-based spatiotemporal saliency computation model for saliency detection in videos. First, we construct the tensor representation of video frames. Then, the spatiotemporal saliency can be directly computed by the tensor distance between different tensors, which can preserve the complete temporal and spatial structure information of object in the spatiotemporal domain. Experimental results demonstrate that our method can achieve encouraging performance in comparison with the state-of-the-art methods.
Akkerman, Erik M.
2010-01-01
Both in diffusion tensor imaging (DTI) and in generalized diffusion tensor imaging (GDTI) the relation between the diffusion tensor and the measured apparent diffusion coefficients is given by a tensorial equation, which needs to be inverted in order to solve the diffusion tensor. The traditional
Efficient Tensor Strategy for Recommendation
Directory of Open Access Journals (Sweden)
Aboagye Emelia Opoku
2017-07-01
Full Text Available The era of big data has witnessed the explosion of tensor datasets, and large scale Probabilistic Tensor Factorization (PTF analysis is important to accommodate such increasing trend of data. Sparsity, and Cold-Start are some of the inherent problems of recommender systems in the era of big data. This paper proposes a novel Sentiment-Based Probabilistic Tensor Analysis technique senti-PTF to address the problems. The propose framework first applies a Natural Language Processing technique to perform sentiment analysis taking advantage of the huge sums of textual data generated available from the social media which are predominantly left untouched. Although some current studies do employ review texts, many of them do not consider how sentiments in reviews influence recommendation algorithm for prediction. There is therefore this big data text analytics gap whose modeling is computationally expensive. From our experiments, our novel machine learning sentiment-based tensor analysis is computationally less expensive, and addresses the cold-start problem, for optimal recommendation prediction.
Weyl tensors for asymmetric complex curvatures
International Nuclear Information System (INIS)
Oliveira, C.G.
Considering a second rank Hermitian field tensor and a general Hermitian connection the associated complex curvature tensor is constructed. The Weyl tensor that corresponds to this complex curvature is determined. The formalism is applied to the Weyl unitary field theory and to the Moffat gravitational theory. (Author) [pt
Spherical Tensor Calculus for Local Adaptive Filtering
Reisert, Marco; Burkhardt, Hans
In 3D image processing tensors play an important role. While rank-1 and rank-2 tensors are well understood and commonly used, higher rank tensors are rare. This is probably due to their cumbersome rotation behavior which prevents a computationally efficient use. In this chapter we want to introduce the notion of a spherical tensor which is based on the irreducible representations of the 3D rotation group. In fact, any ordinary cartesian tensor can be decomposed into a sum of spherical tensors, while each spherical tensor has a quite simple rotation behavior. We introduce so called tensorial harmonics that provide an orthogonal basis for spherical tensor fields of any rank. It is just a generalization of the well known spherical harmonics. Additionally we propose a spherical derivative which connects spherical tensor fields of different degree by differentiation. Based on the proposed theory we present two applications. We propose an efficient algorithm for dense tensor voting in 3D, which makes use of tensorial harmonics decomposition of the tensor-valued voting field. In this way it is possible to perform tensor voting by linear-combinations of convolutions in an efficient way. Secondly, we propose an anisotropic smoothing filter that uses a local shape and orientation adaptive filter kernel which can be computed efficiently by the use spherical derivatives.
Teh, Irvin; McClymont, Darryl; Zdora, Marie-Christine; Whittington, Hannah J; Davidoiu, Valentina; Lee, Jack; Lygate, Craig A; Rau, Christoph; Zanette, Irene; Schneider, Jürgen E
2017-03-10
Diffusion tensor imaging (DTI) is widely used to assess tissue microstructure non-invasively. Cardiac DTI enables inference of cell and sheetlet orientations, which are altered under pathological conditions. However, DTI is affected by many factors, therefore robust validation is critical. Existing histological validation is intrinsically flawed, since it requires further tissue processing leading to sample distortion, is routinely limited in field-of-view and requires reconstruction of three-dimensional volumes from two-dimensional images. In contrast, synchrotron radiation imaging (SRI) data enables imaging of the heart in 3D without further preparation following DTI. The objective of the study was to validate DTI measurements based on structure tensor analysis of SRI data. One isolated, fixed rat heart was imaged ex vivo with DTI and X-ray phase contrast SRI, and reconstructed at 100 μm and 3.6 μm isotropic resolution respectively. Structure tensors were determined from the SRI data and registered to the DTI data. Excellent agreement in helix angles (HA) and transverse angles (TA) was observed between the DTI and structure tensor synchrotron radiation imaging (STSRI) data, where HA DTI-STSRI = -1.4° ± 23.2° and TA DTI-STSRI = -1.4° ± 35.0° (mean ± 1.96 standard deviation across all voxels in the left ventricle). STSRI confirmed that the primary eigenvector of the diffusion tensor corresponds with the cardiomyocyte long-axis across the whole myocardium. We have used STSRI as a novel and high-resolution gold standard for the validation of DTI, allowing like-with-like comparison of three-dimensional tissue structures in the same intact heart free of distortion. This represents a critical step forward in independently verifying the structural basis and informing the interpretation of cardiac DTI data, thereby supporting the further development and adoption of DTI in structure-based electro-mechanical modelling and routine clinical
Newlander, Shawn M; Chu, Alan; Sinha, Usha S; Lu, Po H; Bartzokis, George
2014-02-01
To identify regional differences in apparent diffusion coefficient (ADC) and fractional anisotropy (FA) using customized preprocessing before voxel-based analysis (VBA) in 14 normal subjects with the specific genes that decrease (apolipoprotein [APO] E ε2) and that increase (APOE ε4) the risk of Alzheimer's disease. Diffusion tensor images (DTI) acquired at 1.5 Tesla were denoised with a total variation tensor regularization algorithm before affine and nonlinear registration to generate a common reference frame for the image volumes of all subjects. Anisotropic and isotropic smoothing with varying kernel sizes was applied to the aligned data before VBA to determine regional differences between cohorts segregated by allele status. VBA on the denoised tensor data identified regions of reduced FA in APOE ε4 compared with the APOE ε2 healthy older carriers. The most consistent results were obtained using the denoised tensor and anisotropic smoothing before statistical testing. In contrast, isotropic smoothing identified regional differences for small filter sizes alone, emphasizing that this method introduces bias in FA values for higher kernel sizes. Voxel-based DTI analysis can be performed on low signal to noise ratio images to detect subtle regional differences in cohorts using the proposed preprocessing techniques. Copyright © 2013 Wiley Periodicals, Inc.
Tape, C.; Alvizuri, C. R.; Silwal, V.; Tape, W.
2017-12-01
When considered as a point source, a seismic source can be characterized in terms of its origin time, hypocenter, moment tensor, and source time function. The seismologist's task is to estimate these parameters--and their uncertainties--from three-component ground motion recorded at irregularly spaced stations. We will focus on one portion of this problem: the estimation of the moment tensor and its uncertainties. With magnitude estimated separately, we are left with five parameters describing the normalized moment tensor. A lune of normalized eigenvalue triples can be used to visualize the two parameters (lune longitude and lune latitude) describing the source type, while the conventional strike, dip, and rake angles can be used to characterize the orientation. Slight modifications of these five parameters lead to a uniform parameterization of moment tensors--uniform in the sense that equal volumes in the coordinate domain of the parameterization correspond to equal volumes of moment tensors. For a moment tensor m that we have inferred from seismic data for an earthquake, we define P(V) to be the probability that the true moment tensor for the earthquake lies in the neighborhood of m that has fractional volume V. The average value of P(V) is then a measure of our confidence in our inference of m. The calculation of P(V) requires knowing both the probability P(w) and the fractional volume V(w) of the set of moment tensors within a given angular radius w of m. We apply this approach to several different data sets, including nuclear explosions from the Nevada Test Site, volcanic events from Uturuncu (Bolivia), and earthquakes. Several challenges remain: choosing an appropriate misfit function, handling time shifts between data and synthetic waveforms, and extending the uncertainty estimation to include more source parameters (e.g., hypocenter and source time function).
Population Based Analysis of Directional Information in Serial Deformation Tensor Morphometry
Studholme, Colin; Cardenas, Valerie
2012-01-01
Deformation morphometry provides a sensitive approach to detecting and mapping subtle volume changes in the brain. Population based analyses of this data have been used successfully to detect characteristic changes in different neurodegenerative conditions. However, most studies have been limited to statistical mapping of the scalar volume change at each point in the brain, by evaluating the determinant of the Jacobian of the deformation field. In this paper we describe an approach to spatial normalisation and analysis of the full deformation tensor. The approach employs a spatial relocation and reorientation of tensors of each subject. Using the assumption of small changes, we use a linear modeling of effects of clinical variables on each deformation tensor component across a population. We illustrate the use of this approach by examining the pattern of significance and orientation of the volume change effects in recovery from alcohol abuse. Results show new local structure which was not apparent in the analysis of scalar volume changes. PMID:18044583
A new Weyl-like tensor of geometric origin
Vishwakarma, Ram Gopal
2018-04-01
A set of new tensors of purely geometric origin have been investigated, which form a hierarchy. A tensor of a lower rank plays the role of the potential for the tensor of one rank higher. The tensors have interesting mathematical and physical properties. The highest rank tensor of the hierarchy possesses all the geometrical properties of the Weyl tensor.
Energy Technology Data Exchange (ETDEWEB)
1977-06-01
The economics of a particular hybrid plant must be evaluated with respect to a specific site. This volume focuses on the Roosevelt Hot Springs KGRA. The temperature, pressure, and flow rate data given suggests the site deserves serious consideration for a hybrid plant. Key siting considerations which must be addressed before an economic judgment can be attempted are presented as follows: the availability, quality, and cost of coal; the availability of water; and the availability of transmission. Seismological and climate factors are presented. (MHR)
International Nuclear Information System (INIS)
Bolch, W.E.; Patton, P.W.; Shah, A.P.; Rajon, D.A.; Jokisch, D.W.
2002-01-01
It is generally acknowledged that reference man (70 kg in mass and 170 cm in height) does not adequately represent the stature and physical dimensions of many patients undergoing radionuclide therapy, and thus scaling of radionuclide S values is required for patient specificity. For electron and beta sources uniformly distributed within internal organs, the mean dose from self-irradiation is noted to scale inversely with organ mass, provided no escape of electron energy occurs at the organ boundaries. In the skeleton, this same scaling approach is further assumed to be correct for marrow dosimetry; nevertheless, difficulties in quantitative assessments of marrow mass in specific skeletal regions of the patient make this approach difficult to implement clinically. Instead, scaling of marrow dose is achieved using various anthropometric parameters that presumably scale in the same proportion. In this study, recently developed three-dimensional macrostructural transport models of the femoral head and humeral epiphysis in three individuals (51-year male, 82-year female, and 86-year female) are used to test the abilities of different anthropometric parameters (total body mass, body surface area, etc.) to properly scale radionuclide S values from reference man models. The radionuclides considered are 33 P, 177 Lu, 153 Sm, 186 Re, 89 Sr, 166 Ho, 32 P, 188 Re, and 90 Y localized in either the active marrow or endosteal tissues of the bone trabeculae. S value scaling is additionally conducted in which the 51-year male subject is assigned as the reference individual; scaling parameters are then expanded to include tissue volumes and masses for both active marrow and skeletal spongiosa. The study concludes that, while no single anthropometric parameter emerges as a consistent scaler of reference man S values, lean body mass is indicated as an optimal scaler when the reference S values are based on 3D transport techniques. Furthermore, very exact patient-specific scaling of
Main-coolant-pump shaft-seal guidelines. Volume 3. Specification guidelines. Final report
International Nuclear Information System (INIS)
Fair, C.E.; Greer, A.O.
1983-03-01
This report presents a set of guidelines and criteria to aid in the generation of procurement specifications for Main Coolant Pump Shaft Seals. The noted guidelines are developed from EPRI sponsored nuclear power plant seal operating experience studies, a review of pump and shaft seal literature and discussions with pump and seal designers. This report is preliminary in nature and could be expanded and finalized subsequent to completion of further design, test and evaluation efforts
Spinors, tensors and the covariant form of Dirac's equation
International Nuclear Information System (INIS)
Chen, W.Q.; Cook, A.H.
1986-01-01
The relations between tensors and spinors are used to establish the form of the covariant derivative of a spinor, making use of the fact that certain bilinear combinations of spinors are vectors. The covariant forms of Dirac's equation are thus obtained and examples in specific coordinate systems are displayed. (author)
Comparison of Magnetic Susceptibility Tensor and Diffusion Tensor of the Brain.
Li, Wei; Liu, Chunlei
2013-10-01
Susceptibility tensor imaging (STI) provides a novel approach for noninvasive assessment of the white matter pathways of the brain. Using mouse brain ex vivo , we compared STI with diffusion tensor imaging (DTI), in terms of tensor values, principal tensor values, anisotropy values, and tensor orientations. Despite the completely different biophysical underpinnings, magnetic susceptibility tensors and diffusion tensors show many similarities in the tensor and principal tensor images, for example, the tensors perpendicular to the fiber direction have the highest gray-white matter contrast, and the largest principal tensor is along the fiber direction. Comparison to DTI fractional anisotropy, the susceptibility anisotropy provides much higher sensitivity to the chemical composition of the white matter, especially myelin. The high sensitivity can be further enhanced with the perfusion of ProHance, a gadolinium-based contrast agent. Regarding the tensor orientations, the direction of the largest principal susceptibility tensor agrees with that of diffusion tensors in major white matter fiber bundles. The STI fiber tractography can reconstruct the fiber pathways for the whole corpus callosum and for white matter fiber bundles that are in close contact but in different orientations. There are some differences between susceptibility and diffusion tensor orientations, which are likely due to the limitations in the current STI reconstruction. With the development of more accurate reconstruction methods, STI holds the promise for probing the white matter micro-architectures with more anatomical details and higher chemical sensitivity.
The Physical Interpretation of the Lanczos Tensor
Roberts, Mark D.
1999-01-01
The field equations of general relativity can be written as first order differential equations in the Weyl tensor, the Weyl tensor in turn can be written as a first order differential equation in a three index tensor called the Lanczos tensor. The Lanczos tensor plays a similar role in general relativity to that of the vector potential in electro-magnetic theory. The Aharonov-Bohm effect shows that when quantum mechanics is applied to electro-magnetic theory the vector potential is dynamicall...
Directory of Open Access Journals (Sweden)
Francisco Michel
2011-05-01
Full Text Available Abstract Background Transmission electron microscopy (TEM remains an important technique to investigate the size, shape and surface characteristics of particles at the nanometer scale. Resulting micrographs are two dimensional projections of objects and their interpretation can be difficult. Recently, electron tomography (ET is increasingly used to reveal the morphology of nanomaterials (NM in 3D. In this study, we examined the feasibility to visualize and measure silica and gold NM in suspension using conventional bright field electron tomography. Results The general morphology of gold and silica NM was visualized in 3D by conventional TEM in bright field mode. In orthoslices of the examined NM the surface features of a NM could be seen and measured without interference of higher or lower lying structures inherent to conventional TEM. Segmentation by isosurface rendering allowed visualizing the 3D information of an electron tomographic reconstruction in greater detail than digital slicing. From the 3D reconstructions, the surface area and the volume of the examined NM could be estimated directly and the volume-specific surface area (VSSA was calculated. The mean VSSA of all examined NM was significantly larger than the threshold of 60 m2/cm3. The high correlation between the measured values of area and volume gold nanoparticles with a known spherical morphology and the areas and volumes calculated from the equivalent circle diameter (ECD of projected nanoparticles (NP indicates that the values measured from electron tomographic reconstructions are valid for these gold particles. Conclusion The characterization and definition of the examined gold and silica NM can benefit from application of conventional bright field electron tomography: the NM can be visualized in 3D, while surface features and the VSSA can be measured.
Robust estimation of adaptive tensors of curvature by tensor voting.
Tong, Wai-Shun; Tang, Chi-Keung
2005-03-01
Although curvature estimation from a given mesh or regularly sampled point set is a well-studied problem, it is still challenging when the input consists of a cloud of unstructured points corrupted by misalignment error and outlier noise. Such input is ubiquitous in computer vision. In this paper, we propose a three-pass tensor voting algorithm to robustly estimate curvature tensors, from which accurate principal curvatures and directions can be calculated. Our quantitative estimation is an improvement over the previous two-pass algorithm, where only qualitative curvature estimation (sign of Gaussian curvature) is performed. To overcome misalignment errors, our improved method automatically corrects input point locations at subvoxel precision, which also rejects outliers that are uncorrectable. To adapt to different scales locally, we define the RadiusHit of a curvature tensor to quantify estimation accuracy and applicability. Our curvature estimation algorithm has been proven with detailed quantitative experiments, performing better in a variety of standard error metrics (percentage error in curvature magnitudes, absolute angle difference in curvature direction) in the presence of a large amount of misalignment noise.
Antisymmetric tensor generalizations of affine vector fields.
Houri, Tsuyoshi; Morisawa, Yoshiyuki; Tomoda, Kentaro
2016-02-01
Tensor generalizations of affine vector fields called symmetric and antisymmetric affine tensor fields are discussed as symmetry of spacetimes. We review the properties of the symmetric ones, which have been studied in earlier works, and investigate the properties of the antisymmetric ones, which are the main theme in this paper. It is shown that antisymmetric affine tensor fields are closely related to one-lower-rank antisymmetric tensor fields which are parallelly transported along geodesics. It is also shown that the number of linear independent rank- p antisymmetric affine tensor fields in n -dimensions is bounded by ( n + 1)!/ p !( n - p )!. We also derive the integrability conditions for antisymmetric affine tensor fields. Using the integrability conditions, we discuss the existence of antisymmetric affine tensor fields on various spacetimes.
International Nuclear Information System (INIS)
1995-05-01
DOE is deactivating the PUREX plant at Hanford; this will involve the disposition of about 692,000 liters (183,000 gallons) of surplus nitric acid contaminated with low levels of U and other radionuclides. The nitric acid, designated as low specific activity, is stored in 4 storage tanks at PUREX. Five principal alternatives were evaluated: transfer for reuse (sale to BNF plc), no action, continued storage in Hanford upgraded or new facility, consolidation of DOE surplus acid, and processing the LSA nitric acid as waste. The transfer to BNF plc is the preferred alternative. From the analysis, it is concluded that the proposed disposition and transportation of the acid does not constitute a major federal action significantly affecting the quality of the human environment within the meaning of NEPA; therefore an environmental impact statement is not required
Black holes in vector-tensor theories
Energy Technology Data Exchange (ETDEWEB)
Heisenberg, Lavinia [Institute for Theoretical Studies, ETH Zurich, Clausiusstrasse 47, 8092 Zurich (Switzerland); Kase, Ryotaro; Tsujikawa, Shinji [Department of Physics, Faculty of Science, Tokyo University of Science, 1-3, Kagurazaka, Shinjuku-ku, Tokyo 162-8601 (Japan); Minamitsuji, Masato, E-mail: lavinia.heisenberg@eth-its.ethz.ch, E-mail: r.kase@rs.tus.ac.jp, E-mail: masato.minamitsuji@tecnico.ulisboa.pt, E-mail: shinji@rs.kagu.tus.ac.jp [Centro Multidisciplinar de Astrofisica—CENTRA, Departamento de Fisica, Instituto Superior Tecnico—IST, Universidade de Lisboa—UL, Avenida Rovisco Pais 1, 1049-001 Lisboa (Portugal)
2017-08-01
We study static and spherically symmetric black hole (BH) solutions in second-order generalized Proca theories with nonminimal vector field derivative couplings to the Ricci scalar, the Einstein tensor, and the double dual Riemann tensor. We find concrete Lagrangians which give rise to exact BH solutions by imposing two conditions of the two identical metric components and the constant norm of the vector field. These exact solutions are described by either Reissner-Nordström (RN), stealth Schwarzschild, or extremal RN solutions with a non-trivial longitudinal mode of the vector field. We then numerically construct BH solutions without imposing these conditions. For cubic and quartic Lagrangians with power-law couplings which encompass vector Galileons as the specific cases, we show the existence of BH solutions with the difference between two non-trivial metric components. The quintic-order power-law couplings do not give rise to non-trivial BH solutions regular throughout the horizon exterior. The sixth-order and intrinsic vector-mode couplings can lead to BH solutions with a secondary hair. For all the solutions, the vector field is regular at least at the future or past horizon. The deviation from General Relativity induced by the Proca hair can be potentially tested by future measurements of gravitational waves in the nonlinear regime of gravity.
Filippi, Massimo; Ceccarelli, Antonia; Pagani, Elisabetta; Gatti, Roberto; Rossi, Alice; Stefanelli, Laura; Falini, Andrea; Comi, Giancarlo; Rocca, Maria Assunta
2010-04-15
We used tensor-based morphometry (TBM) to: 1) map gray matter (GM) volume changes associated with motor learning in young healthy individuals; 2) evaluate if GM changes persist three months after cessation of motor training; and 3) assess whether the use of different schemes of motor training during the learning phase could lead to volume modifications of specific GM structures. From 31 healthy subjects, motor functional assessment and brain 3D T1-weighted sequence were obtained: before motor training (time 0), at the end of training (two weeks) (time 2), and three months later (time 3). Fifteen subjects (group A) were trained with goal-directed motor sequences, and 16 (group B) with non purposeful motor actions of the right hand. At time 1 vs. time 0, the whole sample of subjects had GM volume increase in regions of the temporo-occipital lobes, inferior parietal lobule (IPL) and middle frontal gyrus, while at time 2 vs. time 1, an increased GM volume in the middle temporal gyrus was seen. At time 1 vs. time 0, compared to group B, group A had a GM volume increase of the hippocampi, while the opposite comparison showed greater GM volume increase in the IPL and insula in group B vs. group A. Motor learning results in structural GM changes of different brain areas which are part of specific neuronal networks and tend to persist after training is stopped. The scheme applied during the learning phase influences the pattern of such structural changes.
Directory of Open Access Journals (Sweden)
Massimo Filippi
Full Text Available We used tensor-based morphometry (TBM to: 1 map gray matter (GM volume changes associated with motor learning in young healthy individuals; 2 evaluate if GM changes persist three months after cessation of motor training; and 3 assess whether the use of different schemes of motor training during the learning phase could lead to volume modifications of specific GM structures. From 31 healthy subjects, motor functional assessment and brain 3D T1-weighted sequence were obtained: before motor training (time 0, at the end of training (two weeks (time 2, and three months later (time 3. Fifteen subjects (group A were trained with goal-directed motor sequences, and 16 (group B with non purposeful motor actions of the right hand. At time 1 vs. time 0, the whole sample of subjects had GM volume increase in regions of the temporo-occipital lobes, inferior parietal lobule (IPL and middle frontal gyrus, while at time 2 vs. time 1, an increased GM volume in the middle temporal gyrus was seen. At time 1 vs. time 0, compared to group B, group A had a GM volume increase of the hippocampi, while the opposite comparison showed greater GM volume increase in the IPL and insula in group B vs. group A. Motor learning results in structural GM changes of different brain areas which are part of specific neuronal networks and tend to persist after training is stopped. The scheme applied during the learning phase influences the pattern of such structural changes.
Extended vector-tensor theories
Energy Technology Data Exchange (ETDEWEB)
Kimura, Rampei; Naruko, Atsushi; Yoshida, Daisuke, E-mail: rampei@th.phys.titech.ac.jp, E-mail: naruko@th.phys.titech.ac.jp, E-mail: yoshida@th.phys.titech.ac.jp [Department of Physics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551 (Japan)
2017-01-01
Recently, several extensions of massive vector theory in curved space-time have been proposed in many literatures. In this paper, we consider the most general vector-tensor theories that contain up to two derivatives with respect to metric and vector field. By imposing a degeneracy condition of the Lagrangian in the context of ADM decomposition of space-time to eliminate an unwanted mode, we construct a new class of massive vector theories where five degrees of freedom can propagate, corresponding to three for massive vector modes and two for massless tensor modes. We find that the generalized Proca and the beyond generalized Proca theories up to the quartic Lagrangian, which should be included in this formulation, are degenerate theories even in curved space-time. Finally, introducing new metric and vector field transformations, we investigate the properties of thus obtained theories under such transformations.
Scalar-tensor linear inflation
Energy Technology Data Exchange (ETDEWEB)
Artymowski, Michał [Institute of Physics, Jagiellonian University, Łojasiewicza 11, 30-348 Kraków (Poland); Racioppi, Antonio, E-mail: Michal.Artymowski@uj.edu.pl, E-mail: Antonio.Racioppi@kbfi.ee [National Institute of Chemical Physics and Biophysics, Rävala 10, 10143 Tallinn (Estonia)
2017-04-01
We investigate two approaches to non-minimally coupled gravity theories which present linear inflation as attractor solution: a) the scalar-tensor theory approach, where we look for a scalar-tensor theory that would restore results of linear inflation in the strong coupling limit for a non-minimal coupling to gravity of the form of f (φ) R /2; b) the particle physics approach, where we motivate the form of the Jordan frame potential by loop corrections to the inflaton field. In both cases the Jordan frame potentials are modifications of the induced gravity inflationary scenario, but instead of the Starobinsky attractor they lead to linear inflation in the strong coupling limit.
International Nuclear Information System (INIS)
Lankford, S.P.; Pollack, A.; Zagars, G.K.
1996-01-01
Purpose: Although the pretreatment serum prostate specific antigen level (PSAL) is the single most significant predictor of local and biochemical control in prostate cancer patients treated with radiotherapy, it is relatively insensitive for patients with a PSAL in the intermediate range (4-20 ng/ml). PSA density (PSAD) has been shown to be slightly more predictive of outcome than PSAL for this intermediate risk group; however, this improvement is small and of little use clinically. PSA cancer volume (PSACV) is an estimate of cancer volume based on PSA that was recently described by D'Amico and Propert (IJROBP 32:232, 1995) as providing significant and independent prognostic information in addition to PSAL. We report here a detailed comparison between this new prognostic factor, PSAL, and PSAD. Methods and Materials: The records of 356 patients treated with definitive external beam radiotherapy for regionally localized (T1-4, Nx, M0) adenocarcinoma of the prostate were reviewed. Each patient had a PSAL, biopsy Gleason score, and pretreatment prostate volume by transrectal ultrasonography. The median PSAL was 9.3 ng/ml and 66% had Gleason scores in the 2-6 range. The median radiation dose was 66.0 Gy and the median follow-up for those living was 27 months. PSACV is a calculated parameter that takes into account PSAL (total PSA), ultrasonographic prostate volume (estimate of PSA from benign epithelium), and Gleason grade (estimate of PSA per tumor volume). The median PSACV was 1.43 cc. Biochemical failure was defined as increases in two consecutive follow-up PSA levels, one increase by a factor > 1.5, or an absolute increase of > 1 ng/ml. Local failure was defined as a cancer-positive prostate biopsy, usually undertaken because of evidence of biochemical failure. Results: The distributions of PSACV and PSAL were similar and, when normalized by log-transformation, were highly correlated (p 4 cc, as compared to those with a PSACV ≤ 0.5 cc, was over 30%. Conclusion
The GLAS Standard Data Products Specification-Data Dictionary, Version 1.0. Volume 15
Lee, Jeffrey E.
2013-01-01
The Geoscience Laser Altimeter System (GLAS) is the primary instrument for the ICESat (Ice, Cloud and Land Elevation Satellite) laser altimetry mission. ICESat was the benchmark Earth Observing System (EOS) mission for measuring ice sheet mass balance, cloud and aerosol heights, as well as land topography and vegetation characteristics. From 2003 to 2009, the ICESat mission provided multi-year elevation data needed to determine ice sheet mass balance as well as cloud property information, especially for stratospheric clouds common over polar areas. It also provided topography and vegetation data around the globe, in addition to the polar-specific coverage over the Greenland and Antarctic ice sheets.This document contains the data dictionary for the GLAS standard data products. It details the parameters present on GLAS standard data products. Each parameter is defined with a short name, a long name, units on product, type of variable, a long description and products that contain it. The term standard data products refers to those EOS instrument data that are routinely generated for public distribution. These products are distributed by the National Snow and Ice Data Center (NSDIC).
Diffusion tensor optical coherence tomography
Marks, Daniel L.; Blackmon, Richard L.; Oldenburg, Amy L.
2018-01-01
In situ measurements of diffusive particle transport provide insight into tissue architecture, drug delivery, and cellular function. Analogous to diffusion-tensor magnetic resonance imaging (DT-MRI), where the anisotropic diffusion of water molecules is mapped on the millimeter scale to elucidate the fibrous structure of tissue, here we propose diffusion-tensor optical coherence tomography (DT-OCT) for measuring directional diffusivity and flow of optically scattering particles within tissue. Because DT-OCT is sensitive to the sub-resolution motion of Brownian particles as they are constrained by tissue macromolecules, it has the potential to quantify nanoporous anisotropic tissue structure at micrometer resolution as relevant to extracellular matrices, neurons, and capillaries. Here we derive the principles of DT-OCT, relating the detected optical signal from a minimum of six probe beams with the six unique diffusion tensor and three flow vector components. The optimal geometry of the probe beams is determined given a finite numerical aperture, and a high-speed hardware implementation is proposed. Finally, Monte Carlo simulations are employed to assess the ability of the proposed DT-OCT system to quantify anisotropic diffusion of nanoparticles in a collagen matrix, an extracellular constituent that is known to become highly aligned during tumor development.
Inflationary tensor fossils in large-scale structure
Energy Technology Data Exchange (ETDEWEB)
Dimastrogiovanni, Emanuela [School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455 (United States); Fasiello, Matteo [Department of Physics, Case Western Reserve University, Cleveland, OH 44106 (United States); Jeong, Donghui [Department of Astronomy and Astrophysics, The Pennsylvania State University, University Park, PA 16802 (United States); Kamionkowski, Marc, E-mail: ema@physics.umn.edu, E-mail: mrf65@case.edu, E-mail: duj13@psu.edu, E-mail: kamion@jhu.edu [Department of Physics and Astronomy, 3400 N. Charles St., Johns Hopkins University, Baltimore, MD 21218 (United States)
2014-12-01
Inflation models make specific predictions for a tensor-scalar-scalar three-point correlation, or bispectrum, between one gravitational-wave (tensor) mode and two density-perturbation (scalar) modes. This tensor-scalar-scalar correlation leads to a local power quadrupole, an apparent departure from statistical isotropy in our Universe, as well as characteristic four-point correlations in the current mass distribution in the Universe. So far, the predictions for these observables have been worked out only for single-clock models in which certain consistency conditions between the tensor-scalar-scalar correlation and tensor and scalar power spectra are satisfied. Here we review the requirements on inflation models for these consistency conditions to be satisfied. We then consider several examples of inflation models, such as non-attractor and solid-inflation models, in which these conditions are put to the test. In solid inflation the simplest consistency conditions are already violated whilst in the non-attractor model we find that, contrary to the standard scenario, the tensor-scalar-scalar correlator probes directly relevant model-dependent information. We work out the predictions for observables in these models. For non-attractor inflation we find an apparent local quadrupolar departure from statistical isotropy in large-scale structure but that this power quadrupole decreases very rapidly at smaller scales. The consistency of the CMB quadrupole with statistical isotropy then constrains the distance scale that corresponds to the transition from the non-attractor to attractor phase of inflation to be larger than the currently observable horizon. Solid inflation predicts clustering fossils signatures in the current galaxy distribution that may be large enough to be detectable with forthcoming, and possibly even current, galaxy surveys.
International Nuclear Information System (INIS)
D'Amico, Anthony V.; Propert, Kathleen J.
1996-01-01
Purpose: A new clinical pretreatment quantity that closely approximates the true prostate cancer volume is defined. Methods and Materials: The cancer-specific prostate-specific antigen (PSA), PSA density, prostate cancer volume (V Ca ), and the volume fraction of the gland involved with carcinoma (V Ca fx) were calculated for 227 prostate cancer patients managed definitively with external beam radiation therapy. 1. PSA density PSA/ultrasound prostate gland volume 2. Cancer-specific PSA = PSA - [PSA from benign epithelial tissue] 3. V Ca = Cancer-specific PSA/[PSA in serum per cm 3 of cancer] 4. V Ca fx = V Ca /ultrasound prostate gland volume A Cox multiple regression analysis was used to test whether any of these-clinical pretreatment parameters added significantly to PSA in predicting early postradiation PSA failure. Results: The prostate cancer volume (p = 0.039) and the volume fraction of the gland involved by carcinoma (p = 0.035) significantly added to the PSA in predicting postradiation PSA failure. Conversely, the PSA density and the cancer-specific PSA did not add significantly (p > 0.05) to PSA in predicting postradiation PSA failure. The 20-month actuarial PSA failure-free rates for patients with calculated tumor volumes of ≤0.5 cm 3 , 0.5-4.0 cm 3 , and >4.0 cm 3 were 92, 80, and 47%, respectively (p = 0.00004). Conclusion: The volume of prostate cancer (V Ca ) and the resulting volume fraction of cancer both added significantly to PSA in their ability to predict for early postradiation PSA failure. These new parameters may be used to select patients in prospective randomized trials that examine the efficacy of combining radiation and androgen ablative therapy in patients with clinically localized disease, who are at high risk for early postradiation PSA failure
A higher-order tensor vessel tractography for segmentation of vascular structures.
Cetin, Suheyla; Unal, Gozde
2015-10-01
A new vascular structure segmentation method, which is based on a cylindrical flux-based higher order tensor (HOT), is presented. On a vessel structure, the HOT naturally models branching points, which create challenges for vessel segmentation algorithms. In a general linear HOT model embedded in 3D, one has to work with an even order tensor due to an enforced antipodal-symmetry on the unit sphere. However, in scenarios such as in a bifurcation, the antipodally-symmetric tensor embedded in 3D will not be useful. In order to overcome that limitation, we embed the tensor in 4D and obtain a structure that can model asymmetric junction scenarios. During construction of a higher order tensor (e.g. third or fourth order) in 4D, the orientation vectors lie on the unit 3-sphere, in contrast to the unit 2-sphere in 3D tensor modeling. This 4D tensor is exploited in a seed-based vessel segmentation algorithm, where the principal directions of the 4D HOT is obtained by decomposition, and used in a HOT tractography approach. We demonstrate quantitative validation of the proposed algorithm on both synthetic complex tubular structures as well as real cerebral vasculature in Magnetic Resonance Angiography (MRA) datasets and coronary arteries from Computed Tomography Angiography (CTA) volumes.
Sparse alignment for robust tensor learning.
Lai, Zhihui; Wong, Wai Keung; Xu, Yong; Zhao, Cairong; Sun, Mingming
2014-10-01
Multilinear/tensor extensions of manifold learning based algorithms have been widely used in computer vision and pattern recognition. This paper first provides a systematic analysis of the multilinear extensions for the most popular methods by using alignment techniques, thereby obtaining a general tensor alignment framework. From this framework, it is easy to show that the manifold learning based tensor learning methods are intrinsically different from the alignment techniques. Based on the alignment framework, a robust tensor learning method called sparse tensor alignment (STA) is then proposed for unsupervised tensor feature extraction. Different from the existing tensor learning methods, L1- and L2-norms are introduced to enhance the robustness in the alignment step of the STA. The advantage of the proposed technique is that the difficulty in selecting the size of the local neighborhood can be avoided in the manifold learning based tensor feature extraction algorithms. Although STA is an unsupervised learning method, the sparsity encodes the discriminative information in the alignment step and provides the robustness of STA. Extensive experiments on the well-known image databases as well as action and hand gesture databases by encoding object images as tensors demonstrate that the proposed STA algorithm gives the most competitive performance when compared with the tensor-based unsupervised learning methods.
Shape anisotropy: tensor distance to anisotropy measure
Weldeselassie, Yonas T.; El-Hilo, Saba; Atkins, M. S.
2011-03-01
Fractional anisotropy, defined as the distance of a diffusion tensor from its closest isotropic tensor, has been extensively studied as quantitative anisotropy measure for diffusion tensor magnetic resonance images (DT-MRI). It has been used to reveal the white matter profile of brain images, as guiding feature for seeding and stopping in fiber tractography and for the diagnosis and assessment of degenerative brain diseases. Despite its extensive use in DT-MRI community, however, not much attention has been given to the mathematical correctness of its derivation from diffusion tensors which is achieved using Euclidean dot product in 9D space. But, recent progress in DT-MRI has shown that the space of diffusion tensors does not form a Euclidean vector space and thus Euclidean dot product is not appropriate for tensors. In this paper, we propose a novel and robust rotationally invariant diffusion anisotropy measure derived using the recently proposed Log-Euclidean and J-divergence tensor distance measures. An interesting finding of our work is that given a diffusion tensor, its closest isotropic tensor is different for different tensor distance metrics used. We demonstrate qualitatively that our new anisotropy measure reveals superior white matter profile of DT-MR brain images and analytically show that it has a higher signal to noise ratio than fractional anisotropy.
Transposes, L-Eigenvalues and Invariants of Third Order Tensors
Qi, Liqun
2017-01-01
Third order tensors have wide applications in mechanics, physics and engineering. The most famous and useful third order tensor is the piezoelectric tensor, which plays a key role in the piezoelectric effect, first discovered by Curie brothers. On the other hand, the Levi-Civita tensor is famous in tensor calculus. In this paper, we study third order tensors and (third order) hypermatrices systematically, by regarding a third order tensor as a linear operator which transforms a second order t...
Ding, Zi'ang
2016-01-01
Both vector and tensor fields are important mathematical tools used to describe the physics of many phenomena in science and engineering. Effective vector and tensor field visualization techniques are therefore needed to interpret and analyze the corresponding data and achieve new insight into the considered problem. This dissertation is concerned with the extraction of important structural properties from vector and tensor datasets. Specifically, we present a unified approach for the charact...
Śliwczyński, Andrzej; Brzozowska, Melania; Jacyna, Andrzej; Iltchev, Petre; Iwańczuk, Tymoteusz; Wierzba, Waldemar; Marczak, Michał; Orlewska, Katarzyna; Szymański, Piotr; Orlewska, Ewa
2017-01-01
to investigate the drug-class-specific changes in the volume and cost of antidiabetic medications in Poland in 2012-2015. This retrospective analysis was conducted based on the National Health Fund database covering an entire Polish population. The volume of antidiabetic medications is reported according to ATC/DDD methodology, costs-in current international dollars, based on purchasing power parity. During a 4-year observational period the number of patients, consumption of antidiabetic drugs and costs increased by 17%, 21% and 20%, respectively. Biguanides are the basic diabetes medication with a 39% market share. The insulin market is still dominated by human insulins, new antidiabetics (incretins, thiazolidinediones) are practically absent. Insulins had the largest share in diabetes medications expenditures (67% in 2015). The increase in antidiabetic medications costs over the analysed period of time was mainly caused by the increased use of insulin analogues. The observed tendencies correspond to the evidence-based HTA recommendations. The reimbursement status, the ratio of cost to clinical outcomes and data on the long-term safety have a deciding impact on how a drug is used.
International Nuclear Information System (INIS)
Chen, Wenjing; Gemmel, Alexander; Rietzel, Eike
2013-01-01
We propose a patient-specific planning target volume (PTV) to deal with interfractional variations, and test its feasibility in a retrospective treatment-planning study. Instead of using one planning image only, multiple scans are taken on different days. The target and organs at risk (OARs) are delineated on each images. The proposed PTV is generated from a union of those target contours on the planning images, excluding voxels of the OARs, and is denoted the PTV 'GP-OAR' (global prostate-organs at risk). The study is performed using 'plan of the day' adaptive workflow, which selects a daily plan from a library of plans based on a similarity comparison between the daily scan and planning images. The daily plans optimized for GP-OAR volumes are compared with those optimized for PTVs generated from a single prostate contour (PTV SP). Four CT serials of prostate cancer patient datasets are included in the test, and in total 28 fractions are simulated. The results show that the daily chosen GP-OAR plans provide excellent target coverage, with V95 values of the prostate mostly >95%. In addition, dose delivered to the OARs as calculated from applying daily chosen GP-OAR plans is slightly increased but comparable to that calculated from applying daily SP plans. In general, the PTV GP-OARs are able to cover possible target variations while keeping dose delivered to the OARs at a similar level to that of the PTV SPs. (author)
Putra, Ida Bagus O W; Hamid, Agus R A H; Mochtar, Chaidir A; Umbas, Rainy
2016-06-01
To investigate the relationship between age, prostate specific antigen (PSA), and prostate volume (PV) in Indonesian men with histologically proven benign prostatic hyperplasia. Data were generated from our BPH database from June 1994 until December 2013. Subjects were men with a minimum age of 40 years with chief complaint of LUTS or urinary retention, diagnosed with BPH. All patients underwent TRUS-guided prostate biopsy. Patients with PSA level >10 ng/mL were excluded from the study to exclude the possibility of occult prostate cancer. PV was measured with TRUS. Appropriate statistical tests were employed for data analysis. In all, 1638 patients were enrolled in our study. There was a statistically significant difference in PSA (P = 0.03) and PV (P Prostate volume was significantly correlated with PSA. Even though the results were weaker, these results are consistent with results in other sets of population. The results vary between different countries and thus, ethnicities. Indonesia is a populous a sociocultural and ethnically diverse country. Therefore, aside from PSA, age, and PV, when investigating men with BPH, ethnicity may also need to be taken into account.
Mckee, James W.
1990-01-01
This volume (2 of 4) contains the specification, structured flow charts, and code listing for the protocol. The purpose of an autonomous power system on a spacecraft is to relieve humans from having to continuously monitor and control the generation, storage, and distribution of power in the craft. This implies that algorithms will have been developed to monitor and control the power system. The power system will contain computers on which the algorithms run. There should be one control computer system that makes the high level decisions and sends commands to and receive data from the other distributed computers. This will require a communications network and an efficient protocol by which the computers will communicate. One of the major requirements on the protocol is that it be real time because of the need to control the power elements.
Tensor SOM and tensor GTM: Nonlinear tensor analysis by topographic mappings.
Iwasaki, Tohru; Furukawa, Tetsuo
2016-05-01
In this paper, we propose nonlinear tensor analysis methods: the tensor self-organizing map (TSOM) and the tensor generative topographic mapping (TGTM). TSOM is a straightforward extension of the self-organizing map from high-dimensional data to tensorial data, and TGTM is an extension of the generative topographic map, which provides a theoretical background for TSOM using a probabilistic generative model. These methods are useful tools for analyzing and visualizing tensorial data, especially multimodal relational data. For given n-mode relational data, TSOM and TGTM can simultaneously organize a set of n-topographic maps. Furthermore, they can be used to explore the tensorial data space by interactively visualizing the relationships between modes. We present the TSOM algorithm and a theoretical description from the viewpoint of TGTM. Various TSOM variations and visualization techniques are also described, along with some applications to real relational datasets. Additionally, we attempt to build a comprehensive description of the TSOM family by adapting various data structures. Copyright © 2016 Elsevier Ltd. All rights reserved.
3D PATTERN OF BRAIN ABNORMALITIES IN WILLIAMS SYNDROME VISUALIZED USING TENSOR-BASED MORPHOMETRY
Chiang, Ming-Chang; Reiss, Allan L.; Lee, Agatha D.; Bellugi, Ursula; Galaburda, Albert M.; Korenberg, Julie R.; Mills, Debra L.; Toga, Arthur W.; Thompson, Paul M.
2009-01-01
Williams syndrome (WS) is a neurodevelopmental disorder associated with deletion of ~20 contiguous genes in chromosome band 7q11.23. Individuals with WS exhibit mild to moderate mental retardation, but are relatively more proficient in specific language and musical abilities. We used tensor-based morphometry (TBM) to visualize the complex pattern of gray/white matter reductions in WS, based on fluid registration of structural brain images. Methods 3D T1-weighted brain MRIs of 41 WS subjects (age: 29.2±9.2SD years; 23F/18M) and 39 age-matched healthy controls (age: 27.5±7.4 years; 23F/16M) were fluidly registered to a minimum deformation target. Fine-scale volumetric differences were mapped between diagnostic groups. Local regions were identified where regional structure volumes were associated with diagnosis, and with intelligence quotient (IQ) scores. Brain asymmetry was also mapped and compared between diagnostic groups. Results WS subjects exhibited widely distributed brain volume reductions (~10–15% reduction; P < 0.0002, permutation test). After adjusting for total brain volume, the frontal lobes, anterior cingulate, superior temporal gyrus, amygdala, fusiform gyrus and cerebellum were found to be relatively preserved in WS, but parietal and occipital lobes, thalamus and basal ganglia, and midbrain were disproportionally decreased in volume (P < 0.0002). These regional volumes also correlated positively with performance IQ in adult WS subjects (age ≥ 30 years, P = 0.038). Conclusion TBM facilitates 3D visualization of brain volume reductions in WS. Reduced parietal/occipital volumes may be associated with visuospatial deficits in WS. By contrast, frontal lobes, amygdala, and cingulate gyrus are relatively preserved or even enlarged, consistent with unusual affect regulation and language production in WS. PMID:17512756
Glioma grade assessment by using histogram analysis of diffusion tensor imaging-derived maps
International Nuclear Information System (INIS)
Jakab, Andras; Berenyi, Ervin; Molnar, Peter; Emri, Miklos
2011-01-01
Current endeavors in neuro-oncology include morphological validation of imaging methods by histology, including molecular and immunohistochemical techniques. Diffusion tensor imaging (DTI) is an up-to-date methodology of intracranial diagnostics that has gained importance in studies of neoplasia. Our aim was to assess the feasibility of discriminant analysis applied to histograms of preoperative diffusion tensor imaging-derived images for the prediction of glioma grade validated by histomorphology. Tumors of 40 consecutive patients included 13 grade II astrocytomas, seven oligoastrocytomas, six grade II oligodendrogliomas, three grade III oligoastrocytomas, and 11 glioblastoma multiformes. Preoperative DTI data comprised: unweighted (B 0 ) images, fractional anisotropy, longitudinal and radial diffusivity maps, directionally averaged diffusion-weighted imaging, and trace images. Sampling consisted of generating histograms for gross tumor volumes; 25 histogram bins per scalar map were calculated. The histogram bins that allowed the most precise determination of low-grade (LG) or high-grade (HG) classification were selected by multivariate discriminant analysis. Accuracy of the model was defined by the success rate of the leave-one-out cross-validation. Statistical descriptors of voxel value distribution did not differ between LG and HG tumors and did not allow classification. The histogram model had 88.5% specificity and 85.7% sensitivity in the separation of LG and HG gliomas; specificity was improved when cases with oligodendroglial components were omitted. Constructing histograms of preoperative radiological images over the tumor volume allows representation of the grade and enables discrimination of LG and HG gliomas which has been confirmed by histopathology. (orig.)
International Nuclear Information System (INIS)
Lankford, Scott P.; Pollack, Alan; Zagars, Gunar K.
1997-01-01
Purpose: Although the pretreatment serum prostate-specific antigen level (PSAL) is the single-most significant predictor of local and biochemical control in prostate cancer patients treated with radiotherapy, it is relatively insensitive for patients with a PSAL in the intermediate range (4-20 ng/ml). PSA density (PSAD) has been shown to be slightly more predictive of outcome than PSAL for this intermediate risk group; however, this improvement is small and of little use clinically. PSA cancer volume (PSACV), an estimate of cancer volume based on PSA, has recently been described and has been purported to be more significant t than PSAL in predicting early biochemical failure after radiotherapy. We report a detailed comparison between this new prognostic factor, PSAL, and PSAD. Methods and Materials: The records of 356 patients treated with definitive external beam radiotherapy for regionally localized (T1-4,Nx,M0) adenocarcinoma of the prostate were reviewed. Each patient had a PSAL, biopsy Gleason score, and pretreatment prostate volume by transrectal ultrasonography. The median PSAL was 9.3 ng/ml and 66% had Gleason scores in the 2-6 range. The median radiation dose was 66.0 Gy and the median follow-up for those living was 27 months. PSACV was calculated using a formula which takes into account PSAL, pretreatment prostate ultrasound volume, and Gleason score. The median PSACV was 1.43 cc. Biochemical failure was defined as increases in two consecutive follow-up PSA levels, one increase by a factor > 1.5, or an absolute increase of > 1 ng/ml. Local failure was defined as a cancer-positive prostate biopsy, obtained for evidence of tumor progression. Results: The distributions of PSACV and PSAL were similar and, when normalized by log transformation, were highly correlated (p < 0.0001, linear regression). There was a statistically significant relationship between PSACV and several potential prognostic factors including PSAL, PSAD, stage, Gleason score, and
Alvizuri, Celso R.
rather the confidence, is then given by the 'confidence curve' P( V), where P(V) is the probability that the true moment tensor for the event lies within the neighborhood of M that has fractional volume V. The area under the confidence curve provides a single, abbreviated 'confidence parameter' for M0. We apply the method to data from events in different regions and tectonic settings: 63 small (M w 4) earthquakes in the southern Alaska subduction zone, and 12 earthquakes and 17 nuclear explosions at the Nevada Test Site. Characterization of moment tensor uncertainties puts us in better position to discriminate among moment tensor source types and to assign physical processes to the events.
Applications of tensor functions in creep mechanics
International Nuclear Information System (INIS)
Betten, J.
1991-01-01
Within this contribution a short survey is given of some recent advances in the mathematical modelling of materials behaviour under creep conditions. The mechanical behaviour of anisotropic solids requires a suitable mathematical modelling. The properties of tensor functions with several argument tensors constitute a rational basis for a consistent mathematical modelling of complex material behaviour. This paper presents certain principles, methods, and recent successfull applications of tensor functions in solid mechanics. The rules for specifying irreducible sets of tensor invariants and tensor generators for material tensors of rank two and four are also discussed. Furthermore, it is very important that the scalar coefficients in constitutive and evolutional equations are determined as functions of the integrity basis and experimental data. It is explained in detail that these coefficients can be determined by using tensorial interpolation methods. Some examples for practical use are discussed. (orig./RHM)
Seamless warping of diffusion tensor fields
DEFF Research Database (Denmark)
Xu, Dongrong; Hao, Xuejun; Bansal, Ravi
2008-01-01
To warp diffusion tensor fields accurately, tensors must be reoriented in the space to which the tensors are warped based on both the local deformation field and the orientation of the underlying fibers in the original image. Existing algorithms for warping tensors typically use forward mapping...... of seams, including voxels in which the deformation is extensive. Backward mapping, however, cannot reorient tensors in the template space because information about the directional orientation of fiber tracts is contained in the original, unwarped imaging space only, and backward mapping alone cannot...... transfer that information to the template space. To combine the advantages of forward and backward mapping, we propose a novel method for the spatial normalization of diffusion tensor (DT) fields that uses a bijection (a bidirectional mapping with one-to-one correspondences between image spaces) to warp DT...
Directory of Open Access Journals (Sweden)
Allansdotter-Johnsson Ase
2009-01-01
Full Text Available Abstract Background Knowledge about age-specific normal values for left ventricular mass (LVM, end-diastolic volume (EDV, end-systolic volume (ESV, stroke volume (SV and ejection fraction (EF by cardiac magnetic resonance imaging (CMR is of importance to differentiate between health and disease and to assess the severity of disease. The aims of the study were to determine age and gender specific normal reference values and to explore the normal physiological variation of these parameters from adolescence to late adulthood, in a cross sectional study. Methods Gradient echo CMR was performed at 1.5 T in 96 healthy volunteers (11–81 years, 50 male. Gender-specific analysis of parameters was undertaken in both absolute values and adjusted for body surface area (BSA. Results Age and gender specific normal ranges for LV volumes, mass and function are presented from the second through the eighth decade of life. LVM, ESV and EDV rose during adolescence and declined in adulthood. SV and EF decreased with age. Compared to adult females, adult males had higher BSA-adjusted values of EDV (p = 0.006 and ESV (p Conclusion LV volumes, mass and function vary over a broad age range in healthy individuals. LV volumes and mass both rise in adolescence and decline with age. EF showed a rapid decline in adolescence compared to changes throughout adulthood. These findings demonstrate the need for age and gender specific normal ranges for clinical use.
The Topology of Symmetric Tensor Fields
Levin, Yingmei; Batra, Rajesh; Hesselink, Lambertus; Levy, Yuval
1997-01-01
Combinatorial topology, also known as "rubber sheet geometry", has extensive applications in geometry and analysis, many of which result from connections with the theory of differential equations. A link between topology and differential equations is vector fields. Recent developments in scientific visualization have shown that vector fields also play an important role in the analysis of second-order tensor fields. A second-order tensor field can be transformed into its eigensystem, namely, eigenvalues and their associated eigenvectors without loss of information content. Eigenvectors behave in a similar fashion to ordinary vectors with even simpler topological structures due to their sign indeterminacy. Incorporating information about eigenvectors and eigenvalues in a display technique known as hyperstreamlines reveals the structure of a tensor field. The simplify and often complex tensor field and to capture its important features, the tensor is decomposed into an isotopic tensor and a deviator. A tensor field and its deviator share the same set of eigenvectors, and therefore they have a similar topological structure. A a deviator determines the properties of a tensor field, while the isotopic part provides a uniform bias. Degenerate points are basic constituents of tensor fields. In 2-D tensor fields, there are only two types of degenerate points; while in 3-D, the degenerate points can be characterized in a Q'-R' plane. Compressible and incompressible flows share similar topological feature due to the similarity of their deviators. In the case of the deformation tensor, the singularities of its deviator represent the area of vortex core in the field. In turbulent flows, the similarities and differences of the topology of the deformation and the Reynolds stress tensors reveal that the basic addie-viscosity assuptions have their validity in turbulence modeling under certain conditions.
On improving the efficiency of tensor voting
Moreno, Rodrigo; Garcia, Miguel Angel; Puig, Domenec; Pizarro, Luis; Burgeth, Bernhard; Weickert, Joachim
2011-01-01
This paper proposes two alternative formulations to reduce the high computational complexity of tensor voting, a robust perceptual grouping technique used to extract salient information from noisy data. The first scheme consists of numerical approximations of the votes, which have been derived from an in-depth analysis of the plate and ball voting processes. The second scheme simplifies the formulation while keeping the same perceptual meaning of the original tensor voting: The stick tensor v...
Schrimpf, Martin
2016-01-01
Google's Machine Learning framework TensorFlow was open-sourced in November 2015 [1] and has since built a growing community around it. TensorFlow is supposed to be flexible for research purposes while also allowing its models to be deployed productively. This work is aimed towards people with experience in Machine Learning considering whether they should use TensorFlow in their environment. Several aspects of the framework important for such a decision are examined, such as the heterogenity,...
Efficient Low Rank Tensor Ring Completion
Wang, Wenqi; Aggarwal, Vaneet; Aeron, Shuchin
2017-01-01
Using the matrix product state (MPS) representation of the recently proposed tensor ring decompositions, in this paper we propose a tensor completion algorithm, which is an alternating minimization algorithm that alternates over the factors in the MPS representation. This development is motivated in part by the success of matrix completion algorithms that alternate over the (low-rank) factors. In this paper, we propose a spectral initialization for the tensor ring completion algorithm and ana...
The Riemann-Lovelock Curvature Tensor
Kastor, David
2012-01-01
In order to study the properties of Lovelock gravity theories in low dimensions, we define the kth-order Riemann-Lovelock tensor as a certain quantity having a total 4k-indices, which is kth-order in the Riemann curvature tensor and shares its basic algebraic and differential properties. We show that the kth-order Riemann-Lovelock tensor is determined by its traces in dimensions 2k \\le D
The 1/ N Expansion of Tensor Models with Two Symmetric Tensors
Gurau, Razvan
2018-06-01
It is well known that tensor models for a tensor with no symmetry admit a 1/ N expansion dominated by melonic graphs. This result relies crucially on identifying jackets, which are globally defined ribbon graphs embedded in the tensor graph. In contrast, no result of this kind has so far been established for symmetric tensors because global jackets do not exist. In this paper we introduce a new approach to the 1/ N expansion in tensor models adapted to symmetric tensors. In particular we do not use any global structure like the jackets. We prove that, for any rank D, a tensor model with two symmetric tensors and interactions the complete graph K D+1 admits a 1/ N expansion dominated by melonic graphs.
Complete stress tensor determination by microearthquake analysis
Slunga, R.
2010-12-01
the depth based on the assumptions of a fractured crust, widely vary ing stress field, and a general closeness to instability as found by stress measurements (Jamison and Cook 1976). Wheather this approach is working or not is best answered by applying it to real data. This was provided by the IMO network in Iceland. Along Southern Iceland Seismic Zone (SISZ) more than 200,000 microearthquakes and a few M 5 EQs and 2 M=6.6 EQs have been recorded. The results will be presented it is obvious that the use of the stresses determined from the microearthquake recordings may significa ntly improve earthquake warnings and will make it possible to use the absolute C FS method for more deterministic predictions. Note that the microearthquake meth od only shows the part of the stress field that has caused slip. Volumes with st able stress will not show up. However stress measurements (Brown and Hoek 1978, Slunga 1988) have shown that the crustal stresses in general are close to instabi lity and microearthquake source analysis has shown that a large number of differ ent fractures become unstable within longer time windows. This may explain the e xcellent results given by the Icelandic tests of the absolute stress tensor fiel d as given by the microearthquakes. However I prefer to call this stress apparen t.
Dictionary-Based Tensor Canonical Polyadic Decomposition
Cohen, Jeremy Emile; Gillis, Nicolas
2018-04-01
To ensure interpretability of extracted sources in tensor decomposition, we introduce in this paper a dictionary-based tensor canonical polyadic decomposition which enforces one factor to belong exactly to a known dictionary. A new formulation of sparse coding is proposed which enables high dimensional tensors dictionary-based canonical polyadic decomposition. The benefits of using a dictionary in tensor decomposition models are explored both in terms of parameter identifiability and estimation accuracy. Performances of the proposed algorithms are evaluated on the decomposition of simulated data and the unmixing of hyperspectral images.
Bayesian regularization of diffusion tensor images
DEFF Research Database (Denmark)
Frandsen, Jesper; Hobolth, Asger; Østergaard, Leif
2007-01-01
Diffusion tensor imaging (DTI) is a powerful tool in the study of the course of nerve fibre bundles in the human brain. Using DTI, the local fibre orientation in each image voxel can be described by a diffusion tensor which is constructed from local measurements of diffusion coefficients along...... several directions. The measured diffusion coefficients and thereby the diffusion tensors are subject to noise, leading to possibly flawed representations of the three dimensional fibre bundles. In this paper we develop a Bayesian procedure for regularizing the diffusion tensor field, fully utilizing...
A RENORMALIZATION PROCEDURE FOR TENSOR MODELS AND SCALAR-TENSOR THEORIES OF GRAVITY
SASAKURA, NAOKI
2010-01-01
Tensor models are more-index generalizations of the so-called matrix models, and provide models of quantum gravity with the idea that spaces and general relativity are emergent phenomena. In this paper, a renormalization procedure for the tensor models whose dynamical variable is a totally symmetric real three-tensor is discussed. It is proven that configurations with certain Gaussian forms are the attractors of the three-tensor under the renormalization procedure. Since these Gaussian config...
The tensor network theory library
Al-Assam, S.; Clark, S. R.; Jaksch, D.
2017-09-01
In this technical paper we introduce the tensor network theory (TNT) library—an open-source software project aimed at providing a platform for rapidly developing robust, easy to use and highly optimised code for TNT calculations. The objectives of this paper are (i) to give an overview of the structure of TNT library, and (ii) to help scientists decide whether to use the TNT library in their research. We show how to employ the TNT routines by giving examples of ground-state and dynamical calculations of one-dimensional bosonic lattice system. We also discuss different options for gaining access to the software available at www.tensornetworktheory.org.
Dirac tensor with heavy photon
Energy Technology Data Exchange (ETDEWEB)
Bytev, V.V.; Kuraev, E.A. [Joint Institute of Nuclear Research, Moscow (Russian Federation). Bogoliubov Lab. of Theoretical Physics; Scherbakova, E.S. [Hamburg Univ. (Germany). 1. Inst. fuer Theoretische Physik
2012-01-15
For the large-angles hard photon emission by initial leptons in process of high energy annihilation of e{sup +}e{sup -} {yields} to hadrons the Dirac tensor is obtained, taking into account the lowest order radiative corrections. The case of large-angles emission of two hard photons by initial leptons is considered. This result is being completed by the kinematics case of collinear hard photons emission as well as soft virtual and real photons and can be used for construction of Monte-Carlo generators. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Vacca, P.C.; Whitten, J.E.; Pelchat, J.M.; Arredondo, S.A.; Matson, E.R.; Lewis, S.H.; Collins, D.J.; Santiago, P.A. [Nuclear Regulatory Commission, Washington, DC (United States). Div. of Industrial and Medical Nuclear Safety; Tingle, W. [Dept. of Environment, Health, and Natural Resources, Raleigh, NC (United States). Div. of Radiation Protection
1997-05-01
As part of its redesign of the materials licensing process, NRC is consolidating and updating numerous guidance documents into a single comprehensive repository as described in NUREG-1539 and draft NUREG-1541. NUREG-1556, Vol. 1, is the first program-specific guidance developed for the new process and will serve as a template for subsequent program-specific guidance. This document is intended for use by applicants, licensees, and NRC staff and will also be available to Agreement States. This document supersedes the guidance previously found in draft Regulatory Guide DG-0008, ``Applications for the Use of Sealed Sources in Portable Gauging Devices,`` and in NMSs Policy and guidance Directive 2-07, ``Standard Review Plan for Applications for Use of Sealed Sources in Portable Gauging Devices.`` This final report takes a more risk-informed, performance-based approach to licensing portable gauges, and reduces the information(amount and level of detail) needed to support an application to use these devices. It incorporates many suggests submitted during the comment period on draft NUREG-1556, Volume 1. When published, this final report should be used in preparing portable gauge license applications. NRC staff will use this final report in reviewing these applications.
International Nuclear Information System (INIS)
Famiano, M.A.
1997-01-01
A tissue-equivalent spherical proportional counter is used with a modified amplifier system to measure specific energy deposited from a uniform radiation field for short periods of time (∼1 micros to seconds) in order to extrapolate to dose in sub-micron tissue volumes. The energy deposited during these time intervals is compared to biological repair processes occurring within the same intervals after the initial energy deposition. The signal is integrated over a variable collection time which is adjusted with a square-wave pulse. Charge from particle passages is collected on the anode during the period in which the integrator is triggered, and the signal decays quickly to zero after the integrator feedback switch resets; the process repeats for every triggering pulse. Measurements of energy deposited from x rays, 137 Cs gamma rays, and electrons from a 90 Sr/ 90 Y source for various time intervals are taken. Spectral characteristics as a function of charge collection time are observed and frequency plots of specific energy and collection time-interval are presented. In addition, a threshold energy flux is selected for each radiation type at which the formation of radicals (based on current measurements) in mammalian cells equals the rate at which radicals are repaired
International Nuclear Information System (INIS)
Vacca, P.C.; Whitten, J.E.; Pelchat, J.M.; Arredondo, S.A.; Matson, E.R.; Lewis, S.H.; Collins, D.J.; Santiago, P.A.; Tingle, W.
1997-05-01
As part of its redesign of the materials licensing process, NRC is consolidating and updating numerous guidance documents into a single comprehensive repository as described in NUREG-1539 and draft NUREG-1541. NUREG-1556, Vol. 1, is the first program-specific guidance developed for the new process and will serve as a template for subsequent program-specific guidance. This document is intended for use by applicants, licensees, and NRC staff and will also be available to Agreement States. This document supersedes the guidance previously found in draft Regulatory Guide DG-0008, ''Applications for the Use of Sealed Sources in Portable Gauging Devices,'' and in NMSs Policy and guidance Directive 2-07, ''Standard Review Plan for Applications for Use of Sealed Sources in Portable Gauging Devices.'' This final report takes a more risk-informed, performance-based approach to licensing portable gauges, and reduces the information(amount and level of detail) needed to support an application to use these devices. It incorporates many suggests submitted during the comment period on draft NUREG-1556, Volume 1. When published, this final report should be used in preparing portable gauge license applications. NRC staff will use this final report in reviewing these applications
Partition-based Collaborative Tensor Factorization for POI Recommendation
Institute of Scientific and Technical Information of China (English)
Wenjing Luan; Guanjun Liu; Changjun Jiang; Liang Qi
2017-01-01
The rapid development of location-based social networks (LBSNs) provides people with an opportunity of better understanding their mobility behavior which enables them to decide their next location.For example,it can help travelers to choose where to go next,or recommend salesmen the most potential places to deliver advertisements or sell products.In this paper,a method for recommending points of interest (POIs) is proposed based on a collaborative tensor factorization (CTF) technique.Firstly,a generalized objective function is constructed for collaboratively factorizing a tensor with several feature matrices.Secondly,a 3-mode tensor is used to model all users' check-in behaviors,and three feature matrices are extracted to characterize the time distribution,category distribution and POI correlation,respectively.Thirdly,each user's preference to a POI at a specific time can be estimated by using CTF.In order to further improve the recommendation accuracy,PCTF (Partitionbased CTF) is proposed to fill the missing entries of a tensor after clustering its every mode.Experiments on a real checkin database show that the proposed method can provide more accurate location recommendation.
A Tensor Statistical Model for Quantifying Dynamic Functional Connectivity.
Zhu, Yingying; Zhu, Xiaofeng; Kim, Minjeong; Yan, Jin; Wu, Guorong
2017-06-01
Functional connectivity (FC) has been widely investigated in many imaging-based neuroscience and clinical studies. Since functional Magnetic Resonance Image (MRI) signal is just an indirect reflection of brain activity, it is difficult to accurately quantify the FC strength only based on signal correlation. To address this limitation, we propose a learning-based tensor model to derive high sensitivity and specificity connectome biomarkers at the individual level from resting-state fMRI images. First, we propose a learning-based approach to estimate the intrinsic functional connectivity. In addition to the low level region-to-region signal correlation, latent module-to-module connection is also estimated and used to provide high level heuristics for measuring connectivity strength. Furthermore, sparsity constraint is employed to automatically remove the spurious connections, thus alleviating the issue of searching for optimal threshold. Second, we integrate our learning-based approach with the sliding-window technique to further reveal the dynamics of functional connectivity. Specifically, we stack the functional connectivity matrix within each sliding window and form a 3D tensor where the third dimension denotes for time. Then we obtain dynamic functional connectivity (dFC) for each individual subject by simultaneously estimating the within-sliding-window functional connectivity and characterizing the across-sliding-window temporal dynamics. Third, in order to enhance the robustness of the connectome patterns extracted from dFC, we extend the individual-based 3D tensors to a population-based 4D tensor (with the fourth dimension stands for the training subjects) and learn the statistics of connectome patterns via 4D tensor analysis. Since our 4D tensor model jointly (1) optimizes dFC for each training subject and (2) captures the principle connectome patterns, our statistical model gains more statistical power of representing new subject than current state
International Nuclear Information System (INIS)
Bondt, P. de; Wiele, C. van de; Winter, F. de; Dierckx, R.A.; Sutter, J. de; Backer, G. de
2001-01-01
The aim of this study was to determine normative volumetric data and ejection fraction values derived from gated myocardial single-photon emission tomography (SPET) using the commercially available software algorithm QGS (quantitative gated SPET). From a prospective database of 876 consecutive patients who were referred for a 2-day stress-rest technetium-99m tetrofosmin (925 MBq) gated SPET study, 102 patients (43 men, 59 women) with a low (<10%) pre-test likelihood of coronary disease were included (mean age 57.6 years). For stress imaging, a bicycle protocol was used in 79 of the patients and a dipyridamole protocol in 23. Left ventricular ejection fraction (LVEF) and end-diastolic and -systolic volumes (EDV and ESV) were calculated by QGS. EDV and ESV were corrected for body surface area, indicated by EDVi and ESVi. To allow comparison with previous reports using other imaging modalities, men and women were divided into three age groups (<45 years, ≥45 years but <65 years and ≥65 years). Men showed significantly higher EDVi and ESVi values throughout and lower LVEF values when compared with women in the subgroup ≥65 years (P<0.05, ANOVA). Significant negative and positive correlations were found between age and EDVi and ESVi values for both women and men and between LVEF and age in women (Pearson P≤0.01). LVEF values at bicycle stress were significantly higher than at rest (P=0.000, paired t test), which was the result of a significant decrease in ESV (P=0.003), a phenomenon which did not occur following dipyridamole stress (P=0.409). The data presented suggest that LVEF and EDVi and ESVi as assessed by QGS are strongly gender-specific. Although the physiological significance of these results is uncertain and needs further study, these findings demonstrate that the evaluation of cardiac function and volumes of patients by means of QGS should consider age- and gender-matched normative values. (orig.)
Coban, Soner; Doluoglu, Omer Gokhan; Keles, Ibrahim; Demirci, Hakan; Turkoglu, Ali Riza; Guzelsoy, Muhammet; Karalar, Mustafa; Demirbas, Murat
2016-06-01
To investigate the predictive values of free prostate-specific antigen (fPSA), total PSA (tPSA) and age on the prostate volume. The data of 2148 patients with lower urinary tract symptoms were analyzed retrospectively. The patients who had transrectal ultrasonography guided 10 core biopsies owing to the findings obtained on digital rectal examination and presence of high PSA levels (PSA = 2.5-10 ng/dl), and proven to have BPH histopathologically were included in the study. Age, tPSA, fPSA and the prostate volumes (PV) of the patients were noted. One thousand patients that fulfilled the inclusion criteria were included in the study. The PV of the patients were significantly correlated with age, tPSA and fPSA (p < 0.001 and r = 0.307, p < 0.001 and r = 0.382, p < 0.001 and r = 0.296, respectively). On linear regression model, fPSA was found as a stronger predictive for PV (AUC = 0.75, p < 0.001) when compared to age (AUC = 0.64, p < 0.001), and tPSA (AUC = 0.69, p = 0.013). Although tPSA is an important prognostic factor for predicting PV, the predictive value of fPSA is higher. PV can easily be predicted by using age, and serum tPSA and fPSA levels.
J.L.H.R. Bosch (Ruud); W.C.J. Hop (Wim); C.H. Bangma (Chris); W.J. Kirkels (Wim); F.H. Schröder (Fritz)
1995-01-01
textabstractThe correlation between both prostate specific antigen levels (PSA) and prostate specific antigen density (PSAD) and age, prostate volume parameters, body mass index, and the International Prostate Symptom Score (IPSS) were studied in a community‐based population. A sample of 502 men
3D reconstruction of tensors and vectors
International Nuclear Information System (INIS)
Defrise, Michel; Gullberg, Grant T.
2005-01-01
Here we have developed formulations for the reconstruction of 3D tensor fields from planar (Radon) and line-integral (X-ray) projections of 3D vector and tensor fields. Much of the motivation for this work is the potential application of MRI to perform diffusion tensor tomography. The goal is to develop a theory for the reconstruction of both Radon planar and X-ray or line-integral projections because of the flexibility of MRI to obtain both of these type of projections in 3D. The development presented here for the linear tensor tomography problem provides insight into the structure of the nonlinear MRI diffusion tensor inverse problem. A particular application of tensor imaging in MRI is the potential application of cardiac diffusion tensor tomography for determining in vivo cardiac fiber structure. One difficulty in the cardiac application is the motion of the heart. This presents a need for developing future theory for tensor tomography in a motion field. This means developing a better understanding of the MRI signal for diffusion processes in a deforming media. The techniques developed may allow the application of MRI tensor tomography for the study of structure of fiber tracts in the brain, atherosclerotic plaque, and spine in addition to fiber structure in the heart. However, the relations presented are also applicable to other fields in medical imaging such as diffraction tomography using ultrasound. The mathematics presented can also be extended to exponential Radon transform of tensor fields and to other geometric acquisitions such as cone beam tomography of tensor fields
Estimation of the magnetic field gradient tensor using the Swarm constellation
DEFF Research Database (Denmark)
Kotsiaros, Stavros; Finlay, Chris; Olsen, Nils
2014-01-01
For the first time, part of the magnetic field gradient tensor is estimated in space by the Swarm mission. We investigate the possibility of a more complete estimation of the gradient tensor exploiting the Swarm constellation. The East-West gradients can be approximated by observations from...... deviations compared to conventional vector observations at almost all latitudes. Analytical and numerical analysis of the spectral properties of the gradient tensor shows that specific combinations of the East-West and North-South gradients have almost identical signal content to the radial gradient...
Raman scattering tensors of tyrosine.
Tsuboi, M; Ezaki, Y; Aida, M; Suzuki, M; Yimit, A; Ushizawa, K; Ueda, T
1998-01-01
Polarized Raman scattering measurements have been made of a single crystal of L-tyrosine by the use of a Raman microscope with the 488.0-nm exciting beam from an argon ion laser. The L-tyrosine crystal belongs to the space group P2(1)2(1)2(1) (orthorhombic), and Raman scattering intensities corresponding to the aa, bb, cc, ab and ac components of the crystal Raman tensor have been determined for each prominent Raman band. A similar set of measurements has been made of L-tyrosine-d4, in which four hydrogen atoms on the benzene ring are replaced by deuterium atoms. The effects of NH3-->ND3 and OH-->OD on the Raman spectrum have also been examined. In addition, depolarization ratios of some bands of L-tyrosine in aqueous solutions of pH 13 and pH 1 were examined. For comparison with these experimental results, on the other hand, ab initio molecular orbital calculations have been made of the normal modes of vibration and their associated polarizability oscillations of the L-tyrosine molecule. On the basis of these experimental data and by referring to the results of the calculations, discussions have been presented on the Raman tensors associated to some Raman bands, including those at 829 cm-1 (benzene ring breathing), 642 cm-1 (benzene ring deformation), and 432 cm-1 (C alpha-C beta-C gamma bending).
Algebraic classification of the Weyl tensor in higher dimensions based on its 'superenergy' tensor
International Nuclear Information System (INIS)
Senovilla, Jose M M
2010-01-01
The algebraic classification of the Weyl tensor in the arbitrary dimension n is recovered by means of the principal directions of its 'superenergy' tensor. This point of view can be helpful in order to compute the Weyl aligned null directions explicitly, and permits one to obtain the algebraic type of the Weyl tensor by computing the principal eigenvalue of rank-2 symmetric future tensors. The algebraic types compatible with states of intrinsic gravitational radiation can then be explored. The underlying ideas are general, so that a classification of arbitrary tensors in the general dimension can be achieved. (fast track communication)
Gravitational Metric Tensor Exterior to Rotating Homogeneous ...
African Journals Online (AJOL)
The covariant and contravariant metric tensors exterior to a homogeneous spherical body rotating uniformly about a common φ axis with constant angular velocity ω is constructed. The constructed metric tensors in this gravitational field have seven non-zero distinct components.The Lagrangian for this gravitational field is ...
Tensor Network Quantum Virtual Machine (TNQVM)
Energy Technology Data Exchange (ETDEWEB)
2016-11-18
There is a lack of state-of-the-art quantum computing simulation software that scales on heterogeneous systems like Titan. Tensor Network Quantum Virtual Machine (TNQVM) provides a quantum simulator that leverages a distributed network of GPUs to simulate quantum circuits in a manner that leverages recent results from tensor network theory.
Tensor product varieties and crystals. GL case
Malkin, Anton
2001-01-01
The role of Spaltenstein varieties in the tensor product for GL is explained. In particular a direct (non-combinatorial) proof of the fact that the number of irreducible components of a Spaltenstein variety is equal to a Littlewood-Richardson coefficient (i.e. certain tensor product multiplicity) is obtained.
Halpern, Joshua A; Shoag, Jonathan E; Artis, Amanda S; Ballman, Karla V; Sedrakyan, Art; Hershman, Dawn L; Wright, Jason D; Shih, Ya Chen Tina; Hu, Jim C
2017-02-01
Studies demonstrate that use of prostate-specific antigen screening decreased significantly following the US Preventive Services Task Force (USPSTF) recommendation against prostate-specific antigen screening in 2012. To determine downstream effects on practice patterns in prostate cancer diagnosis and treatment following the 2012 USPSTF recommendation. Procedural volumes of certifying and recertifying urologists from 2009 through 2016 were evaluated for variation in prostate biopsy and radical prostatectomy (RP) volume. Trends were confirmed using the New York Statewide Planning and Research Cooperative System and Nationwide Inpatient Sample. The study included a representative sample of urologists across practice settings and nationally representative sample of all RP discharges. We obtained operative case logs from the American Board of Urology and identified urologists performing at least 1 prostate biopsy (n = 5173) or RP (n = 3748), respectively. The 2012 USPSTF recommendation against routine population-wide prostate-specific antigen screening. Change in median biopsy and RP volume per urologist and national procedural volume. Following the USPSTF recommendation, median biopsy volume per urologist decreased from 29 to 21 (interquartile range [IQR}, 12-34; P prostate biopsy and RP volumes decreased significantly. A panoramic vantage point is needed to evaluate the long-term consequences of the 2012 USPSTF recommendation.
Nichols, John H; Loeb, Stacy; Metter, E Jeffrey; Ferrucci, Luigi; Carter, H Ballentine
2012-05-01
Study Type--Prognostic (cohort). Level of Evidence 2b. What's known on the subject? And what does the study add? Previous studies have attempted to characterize the normal biological variability in PSA among men without prostate cancer. These reports suggest that PSA variability is unrelated to age, but there are conflicting data on its association with the baseline PSA level. There are limited published data regarding the effects of prostate volume on PSA variability. A prior study assessing whether prostate volume changes would confound the use of PSA velocity in clinical practice reported that prostate volume changes were not significantly related to PSA changes. This study did not directly address the effect of baseline prostate volume on serial PSA variability. The objective of the current study was to further examine the relationship between prostate volume and PSA variability. Our hypothesis was that larger baseline prostate volume would be associated with increased PSA variability in men without known prostate cancer and in those with suspected small-volume disease. The results of the study suggest that baseline PSA, not prostate volume, is the primary driver of PSA variability in these populations. • To clarify the relationship between serial prostate-specific antigen (PSA) variability and prostate volume in both cancer-free participants from the Baltimore Longitudinal Study of Aging (BLSA) and patients with low-risk prostate cancer from the Johns Hopkins Active Surveillance Program (AS). • In all, 287 men from the BLSA and 131 patients from the AS were included in the analysis, all with at least two PSA measurements and concurrent prostate volume measurements. • PSA variability was calculated in ng/mL per year, and a linear mixed-effects model was used to determine the relative effects of prostate volume, baseline PSA and age on PSA change over time. • In a model with prostate volume, age and baseline PSA, there was no significant relationship
Differential invariants for higher-rank tensors. A progress report
International Nuclear Information System (INIS)
Tapial, V.
2004-07-01
We outline the construction of differential invariants for higher-rank tensors. In section 2 we outline the general method for the construction of differential invariants. A first result is that the simplest tensor differential invariant contains derivatives of the same order as the rank of the tensor. In section 3 we review the construction for the first-rank tensors (vectors) and second-rank tensors (metrics). In section 4 we outline the same construction for higher-rank tensors. (author)
Beyond Low Rank: A Data-Adaptive Tensor Completion Method
Zhang, Lei; Wei, Wei; Shi, Qinfeng; Shen, Chunhua; Hengel, Anton van den; Zhang, Yanning
2017-01-01
Low rank tensor representation underpins much of recent progress in tensor completion. In real applications, however, this approach is confronted with two challenging problems, namely (1) tensor rank determination; (2) handling real tensor data which only approximately fulfils the low-rank requirement. To address these two issues, we develop a data-adaptive tensor completion model which explicitly represents both the low-rank and non-low-rank structures in a latent tensor. Representing the no...
Unique characterization of the Bel-Robinson tensor
International Nuclear Information System (INIS)
Bergqvist, G; Lankinen, P
2004-01-01
We prove that a completely symmetric and trace-free rank-4 tensor is, up to sign, a Bel-Robinson-type tensor, i.e., the superenergy tensor of a tensor with the same algebraic symmetries as the Weyl tensor, if and only if it satisfies a certain quadratic identity. This may be seen as the first Rainich theory result for rank-4 tensors
Mazzini, Virginia; Craig, Vincent S J
2017-10-01
The importance of electrolyte solutions cannot be overstated. Beyond the ionic strength of electrolyte solutions the specific nature of the ions present is vital in controlling a host of properties. Therefore ion specificity is fundamentally important in physical chemistry, engineering and biology. The observation that the strengths of the effect of ions often follows well established series suggests that a single predictive and quantitative description of specific-ion effects covering a wide range of systems is possible. Such a theory would revolutionise applications of physical chemistry from polymer precipitation to drug design. Current approaches to understanding specific-ion effects involve consideration of the ions themselves, the solvent and relevant interfaces and the interactions between them. Here we investigate the specific-ion effects trends of standard partial molar volumes and electrostrictive volumes of electrolytes in water and eleven non-aqueous solvents. We choose these measures as they relate to bulk properties at infinite dilution, therefore they are the simplest electrolyte systems. This is done to test the hypothesis that the ions alone exhibit a specific-ion effect series that is independent of the solvent and unrelated to surface properties. The specific-ion effects trends of standard partial molar volumes and normalised electrostrictive volumes examined in this work show a fundamental ion-specific series that is reproduced across the solvents, which is the Hofmeister series for anions and the reverse lyotropic series for cations, supporting the hypothesis. This outcome is important in demonstrating that ion specificity is observed at infinite dilution and demonstrates that the complexity observed in the manifestation of specific-ion effects in a very wide range of systems is due to perturbations of solvent, surfaces and concentration on the underlying fundamental series. This knowledge will guide a general understanding of specific
Tensor completion and low-n-rank tensor recovery via convex optimization
International Nuclear Information System (INIS)
Gandy, Silvia; Yamada, Isao; Recht, Benjamin
2011-01-01
In this paper we consider sparsity on a tensor level, as given by the n-rank of a tensor. In an important sparse-vector approximation problem (compressed sensing) and the low-rank matrix recovery problem, using a convex relaxation technique proved to be a valuable solution strategy. Here, we will adapt these techniques to the tensor setting. We use the n-rank of a tensor as a sparsity measure and consider the low-n-rank tensor recovery problem, i.e. the problem of finding the tensor of the lowest n-rank that fulfills some linear constraints. We introduce a tractable convex relaxation of the n-rank and propose efficient algorithms to solve the low-n-rank tensor recovery problem numerically. The algorithms are based on the Douglas–Rachford splitting technique and its dual variant, the alternating direction method of multipliers
Towards a tensor calculus for κ-supersymmetry
International Nuclear Information System (INIS)
Ivanov, E.A.; Kapustnikov, A.A.
1991-05-01
We present a new manifestly space-time and world-volume supersymmetric formulation of the simplest super p-branes, massive d=2, N=1 superparticle and d=4, N=1 superstring, in terms of properly constrained world-line and world-sheet superfields. We identify the relevant κ-supersymmetries with a kind of local supersymmetry in the world-volume superspaces and, based on this, develop a tensor calculus for constructing higher-order supersymmetric and κ-invariant corrections to the corresponding minimal super p-brane actions. The latter are represented by pure Wess-Zumino terms in the world-volume superspaces. A ''double analyticity'' principle for extending this superfield approach to other super p-branes is suggested. (author). 14 refs
Weyl curvature tensor in static spherical sources
International Nuclear Information System (INIS)
Ponce de Leon, J.
1988-01-01
The role of the Weyl curvature tensor in static sources of the Schwarzschild field is studied. It is shown that in general the contribution from the Weyl curvature tensor (the ''purely gravitational field energy'') to the mass-energy inside the body may be positive, negative, or zero. It is proved that a positive (negative) contribution from the Weyl tensor tends to increase (decrease) the effective gravitational mass, the red-shift (from a point in the sphere to infinity), as well as the gravitational force which acts on a constituent matter element of a body. It is also proved that the contribution from the Weyl tensor always is negative in sources with surface gravitational potential larger than (4/9. It is pointed out that large negative contributions from the Weyl tensor could give rise to the phenomenon of gravitational repulsion. A simple example which illustrates the results is discussed
A recursive reduction of tensor Feynman integrals
International Nuclear Information System (INIS)
Diakonidis, T.; Riemann, T.; Tausk, J.B.; Fleischer, J.
2009-07-01
We perform a recursive reduction of one-loop n-point rank R tensor Feynman integrals [in short: (n,R)-integrals] for n≤6 with R≤n by representing (n,R)-integrals in terms of (n,R-1)- and (n-1,R-1)-integrals. We use the known representation of tensor integrals in terms of scalar integrals in higher dimension, which are then reduced by recurrence relations to integrals in generic dimension. With a systematic application of metric tensor representations in terms of chords, and by decomposing and recombining these representations, we find the recursive reduction for the tensors. The procedure represents a compact, sequential algorithm for numerical evaluations of tensor Feynman integrals appearing in next-to-leading order contributions to massless and massive three- and four-particle production at LHC and ILC, as well as at meson factories. (orig.)
On Lovelock analogs of the Riemann tensor
Camanho, Xián O.; Dadhich, Naresh
2016-03-01
It is possible to define an analog of the Riemann tensor for Nth order Lovelock gravity, its characterizing property being that the trace of its Bianchi derivative yields the corresponding analog of the Einstein tensor. Interestingly there exist two parallel but distinct such analogs and the main purpose of this note is to reconcile both formulations. In addition we will introduce a simple tensor identity and use it to show that any pure Lovelock vacuum in odd d=2N+1 dimensions is Lovelock flat, i.e. any vacuum solution of the theory has vanishing Lovelock-Riemann tensor. Further, in the presence of cosmological constant it is the Lovelock-Weyl tensor that vanishes.
Aagaard, James S.; And Others
This two-volume document specifies a protocol that was developed using the Reference Model for Open Systems Interconnection (OSI), which provides a framework for communications within a heterogeneous network environment. The protocol implements the features necessary for bibliographic searching, record maintenance, and mail transfer between…
Tri-Clustered Tensor Completion for Social-Aware Image Tag Refinement.
Tang, Jinhui; Shu, Xiangbo; Qi, Guo-Jun; Li, Zechao; Wang, Meng; Yan, Shuicheng; Jain, Ramesh
2017-08-01
Social image tag refinement, which aims to improve tag quality by automatically completing the missing tags and rectifying the noise-corrupted ones, is an essential component for social image search. Conventional approaches mainly focus on exploring the visual and tag information, without considering the user information, which often reveals important hints on the (in)correct tags of social images. Towards this end, we propose a novel tri-clustered tensor completion framework to collaboratively explore these three kinds of information to improve the performance of social image tag refinement. Specifically, the inter-relations among users, images and tags are modeled by a tensor, and the intra-relations between users, images and tags are explored by three regularizations respectively. To address the challenges of the super-sparse and large-scale tensor factorization that demands expensive computing and memory cost, we propose a novel tri-clustering method to divide the tensor into a certain number of sub-tensors by simultaneously clustering users, images and tags into a bunch of tri-clusters. And then we investigate two strategies to complete these sub-tensors by considering (in)dependence between the sub-tensors. Experimental results on a real-world social image database demonstrate the superiority of the proposed method compared with the state-of-the-art methods.
Evidence for Nuclear Tensor Polarization of Deuterium Molecules in Storage Cells
International Nuclear Information System (INIS)
van den Brand, J.; Bulten, H.; Zhou, Z.; Unal, O.; van den Brand, J.; Ferro-Luzzi, M.; Botto, T.; Bouwhuis, M.; Heimberg, P.; de Jager, C.; de Lange, D.; Nooren, G.; Papadakis, N.; Passchier, I.; Poolman, H.; Steijger, J.; Vodinas, N.; de Vries, H.; van den Brand, J.; Ferro-Luzzi, M.; Lang, J.; Alarcon, R.; Dolfini, S.; Ent, R.; Higinbotham, D.
1997-01-01
Deuterium molecules were obtained by recombination, on a copper surface, of deuterium atoms prepared in specific hyperfine states. The molecules were stored for about 5ms in an open-ended cylindrical cell, placed in a 23mT magnetic field, and their tensor polarization was measured by elastic scattering of 704MeV electrons. The results of the measurements are consistent with the deuterium molecules retaining the tensor polarization of the initial atoms. copyright 1997 The American Physical Society
Stefanou, Maria-Ioanna; Lumsden, Daniel E; Ashmore, Jonathan; Ashkan, Keyoumars; Lin, Jean-Pierre; Charles-Edwards, Geoffrey
2016-10-01
Non-invasive measures of corticospinal tract (CST) integrity may help to guide clinical interventions, particularly in children and young people (CAYP) with motor disorders. We compared diffusion tensor imaging (DTI) metrics extracted from the CST generated by tensor and non-tensor based tractography algorithms. For a group of 25 CAYP undergoing clinical evaluation, the CST was reconstructed using (1) deterministic tensor-based tractography algorithm, (2) probabilistic tensor-based, and (3) constrained spherical deconvolution (CSD)-derived tractography algorithms. Choice of tractography algorithm significantly altered the results of tracking. Larger tracts were consistently defined with CSD, with differences in FA but not MD values for tracts to the pre- or post-central gyrus. Differences between deterministic and probabilistic tensor-based algorithms were minimal. Non-tensor reconstructed tracts appeared to be more anatomically representative. Examining metrics along the tract, difference in FA values appeared to be greatest in voxels with predominantly single-fibre orientations. Less pronounced differences were seen outwith of these regions. With an increasing interest in the applications of tractography analysis at all stages of movement disorder surgery, it is important that clinicians remain alert to the consequences of choice of tractography algorithm on subsequently generated tracts, including differences in volumes, anatomical reconstruction, and DTI metrics, the latter of which will have global as well as more regional effects. Tract-wide analysis of DTI based metrics is of limited utility, and a more segmental approach to analysis may be appropriate, particularly if disruption to a focal region of a white matter pathway is anticipated.
International Nuclear Information System (INIS)
Cain, Peter A; Ahl, Ragnhild; Hedstrom, Erik; Ugander, Martin; Allansdotter-Johnsson, Ase; Friberg, Peter; Arheden, Hakan
2009-01-01
Knowledge about age-specific normal values for left ventricular mass (LVM), end-diastolic volume (EDV), end-systolic volume (ESV), stroke volume (SV) and ejection fraction (EF) by cardiac magnetic resonance imaging (CMR) is of importance to differentiate between health and disease and to assess the severity of disease. The aims of the study were to determine age and gender specific normal reference values and to explore the normal physiological variation of these parameters from adolescence to late adulthood, in a cross sectional study. Gradient echo CMR was performed at 1.5 T in 96 healthy volunteers (11–81 years, 50 male). Gender-specific analysis of parameters was undertaken in both absolute values and adjusted for body surface area (BSA). Age and gender specific normal ranges for LV volumes, mass and function are presented from the second through the eighth decade of life. LVM, ESV and EDV rose during adolescence and declined in adulthood. SV and EF decreased with age. Compared to adult females, adult males had higher BSA-adjusted values of EDV (p = 0.006) and ESV (p < 0.001), similar SV (p = 0.51) and lower EF (p = 0.014). No gender differences were seen in the youngest, 11–15 year, age range. LV volumes, mass and function vary over a broad age range in healthy individuals. LV volumes and mass both rise in adolescence and decline with age. EF showed a rapid decline in adolescence compared to changes throughout adulthood. These findings demonstrate the need for age and gender specific normal ranges for clinical use
Efficient Tensor Completion for Color Image and Video Recovery: Low-Rank Tensor Train.
Bengua, Johann A; Phien, Ho N; Tuan, Hoang Duong; Do, Minh N
2017-05-01
This paper proposes a novel approach to tensor completion, which recovers missing entries of data represented by tensors. The approach is based on the tensor train (TT) rank, which is able to capture hidden information from tensors thanks to its definition from a well-balanced matricization scheme. Accordingly, new optimization formulations for tensor completion are proposed as well as two new algorithms for their solution. The first one called simple low-rank tensor completion via TT (SiLRTC-TT) is intimately related to minimizing a nuclear norm based on TT rank. The second one is from a multilinear matrix factorization model to approximate the TT rank of a tensor, and is called tensor completion by parallel matrix factorization via TT (TMac-TT). A tensor augmentation scheme of transforming a low-order tensor to higher orders is also proposed to enhance the effectiveness of SiLRTC-TT and TMac-TT. Simulation results for color image and video recovery show the clear advantage of our method over all other methods.
Effective field theory approaches for tensor potentials
Energy Technology Data Exchange (ETDEWEB)
Jansen, Maximilian
2016-11-14
Effective field theories are a widely used tool to study physical systems at low energies. We apply them to systematically analyze two and three particles interacting via tensor potentials. Two examples are addressed: pion interactions for anti D{sup 0}D{sup *0} scattering to dynamically generate the X(3872) and dipole interactions for two and three bosons at low energies. For the former, the one-pion exchange and for the latter, the long-range dipole force induce a tensor-like structure of the potential. We apply perturbative as well as non-perturbative methods to determine low-energy observables. The X(3872) is of major interest in modern high-energy physics. Its exotic characteristics require approaches outside the range of the quark model for baryons and mesons. Effective field theories represent such methods and provide access to its peculiar nature. We interpret the X(3872) as a hadronic molecule consisting of neutral D and D{sup *} mesons. It is possible to apply an effective field theory with perturbative pions. Within this framework, we address chiral as well as finite volume extrapolations for low-energy observables, such as the binding energy and the scattering length. We show that the two-point correlation function for the D{sup *0} meson has to be resummed to cure infrared divergences. Moreover, next-to-leading order coupling constants, which were introduced by power counting arguments, appear to be essential to renormalize the scattering amplitude. The binding energy as well as the scattering length display a moderate dependence on the light quark masses. The X(3872) is most likely deeper bound for large light quark masses. In a finite volume on the other hand, the binding energy significantly increases. The dependence on the light quark masses and the volume size can be simultaneously obtained. For bosonic dipoles we apply a non-perturbative, numerical approach. We solve the Lippmann-Schwinger equation for the two-dipole system and the Faddeev
Hoefnagels, Friso W A; de Witt Hamer, Philip C; Pouwels, Petra J W; Barkhof, Frederik; Vandertop, W Peter
2017-09-01
To explore quantitatively and qualitatively how the number of gradient directions (NGD) and spatial resolution (SR) affect diffusion tensor imaging (DTI) tractography in patients planned for brain tumor surgery, using routine clinical magnetic resonance imaging protocols. Of 67 patients with intracerebral lesions who had 2 different DTI scans, 3 DTI series were reconstructed to compare the effects of NGD and SR. Tractographies for 4 clinically relevant tracts (corticospinal tract, superior longitudinal fasciculus, optic radiation, and inferior fronto-occipital fasciculus) were constructed with a probabilistic tracking algorithm and automated region of interest placement and compared for 3 quantitative measurements: tract volume, median fiber density, and mean fractional anisotropy, using linear mixed-effects models. The mean tractography volume and intersubject reliability were visually compared across scanning protocols, to assess the clinical relevance of the quantitative differences. Both NGD and SR significantly influenced tract volume, median fiber density, and mean fractional anisotropy, but not to the same extent. In particular, higher NGD increased tract volume and median fiber density. More importantly, these effects further increased when tracts were affected by disease. The effects were tract specific, but not dependent on threshold. The superior longitudinal fasciculus and inferior fronto-occipital fasciculus showed the most significant differences. Qualitative assessment showed larger tract volumes given a fixed confidence level, and better intersubject reliability for the higher NGD protocol. SR in the range we considered seemed less relevant than NGD. This study indicates that, under time constraints of clinical imaging, a higher number of diffusion gradients is more important than spatial resolution for superior DTI probabilistic tractography in patients undergoing brain tumor surgery. Copyright © 2017 Elsevier Inc. All rights reserved.
Tensor network method for reversible classical computation
Yang, Zhi-Cheng; Kourtis, Stefanos; Chamon, Claudio; Mucciolo, Eduardo R.; Ruckenstein, Andrei E.
2018-03-01
We develop a tensor network technique that can solve universal reversible classical computational problems, formulated as vertex models on a square lattice [Nat. Commun. 8, 15303 (2017), 10.1038/ncomms15303]. By encoding the truth table of each vertex constraint in a tensor, the total number of solutions compatible with partial inputs and outputs at the boundary can be represented as the full contraction of a tensor network. We introduce an iterative compression-decimation (ICD) scheme that performs this contraction efficiently. The ICD algorithm first propagates local constraints to longer ranges via repeated contraction-decomposition sweeps over all lattice bonds, thus achieving compression on a given length scale. It then decimates the lattice via coarse-graining tensor contractions. Repeated iterations of these two steps gradually collapse the tensor network and ultimately yield the exact tensor trace for large systems, without the need for manual control of tensor dimensions. Our protocol allows us to obtain the exact number of solutions for computations where a naive enumeration would take astronomically long times.
On improving the efficiency of tensor voting.
Moreno, Rodrigo; Garcia, Miguel Angel; Puig, Domenec; Pizarro, Luis; Burgeth, Bernhard; Weickert, Joachim
2011-11-01
This paper proposes two alternative formulations to reduce the high computational complexity of tensor voting, a robust perceptual grouping technique used to extract salient information from noisy data. The first scheme consists of numerical approximations of the votes, which have been derived from an in-depth analysis of the plate and ball voting processes. The second scheme simplifies the formulation while keeping the same perceptual meaning of the original tensor voting: The stick tensor voting and the stick component of the plate tensor voting must reinforce surfaceness, the plate components of both the plate and ball tensor voting must boost curveness, whereas junctionness must be strengthened by the ball component of the ball tensor voting. Two new parameters have been proposed for the second formulation in order to control the potentially conflictive influence of the stick component of the plate vote and the ball component of the ball vote. Results show that the proposed formulations can be used in applications where efficiency is an issue since they have a complexity of order O(1). Moreover, the second proposed formulation has been shown to be more appropriate than the original tensor voting for estimating saliencies by appropriately setting the two new parameters.
Covariant conserved currents for scalar-tensor Horndeski theory
Schmidt, J.; Bičák, J.
2018-04-01
The scalar-tensor theories have become popular recently in particular in connection with attempts to explain present accelerated expansion of the universe, but they have been considered as a natural extension of general relativity long time ago. The Horndeski scalar-tensor theory involving four invariantly defined Lagrangians is a natural choice since it implies field equations involving at most second derivatives. Following the formalisms of defining covariant global quantities and conservation laws for perturbations of spacetimes in standard general relativity, we extend these methods to the general Horndeski theory and find the covariant conserved currents for all four Lagrangians. The current is also constructed in the case of linear perturbations involving both metric and scalar fields. As a specific illustration, we derive a superpotential that leads to the covariantly conserved current in the Branse-Dicke theory.
Tensor harmonic analysis on homogenous space
International Nuclear Information System (INIS)
Wrobel, G.
1997-01-01
The Hilbert space of tensor functions on a homogenous space with the compact stability group is considered. The functions are decomposed onto a sum of tensor plane waves (defined in the text), components of which are transformed by irreducible representations of the appropriate transformation group. The orthogonality relation and the completeness relation for tensor plane waves are found. The decomposition constitutes a unitary transformation, which allows to obtain the Parseval equality. The Fourier components can be calculated by means of the Fourier transformation, the form of which is given explicitly. (author)
Abelian gauge theories with tensor gauge fields
International Nuclear Information System (INIS)
Kapuscik, E.
1984-01-01
Gauge fields of arbitrary tensor type are introduced. In curved space-time the gravitational field serves as a bridge joining different gauge fields. The theory of second order tensor gauge field is developed on the basis of close analogy to Maxwell electrodynamics. The notion of tensor current is introduced and an experimental test of its detection is proposed. The main result consists in a coupled set of field equations representing a generalization of Maxwell theory in which the Einstein equivalence principle is not satisfied. (author)
Local Tensor Radiation Conditions For Elastic Waves
DEFF Research Database (Denmark)
Krenk, S.; Kirkegaard, Poul Henning
2001-01-01
A local boundary condition is formulated, representing radiation of elastic waves from an arbitrary point source. The boundary condition takes the form of a tensor relation between the stress at a point on an arbitrarily oriented section and the velocity and displacement vectors at the point....... The tensor relation generalizes the traditional normal incidence impedance condition by accounting for the angle between wave propagation and the surface normal and by including a generalized stiffness term due to spreading of the waves. The effectiveness of the local tensor radiation condition...
Scalable Tensor Factorizations with Missing Data
DEFF Research Database (Denmark)
Acar, Evrim; Dunlavy, Daniel M.; Kolda, Tamara G.
2010-01-01
of missing data, many important data sets will be discarded or improperly analyzed. Therefore, we need a robust and scalable approach for factorizing multi-way arrays (i.e., tensors) in the presence of missing data. We focus on one of the most well-known tensor factorizations, CANDECOMP/PARAFAC (CP...... is shown to successfully factor tensors with noise and up to 70% missing data. Moreover, our approach is significantly faster than the leading alternative and scales to larger problems. To show the real-world usefulness of CP-WOPT, we illustrate its applicability on a novel EEG (electroencephalogram...
Tensor products of higher almost split sequences
Pasquali, Andrea
2015-01-01
We investigate how the higher almost split sequences over a tensor product of algebras are related to those over each factor. Herschend and Iyama gave a precise criterion for when the tensor product of an $n$-representation finite algebra and an $m$-representation finite algebra is $(n+m)$-representation finite. In this case we give a complete description of the higher almost split sequences over the tensor product by expressing every higher almost split sequence as the mapping cone of a suit...
Scalable tensor factorizations for incomplete data
DEFF Research Database (Denmark)
Acar, Evrim; Dunlavy, Daniel M.; KOlda, Tamara G.
2011-01-01
to factorize data sets with missing values with the goal of capturing the underlying latent structure of the data and possibly reconstructing missing values (i.e., tensor completion). We focus on one of the most well-known tensor factorizations that captures multi-linear structure, CANDECOMP/PARAFAC (CP...... experiments, our algorithm is shown to successfully factorize tensors with noise and up to 99% missing data. A unique aspect of our approach is that it scales to sparse large-scale data, e.g., 1000 × 1000 × 1000 with five million known entries (0.5% dense). We further demonstrate the usefulness of CP...
Relationship between timed 25-foot walk and diffusion tensor imaging in multiple sclerosis.
Klineova, Sylvia; Farber, Rebecca; Saiote, Catarina; Farrell, Colleen; Delman, Bradley N; Tanenbaum, Lawrence N; Friedman, Joshua; Inglese, Matilde; Lublin, Fred D; Krieger, Stephen
2016-01-01
The majority of multiple sclerosis patients experience impaired walking ability, which impacts quality of life. Timed 25-foot walk is commonly used to gauge gait impairment but results can be broadly variable. Objective biological markers that correlate closely with patients' disability are needed. Diffusion tensor imaging, quantifying fiber tract integrity, might provide such information. In this project we analyzed relationships between timed 25-foot walk, conventional and diffusion tensor imaging magnetic resonance imaging markers. A cohort of gait impaired multiple sclerosis patients underwent brain and cervical spinal cord magnetic resonance imaging. Diffusion tensor imaging mean diffusivity and fractional anisotropy were measured on the brain corticospinal tracts and spinal restricted field of vision at C2/3. We analyzed relationships between baseline timed 25-foot walk, conventional and diffusion tensor imaging magnetic resonance imaging markers. Multivariate linear regression analysis showed a statistically significant association between several magnetic resonance imaging and diffusion tensor imaging metrics and timed 25-foot walk: brain mean diffusivity corticospinal tracts (p = 0.004), brain corticospinal tracts axial and radial diffusivity (P = 0.004 and 0.02), grey matter volume (p = 0.05), white matter volume (p = 0.03) and normalized brain volume (P = 0.01). The linear regression model containing mean diffusivity corticospinal tracts and controlled for gait assistance was the best fit model (p = 0.004). Our results suggest an association between diffusion tensor imaging metrics and gait impairment, evidenced by brain mean diffusivity corticospinal tracts and timed 25-foot walk.
Voxel-based clustered imaging by multiparameter diffusion tensor images for glioma grading.
Inano, Rika; Oishi, Naoya; Kunieda, Takeharu; Arakawa, Yoshiki; Yamao, Yukihiro; Shibata, Sumiya; Kikuchi, Takayuki; Fukuyama, Hidenao; Miyamoto, Susumu
2014-01-01
Gliomas are the most common intra-axial primary brain tumour; therefore, predicting glioma grade would influence therapeutic strategies. Although several methods based on single or multiple parameters from diagnostic images exist, a definitive method for pre-operatively determining glioma grade remains unknown. We aimed to develop an unsupervised method using multiple parameters from pre-operative diffusion tensor images for obtaining a clustered image that could enable visual grading of gliomas. Fourteen patients with low-grade gliomas and 19 with high-grade gliomas underwent diffusion tensor imaging and three-dimensional T1-weighted magnetic resonance imaging before tumour resection. Seven features including diffusion-weighted imaging, fractional anisotropy, first eigenvalue, second eigenvalue, third eigenvalue, mean diffusivity and raw T2 signal with no diffusion weighting, were extracted as multiple parameters from diffusion tensor imaging. We developed a two-level clustering approach for a self-organizing map followed by the K-means algorithm to enable unsupervised clustering of a large number of input vectors with the seven features for the whole brain. The vectors were grouped by the self-organizing map as protoclusters, which were classified into the smaller number of clusters by K-means to make a voxel-based diffusion tensor-based clustered image. Furthermore, we also determined if the diffusion tensor-based clustered image was really helpful for predicting pre-operative glioma grade in a supervised manner. The ratio of each class in the diffusion tensor-based clustered images was calculated from the regions of interest manually traced on the diffusion tensor imaging space, and the common logarithmic ratio scales were calculated. We then applied support vector machine as a classifier for distinguishing between low- and high-grade gliomas. Consequently, the sensitivity, specificity, accuracy and area under the curve of receiver operating characteristic
1974-01-01
All general purpose equipment items contained in the final carry-on laboratory (COL) design concepts are described in terms of specific requirements identified for COL use, hardware status, and technical parameters such as weight, volume, power, range, and precision. Estimated costs for each item are given, along with projected development times.
International Nuclear Information System (INIS)
Franconi, Antoine; Joo', Julien; Zibo, Idde
1981-01-01
This volume contains the detailed study of mineral substances industrially exploited to date : uranium, coal, non metallic building materials and public activities, and non conventionally exploited substances, that are : tin, columbite-tantalite, tungsten, gold, phosphates and evaporates [fr
General projective relativity and the vector-tensor gravitational field
International Nuclear Information System (INIS)
Arcidiacono, G.
1986-01-01
In the general projective relativity, the induced 4-dimensional metric is symmetric in three cases, and we obtain the vector-tensor, the scalar-tensor, and the scalar-vector-tensor theories of gravitation. In this work we examine the vector-tensor theory, similar to the Veblen's theory, but with a different physical interpretation
Tucker tensor analysis of Matern functions in spatial statistics
Litvinenko, Alexander
2018-04-20
Low-rank Tucker tensor methods in spatial statistics 1. Motivation: improve statistical models 2. Motivation: disadvantages of matrices 3. Tools: Tucker tensor format 4. Tensor approximation of Matern covariance function via FFT 5. Typical statistical operations in Tucker tensor format 6. Numerical experiments
TensorFlow Agents: Efficient Batched Reinforcement Learning in TensorFlow
Hafner, Danijar; Davidson, James; Vanhoucke, Vincent
2017-01-01
We introduce TensorFlow Agents, an efficient infrastructure paradigm for building parallel reinforcement learning algorithms in TensorFlow. We simulate multiple environments in parallel, and group them to perform the neural network computation on a batch rather than individual observations. This allows the TensorFlow execution engine to parallelize computation, without the need for manual synchronization. Environments are stepped in separate Python processes to progress them in parallel witho...
Reconstruction of convex bodies from surface tensors
DEFF Research Database (Denmark)
Kousholt, Astrid; Kiderlen, Markus
. The output of the reconstruction algorithm is a polytope P, where the surface tensors of P and K are identical up to rank s. We establish a stability result based on a generalization of Wirtinger’s inequality that shows that for large s, two convex bodies are close in shape when they have identical surface...... that are translates of each other. An algorithm for reconstructing an unknown convex body in R 2 from its surface tensors up to a certain rank is presented. Using the reconstruction algorithm, the shape of an unknown convex body can be approximated when only a finite number s of surface tensors are available...... tensors up to rank s. This is used to establish consistency of the developed reconstruction algorithm....
Energy-momentum tensor in scalar QED
International Nuclear Information System (INIS)
Joglekar, S.D.; Misra, A.
1988-01-01
We consider the renormalization of the energy-momentum tensor in scalar quantum electrodynamics. We show the need for adding an improvement term to the conventional energy-momentum tensor. We consider two possible forms for the improvement term: (i) one in which the improvement coefficient is a finite function of bare parameters of the theory (so that the energy-momentum tensor can be obtained from an action that is a finite function of bare quantities); (ii) one in which the improvement coefficient is a finite quantity, i.e., a finite function of renormalized parameters. We establish a negative result; viz., neither form leads to a finite energy-momentum tensor to O(e 2 λ/sup n/). .AE
Unsupervised Tensor Mining for Big Data Practitioners.
Papalexakis, Evangelos E; Faloutsos, Christos
2016-09-01
Multiaspect data are ubiquitous in modern Big Data applications. For instance, different aspects of a social network are the different types of communication between people, the time stamp of each interaction, and the location associated to each individual. How can we jointly model all those aspects and leverage the additional information that they introduce to our analysis? Tensors, which are multidimensional extensions of matrices, are a principled and mathematically sound way of modeling such multiaspect data. In this article, our goal is to popularize tensors and tensor decompositions to Big Data practitioners by demonstrating their effectiveness, outlining challenges that pertain to their application in Big Data scenarios, and presenting our recent work that tackles those challenges. We view this work as a step toward a fully automated, unsupervised tensor mining tool that can be easily and broadly adopted by practitioners in academia and industry.
Calculus of tensors and differential forms
Sinha, Rajnikant
2014-01-01
Calculus of tensors and differential forms is an introductory-level textbook. Through this book, students will familiarize themselves with tools they need in order to use for further study on general relativity and research, such as affine tensors, tensor calculus on manifolds, relative tensors, Lie derivatives, wedge products, differential forms, and Stokes' theorem. The treatment is concrete and in detail, so that abstract concepts do not deter even physics and engineering students. This self contained book requires undergraduate-level calculus of several variables and linear algebra as prerequisite. Fubini's theorem in real analysis, to be used in Stokes' theorem, has been proved earlier than Stokes' theorem so that students don't have to search elsewhere.
Potentials for transverse trace-free tensors
International Nuclear Information System (INIS)
Conboye, Rory; Murchadha, Niall Ó
2014-01-01
In constructing and understanding initial conditions in the 3 + 1 formalism for numerical relativity, the transverse and trace-free (TT) part of the extrinsic curvature plays a key role. We know that TT tensors possess two degrees of freedom per space point. However, finding an expression for a TT tensor depending on only two scalar functions is a non-trivial task. Assuming either axial or translational symmetry, expressions depending on two scalar potentials alone are derived here for all TT tensors in flat 3-space. In a more general spatial slice, only one of these potentials is found, the same potential given in (Baker and Puzio 1999 Phys. Rev. D 59 044030) and (Dain 2001 Phys. Rev. D 64 124002), with the remaining equations reduced to a partial differential equation, depending on boundary conditions for a solution. As an exercise, we also derive the potentials which give the Bowen-York curvature tensor in flat space. (paper)
Correlators in tensor models from character calculus
Directory of Open Access Journals (Sweden)
A. Mironov
2017-11-01
Full Text Available We explain how the calculations of [20], which provided the first evidence for non-trivial structures of Gaussian correlators in tensor models, are efficiently performed with the help of the (Hurwitz character calculus. This emphasizes a close similarity between technical methods in matrix and tensor models and supports a hope to understand the emerging structures in very similar terms. We claim that the 2m-fold Gaussian correlators of rank r tensors are given by r-linear combinations of dimensions with the Young diagrams of size m. The coefficients are made from the characters of the symmetric group Sm and their exact form depends on the choice of the correlator and on the symmetries of the model. As the simplest application of this new knowledge, we provide simple expressions for correlators in the Aristotelian tensor model as tri-linear combinations of dimensions.
Loop optimization for tensor network renormalization
Yang, Shuo; Gu, Zheng-Cheng; Wen, Xiao-Gang
We introduce a tensor renormalization group scheme for coarse-graining a two-dimensional tensor network, which can be successfully applied to both classical and quantum systems on and off criticality. The key idea of our scheme is to deform a 2D tensor network into small loops and then optimize tensors on each loop. In this way we remove short-range entanglement at each iteration step, and significantly improve the accuracy and stability of the renormalization flow. We demonstrate our algorithm in the classical Ising model and a frustrated 2D quantum model. NSF Grant No. DMR-1005541 and NSFC 11274192, BMO Financial Group, John Templeton Foundation, Government of Canada through Industry Canada, Province of Ontario through the Ministry of Economic Development & Innovation.
An introduction to linear algebra and tensors
Akivis, M A; Silverman, Richard A
1978-01-01
Eminently readable, completely elementary treatment begins with linear spaces and ends with analytic geometry, covering multilinear forms, tensors, linear transformation, and more. 250 problems, most with hints and answers. 1972 edition.
Algebraic classification of the conformal tensor
International Nuclear Information System (INIS)
Ares de Parga, Gonzalo; Chavoya, O.; Lopez B, J.L.; Ovando Z, Gerardo
1989-01-01
Starting from the Petrov matrix method, we deduce a new algorithm (adaptable to computers), within the Newman-Penrose formalism, to obtain the algebraic type of the Weyl tensor in general relativity. (author)
Effects of tensor forces in nuclei
International Nuclear Information System (INIS)
Tanihata, Isao
2013-01-01
Recent studies of nuclei far from the stability line have revealed drastic changes in nuclear orbitals and reported the appearance of new magic numbers and the disappearance of magic numbers observed at the stability line. One of the important reasons for such changes is considered to be because of the effect of tensor forces on nuclear structure. Although the role of tensor forces in binding very light nuclei such as deuterons and 4 He has been known, direct experimental evidence for the effect on nuclear structure is scarce. In this paper, I review known effects of tensor forces in nuclei and then discuss the recently raised question of s–p wave mixing in a halo nucleus of 11 Li. Following these reviews, the development of a new experiment to see the high-momentum components due to the tensor forces is discussed and some of the new data are presented. (paper)
The energy–momentum tensor(s in classical gauge theories
Directory of Open Access Journals (Sweden)
Daniel N. Blaschke
2016-11-01
Full Text Available We give an introduction to, and review of, the energy–momentum tensors in classical gauge field theories in Minkowski space, and to some extent also in curved space–time. For the canonical energy–momentum tensor of non-Abelian gauge fields and of matter fields coupled to such fields, we present a new and simple improvement procedure based on gauge invariance for constructing a gauge invariant, symmetric energy–momentum tensor. The relationship with the Einstein–Hilbert tensor following from the coupling to a gravitational field is also discussed.
Hayakawa, Yayoi K; Sasaki, Hiroki; Takao, Hidemasa; Mori, Harushi; Hayashi, Naoto; Kunimatsu, Akira; Aoki, Shigeki; Ohtomo, Kuni
2013-01-25
Brain structural changes accompany major depressive disorder, but whether subclinical depression is accompanied by similar changes in brain volume and white matter integrity is unknown. By using voxel-based morphometry (VBM) of the gray matter and tract-specific analysis based on diffusion tensor imaging (DTI) of the white matter, we explored the extent to which abnormalities could be identified in specific brain structures of healthy adults with subclinical depression. The subjects were 21 community-dwelling adults with subclinical depression, as measured by their Center for Epidemiologic Studies Depression Scale (CES-D) scores. They were not demented and had no neurological or psychiatric history. We collected brain magnetic resonance images of the patients and of 21 matched control subjects, and we used VBM to analyze the differences in regional gray matter volume between the two groups. Moreover, we examined the white matter integrity by using tract-specific analysis based on the gray matter volume changes revealed by VBM. VBM revealed that the volumes of both anterior cingulate gyri and the right rectal gyrus were smaller in subclinically depressed women than in control women. Calculation of DTI measures in the anterior cingulum bundle revealed a positive correlation between CES-D scale score and radial diffusivity in the right anterior cingulum in subclinically depressed women. The small sample size limits the stability of the reported findings. Gray matter volume reduction and white matter integrity change in specific frontal brain regions may be associated with depressive symptoms in women, even at a subclinical level. Copyright © 2012 Elsevier B.V. All rights reserved.
Geometric decomposition of the conformation tensor in viscoelastic turbulence
Hameduddin, Ismail; Meneveau, Charles; Zaki, Tamer A.; Gayme, Dennice F.
2018-05-01
This work introduces a mathematical approach to analysing the polymer dynamics in turbulent viscoelastic flows that uses a new geometric decomposition of the conformation tensor, along with associated scalar measures of the polymer fluctuations. The approach circumvents an inherent difficulty in traditional Reynolds decompositions of the conformation tensor: the fluctuating tensor fields are not positive-definite and so do not retain the physical meaning of the tensor. The geometric decomposition of the conformation tensor yields both mean and fluctuating tensor fields that are positive-definite. The fluctuating tensor in the present decomposition has a clear physical interpretation as a polymer deformation relative to the mean configuration. Scalar measures of this fluctuating conformation tensor are developed based on the non-Euclidean geometry of the set of positive-definite tensors. Drag-reduced viscoelastic turbulent channel flow is then used an example case study. The conformation tensor field, obtained using direct numerical simulations, is analysed using the proposed framework.
Estimation of Uncertainties of Full Moment Tensors
2017-10-06
For our moment tensor inversions, we use the ‘cut-and-paste’ ( CAP ) code of Zhu and Helmberger (1996) and Zhu and Ben-Zion (2013), with some...modifications. For the misfit function we use an L1 norm Silwal and Tape (2016), and we incorporate the number of misfitting polarities into the waveform... norm of the eigenvalue triple provides the magnitude of the moment tensor, leaving two free parameters to define the source type. In the same year
Superconformal tensor calculus in five dimensions
International Nuclear Information System (INIS)
Fujita, Tomoyuki; Ohashi, Keisuke
2001-01-01
We present a full superconformal tensor calculus in five spacetime dimensions in which the Weyl multiplet has 32 Bose plus 32 Fermi degrees of freedom. It is derived using dimensional reduction from the 6D superconformal tensor calculus. We present two types of 32+32 Weyl multiplets, a vector multiplet, linear multiplet, hypermultiplet and nonlinear multiplet. Their superconformal transformation laws and the embedding and invariant action formulas are given. (author)
Goldsborough, Peter
2016-01-01
Deep learning is a branch of artificial intelligence employing deep neural network architectures that has significantly advanced the state-of-the-art in computer vision, speech recognition, natural language processing and other domains. In November 2015, Google released $\\textit{TensorFlow}$, an open source deep learning software library for defining, training and deploying machine learning models. In this paper, we review TensorFlow and put it in context of modern deep learning concepts and ...
Geometrical foundations of tensor calculus and relativity
Schuller , Frédéric; Lorent , Vincent
2006-01-01
Manifolds, particularly space curves: basic notions 1 The first groundform, the covariant metric tensor 11 The second groundform, Meusnier's theorem 19 Transformation groups in the plane 28 Co- and contravariant components for a special affine transformation in the plane 29 Surface vectors 32 Elements of tensor calculus 36 Generalization of the first groundform to the space 46 The covariant (absolute) derivation 57 Examples from elasticity theory 61 Geodesic lines 63 Main curvatur...
Measuring Nematic Susceptibilities from the Elastoresistivity Tensor
Hristov, A. T.; Shapiro, M. C.; Hlobil, Patrick; Maharaj, Akash; Chu, Jiun-Haw; Fisher, Ian
The elastoresistivity tensor mijkl relates changes in resistivity to the strain on a material. As a fourth-rank tensor, it contains considerably more information about the material than the simpler (second-rank) resistivity tensor; in particular, certain elastoresistivity coefficients can be related to thermodynamic susceptibilities and serve as a direct probe of symmetry breaking at a phase transition. The aim of this talk is twofold. First, we enumerate how symmetry both constrains the structure of the elastoresistivity tensor into an easy-to-understand form and connects tensor elements to thermodynamic susceptibilities. In the process, we generalize previous studies of elastoresistivity to include the effects of magnetic field. Second, we describe an approach to measuring quantities in the elastoresistivity tensor with a novel transverse measurement, which is immune to relative strain offsets. These techniques are then applied to BaFe2As2 in a proof of principle measurement. This work is supported by the Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under Contract DE-AC02-76SF00515.
Zaitchik, Deborah; Solomon, Gregg E. A.
2009-01-01
Two studies investigated whether patients with Alzheimer’s disease (AD) suffer high-level and category-specific impairment in the conceptual domain of living things. In Study 1, AD patients and healthy young and healthy elderly controls took part in three tasks: the Conservation of Species, Volume, and Belief. All 3 tasks required tracking an object’s identity in the face of irrelevant but salient transformations. Healthy young and elderly controls performed at or near ceiling on all tasks. AD patients were at or near ceiling on the Volume and Belief tasks, but only about half succeeded on the Species task. Study 2 demonstrated that the results were not due to simple task demands. AD patients’ failure to conserve species indicates that they are impaired in their theoretical understanding of living things, and their success on the Volume and Belief tasks suggests that the impairment is domain-specific. Two hypotheses are put forward to explain the phenomenon: the first, a category-specific account, holds that the intuitive theory of biology undergoes pervasive degradation; the second, a hybrid domain-general/domain-specific account, holds that impairment to domain-general processes such as executive function interacts with core cognition, the primitive elements that are the foundation of domain-specific knowledge. PMID:20043252
International Nuclear Information System (INIS)
Knapp, F.R. Jr.; Beets, A.L.; Mirzadeh, S.; Guhlke, S.; Univ. of Bonn
1998-03-01
In this paper the authors describe the first application of a simple and inexpensive post elution tandem cation-anion exchange column system which is based on generator elution with salts of weak acids such as ammonium acetate instead of saline solution to provide very high specific volume solutions of technetium-99m and rhenium-188 from clinical scale molybdenum-99/technetium-99m generator prepared from low specific activity (n,y) molybdenum-99, and tungsten-188/rhenium-188 generators, respectively. Initial passage of the bolus through a strong cation exchange cartridge converts the ammonium acetate to acetic acid which is essentially not ionized at the acidic pH, allowing specific subsequent amine type (QMA SepPak trademark) anion exchange cartridge column trapping of the microscopic levels of the pertechnetate or perrhenate. Subsequent elution of the anion cartridge with a small volume ( 500 mCi/mL) from the alumina-based tungsten-188/rhenium-188 generator
Ramskov, Daniel; Rasmussen, Sten; Sørensen, Henrik; Parner, Erik Thorlund; Lind, Martin; Nielsen, Rasmus
2018-06-12
Study Design Randomized clinical trial, etiology. Background Training intensity and volume have been proposed to be associated with specific running-related injuries. If such an association exists, secondary preventive measures could be initiated by clinicians based on symptoms of a specific injury diagnosis. Objectives To test the following hypotheses: (i) A running schedule focusing on intensity will increase the risk of sustaining Achilles tendinopathy, gastrocnemius injuries and plantar fasciitis compared with hypothesized volume-related injuries. (ii) A running schedule focusing on running volume will increase the risk of sustaining patellofemoral pain syndrome, iliotibial band syndrome and patellar tendinopathy compared with hypothesized intensity-related injuries. Methods Healthy recreational runners were included in a 24-week follow-up, divided into 8-week preconditioning and 16-week specific focus-training. Participants were randomized to one of two running schedules: Schedule Intensity(Sch-I) or Schedule Volume(Sch-V). Sch-I progressed the amount of high intensity running (≥88% VO2max) each week. Sch-V progressed total weekly running volume. Global positioning system watch or smartphone collected data on running. Running-related injuries were diagnosed based on a clinical examination. Estimates were risk difference (RD) and 95%CI. Results Of 447 runners, a total of 80 sustained an injury (Sch-I n=36; Sch-V n=44). Risk of intensity injuries in Sch-I were: RD 2-weeks =-0.8%[-5.0;3.4]; RD 4-weeks =-0.8%[-6.7;5.1]; RD 8-weeks =-2.0%[-9.2;5.1]; RD 16-weeks =-5.1%[-16.5;6.3]. Risk of volume injuries in Sch-V were: RD 2-weeks =-0.9%[-5.0;3.2]; RD 4-weeks =-2.0%[-7.5;3.5]; RD 8-weeks =-3.2%[-9.1;2.7]; RD 16-weeks =-3.4%[-13.2;6.2]. Conclusion No difference in risk of hypothesized intensity and volume specific running-related injuries exist between running schedules focused on progression in either running intensity or volume. Level of Evidence Etiology, level 1
On the concircular curvature tensor of Riemannian manifolds
International Nuclear Information System (INIS)
Rahman, M.S.; Lal, S.
1990-06-01
Definition of the concircular curvature tensor, Z hijk , along with Z-tensor, Z ij , is given and some properties of Z hijk are described. Tensors identical with Z hijk are shown. A necessary and sufficient condition that a Riemannian V n has zero Z-tensor is found. A number of theorems on concircular symmetric space, concircular recurrent space (Z n -space) and Z n -space with zero Z-tensor are deduced. (author). 6 refs
(Ln-bar, g)-spaces. Special tensor fields
International Nuclear Information System (INIS)
Manoff, S.; Dimitrov, B.
1998-01-01
The Kronecker tensor field, the contraction tensor field, as well as the multi-Kronecker and multi-contraction tensor fields are determined and the action of the covariant differential operator, the Lie differential operator, the curvature operator, and the deviation operator on these tensor fields is established. The commutation relations between the operators Sym and Asym and the covariant and Lie differential operators are considered acting on symmetric and antisymmetric tensor fields over (L n bar, g)-spaces
Bili, Eleni; Bili, Authors Eleni; Dampala, Kaliopi; Iakovou, Ioannis; Tsolakidis, Dimitrios; Giannakou, Anastasia; Tarlatzis, Basil C
2014-08-01
The aim of this study was to determine the performance of prostate specific antigen (PSA) and ultrasound parameters, such as ovarian volume and outline, in the diagnosis of polycystic ovary syndrome (PCOS). This prospective, observational, case-controlled study included 43 women with PCOS, and 40 controls. Between day 3 and 5 of the menstrual cycle, fasting serum samples were collected and transvaginal ultrasound was performed. The diagnostic performance of each parameter [total PSA (tPSA), total-to-free PSA ratio (tPSA:fPSA), ovarian volume, ovarian outline] was estimated by means of receiver operating characteristic (ROC) analysis, along with area under the curve (AUC), threshold, sensitivity, specificity as well as positive (+) and negative (-) likelihood ratios (LRs). Multivariate logistical regression models, using ovarian volume and ovarian outline, were constructed. The tPSA and tPSA:fPSA ratio resulted in AUC of 0.74 and 0.70, respectively, with moderate specificity/sensitivity and insufficient LR+/- values. In the multivariate logistic regression model, the combination of ovarian volume and outline had a sensitivity of 97.7% and a specificity of 97.5% in the diagnosis of PCOS, with +LR and -LR values of 39.1 and 0.02, respectively. In women with PCOS, tPSA and tPSA:fPSA ratio have similar diagnostic performance. The use of a multivariate logistic regression model, incorporating ovarian volume and outline, offers very good diagnostic accuracy in distinguishing women with PCOS patients from controls. Copyright © 2014 Elsevier Ireland Ltd. All rights reserved.
A closed-form solution to tensor voting: theory and applications.
Wu, Tai-Pang; Yeung, Sai-Kit; Jia, Jiaya; Tang, Chi-Keung; Medioni, Gérard
2012-08-01
We prove a closed-form solution to tensor voting (CFTV): Given a point set in any dimensions, our closed-form solution provides an exact, continuous, and efficient algorithm for computing a structure-aware tensor that simultaneously achieves salient structure detection and outlier attenuation. Using CFTV, we prove the convergence of tensor voting on a Markov random field (MRF), thus termed as MRFTV, where the structure-aware tensor at each input site reaches a stationary state upon convergence in structure propagation. We then embed structure-aware tensor into expectation maximization (EM) for optimizing a single linear structure to achieve efficient and robust parameter estimation. Specifically, our EMTV algorithm optimizes both the tensor and fitting parameters and does not require random sampling consensus typically used in existing robust statistical techniques. We performed quantitative evaluation on its accuracy and robustness, showing that EMTV performs better than the original TV and other state-of-the-art techniques in fundamental matrix estimation for multiview stereo matching. The extensions of CFTV and EMTV for extracting multiple and nonlinear structures are underway.
TensorCalculator: exploring the evolution of mechanical stress in the CCMV capsid
Kononova, Olga; Maksudov, Farkhad; Marx, Kenneth A.; Barsegov, Valeri
2018-01-01
A new computational methodology for the accurate numerical calculation of the Cauchy stress tensor, stress invariants, principal stress components, von Mises and Tresca tensors is developed. The methodology is based on the atomic stress approach which permits the calculation of stress tensors, widely used in continuum mechanics modeling of materials properties, using the output from the MD simulations of discrete atomic and C_α -based coarse-grained structural models of biological particles. The methodology mapped into the software package TensorCalculator was successfully applied to the empty cowpea chlorotic mottle virus (CCMV) shell to explore the evolution of mechanical stress in this mechanically-tested specific example of a soft virus capsid. We found an inhomogeneous stress distribution in various portions of the CCMV structure and stress transfer from one portion of the virus structure to another, which also points to the importance of entropic effects, often ignored in finite element analysis and elastic network modeling. We formulate a criterion for elastic deformation using the first principal stress components. Furthermore, we show that von Mises and Tresca stress tensors can be used to predict the onset of a viral capsid’s mechanical failure, which leads to total structural collapse. TensorCalculator can be used to study stress evolution and dynamics of defects in viral capsids and other large-size protein assemblies.
Real-time MR diffusion tensor and Q-ball imaging using Kalman filtering
International Nuclear Information System (INIS)
Poupon, C.; Roche, A.; Dubois, J.; Mangin, J.F.; Poupon, F.
2008-01-01
Diffusion magnetic resonance imaging (dMRI) has become an established research tool for the investigation of tissue structure and orientation. In this paper, we present a method for real-time processing of diffusion tensor and Q-ball imaging. The basic idea is to use Kalman filtering framework to fit either the linear tensor or Q-ball model. Because the Kalman filter is designed to be an incremental algorithm, it naturally enables updating the model estimate after the acquisition of any new diffusion-weighted volume. Processing diffusion models and maps during ongoing scans provides a new useful tool for clinicians, especially when it is not possible to predict how long a subject may remain still in the magnet. First, we introduce the general linear models corresponding to the two diffusion tensor and analytical Q-ball models of interest. Then, we present the Kalman filtering framework and we focus on the optimization of the diffusion orientation sets in order to speed up the convergence of the online processing. Last, we give some results on a healthy volunteer for the online tensor and the Q-ball model, and we make some comparisons with the conventional offline techniques used in the literature. We could achieve full real-time for diffusion tensor imaging and deferred time for Q-ball imaging, using a single workstation. (authors)
A review of anisotropic conductivity models of brain white matter based on diffusion tensor imaging.
Wu, Zhanxiong; Liu, Yang; Hong, Ming; Yu, Xiaohui
2018-06-01
The conductivity of brain tissues is not only essential for electromagnetic source estimation (ESI), but also a key reflector of the brain functional changes. Different from the other brain tissues, the conductivity of whiter matter (WM) is highly anisotropic and a tensor is needed to describe it. The traditional electrical property imaging methods, such as electrical impedance tomography (EIT) and magnetic resonance electrical impedance tomography (MREIT), usually fail to image the anisotropic conductivity tensor of WM with high spatial resolution. The diffusion tensor imaging (DTI) is a newly developed technique that can fulfill this purpose. This paper reviews the existing anisotropic conductivity models of WM based on the DTI and discusses their advantages and disadvantages, as well as identifies opportunities for future research on this subject. It is crucial to obtain the linear conversion coefficient between the eigenvalues of anisotropic conductivity tensor and diffusion tensor, since they share the same eigenvectors. We conclude that the electrochemical model is suitable for ESI analysis because the conversion coefficient can be directly obtained from the concentration of ions in extracellular liquid and that the volume fraction model is appropriate to study the influence of WM structural changes on electrical conductivity. Graphical abstract ᅟ.
Low Multilinear Rank Approximation of Tensors and Application in Missing Traffic Data
Directory of Open Access Journals (Sweden)
Huachun Tan
2014-02-01
Full Text Available The problem of missing data in multiway arrays (i.e., tensors is common in many fields such as bibliographic data analysis, image processing, and computer vision. We consider the problems of approximating a tensor by another tensor with low multilinear rank in the presence of missing data and possibly reconstructing it (i.e., tensor completion. In this paper, we propose a weighted Tucker model which models only the known elements for capturing the latent structure of the data and reconstructing the missing elements. To treat the nonuniqueness of the proposed weighted Tucker model, a novel gradient descent algorithm based on a Grassmann manifold, which is termed Tucker weighted optimization (Tucker-Wopt, is proposed for guaranteeing the global convergence to a local minimum of the problem. Based on extensive experiments, Tucker-Wopt is shown to successfully reconstruct tensors with noise and up to 95% missing data. Furthermore, the experiments on traffic flow volume data demonstrate the usefulness of our algorithm on real-world application.
Marin Quintero, Maider J.
2013-01-01
The structure tensor for vector valued images is most often defined as the average of the scalar structure tensors in each band. The problem with this definition is the assumption that all bands provide the same amount of edge information giving them the same weights. As a result non-edge pixels can be reinforced and edges can be weakened…
Auriat, A M; Borich, M R; Snow, N J; Wadden, K P; Boyd, L A
2015-01-01
Diffusion tensor imaging (DTI)-based tractography has been used to demonstrate functionally relevant differences in white matter pathway status after stroke. However, it is now known that the tensor model is insensitive to the complex fiber architectures found in the vast majority of voxels in the human brain. The inability to resolve intra-voxel fiber orientations may have important implications for the utility of standard DTI-based tract reconstruction methods. Intra-voxel fiber orientations can now be identified using novel, tensor-free approaches. Constrained spherical deconvolution (CSD) is one approach to characterize intra-voxel diffusion behavior. In the current study, we performed DTI- and CSD-based tract reconstruction of the corticospinal tract (CST) and corpus callosum (CC) to test the hypothesis that characterization of complex fiber orientations may improve the robustness of fiber tract reconstruction and increase the sensitivity to identify functionally relevant white matter abnormalities in individuals with chronic stroke. Diffusion weighted magnetic resonance imaging was performed in 27 chronic post-stroke participants and 12 healthy controls. Transcallosal pathways and the CST bilaterally were reconstructed using DTI- and CSD-based tractography. Mean fractional anisotropy (FA), apparent diffusion coefficient (ADC), axial diffusivity (AD), and radial diffusivity (RD) were calculated across the tracts of interest. The total number and volume of reconstructed tracts was also determined. Diffusion measures were compared between groups (Stroke, Control) and methods (CSD, DTI). The relationship between post-stroke motor behavior and diffusion measures was evaluated. Overall, CSD methods identified more tracts than the DTI-based approach for both CC and CST pathways. Mean FA, ADC, and RD differed between DTI and CSD for CC-mediated tracts. In these tracts, we discovered a difference in FA for the CC between stroke and healthy control groups using CSD but
Directory of Open Access Journals (Sweden)
A.M. Auriat
2015-01-01
Full Text Available Diffusion tensor imaging (DTI-based tractography has been used to demonstrate functionally relevant differences in white matter pathway status after stroke. However, it is now known that the tensor model is insensitive to the complex fiber architectures found in the vast majority of voxels in the human brain. The inability to resolve intra-voxel fiber orientations may have important implications for the utility of standard DTI-based tract reconstruction methods. Intra-voxel fiber orientations can now be identified using novel, tensor-free approaches. Constrained spherical deconvolution (CSD is one approach to characterize intra-voxel diffusion behavior. In the current study, we performed DTI- and CSD-based tract reconstruction of the corticospinal tract (CST and corpus callosum (CC to test the hypothesis that characterization of complex fiber orientations may improve the robustness of fiber tract reconstruction and increase the sensitivity to identify functionally relevant white matter abnormalities in individuals with chronic stroke. Diffusion weighted magnetic resonance imaging was performed in 27 chronic post-stroke participants and 12 healthy controls. Transcallosal pathways and the CST bilaterally were reconstructed using DTI- and CSD-based tractography. Mean fractional anisotropy (FA, apparent diffusion coefficient (ADC, axial diffusivity (AD, and radial diffusivity (RD were calculated across the tracts of interest. The total number and volume of reconstructed tracts was also determined. Diffusion measures were compared between groups (Stroke, Control and methods (CSD, DTI. The relationship between post-stroke motor behavior and diffusion measures was evaluated. Overall, CSD methods identified more tracts than the DTI-based approach for both CC and CST pathways. Mean FA, ADC, and RD differed between DTI and CSD for CC-mediated tracts. In these tracts, we discovered a difference in FA for the CC between stroke and healthy control groups
Tensor network state correspondence and holography
Singh, Sukhwinder
2018-01-01
In recent years, tensor network states have emerged as a very useful conceptual and simulation framework to study quantum many-body systems at low energies. In this paper, we describe a particular way in which any given tensor network can be viewed as a representation of two different quantum many-body states. The two quantum many-body states are said to correspond to each other by means of the tensor network. We apply this "tensor network state correspondence"—a correspondence between quantum many-body states mediated by tensor networks as we describe—to the multi-scale entanglement renormalization ansatz (MERA) representation of ground states of one dimensional (1D) quantum many-body systems. Since the MERA is a 2D hyperbolic tensor network (the extra dimension is identified as the length scale of the 1D system), the two quantum many-body states obtained from the MERA, via tensor network state correspondence, are seen to live in the bulk and on the boundary of a discrete hyperbolic geometry. The bulk state so obtained from a MERA exhibits interesting features, some of which caricature known features of the holographic correspondence of String theory. We show how (i) the bulk state admits a description in terms of "holographic screens", (ii) the conformal field theory data associated with a critical ground state can be obtained from the corresponding bulk state, in particular, how pointlike boundary operators are identified with extended bulk operators. (iii) We also present numerical results to illustrate that bulk states, dual to ground states of several critical spin chains, have exponentially decaying correlations, and that the bulk correlation length generally decreases with increase in central charge for these spin chains.
Killing-Yano tensors, rank-2 Killing tensors, and conserved quantities in higher dimensions
Energy Technology Data Exchange (ETDEWEB)
Krtous, Pavel [Institute of Theoretical Physics, Charles University, V Holesovickach 2, Prague (Czech Republic); Kubiznak, David [Institute of Theoretical Physics, Charles University, V Holesovickach 2, Prague (Czech Republic); Page, Don N. [Theoretical Physics Institute, University of Alberta, Edmonton T6G 2G7, Alberta (Canada); Frolov, Valeri P. [Theoretical Physics Institute, University of Alberta, Edmonton T6G 2G7, Alberta (Canada)
2007-02-15
From the metric and one Killing-Yano tensor of rank D-2 in any D-dimensional spacetime with such a principal Killing-Yano tensor, we show how to generate k = [(D+1)/2] Killing-Yano tensors, of rank D-2j for all 0 {<=} j {<=} k-1, and k rank-2 Killing tensors, giving k constants of geodesic motion that are in involution. For the example of the Kerr-NUT-AdS spacetime (hep-th/0604125) with its principal Killing-Yano tensor (gr-qc/0610144), these constants and the constants from the k Killing vectors give D independent constants in involution, making the geodesic motion completely integrable (hep-th/0611083). The constants of motion are also related to the constants recently obtained in the separation of the Hamilton-Jacobi and Klein-Gordon equations (hep-th/0611245)
Killing-Yano tensors, rank-2 Killing tensors, and conserved quantities in higher dimensions
International Nuclear Information System (INIS)
Krtous, Pavel; Kubiznak, David; Page, Don N.; Frolov, Valeri P.
2007-01-01
From the metric and one Killing-Yano tensor of rank D-2 in any D-dimensional spacetime with such a principal Killing-Yano tensor, we show how to generate k = [(D+1)/2] Killing-Yano tensors, of rank D-2j for all 0 ≤ j ≤ k-1, and k rank-2 Killing tensors, giving k constants of geodesic motion that are in involution. For the example of the Kerr-NUT-AdS spacetime (hep-th/0604125) with its principal Killing-Yano tensor (gr-qc/0610144), these constants and the constants from the k Killing vectors give D independent constants in involution, making the geodesic motion completely integrable (hep-th/0611083). The constants of motion are also related to the constants recently obtained in the separation of the Hamilton-Jacobi and Klein-Gordon equations (hep-th/0611245)
International Nuclear Information System (INIS)
Franconi, Antoine; Joo', Julien; Zibo, Idde
1981-01-01
This volume describes Niger Republic mineral substances capable of rising economic interest. After relating minerals occurrence , indices and deposits types, conclusions and recommendations have been made for mineral prospecting. Mineral substances described are : Copper, lead and zinc, molybdena, iron, manganese, titanium, vanadium, nickel and chrome ( cobalt and platinoid ), lithium, lignite, diamond and diverse substances rare earth, beryllium, silver, bismuth arsenic and antimony, barytine, alunite, talc and asbestos ( graphite and diatomite) [fr
Susceptibility tensor imaging (STI) of the brain.
Li, Wei; Liu, Chunlei; Duong, Timothy Q; van Zijl, Peter C M; Li, Xu
2017-04-01
Susceptibility tensor imaging (STI) is a recently developed MRI technique that allows quantitative determination of orientation-independent magnetic susceptibility parameters from the dependence of gradient echo signal phase on the orientation of biological tissues with respect to the main magnetic field. By modeling the magnetic susceptibility of each voxel as a symmetric rank-2 tensor, individual magnetic susceptibility tensor elements as well as the mean magnetic susceptibility and magnetic susceptibility anisotropy can be determined for brain tissues that would still show orientation dependence after conventional scalar-based quantitative susceptibility mapping to remove such dependence. Similar to diffusion tensor imaging, STI allows mapping of brain white matter fiber orientations and reconstruction of 3D white matter pathways using the principal eigenvectors of the susceptibility tensor. In contrast to diffusion anisotropy, the main determinant factor of the susceptibility anisotropy in brain white matter is myelin. Another unique feature of the susceptibility anisotropy of white matter is its sensitivity to gadolinium-based contrast agents. Mechanistically, MRI-observed susceptibility anisotropy is mainly attributed to the highly ordered lipid molecules in the myelin sheath. STI provides a consistent interpretation of the dependence of phase and susceptibility on orientation at multiple scales. This article reviews the key experimental findings and physical theories that led to the development of STI, its practical implementations, and its applications for brain research. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.
Susceptibility Tensor Imaging (STI) of the Brain
Li, Wei; Liu, Chunlei; Duong, Timothy Q.; van Zijl, Peter C.M.; Li, Xu
2016-01-01
Susceptibility tensor imaging (STI) is a recently developed MRI technique that allows quantitative determination of orientation-independent magnetic susceptibility parameters from the dependence of gradient echo signal phase on the orientation of biological tissues with respect to the main magnetic field. By modeling the magnetic susceptibility of each voxel as a symmetric rank-2 tensor, individual magnetic susceptibility tensor elements as well as the mean magnetic susceptibility (MMS) and magnetic susceptibility anisotropy (MSA) can be determined for brain tissues that would still show orientation dependence after conventional scalar-based quantitative susceptibility mapping (QSM) to remove such dependence. Similar to diffusion tensor imaging (DTI), STI allows mapping of brain white matter fiber orientations and reconstruction of 3D white matter pathways using the principal eigenvectors of the susceptibility tensor. In contrast to diffusion anisotropy, the main determinant factor of susceptibility anisotropy in brain white matter is myelin. Another unique feature of susceptibility anisotropy of white matter is its sensitivity to gadolinium-based contrast agents. Mechanistically, MRI-observed susceptibility anisotropy is mainly attributed to the highly ordered lipid molecules in myelin sheath. STI provides a consistent interpretation of the dependence of phase and susceptibility on orientation at multiple scales. This article reviews the key experimental findings and physical theories that led to the development of STI, its practical implementations, and its applications for brain research. PMID:27120169
Off-shell N = 2 tensor supermultiplets
International Nuclear Information System (INIS)
Wit, Bernard de; Saueressig, Frank
2006-01-01
A multiplet calculus is presented for an arbitrary number n of N = 2 tensor supermultiplets. For rigid supersymmetry the known couplings are reproduced. In the superconformal case the target spaces parametrized by the scalar fields are cones over (3n-1)-dimensional spaces encoded in homogeneous SU(2) invariant potentials, subject to certain constraints. The coupling to conformal supergravity enables the derivation of a large class of supergravity Lagrangians with vector and tensor multiplets and hypermultiplets. Dualizing the tensor fields into scalars leads to hypermultiplets with hyperkaehler or quaternion-Kaehler target spaces with at least n abelian isometries. It is demonstrated how to use the calculus for the construction of Lagrangians containing higher-derivative couplings of tensor multiplets. For the application of the c-map between vector and tensor supermultiplets to Lagrangians with higher-order derivatives, an off-shell version of this map is proposed. Various other implications of the results are discussed. As an example an elegant derivation of the classification of 4-dimensional quaternion-Kaehler manifolds with two commuting isometries is given
Watson, Kathleen Bachtel; Dai, Shifan; Paul, Prabasaj; Carlson, Susan A; Carroll, Dianna D; Fulton, Janet
2016-11-01
Previous studies have examined participation in specific leisure-time physical activities (PA) among US adults. The purpose of this study was to identify specific activities that contribute substantially to total volume of leisure-time PA in US adults. Proportion of total volume of leisure-time PA moderate-equivalent minutes attributable to 9 specific types of activities was estimated using self-reported data from 21,685 adult participants (≥ 18 years) in the National Health and Nutrition Examination Survey 1999-2006. Overall, walking (28%), sports (22%), and dancing (9%) contributed most to PA volume. Attributable proportion was higher among men than women for sports (30% vs. 11%) and higher among women than men for walking (36% vs. 23%), dancing (16% vs. 4%), and conditioning exercises (10% vs. 5%). The proportion was lower for walking, but higher for sports, among active adults than those insufficiently active and increased with age for walking. Compared with other racial/ethnic groups, the proportion was lower for sports among non-Hispanic white men and for dancing among non-Hispanic white women. Walking, sports, and dance account for the most activity time among US adults overall, yet some demographic variations exist. Strategies for PA promotion should be tailored to differences across population subgroups.
Reliable Dual Tensor Model Estimation in Single and Crossing Fibers Based on Jeffreys Prior
Yang, Jianfei; Poot, Dirk H. J.; Caan, Matthan W. A.; Su, Tanja; Majoie, Charles B. L. M.; van Vliet, Lucas J.; Vos, Frans M.
2016-01-01
Purpose This paper presents and studies a framework for reliable modeling of diffusion MRI using a data-acquisition adaptive prior. Methods Automated relevance determination estimates the mean of the posterior distribution of a rank-2 dual tensor model exploiting Jeffreys prior (JARD). This data-acquisition prior is based on the Fisher information matrix and enables the assessment whether two tensors are mandatory to describe the data. The method is compared to Maximum Likelihood Estimation (MLE) of the dual tensor model and to FSL’s ball-and-stick approach. Results Monte Carlo experiments demonstrated that JARD’s volume fractions correlated well with the ground truth for single and crossing fiber configurations. In single fiber configurations JARD automatically reduced the volume fraction of one compartment to (almost) zero. The variance in fractional anisotropy (FA) of the main tensor component was thereby reduced compared to MLE. JARD and MLE gave a comparable outcome in data simulating crossing fibers. On brain data, JARD yielded a smaller spread in FA along the corpus callosum compared to MLE. Tract-based spatial statistics demonstrated a higher sensitivity in detecting age-related white matter atrophy using JARD compared to both MLE and the ball-and-stick approach. Conclusions The proposed framework offers accurate and precise estimation of diffusion properties in single and dual fiber regions. PMID:27760166
International Nuclear Information System (INIS)
Huf, P A; Carminati, J
2015-01-01
In this paper we: (1) introduce TensorPack, a software package for the algebraic manipulation of tensors in covariant index format in Maple; (2) briefly demonstrate the use of the package with an orthonormal tensor proof of the shearfree conjecture for dust. TensorPack is based on the Riemann and Canon tensor software packages and uses their functions to express tensors in an indexed covariant format. TensorPack uses a string representation as input and provides functions for output in index form. It extends the functionality to basic algebra of tensors, substitution, covariant differentiation, contraction, raising/lowering indices, symmetry functions and other accessory functions. The output can be merged with text in the Maple environment to create a full working document with embedded dynamic functionality. The package offers potential for manipulation of indexed algebraic tensor expressions in a flexible software environment. (paper)
Energy-momentum tensor in the fermion-pairing model
International Nuclear Information System (INIS)
Kawati, S.; Miyata, H.
1980-01-01
The symmetric energy-momentum tensor for the self-interacting fermion theory (psi-barpsi) 2 is expressed in terms of the collective mode within the Hartree approximation. The divergent part of the energy-momentum tensor for the fermion theory induces an effective energy-momentum tensor for the collective mode, and this effective energy-momentum tensor automatically has the Callan-Coleman-Jackiw improved form. The renormalized energy-momentum tensor is structurally equivalent to the Callan-Coleman-Jackiw improved tensor for the Yukawa theory
(Ln-bar, g)-spaces. Ordinary and tensor differentials
International Nuclear Information System (INIS)
Manoff, S.; Dimitrov, B.
1998-01-01
Different types of differentials as special cases of differential operators acting on tensor fields over (L n bar, g)-spaces are considered. The ordinary differential, the covariant differential as a special case of the covariant differential operator, and the Lie differential as a special case of the Lie differential operator are investigated. The tensor differential and its special types (Covariant tensor differential, and Lie tensor differential) are determined and their properties are discussed. Covariant symmetric and antisymmetric (external) tensor differentials, Lie symmetric, and Lie antisymmetric (external) tensor differentials are determined and considered over (L n bar, g)-spaces
1973-01-01
A specification catalog to define the equipment to be used for conducting life sciences experiments in a space laboratory is presented. The specification sheets list the purpose of the equipment item, and any specific technical requirements which can be identified. The status of similar hardware for ground use is stated with comments regarding modifications required to achieve spaceflight qualified hardware. Pertinent sketches, commercial catalog sheets, or drawings of the applicable equipment are included.
Image processing tensor transform and discrete tomography with Matlab
Grigoryan, Artyom M
2012-01-01
Focusing on mathematical methods in computer tomography, Image Processing: Tensor Transform and Discrete Tomography with MATLAB(R) introduces novel approaches to help in solving the problem of image reconstruction on the Cartesian lattice. Specifically, it discusses methods of image processing along parallel rays to more quickly and accurately reconstruct images from a finite number of projections, thereby avoiding overradiation of the body during a computed tomography (CT) scan. The book presents several new ideas, concepts, and methods, many of which have not been published elsewhere. New co
Federated Tensor Factorization for Computational Phenotyping
Kim, Yejin; Sun, Jimeng; Yu, Hwanjo; Jiang, Xiaoqian
2017-01-01
Tensor factorization models offer an effective approach to convert massive electronic health records into meaningful clinical concepts (phenotypes) for data analysis. These models need a large amount of diverse samples to avoid population bias. An open challenge is how to derive phenotypes jointly across multiple hospitals, in which direct patient-level data sharing is not possible (e.g., due to institutional policies). In this paper, we developed a novel solution to enable federated tensor factorization for computational phenotyping without sharing patient-level data. We developed secure data harmonization and federated computation procedures based on alternating direction method of multipliers (ADMM). Using this method, the multiple hospitals iteratively update tensors and transfer secure summarized information to a central server, and the server aggregates the information to generate phenotypes. We demonstrated with real medical datasets that our method resembles the centralized training model (based on combined datasets) in terms of accuracy and phenotypes discovery while respecting privacy. PMID:29071165
Tensor calculus for engineers and physicists
de Souza Sánchez Filho, Emil
2016-01-01
This textbook provides a rigorous approach to tensor manifolds in several aspects relevant for Engineers and Physicists working in industry or academia. With a thorough, comprehensive, and unified presentation, this book offers insights into several topics of tensor analysis, which covers all aspects of N dimensional spaces. The main purpose of this book is to give a self-contained yet simple, correct and comprehensive mathematical explanation of tensor calculus for undergraduate and graduate students and for professionals. In addition to many worked problems, this book features a selection of examples, solved step by step. Although no emphasis is placed on special and particular problems of Engineering or Physics, the text covers the fundamentals of these fields of science. The book makes a brief introduction into the basic concept of the tensorial formalism so as to allow the reader to make a quick and easy review of the essential topics that enable having the grounds for the subsequent themes, without need...
Exploring extra dimensions through inflationary tensor modes
Im, Sang Hui; Nilles, Hans Peter; Trautner, Andreas
2018-03-01
Predictions of inflationary schemes can be influenced by the presence of extra dimensions. This could be of particular relevance for the spectrum of gravitational waves in models where the extra dimensions provide a brane-world solution to the hierarchy problem. Apart from models of large as well as exponentially warped extra dimensions, we analyze the size of tensor modes in the Linear Dilaton scheme recently revived in the discussion of the "clockwork mechanism". The results are model dependent, significantly enhanced tensor modes on one side and a suppression on the other. In some cases we are led to a scheme of "remote inflation", where the expansion is driven by energies at a hidden brane. In all cases where tensor modes are enhanced, the requirement of perturbativity of gravity leads to a stringent upper limit on the allowed Hubble rate during inflation.
On an uninterpretated tensor in Dirac's theory
International Nuclear Information System (INIS)
Costa de Beauregard, O.
1989-01-01
Franz, in 1935, deduced systematically from the Dirac equation 10 tensorial equations, 5 with a mechanical interpretation, 5 with an electromagnetic interpretation, which are also consequences of Kemmer's formalism for spins 1 and 0; Durand, in 1944, operating similarly with the second order Dirac equation, obtained, 10 equations, 5 of which expressing the divergences of the Gordon type tensors. Of these equations, together with the tensors they imply, some are easily interpreted by reference to the classical theories, some other remain uniterpreted. Recently (1988) we proposed a theory of the coupling between Einstein's gravity field and the 5 Franz mechanical equations, yielding as a bonus the complete interpretation of the 5 Franz mechanical equations. This is an incitation to reexamine the 5 electromagnetic equations. We show here that two of these, together with one of the Durand equations, implying the same tensor, remain uninterpreted. This is proposed as a challenge to the reader's sagacity [fr
The Riemann-Lovelock curvature tensor
International Nuclear Information System (INIS)
Kastor, David
2012-01-01
In order to study the properties of Lovelock gravity theories in low dimensions, we define the kth-order Riemann-Lovelock tensor as a certain quantity having a total 4k-indices, which is kth order in the Riemann curvature tensor and shares its basic algebraic and differential properties. We show that the kth-order Riemann-Lovelock tensor is determined by its traces in dimensions 2k ≤ D < 4k. In D = 2k + 1 this identity implies that all solutions of pure kth-order Lovelock gravity are 'Riemann-Lovelock' flat. It is verified that the static, spherically symmetric solutions of these theories, which are missing solid angle spacetimes, indeed satisfy this flatness property. This generalizes results from Einstein gravity in D = 3, which corresponds to the k = 1 case. We speculate about some possible further consequences of Riemann-Lovelock curvature. (paper)
Diffusion tensor smoothing through weighted Karcher means
Carmichael, Owen; Chen, Jun; Paul, Debashis; Peng, Jie
2014-01-01
Diffusion tensor magnetic resonance imaging (MRI) quantifies the spatial distribution of water Diffusion at each voxel on a regular grid of locations in a biological specimen by Diffusion tensors– 3 × 3 positive definite matrices. Removal of noise from DTI is an important problem due to the high scientific relevance of DTI and relatively low signal to noise ratio it provides. Leading approaches to this problem amount to estimation of weighted Karcher means of Diffusion tensors within spatial neighborhoods, under various metrics imposed on the space of tensors. However, it is unclear how the behavior of these estimators varies with the magnitude of DTI sensor noise (the noise resulting from the thermal e!ects of MRI scanning) as well as the geometric structure of the underlying Diffusion tensor neighborhoods. In this paper, we combine theoretical analysis, empirical analysis of simulated DTI data, and empirical analysis of real DTI scans to compare the noise removal performance of three kernel-based DTI smoothers that are based on Euclidean, log-Euclidean, and affine-invariant metrics. The results suggest, contrary to conventional wisdom, that imposing a simplistic Euclidean metric may in fact provide comparable or superior noise removal, especially in relatively unstructured regions and/or in the presence of moderate to high levels of sensor noise. On the contrary, log-Euclidean and affine-invariant metrics may lead to better noise removal in highly structured anatomical regions, especially when the sensor noise is of low magnitude. These findings emphasize the importance of considering the interplay of sensor noise magnitude and tensor field geometric structure when assessing Diffusion tensor smoothing options. They also point to the necessity for continued development of smoothing methods that perform well across a large range of scenarios. PMID:25419264
Aspects of the Antisymmetric Tensor Field
Lahiri, Amitabha
1991-02-01
With the possible exception of gravitation, fundamental interactions are generally described by theories of point particles interacting via massless gauge fields. Since the advent of string theories the picture of physical interaction has changed to accommodate one in which extended objects interact with each other. The generalization of the gauge theories to extended objects leads to theories of antisymmetric tensor fields. At scales corresponding to present-day laboratory experiments one expects to see only point particles, their interactions modified by the presence of antisymmetric tensor fields in the theory. Therefore, in order to establish the validity of any theory with antisymmetric tensor fields one needs to look for manifestations of these fields at low energies. The principal problem of gauge theories is the failure to provide a suitable explanation for the generation of masses for the fields in the theory. While there is a known mechanism (spontaneous symmetry breaking) for generating masses for both the matter fields and the gauge fields, the lack of experimental evidence in support of an elementary scalar field suggests that one look for alternative ways of generating masses for the fields. The interaction of gauge fields with an antisymmetric tensor field seems to be an attractive way of doing so, especially since all indications point to the possibility that there will be no remnant degrees of freedom. On the other hand the interaction of such a field with black holes suggest an independent way of verifying the existence of such fields. In this dissertation the origins of the antisymmetric tensor field are discussed in terms of string theory. The interaction of black holes with such a field is discussed next. The last chapter discusses the effects of an antisymmetric tensor field on quantum electrodynamics when the fields are minimally coupled.
Tensor hypercontraction. II. Least-squares renormalization
Parrish, Robert M.; Hohenstein, Edward G.; Martínez, Todd J.; Sherrill, C. David
2012-12-01
The least-squares tensor hypercontraction (LS-THC) representation for the electron repulsion integral (ERI) tensor is presented. Recently, we developed the generic tensor hypercontraction (THC) ansatz, which represents the fourth-order ERI tensor as a product of five second-order tensors [E. G. Hohenstein, R. M. Parrish, and T. J. Martínez, J. Chem. Phys. 137, 044103 (2012)], 10.1063/1.4732310. Our initial algorithm for the generation of the THC factors involved a two-sided invocation of overlap-metric density fitting, followed by a PARAFAC decomposition, and is denoted PARAFAC tensor hypercontraction (PF-THC). LS-THC supersedes PF-THC by producing the THC factors through a least-squares renormalization of a spatial quadrature over the otherwise singular 1/r12 operator. Remarkably, an analytical and simple formula for the LS-THC factors exists. Using this formula, the factors may be generated with O(N^5) effort if exact integrals are decomposed, or O(N^4) effort if the decomposition is applied to density-fitted integrals, using any choice of density fitting metric. The accuracy of LS-THC is explored for a range of systems using both conventional and density-fitted integrals in the context of MP2. The grid fitting error is found to be negligible even for extremely sparse spatial quadrature grids. For the case of density-fitted integrals, the additional error incurred by the grid fitting step is generally markedly smaller than the underlying Coulomb-metric density fitting error. The present results, coupled with our previously published factorizations of MP2 and MP3, provide an efficient, robust O(N^4) approach to both methods. Moreover, LS-THC is generally applicable to many other methods in quantum chemistry.
Diffusion tensor imaging in spinal cord compression
International Nuclear Information System (INIS)
Wang, Wei; Qin, Wen; Hao, Nanxin; Wang, Yibin; Zong, Genlin
2012-01-01
Background Although diffusion tensor imaging has been successfully applied in brain research for decades, several main difficulties have hindered its extended utilization in spinal cord imaging. Purpose To assess the feasibility and clinical value of diffusion tensor imaging and tractography for evaluating chronic spinal cord compression. Material and Methods Single-shot spin-echo echo-planar DT sequences were scanned in 42 spinal cord compression patients and 49 healthy volunteers. The mean values of the apparent diffusion coefficient and fractional anisotropy were measured in region of interest at the cervical and lower thoracic spinal cord. The patients were divided into two groups according to the high signal on T2WI (the SCC-HI group and the SCC-nHI group for with or without high signal). A one-way ANOVA was used. Diffusion tensor tractography was used to visualize the morphological features of normal and impaired white matter. Results There were no statistically significant differences in the apparent diffusion coefficient and fractional anisotropy values between the different spinal cord segments of the normal subjects. All of the patients in the SCC-HI group had increased apparent diffusion coefficient values and decreased fractional anisotropy values at the lesion level compared to the normal controls. However, there were no statistically significant diffusion index differences between the SCC-nHI group and the normal controls. In the diffusion tensor imaging maps, the normal spinal cord sections were depicted as fiber tracts that were color-encoded to a cephalocaudal orientation. The diffusion tensor images were compressed to different degrees in all of the patients. Conclusion Diffusion tensor imaging and tractography are promising methods for visualizing spinal cord tracts and can provide additional information in clinical studies in spinal cord compression
Prediction of myelopathic level in cervical spondylotic myelopathy using diffusion tensor imaging.
Wang, Shu-Qiang; Li, Xiang; Cui, Jiao-Long; Li, Han-Xiong; Luk, Keith D K; Hu, Yong
2015-06-01
To investigate the use of a newly designed machine learning-based classifier in the automatic identification of myelopathic levels in cervical spondylotic myelopathy (CSM). In all, 58 normal volunteers and 16 subjects with CSM were recruited for diffusion tensor imaging (DTI) acquisition. The eigenvalues were extracted as the selected features from DTI images. Three classifiers, naive Bayesian, support vector machine, and support tensor machine, and fractional anisotropy (FA) were employed to identify myelopathic levels. The results were compared with clinical level diagnosis results and accuracy, sensitivity, and specificity were calculated to evaluate the performance of the developed classifiers. The accuracy by support tensor machine was the highest (93.62%) among the three classifiers. The support tensor machine also showed excellent capacity to identify true positives (sensitivity: 84.62%) and true negatives (specificity: 97.06%). The accuracy by FA value was the lowest (76%) in all the methods. The classifiers-based method using eigenvalues had a better performance in identifying the levels of CSM than the diagnosis using FA values. The support tensor machine was the best among three classifiers. © 2014 Wiley Periodicals, Inc.
Bound-Preserving Reconstruction of Tensor Quantities for Remap in ALE Fluid Dynamics
Energy Technology Data Exchange (ETDEWEB)
Klima, Matej [Czech Technical Univ. in Prague, Praha (Czech Republic); Kucharik, MIlan [Czech Technical Univ. in Prague, Praha (Czech Republic); Shashkov, Mikhail Jurievich [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Velechovsky, Jan [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-01-06
We analyze several new and existing approaches for limiting tensor quantities in the context of deviatoric stress remapping in an ALE numerical simulation of elastic flow. Remapping and limiting of the tensor component-by-component is shown to violate radial symmetry of derived variables such as elastic energy or force. Therefore, we have extended the symmetry-preserving Vector Image Polygon algorithm, originally designed for limiting vector variables. This limiter constrains the vector (in our case a vector of independent tensor components) within the convex hull formed by the vectors from surrounding cells – an equivalent of the discrete maximum principle in scalar variables. We compare this method with a limiter designed specifically for deviatoric stress limiting which aims to constrain the J_{2} invariant that is proportional to the specific elastic energy and scale the tensor accordingly. We also propose a method which involves remapping and limiting the J_{2} invariant independently using known scalar techniques. The deviatoric stress tensor is then scaled to match this remapped invariant, which guarantees conservation in terms of elastic energy.
Kronecker-Basis-Representation Based Tensor Sparsity and Its Applications to Tensor Recovery.
Xie, Qi; Zhao, Qian; Meng, Deyu; Xu, Zongben
2017-08-02
It is well known that the sparsity/low-rank of a vector/matrix can be rationally measured by nonzero-entries-number ($l_0$ norm)/nonzero- singular-values-number (rank), respectively. However, data from real applications are often generated by the interaction of multiple factors, which obviously cannot be sufficiently represented by a vector/matrix, while a high order tensor is expected to provide more faithful representation to deliver the intrinsic structure underlying such data ensembles. Unlike the vector/matrix case, constructing a rational high order sparsity measure for tensor is a relatively harder task. To this aim, in this paper we propose a measure for tensor sparsity, called Kronecker-basis-representation based tensor sparsity measure (KBR briefly), which encodes both sparsity insights delivered by Tucker and CANDECOMP/PARAFAC (CP) low-rank decompositions for a general tensor. Then we study the KBR regularization minimization (KBRM) problem, and design an effective ADMM algorithm for solving it, where each involved parameter can be updated with closed-form equations. Such an efficient solver makes it possible to extend KBR to various tasks like tensor completion and tensor robust principal component analysis. A series of experiments, including multispectral image (MSI) denoising, MSI completion and background subtraction, substantiate the superiority of the proposed methods beyond state-of-the-arts.
Chen, Zhenrui; Tie, Yanmei; Olubiyi, Olutayo; Rigolo, Laura; Mehrtash, Alireza; Norton, Isaiah; Pasternak, Ofer; Rathi, Yogesh; Golby, Alexandra J; O'Donnell, Lauren J
2015-01-01
Diffusion imaging tractography is increasingly used to trace critical fiber tracts in brain tumor patients to reduce the risk of post-operative neurological deficit. However, the effects of peritumoral edema pose a challenge to conventional tractography using the standard diffusion tensor model. The aim of this study was to present a novel technique using a two-tensor unscented Kalman filter (UKF) algorithm to track the arcuate fasciculus (AF) in brain tumor patients with peritumoral edema. Ten right-handed patients with left-sided brain tumors in the vicinity of language-related cortex and evidence of significant peritumoral edema were retrospectively selected for the study. All patients underwent 3-Tesla magnetic resonance imaging (MRI) including a diffusion-weighted dataset with 31 directions. Fiber tractography was performed using both single-tensor streamline and two-tensor UKF tractography. A two-regions-of-interest approach was applied to perform the delineation of the AF. Results from the two different tractography algorithms were compared visually and quantitatively. Using single-tensor streamline tractography, the AF appeared disrupted in four patients and contained few fibers in the remaining six patients. Two-tensor UKF tractography delineated an AF that traversed edematous brain areas in all patients. The volume of the AF was significantly larger on two-tensor UKF than on single-tensor streamline tractography (p tensor UKF tractography provides the ability to trace a larger volume AF than single-tensor streamline tractography in the setting of peritumoral edema in brain tumor patients.
Examining the consistency relations describing the three-point functions involving tensors
International Nuclear Information System (INIS)
Sreenath, V.; Sriramkumar, L.
2014-01-01
It is well known that the non-Gaussianity parameter f NL characterizing the scalar bi-spectrum can be expressed in terms of the scalar spectral index in the squeezed limit, a property that is referred to as the consistency relation. In contrast to the scalar bi-spectrum, the three-point cross-correlations involving scalars and tensors and the tensor bi-spectrum have not received adequate attention, which can be largely attributed to the fact that the tensors had remained undetected at the level of the power spectrum until very recently. The detection of the imprints of the primordial tensor perturbations by BICEP2 and its indication of a rather high tensor-to-scalar ratio, if confirmed, can open up a new window for understanding the tensor perturbations, not only at the level of the power spectrum, but also in the realm of non-Gaussianities. In this work, we consider the consistency relations associated with the three-point cross-correlations involving scalars and tensors as well as the tensor bi-spectrum in inflationary models driven by a single, canonical, scalar field. Characterizing the cross-correlations in terms of the dimensionless non-Gaussianity parameters C NL R and C NL γ that we had introduced earlier, we express the consistency relations governing the cross-correlations as relations between these non-Gaussianity parameters and the scalar or tensor spectral indices, in a fashion similar to that of the purely scalar case. We also discuss the corresponding relation for the non-Gaussianity parameter h NL used to describe the tensor bi-spectrum. We analytically establish these consistency relations explicitly in the following two situations: a simple example involving a specific case of power law inflation and a non-trivial scenario in the so-called Starobinsky model that is governed by a linear potential with a sharp change in its slope. We also numerically verify the consistency relations in three types of inflationary models that permit deviations from
Improving Tensor Based Recommenders with Clustering
DEFF Research Database (Denmark)
Leginus, Martin; Dolog, Peter; Zemaitis, Valdas
2012-01-01
Social tagging systems (STS) model three types of entities (i.e. tag-user-item) and relationships between them are encoded into a 3-order tensor. Latent relationships and patterns can be discovered by applying tensor factorization techniques like Higher Order Singular Value Decomposition (HOSVD),...... of the recommendations and execution time are improved and memory requirements are decreased. The clustering is motivated by the fact that many tags in a tag space are semantically similar thus the tags can be grouped. Finally, promising experimental results are presented...
Tensor modes in pure natural inflation
Nomura, Yasunori; Yamazaki, Masahito
2018-05-01
We study tensor modes in pure natural inflation [1], a recently-proposed inflationary model in which an axionic inflaton couples to pure Yang-Mills gauge fields. We find that the tensor-to-scalar ratio r is naturally bounded from below. This bound originates from the finiteness of the number of metastable branches of vacua in pure Yang-Mills theories. Details of the model can be probed by future cosmic microwave background experiments and improved lattice gauge theory calculations of the θ-angle dependence of the vacuum energy.
Jang, Hojin; Plis, Sergey M; Calhoun, Vince D; Lee, Jong-Hwan
2017-01-15
Feedforward deep neural networks (DNNs), artificial neural networks with multiple hidden layers, have recently demonstrated a record-breaking performance in multiple areas of applications in computer vision and speech processing. Following the success, DNNs have been applied to neuroimaging modalities including functional/structural magnetic resonance imaging (MRI) and positron-emission tomography data. However, no study has explicitly applied DNNs to 3D whole-brain fMRI volumes and thereby extracted hidden volumetric representations of fMRI that are discriminative for a task performed as the fMRI volume was acquired. Our study applied fully connected feedforward DNN to fMRI volumes collected in four sensorimotor tasks (i.e., left-hand clenching, right-hand clenching, auditory attention, and visual stimulus) undertaken by 12 healthy participants. Using a leave-one-subject-out cross-validation scheme, a restricted Boltzmann machine-based deep belief network was pretrained and used to initialize weights of the DNN. The pretrained DNN was fine-tuned while systematically controlling weight-sparsity levels across hidden layers. Optimal weight-sparsity levels were determined from a minimum validation error rate of fMRI volume classification. Minimum error rates (mean±standard deviation; %) of 6.9 (±3.8) were obtained from the three-layer DNN with the sparsest condition of weights across the three hidden layers. These error rates were even lower than the error rates from the single-layer network (9.4±4.6) and the two-layer network (7.4±4.1). The estimated DNN weights showed spatial patterns that are remarkably task-specific, particularly in the higher layers. The output values of the third hidden layer represented distinct patterns/codes of the 3D whole-brain fMRI volume and encoded the information of the tasks as evaluated from representational similarity analysis. Our reported findings show the ability of the DNN to classify a single fMRI volume based on the
Diffusion tensor metrics as biomarkers in Alzheimer's disease.
Directory of Open Access Journals (Sweden)
Julio Acosta-Cabronero
Full Text Available Although diffusion tensor imaging has been a major research focus for Alzheimer's disease in recent years, it remains unclear whether it has sufficient stability to have biomarker potential. To date, frequently inconsistent results have been reported, though lack of standardisation in acquisition and analysis make such discrepancies difficult to interpret. There is also, at present, little knowledge of how the biometric properties of diffusion tensor imaging might evolve in the course of Alzheimer's disease.The biomarker question was addressed in this study by adopting a standardised protocol both for the whole brain (tract-based spatial statistics, and for a region of interest: the midline corpus callosum. In order to study the evolution of tensor changes, cross-sectional data from very mild (N = 21 and mild (N = 22 Alzheimer's disease patients were examined as well as a longitudinal cohort (N = 16 that had been rescanned at 12 months.The results revealed that increased axial and mean diffusivity are the first abnormalities to occur and that the first region to develop such significant differences was mesial parietal/splenial white matter; these metrics, however, remained relatively static with advancing disease indicating they are suitable as 'state-specific' markers. In contrast, increased radial diffusivity, and therefore decreased fractional anisotropy-though less detectable early-became increasingly abnormal with disease progression, and, in the splenium of the corpus callosum, correlated significantly with dementia severity; these metrics therefore appear 'stage-specific' and would be ideal for monitoring disease progression. In addition, the cross-sectional and longitudinal analyses showed that the progressive abnormalities in radial diffusivity and fractional anisotropy always occurred in areas that had first shown an increase in axial and mean diffusivity. Given that the former two metrics correlate with dementia severity
Gloger, Oliver; Tönnies, Klaus; Mensel, Birger; Völzke, Henry
2015-11-01
In epidemiological studies as well as in clinical practice the amount of produced medical image data strongly increased in the last decade. In this context organ segmentation in MR volume data gained increasing attention for medical applications. Especially in large-scale population-based studies organ volumetry is highly relevant requiring exact organ segmentation. Since manual segmentation is time-consuming and prone to reader variability, large-scale studies need automatized methods to perform organ segmentation. Fully automatic organ segmentation in native MR image data has proven to be a very challenging task. Imaging artifacts as well as inter- and intrasubject MR-intensity differences complicate the application of supervised learning strategies. Thus, we propose a modularized framework of a two-stepped probabilistic approach that generates subject-specific probability maps for renal parenchyma tissue, which are refined subsequently by using several, extended segmentation strategies. We present a three class-based support vector machine recognition system that incorporates Fourier descriptors as shape features to recognize and segment characteristic parenchyma parts. Probabilistic methods use the segmented characteristic parenchyma parts to generate high quality subject-specific parenchyma probability maps. Several refinement strategies including a final shape-based 3D level set segmentation technique are used in subsequent processing modules to segment renal parenchyma. Furthermore, our framework recognizes and excludes renal cysts from parenchymal volume, which is important to analyze renal functions. Volume errors and Dice coefficients show that our presented framework outperforms existing approaches.
International Nuclear Information System (INIS)
Gloger, Oliver; Völzke, Henry; Tönnies, Klaus; Mensel, Birger
2015-01-01
In epidemiological studies as well as in clinical practice the amount of produced medical image data strongly increased in the last decade. In this context organ segmentation in MR volume data gained increasing attention for medical applications. Especially in large-scale population-based studies organ volumetry is highly relevant requiring exact organ segmentation. Since manual segmentation is time-consuming and prone to reader variability, large-scale studies need automatized methods to perform organ segmentation. Fully automatic organ segmentation in native MR image data has proven to be a very challenging task. Imaging artifacts as well as inter- and intrasubject MR-intensity differences complicate the application of supervised learning strategies. Thus, we propose a modularized framework of a two-stepped probabilistic approach that generates subject-specific probability maps for renal parenchyma tissue, which are refined subsequently by using several, extended segmentation strategies. We present a three class-based support vector machine recognition system that incorporates Fourier descriptors as shape features to recognize and segment characteristic parenchyma parts. Probabilistic methods use the segmented characteristic parenchyma parts to generate high quality subject-specific parenchyma probability maps. Several refinement strategies including a final shape-based 3D level set segmentation technique are used in subsequent processing modules to segment renal parenchyma. Furthermore, our framework recognizes and excludes renal cysts from parenchymal volume, which is important to analyze renal functions. Volume errors and Dice coefficients show that our presented framework outperforms existing approaches. (paper)
International Nuclear Information System (INIS)
1995-04-01
This NUREG contains the improved Standard Technical Specifications (STS) for Babcock and Wilcox (B ampersand W) plants. Revision 1 incorporates the cumulative changes to Revision 0, which was published in September 1992. The changes reflected in Revision 1 resulted from the experience gained from license amendment applications to convert to these improved STS or to adopt partial improvements to existing technical specifications. This NUREG is the result of extensive public technical meetings and discussions between the Nuclear Regulatory Commission (NRC) staff and various nuclear power plant licensees, Nuclear Steam Supply System (NSSS) Owners Groups, specifically the B ampersand W Owners Group (BWOG), NSSS vendors, and the Nuclear Energy Institute (NEI). The improved STS were developed based on the criteria in the Final Commission Policy Statement on Technical Specifications Improvements for Nuclear Power Reactors, dated July 22, 1993 (58 FR 39132). Licensees are encouraged to upgrade their technical specifications consistent with those criteria and conforming, to the extent practical and consistent with the licensing basis for the facility, to Revision 1 to the improved STS. The Commission continues to place the highest priority on requests for complete conversions to the improved STS. Licensees adopting portions of the improved STS to existing technical specifications should adopt all related requirements, as applicable, to achieve a high degree of standardization and consistency
Poya, Roman; Gil, Antonio J.; Ortigosa, Rogelio
2017-07-01
The paper presents aspects of implementation of a new high performance tensor contraction framework for the numerical analysis of coupled and multi-physics problems on streaming architectures. In addition to explicit SIMD instructions and smart expression templates, the framework introduces domain specific constructs for the tensor cross product and its associated algebra recently rediscovered by Bonet et al. (2015, 2016) in the context of solid mechanics. The two key ingredients of the presented expression template engine are as follows. First, the capability to mathematically transform complex chains of operations to simpler equivalent expressions, while potentially avoiding routes with higher levels of computational complexity and, second, to perform a compile time depth-first or breadth-first search to find the optimal contraction indices of a large tensor network in order to minimise the number of floating point operations. For optimisations of tensor contraction such as loop transformation, loop fusion and data locality optimisations, the framework relies heavily on compile time technologies rather than source-to-source translation or JIT techniques. Every aspect of the framework is examined through relevant performance benchmarks, including the impact of data parallelism on the performance of isomorphic and nonisomorphic tensor products, the FLOP and memory I/O optimality in the evaluation of tensor networks, the compilation cost and memory footprint of the framework and the performance of tensor cross product kernels. The framework is then applied to finite element analysis of coupled electro-mechanical problems to assess the speed-ups achieved in kernel-based numerical integration of complex electroelastic energy functionals. In this context, domain-aware expression templates combined with SIMD instructions are shown to provide a significant speed-up over the classical low-level style programming techniques.
Tucker Tensor analysis of Matern functions in spatial statistics
Litvinenko, Alexander; Keyes, David E.; Khoromskaia, Venera; Khoromskij, Boris N.; Matthies, Hermann G.
2018-01-01
in a low-rank tensor format. We apply the Tucker and canonical tensor decompositions to a family of Matern- and Slater-type functions with varying parameters and demonstrate numerically that their approximations exhibit exponentially fast convergence
Directory of Open Access Journals (Sweden)
Fábio Pascotto de Oliveira
2011-06-01
Full Text Available There are individuals who have a progressive language deficit without presenting cognitive deficits in other areas. One of the diseases related to this presentation is primary progressive aphasia (PPA. OBJECTIVE: Identify by means of diffusion tensor imaging (DTI and measurements of cortical volume, brain areas that lead to dysphasia when presenting signs of impaired connectivity or reduced volume. METHOD: Four patients with PPA were evaluated using DTI, and measurements of cortical volumes in temporal areas. These patients were compared with two normal volunteers. RESULTS: There is a trend to a difference in the number and volume of related fibers between control group and patients with PPA. Comparing cortical volumes in temporal areas between groups yielded a trend to a smaller volume in PPA patients. CONCLUSION: Patients with PPA have a trend to impairment in cortical and subcortical levels regarding relevant areas.
International Nuclear Information System (INIS)
Loft, S.M.; Dale, R.G.
1990-01-01
Anderson (1986) has proposed an analytical method for deriving volume-dose histograms relating to three-dimensional brachytherapy distributions. Because the mathematical transformation allows the otherwise dominant effects of the inverse-square fall-off about individual sources to be effectively suppressed, resulting histograms provide the potential for visually and numerically assessing overall quality of a brachytherapy treatment. In this paper the Anderson equations have been combined with the radial-dose polynomials of Dale, which are applicable to a number of tissue/nuclide combinations, and the predictions of the combined formalism used to further investigate the physical aspects of brachytherapy dosimetry. The problems associated with the dosimetry of low-energy γ-emitters such as 125 I are once again highlighted, as are potential advantages of using a radionuclide with an intermediate γ-ray energy. (author)
Tensor completion for PDEs with uncertain coefficients and Bayesian Update
Litvinenko, Alexander
2017-03-05
In this work, we tried to show connections between Bayesian update and tensor completion techniques. Usually, only a small/sparse vector/tensor of measurements is available. The typical measurement is a function of the solution. The solution of a stochastic PDE is a tensor, the measurement as well. The idea is to use completion techniques to compute all "missing" values of the measurement tensor and only then apply the Bayesian technique.
Tensor completion for PDEs with uncertain coefficients and Bayesian Update
Litvinenko, Alexander
2017-01-01
In this work, we tried to show connections between Bayesian update and tensor completion techniques. Usually, only a small/sparse vector/tensor of measurements is available. The typical measurement is a function of the solution. The solution of a stochastic PDE is a tensor, the measurement as well. The idea is to use completion techniques to compute all "missing" values of the measurement tensor and only then apply the Bayesian technique.
Concatenated image completion via tensor augmentation and completion
Bengua, Johann A.; Tuan, Hoang D.; Phien, Ho N.; Do, Minh N.
2016-01-01
This paper proposes a novel framework called concatenated image completion via tensor augmentation and completion (ICTAC), which recovers missing entries of color images with high accuracy. Typical images are second- or third-order tensors (2D/3D) depending if they are grayscale or color, hence tensor completion algorithms are ideal for their recovery. The proposed framework performs image completion by concatenating copies of a single image that has missing entries into a third-order tensor,...
Rofes, L; Arreola, V; Mukherjee, R; Clavé, P
2014-01-01
Background Oropharyngeal dysphagia (OD) is an underdiagnosed digestive disorder that causes severe nutritional and respiratory complications. Our aim was to determine the accuracy of the Eating Assessment Tool (EAT-10) and the Volume-Viscosity Swallow Test (V-VST) for clinical evaluation of OD. Methods We studied 120 patients with swallowing difficulties and 14 healthy subjects. OD was evaluated by the 10-item screening questionnaire EAT-10 and the bedside method V-VST, videofluoroscopy (VFS) being the reference standard. The V-VST is an effort test that uses boluses of different volumes and viscosities to identify clinical signs of impaired efficacy (impaired labial seal, piecemeal deglutition, and residue) and impaired safety of swallow (cough, voice changes, and oxygen desaturation ≥3%). Discriminating ability was assessed by the AUC of the ROC curve and sensitivity and specificity values. Key Results According to VFS, prevalence of OD was 87%, 75.6% with impaired efficacy and 80.9% with impaired safety of swallow including 17.6% aspirations. The EAT-10 showed a ROC AUC of 0.89 for OD with an optimal cut-off at 2 (0.89 sensitivity and 0.82 specificity). The V-VST showed 0.94 sensitivity and 0.88 specificity for OD, 0.79 sensitivity and 0.75 specificity for impaired efficacy, 0.87 sensitivity and 0.81 specificity for impaired safety, and 0.91 sensitivity and 0.28 specificity for aspirations. Conclusions & Inferences Clinical methods for screening (EAT-10) and assessment (V-VST) of OD offer excellent psychometric proprieties that allow adequate management of OD. Their universal application among at-risk populations will improve the identification of patients with OD at risk for malnutrition and aspiration pneumonia. PMID:24909661
Abelian tensor models on the lattice
Chaudhuri, Soumyadeep; Giraldo-Rivera, Victor I.; Joseph, Anosh; Loganayagam, R.; Yoon, Junggi
2018-04-01
We consider a chain of Abelian Klebanov-Tarnopolsky fermionic tensor models coupled through quartic nearest-neighbor interactions. We characterize the gauge-singlet spectrum for small chains (L =2 ,3 ,4 ,5 ) and observe that the spectral statistics exhibits strong evidence in favor of quasi-many-body localization.
Tensor squeezed limits and the Higuchi bound
Energy Technology Data Exchange (ETDEWEB)
Bordin, Lorenzo [SISSA, via Bonomea 265, 34136, Trieste (Italy); Creminelli, Paolo [Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151, Trieste (Italy); Mirbabayi, Mehrdad [Institute for Advanced Study, Princeton, NJ 08540 (United States); Noreña, Jorge, E-mail: lbordin@sissa.it, E-mail: creminel@ictp.it, E-mail: mehrdadm@ias.edu, E-mail: jorge.norena@pucv.cl [Instituto de Física, Pontificia Universidad Católica de Valparaíso, Avenida Universidad 330, Curauma, Valparaíso (Chile)
2016-09-01
We point out that tensor consistency relations—i.e. the behavior of primordial correlation functions in the limit a tensor mode has a small momentum—are more universal than scalar consistency relations. They hold in the presence of multiple scalar fields and as long as anisotropies are diluted exponentially fast. When de Sitter isometries are approximately respected during inflation this is guaranteed by the Higuchi bound, which forbids the existence of light particles with spin: de Sitter space can support scalar hair but no curly hair. We discuss two indirect ways to look for the violation of tensor consistency relations in observations, as a signature of models in which inflation is not a strong isotropic attractor, such as solid inflation: (a) graviton exchange contribution to the scalar four-point function; (b) quadrupolar anisotropy of the scalar power spectrum due to super-horizon tensor modes. This anisotropy has a well-defined statistics which can be distinguished from cases in which the background has a privileged direction.
Higher-order tensors in diffusion imaging
Schultz, T.; Fuster, A.; Ghosh, A.; Deriche, R.; Florack, L.M.J.; Lim, L.H.; Westin, C.-F.; Vilanova, A.; Burgeth, B.
2014-01-01
Diffusion imaging is a noninvasive tool for probing the microstructure of fibrous nerve and muscle tissue. Higher-order tensors provide a powerful mathematical language to model and analyze the large and complex data that is generated by its modern variants such as High Angular Resolution Diffusion
Visualization and processing of tensor fields
Weickert, Joachim
2007-01-01
Presents information on the visualization and processing of tensor fields. This book serves as an overview for the inquiring scientist, as a basic foundation for developers and practitioners, and as a textbook for specialized classes and seminars for graduate and doctoral students.
Curvature tensor copies in affine geometry
International Nuclear Information System (INIS)
Srivastava, P.P.
1981-01-01
The sets of space-time and spin-connections which give rise to the same curvature tensor are constructed. The corresponding geometries are compared. Results are illustrated by an explicit calculation and comment on the copies in Einstein-Cartan and Weyl-Cartan geometries. (Author) [pt
Positivity of linear maps under tensor powers
Energy Technology Data Exchange (ETDEWEB)
Müller-Hermes, Alexander, E-mail: muellerh@ma.tum.de; Wolf, Michael M., E-mail: m.wolf@tum.de [Zentrum Mathematik, Technische Universität München, 85748 Garching (Germany); Reeb, David, E-mail: reeb.qit@gmail.com [Zentrum Mathematik, Technische Universität München, 85748 Garching (Germany); Institute for Theoretical Physics, Leibniz Universität Hannover, 30167 Hannover (Germany)
2016-01-15
We investigate linear maps between matrix algebras that remain positive under tensor powers, i.e., under tensoring with n copies of themselves. Completely positive and completely co-positive maps are trivial examples of this kind. We show that for every n ∈ ℕ, there exist non-trivial maps with this property and that for two-dimensional Hilbert spaces there is no non-trivial map for which this holds for all n. For higher dimensions, we reduce the existence question of such non-trivial “tensor-stable positive maps” to a one-parameter family of maps and show that an affirmative answer would imply the existence of non-positive partial transpose bound entanglement. As an application, we show that any tensor-stable positive map that is not completely positive yields an upper bound on the quantum channel capacity, which for the transposition map gives the well-known cb-norm bound. We, furthermore, show that the latter is an upper bound even for the local operations and classical communications-assisted quantum capacity, and that moreover it is a strong converse rate for this task.
An introduction to diffusion tensor image analysis.
O'Donnell, Lauren J; Westin, Carl-Fredrik
2011-04-01
Diffusion tensor magnetic resonance imaging (DTI) is a relatively new technology that is popular for imaging the white matter of the brain. This article provides a basic and broad overview of DTI to enable the reader to develop an intuitive understanding of these types of data, and an awareness of their strengths and weaknesses. Copyright © 2011 Elsevier Inc. All rights reserved.
Primordial tensor modes from quantum corrected inflation
DEFF Research Database (Denmark)
Joergensen, Jakob; Sannino, Francesco; Svendsen, Ole
2014-01-01
. Finally we confront these theories with the Planck and BICEP2 data. We demonstrate that the discovery of primordial tensor modes by BICEP2 require the presence of sizable quantum departures from the $\\phi^4$-Inflaton model for the non-minimally coupled scenario which we parametrize and quantify. We...
From stochastic completion fields to tensor voting
Almsick, van M.A.; Duits, R.; Franken, E.M.; Haar Romenij, ter B.M.; Olsen, O.F.; Florack, L.M.J.; Kuijper, A.
2005-01-01
Several image processing algorithms imitate the lateral interaction of neurons in the visual striate cortex V1 to account for the correlations along contours and lines. Here we focus on two methodologies: tensor voting by Guy and Medioni, and stochastic completion fields by Mumford, Williams and
Positivity of linear maps under tensor powers
International Nuclear Information System (INIS)
Müller-Hermes, Alexander; Wolf, Michael M.; Reeb, David
2016-01-01
We investigate linear maps between matrix algebras that remain positive under tensor powers, i.e., under tensoring with n copies of themselves. Completely positive and completely co-positive maps are trivial examples of this kind. We show that for every n ∈ ℕ, there exist non-trivial maps with this property and that for two-dimensional Hilbert spaces there is no non-trivial map for which this holds for all n. For higher dimensions, we reduce the existence question of such non-trivial “tensor-stable positive maps” to a one-parameter family of maps and show that an affirmative answer would imply the existence of non-positive partial transpose bound entanglement. As an application, we show that any tensor-stable positive map that is not completely positive yields an upper bound on the quantum channel capacity, which for the transposition map gives the well-known cb-norm bound. We, furthermore, show that the latter is an upper bound even for the local operations and classical communications-assisted quantum capacity, and that moreover it is a strong converse rate for this task
Tensors in image processing and computer vision
De Luis García, Rodrigo; Tao, Dacheng; Li, Xuelong
2009-01-01
Tensor signal processing is an emerging field with important applications to computer vision and image processing. This book presents the developments in this branch of signal processing, offering research and discussions by experts in the area. It is suitable for advanced students working in the area of computer vision and image processing.
Tensor B mode and stochastic Faraday mixing
Giovannini, Massimo
2014-01-01
This paper investigates the Faraday effect as a different source of B mode polarization. The E mode polarization is Faraday rotated provided a stochastic large-scale magnetic field is present prior to photon decoupling. In the first part of the paper we discuss the case where the tensor modes of the geometry are absent and we argue that the B mode recently detected by the Bicep2 collaboration cannot be explained by a large-scale magnetic field rotating, through the Faraday effect, the well established E mode polarization. In this case, the observed temperature autocorrelations would be excessively distorted by the magnetic field. In the second part of the paper the formation of Faraday rotation is treated as a stationary, random and Markovian process with the aim of generalizing a set of scaling laws originally derived in the absence of the tensor modes of the geometry. We show that the scalar, vector and tensor modes of the brightness perturbations can all be Faraday rotated even if the vector and tensor par...
Tensor operators in R-matrix approach
International Nuclear Information System (INIS)
Bytsko, A.G.; Rossijskaya Akademiya Nauk, St. Petersburg
1995-12-01
The definitions and some properties (e.g. the Wigner-Eckart theorem, the fusion procedure) of covariant and contravariant q-tensor operators for quasitriangular quantum Lie algebras are formulated in the R-matrix language. The case of U q (sl(n)) (in particular, for n=2) is discussed in more detail. (orig.)
Tensors, differential forms, and variational principles
Lovelock, David
1989-01-01
Incisive, self-contained account of tensor analysis and the calculus of exterior differential forms, interaction between the concept of invariance and the calculus of variations. Emphasis is on analytical techniques, with large number of problems, from routine manipulative exercises to technically difficult assignments.
Tensor algebra and tensor analysis for engineers with applications to continuum mechanics
Itskov, Mikhail
2015-01-01
This is the fourth and revised edition of a well-received book that aims at bridging the gap between the engineering course of tensor algebra on the one side and the mathematical course of classical linear algebra on the other side. In accordance with the contemporary way of scientific publications, a modern absolute tensor notation is preferred throughout. The book provides a comprehensible exposition of the fundamental mathematical concepts of tensor calculus and enriches the presented material with many illustrative examples. In addition, the book also includes advanced chapters dealing with recent developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics. Hence, this monograph addresses graduate students as well as scientists working in this field. In each chapter numerous exercises are included, allowing for self-study and intense practice. Solutions to the exercises are also provided.
Baust, Maximilian; Weinmann, Andreas; Wieczorek, Matthias; Lasser, Tobias; Storath, Martin; Navab, Nassir
2016-08-01
In this paper, we consider combined TV denoising and diffusion tensor fitting in DTI using the affine-invariant Riemannian metric on the space of diffusion tensors. Instead of first fitting the diffusion tensors, and then denoising them, we define a suitable TV type energy functional which incorporates the measured DWIs (using an inverse problem setup) and which measures the nearness of neighboring tensors in the manifold. To approach this functional, we propose generalized forward- backward splitting algorithms which combine an explicit and several implicit steps performed on a decomposition of the functional. We validate the performance of the derived algorithms on synthetic and real DTI data. In particular, we work on real 3D data. To our knowledge, the present paper describes the first approach to TV regularization in a combined manifold and inverse problem setup.
The nonabelian tensor square of a bieberbach group with ...
African Journals Online (AJOL)
The main objective of this paper is to compute the nonabelian tensor square of one Bieberbach group with elementary abelian 2-group point group of dimension three by using the computational method of the nonabelian tensor square for polycyclic groups. The finding of the computation showed that the nonabelian tensor ...
[An Improved Spectral Quaternion Interpolation Method of Diffusion Tensor Imaging].
Xu, Yonghong; Gao, Shangce; Hao, Xiaofei
2016-04-01
Diffusion tensor imaging(DTI)is a rapid development technology in recent years of magnetic resonance imaging.The diffusion tensor interpolation is a very important procedure in DTI image processing.The traditional spectral quaternion interpolation method revises the direction of the interpolation tensor and can preserve tensors anisotropy,but the method does not revise the size of tensors.The present study puts forward an improved spectral quaternion interpolation method on the basis of traditional spectral quaternion interpolation.Firstly,we decomposed diffusion tensors with the direction of tensors being represented by quaternion.Then we revised the size and direction of the tensor respectively according to different situations.Finally,we acquired the tensor of interpolation point by calculating the weighted average.We compared the improved method with the spectral quaternion method and the Log-Euclidean method by the simulation data and the real data.The results showed that the improved method could not only keep the monotonicity of the fractional anisotropy(FA)and the determinant of tensors,but also preserve the tensor anisotropy at the same time.In conclusion,the improved method provides a kind of important interpolation method for diffusion tensor image processing.
Tensor based structure estimation in multi-channel images
DEFF Research Database (Denmark)
Schou, Jesper; Dierking, Wolfgang; Skriver, Henning
2000-01-01
. In the second part tensors are used for representing the structure information. This approach has the advantage, that tensors can be averaged either spatially or by applying several images, and the resulting tensor provides information of the average strength as well as orientation of the structure...
Relativistic particles with spin and antisymmetric tensor fields
International Nuclear Information System (INIS)
Sandoval Junior, L.
1990-09-01
A study is made on antisymmetric tensor fields particularly on second order tensor field as far as his equivalence to other fields and quantization through the path integral are concerned. Also, a particle model is studied which has been recently proposed and reveals to be equivalent to antisymmetric tensor fields of any order. (L.C.J.A.)
Dasenbrock, Hormuzdiyar H; Smith, Seth A; Ozturk, Arzu; Farrell, Sheena K; Calabresi, Peter A; Reich, Daniel S
2011-04-01
Visual disability is common in multiple sclerosis, but its relationship to abnormalities of the optic tracts remains unknown. Because they are only rarely affected by lesions, the optic tracts may represent a good model for assessing the imaging properties of normal-appearing white matter in multiple sclerosis. Whole-brain diffusion tensor imaging was performed on 34 individuals with multiple sclerosis and 26 healthy volunteers. The optic tracts were reconstructed by tractography, and tract-specific diffusion indices were quantified. In the multiple-sclerosis group, peripapillary retinal nerve-fiber-layer thickness and total macular volume were measured by optical coherence tomography, and visual acuity at 100%, 2.5%, and 1.25% contrast was examined. After adjusting for age and sex, optic-tract mean and perpendicular diffusivity were higher (P=.002) in multiple sclerosis. Lower optic-tract fractional anisotropy was correlated with retinal nerve-fiber-layer thinning (r=.51, P=.003) and total-macular-volume reduction (r=.59, P=.002). However, optic-tract diffusion indices were not specifically correlated with visual acuity or with their counterparts in the optic radiation. Optic-tract diffusion abnormalities are associated with retinal damage, suggesting that both may be related to optic-nerve injury, but do not appear to contribute strongly to visual disability in multiple sclerosis. Copyright © 2010 by the American Society of Neuroimaging.
International Nuclear Information System (INIS)
Knapp, F.F. Jr.; Beets, A.L.; Mirzadeh, S.; Guhlke, S.
1998-01-01
In this paper we describe the first application of our simple and inexpensive post-elution tandem cation/anion exchange column system which is based on generator elution with salts of weak acids such as ammonium acetate instead of saline solution to provide very high specific volume solutions of technetium-99m and rhenium-188 from clinical-scale molybdenum-99/technetium-99m generator prepared from low specific activity (n,y) molybdenum-99, and tungsten-188/rhenium-188 generators, respectively. Initial passage of the bolus through a strong cation exchange cartridge converts the ammonium acetate to acetic acid which is essentially not ionized at the acidic pH, allowing specific subsequent amine-type (QMA SepPak TM ) anion exchange cartridge column trapping of the microscopic levels of the pertechnetate or perrhenate. Subsequent elution of the anion cartridge with a small volume ( 500 mCi/mL) from the alumina-based tungsten-188/rhenium-188 generator. (author)
Morphometric study of tensor of vastus intermedius in South Indian population.
Veeramani, Raveendranath; Gnanasekaran, Dhivyalakshmi
2017-03-01
Tensor of vastus intermedius is a newly discovered muscle located between vastus lateralis and vastus intermedius. The purpose of this study was to investigate the detailed morphology of tensor of vastus intermedius, specifically to provide data pertaining to the attachments, innervations, variation in the types and its morphometry in South Indian population. The tensor of vastus intermedius was studied in thirty six cadaveric lower limbs using macrodissection techniques. The origin of the muscle was from upper part of intertrochanteric line and anterior part of greater trochanter of femur inserted to medial aspect of upper border of patella. The muscle was classified into four types based on the origin and also the aponeurosis course with independent type (type 1) being common. The mean and standard deviation of the length of tensor of vastus intermedius and aponeurosis were 145.40±37.55 mm and 193.55±42.32 mm, respectively. The results of the study suggest that tensor of vastus intermedius is variable and the information provided regarding the attachments, types and quantitative data will contribute to the existing knowledge of the muscle.
Correlation functions of the energy-momentum tensor in SU(2) gauge theory at finite temperature
DEFF Research Database (Denmark)
Huebner, K.; Karsch, F.; Pica, Claudio
2008-01-01
We calculate correlation functions of the energy-momentum tensor in the vicinity of the deconfinement phase transition of (3+1)-dimensional SU(2) gauge theory and discuss their critical behavior in the vicinity of the second order deconfinement transition. We show that correlation functions...... of the trace of the energy momentum tensor diverge uniformly at the critical point in proportion to the specific heat singularity. Correlation functions of the pressure, on the other hand, stay finite at the critical point. We discuss the consequences of these findings for the analysis of transport...... coefficients, in particular the bulk viscosity, in the vicinity of a second order phase transition point....
Zhang, Hai-Min; Yan, Yang; Wang, Fang; Gu, Wen-Yu; Hu, Guang-Hui; Zheng, Jun-Hua
2014-01-01
As a definite diagnosis of prostate cancer, puncture biopsy of the prostate is invasive method. The aim of this study was to evaluate the value of OPSAD (the ratio of PSA to the outer gland volume of prostate) as a non-invasive screening and diagnosis method for prostate cancer in a select population. The diagnosis data of 490 subjects undergoing ultrasound-guided biopsy of the prostate were retrospectively analyzed. This included 133 patients with prostate cancer, and 357 patients with benign prostate hyperplasia (BPH). The OPSAD was significantly greater in patients with prostate cancer (1.87 ± 1.26 ng/ml(2)) than those with BPH (0.44 ± 0.21 ng/ml(2)) (P prostate cancer. In the different groups divided according to the Gleason score of prostate cancer, OPSAD is elevated with the rise of the Gleason score. OPSAD may be used as a new indicator for the diagnosis and prognosis of prostate cancer, and it can reduce the use of unnecessary puncture biopsy of the prostate.
International Nuclear Information System (INIS)
Hoyos Madrigal, Bibian
2000-01-01
A new generalized correction equation for specific volume of hydrocarbon pure liquids is proposed. Which can be used in a wide temperature range and that do not require additional parameters for each substance. The equation was developed for the normal hydrocarbon series from methane to octane and the obtained results applied to other substances are analysed. A comparison is also made with the equation proposed by Peneloux et al. (1982) resulting. In all cases, in a better performance of the equation proposed in this work
Joly, Florian; Soulez, Gilles; Garcia, Damien; Lessard, Simon; Kauffmann, Claude
2018-01-01
Abdominal aortic aneurysms (AAA) are localized, commonly-occurring dilations of the aorta. When equilibrium between blood pressure (loading) and wall mechanical resistance is lost, rupture ensues, and patient death follows, if not treated immediately. Experimental and numerical analyses of flow patterns in arteries show direct correlations between wall shear stress and wall mechano-adaptation with the development of zones prone to thrombus formation. For further insights into AAA flow topology/growth interaction, a workout of patient-specific computational flow dynamics (CFD) is proposed to compute finite-time Lyapunov exponents and extract Lagrangian-coherent structures (LCS). This computational model was first compared with 4-D phase-contrast magnetic resonance imaging (MRI) in 5 patients. To better understand the impact of flow topology and transport on AAA growth, hyperbolic, repelling LCS were computed in 1 patient during 8-year follow-up, including 9 volumetric morphologic AAA measures by computed tomography-angiography (CTA). LCS defined barriers to Lagrangian jet cores entering AAA. Domains enclosed between LCS and the aortic wall were considered to be stagnation zones. Their evolution was studied during AAA growth. Good correlation - 2-D cross-correlation coefficients of 0.65, 0.86 and 0.082 (min, max, SD) - was obtained between numerical simulations and 4-D MRI acquisitions in 6 specific cross-sections from 4 patients. In follow-up study, LCS divided AAA lumens into 3 dynamically-isolated zones: 2 stagnation volumes lying in dilated portions of the AAA, and circulating volume connecting the inlet to the outlet. The volume of each zone was tracked over time. Although circulating volume remained unchanged during 8-year follow-up, the AAA lumen and main stagnation zones grew significantly (8 cm 3 /year and 6 cm 3 /year, respectively). This study reveals that transient transport topology can be quantified in patient-specific AAA during disease progression
Tensor-based cortical surface morphometry via weighted spherical harmonic representation.
Chung, Moo K; Dalton, Kim M; Davidson, Richard J
2008-08-01
We present a new tensor-based morphometric framework that quantifies cortical shape variations using a local area element. The local area element is computed from the Riemannian metric tensors, which are obtained from the smooth functional parametrization of a cortical mesh. For the smooth parametrization, we have developed a novel weighted spherical harmonic (SPHARM) representation, which generalizes the traditional SPHARM as a special case. For a specific choice of weights, the weighted-SPHARM is shown to be the least squares approximation to the solution of an isotropic heat diffusion on a unit sphere. The main aims of this paper are to present the weighted-SPHARM and to show how it can be used in the tensor-based morphometry. As an illustration, the methodology has been applied in the problem of detecting abnormal cortical regions in the group of high functioning autistic subjects.
On Adapting the Tensor Voting Framework to Robust Color Image Denoising
Moreno, Rodrigo; Garcia, Miguel Angel; Puig, Domenec; Julià, Carme
This paper presents an adaptation of the tensor voting framework for color image denoising, while preserving edges. Tensors are used in order to encode the CIELAB color channels, the uniformity and the edginess of image pixels. A specific voting process is proposed in order to propagate color from a pixel to its neighbors by considering the distance between pixels, the perceptual color difference (by using an optimized version of CIEDE2000), a uniformity measurement and the likelihood of the pixels being impulse noise. The original colors are corrected with those encoded by the tensors obtained after the voting process. Peak to noise ratios and visual inspection show that the proposed methodology has a better performance than state-of-the-art techniques.
Diffusion Tensor Imaging Correlates of Reading Ability in Dysfluent and Non-Impaired Readers
Lebel, Catherine; Shaywitz, Bennett; Holahan, John; Shaywitz, Sally; Marchione, Karen; Beaulieu, Christian
2013-01-01
Many children and adults have specific reading disabilities; insight into the brain structure underlying these difficulties is evolving from imaging. Previous research highlights the left temporal-parietal white matter as important in reading, yet the degree of involvement of other areas remains unclear. Diffusion tensor imaging (DTI) and…
Effects of tensor forces in nuclear spin–orbit splittings from ab initio calculations
Directory of Open Access Journals (Sweden)
Shihang Shen
2018-03-01
Full Text Available A systematic and specific pattern due to the effects of the tensor forces is found in the evolution of spin–orbit splittings in neutron drops. This result is obtained from relativistic Brueckner–Hartree–Fock theory using the bare nucleon–nucleon interaction. It forms an important guide for future microscopic derivations of relativistic and nonrelativistic nuclear energy density functionals.
The total energy-momentum tensor for electromagnetic fields in a dielectric
Crenshaw, Michael E.
2017-08-01
Radiation pressure is an observable consequence of optically induced forces on materials. On cosmic scales, radiation pressure is responsible for the bending of the tails of comets as they pass near the sun. At a much smaller scale, optically induced forces are being investigated as part of a toolkit for micromanipulation and nanofabrication technology [1]. A number of practical applications of the mechanical effects of light-matter interaction are discussed by Qiu, et al. [2]. The promise of the nascent nanophotonic technology for manufacturing small, low-power, high-sensitivity sensors and other devices has likely motivated the substantial current interest in optical manipulation of materials at the nanoscale, see, for example, Ref. [2] and the references therein. While substantial progress toward optical micromanipulation has been achieved, e.g. optical tweezers [1], in this report we limit our consideration to the particular issue of optically induced forces on a transparent dielectric material. As a matter of electromagnetic theory, these forces remain indeterminate and controversial. Due to the potential applications in nanotechnology, the century-old debate regarding these forces, and the associated momentums, has ramped up considerably in the physics community. The energy-momentum tensor is the centerpiece of conservation laws for the unimpeded, inviscid, incompressible flow of non-interacting particles in the continuum limit in an otherwise empty volume. The foundations of the energy-momentum tensor and the associated tensor conservation theory come to electrodynamics from classical continuum dynamics by applying the divergence theorem to a Taylor series expansion of a property density field of a continuous flow in an otherwise empty volume. The dust tensor is a particularly simple example of an energy-momentum tensor that deals with particles of matter in the continuum limit in terms of the mass density ρm, energy density ρmc 2 , and momentum density
International Nuclear Information System (INIS)
1996-05-01
This report describes and summarizes a probabilistic evaluation of ground motions for the Idaho National Engineering Laboratory (INEL). The purpose of this evaluation is to provide a basis for updating the seismic design criteria for the INEL. In this study, site-specific seismic hazard curves were developed for seven facility sites as prescribed by DOE Standards 1022-93 and 1023-96. These sites include the: Advanced Test Reactor (ATR); Argonne National Laboratory West (ANL); Idaho Chemical Processing Plant (ICPP or CPP); Power Burst Facility (PBF); Radioactive Waste Management Complex (RWMC); Naval Reactor Facility (NRF); and Test Area North (TAN). The results, probabilistic peak ground accelerations and uniform hazard spectra, contained in this report are not to be used for purposes of seismic design at INEL. A subsequent study will be performed to translate the results of this probabilistic seismic hazard analysis to site-specific seismic design values for the INEL as per the requirements of DOE Standard 1020-94. These site-specific seismic design values will be incorporated into the INEL Architectural and Engineering Standards
Sundram, Frederick; Campbell, Linda E.; Azuma, Rayna; Daly, Eileen; Bloemen, Oswald J. N.; Barker, Gareth J.; Chitnis, Xavier; Jones, Derek K.; van Amelsvoort, Therese; Murphy, Kieran C.; Murphy, Declan G. M.
2010-01-01
Young people with 22q11 Deletion Syndrome (22q11DS) are at substantial risk for developing psychosis and have significant differences in white matter (WM) volume. However, there are few in vivo studies of both WM microstructural integrity (as measured using Diffusion Tensor (DT)-MRI) and WM volume
Massless and massive quanta resulting from a mediumlike metric tensor
International Nuclear Information System (INIS)
Soln, J.
1985-01-01
A simple model of the ''primordial'' scalar field theory is presented in which the metric tensor is a generalization of the metric tensor from electrodynamics in a medium. The radiation signal corresponding to the scalar field propagates with a velocity that is generally less than c. This signal can be associated simultaneously with imaginary and real effective (momentum-dependent) masses. The requirement that the imaginary effective mass vanishes, which we take to be the prerequisite for the vacuumlike signal propagation, leads to the ''spontaneous'' splitting of the metric tensor into two distinct metric tensors: one metric tensor gives rise to masslesslike radiation and the other to a massive particle. (author)
Gaussian mixtures on tensor fields for segmentation: applications to medical imaging.
de Luis-García, Rodrigo; Westin, Carl-Fredrik; Alberola-López, Carlos
2011-01-01
In this paper, we introduce a new approach for tensor field segmentation based on the definition of mixtures of Gaussians on tensors as a statistical model. Working over the well-known Geodesic Active Regions segmentation framework, this scheme presents several interesting advantages. First, it yields a more flexible model than the use of a single Gaussian distribution, which enables the method to better adapt to the complexity of the data. Second, it can work directly on tensor-valued images or, through a parallel scheme that processes independently the intensity and the local structure tensor, on scalar textured images. Two different applications have been considered to show the suitability of the proposed method for medical imaging segmentation. First, we address DT-MRI segmentation on a dataset of 32 volumes, showing a successful segmentation of the corpus callosum and favourable comparisons with related approaches in the literature. Second, the segmentation of bones from hand radiographs is studied, and a complete automatic-semiautomatic approach has been developed that makes use of anatomical prior knowledge to produce accurate segmentation results. Copyright © 2010 Elsevier Ltd. All rights reserved.
International Nuclear Information System (INIS)
Adams, S.M.; Cunningham, P.A.; Gray, D.D.; Kumar, K.D.; Witten, A.J.
1976-01-01
A comprehensive study of the data collected as part of the environmental Technical Specifications program for Units 2 and 3 of the Peach Bottom Nuclear Power Plant was conducted for the Office of Regulatory Research of the U.S. Nuclear Regulatory Commission. The program included an analysis of both the hydrothermal and ecological monitoring data collected from 1967 through 1976. Specific recommendations are made for improving both the present hydrothermal and ecological monitoring programs. Hydrothermal monitoring would be improved by more complete reporting of in-plant operating parameters. In addition, the present boat surveys could be discontinued, and monitoring efforts could be directed toward expanding the present thermograph network. Ecological monitoring programs were judged to be of high quality because standardized collection techniques, consistent reporting formats, and statistical analyses were performed on all of the data and were presented in an annual report. Sampling for all trophic groups was adequate for the purposes of assessing power plant induced perturbations. Considering the extensive period of preoperational data (six years) and operational data (three years) available for analysis, consideration could be given to reducing monitoring effort after data have been collected for a period when both units are operating at full capacity. In this way, an assessment of the potential ecological impact of the Peach Bottom facility can be made under conditions of maximum plant induced perturbations
Feature Surfaces in Symmetric Tensor Fields Based on Eigenvalue Manifold.
Palacios, Jonathan; Yeh, Harry; Wang, Wenping; Zhang, Yue; Laramee, Robert S; Sharma, Ritesh; Schultz, Thomas; Zhang, Eugene
2016-03-01
Three-dimensional symmetric tensor fields have a wide range of applications in solid and fluid mechanics. Recent advances in the (topological) analysis of 3D symmetric tensor fields focus on degenerate tensors which form curves. In this paper, we introduce a number of feature surfaces, such as neutral surfaces and traceless surfaces, into tensor field analysis, based on the notion of eigenvalue manifold. Neutral surfaces are the boundary between linear tensors and planar tensors, and the traceless surfaces are the boundary between tensors of positive traces and those of negative traces. Degenerate curves, neutral surfaces, and traceless surfaces together form a partition of the eigenvalue manifold, which provides a more complete tensor field analysis than degenerate curves alone. We also extract and visualize the isosurfaces of tensor modes, tensor isotropy, and tensor magnitude, which we have found useful for domain applications in fluid and solid mechanics. Extracting neutral and traceless surfaces using the Marching Tetrahedra method can cause the loss of geometric and topological details, which can lead to false physical interpretation. To robustly extract neutral surfaces and traceless surfaces, we develop a polynomial description of them which enables us to borrow techniques from algebraic surface extraction, a topic well-researched by the computer-aided design (CAD) community as well as the algebraic geometry community. In addition, we adapt the surface extraction technique, called A-patches, to improve the speed of finding degenerate curves. Finally, we apply our analysis to data from solid and fluid mechanics as well as scalar field analysis.
Glyph-Based Comparative Visualization for Diffusion Tensor Fields.
Zhang, Changgong; Schultz, Thomas; Lawonn, Kai; Eisemann, Elmar; Vilanova, Anna
2016-01-01
Diffusion Tensor Imaging (DTI) is a magnetic resonance imaging modality that enables the in-vivo reconstruction and visualization of fibrous structures. To inspect the local and individual diffusion tensors, glyph-based visualizations are commonly used since they are able to effectively convey full aspects of the diffusion tensor. For several applications it is necessary to compare tensor fields, e.g., to study the effects of acquisition parameters, or to investigate the influence of pathologies on white matter structures. This comparison is commonly done by extracting scalar information out of the tensor fields and then comparing these scalar fields, which leads to a loss of information. If the glyph representation is kept, simple juxtaposition or superposition can be used. However, neither facilitates the identification and interpretation of the differences between the tensor fields. Inspired by the checkerboard style visualization and the superquadric tensor glyph, we design a new glyph to locally visualize differences between two diffusion tensors by combining juxtaposition and explicit encoding. Because tensor scale, anisotropy type, and orientation are related to anatomical information relevant for DTI applications, we focus on visualizing tensor differences in these three aspects. As demonstrated in a user study, our new glyph design allows users to efficiently and effectively identify the tensor differences. We also apply our new glyphs to investigate the differences between DTI datasets of the human brain in two different contexts using different b-values, and to compare datasets from a healthy and HIV-infected subject.
Tensoral for post-processing users and simulation authors
Dresselhaus, Eliot
1993-01-01
The CTR post-processing effort aims to make turbulence simulations and data more readily and usefully available to the research and industrial communities. The Tensoral language, which provides the foundation for this effort, is introduced here in the form of a user's guide. The Tensoral user's guide is presented in two main sections. Section one acts as a general introduction and guides database users who wish to post-process simulation databases. Section two gives a brief description of how database authors and other advanced users can make simulation codes and/or the databases they generate available to the user community via Tensoral database back ends. The two-part structure of this document conforms to the two-level design structure of the Tensoral language. Tensoral has been designed to be a general computer language for performing tensor calculus and statistics on numerical data. Tensoral's generality allows it to be used for stand-alone native coding of high-level post-processing tasks (as described in section one of this guide). At the same time, Tensoral's specialization to a minute task (namely, to numerical tensor calculus and statistics) allows it to be easily embedded into applications written partly in Tensoral and partly in other computer languages (here, C and Vectoral). Embedded Tensoral, aimed at advanced users for more general coding (e.g. of efficient simulations, for interfacing with pre-existing software, for visualization, etc.), is described in section two of this guide.
International Nuclear Information System (INIS)
Fugal, M; McDonald, D; Jacqmin, D; Koch, N; Ellis, A; Peng, J; Ashenafi, M; Vanek, K
2015-01-01
Purpose: This study explores novel methods to address two significant challenges affecting measurement of patient-specific quality assurance (QA) with IBA’s Matrixx Evolution™ ionization chamber array. First, dose calculation algorithms often struggle to accurately determine dose to the chamber array due to CT artifact and algorithm limitations. Second, finite chamber size and volume averaging effects cause additional deviation from the calculated dose. Methods: QA measurements were taken with the Matrixx positioned on the treatment table in a solid-water Multi-Cube™ phantom. To reduce the effect of CT artifact, the Matrixx CT image set was masked with appropriate materials and densities. Individual ionization chambers were masked as air, while the high-z electronic backplane and remaining solid-water material were masked as aluminum and water, respectively. Dose calculation was done using Varian’s Acuros XB™ (V11) algorithm, which is capable of predicting dose more accurately in non-biologic materials due to its consideration of each material’s atomic properties. Finally, the exported TPS dose was processed using an in-house algorithm (MATLAB) to assign the volume averaged TPS dose to each element of a corresponding 2-D matrix. This matrix was used for comparison with the measured dose. Square fields at regularly-spaced gantry angles, as well as selected patient plans were analyzed. Results: Analyzed plans showed improved agreement, with the average gamma passing rate increasing from 94 to 98%. Correction factors necessary for chamber angular dependence were reduced by 67% compared to factors measured previously, indicating that previously measured factors corrected for dose calculation errors in addition to true chamber angular dependence. Conclusion: By comparing volume averaged dose, calculated with a capable dose engine, on a phantom masked with correct materials and densities, QA results obtained with the Matrixx Evolution™ can be significantly
Energy-momentum tensor of the electromagnetic field
International Nuclear Information System (INIS)
Horndeski, G.W.; Wainwright, J.
1977-01-01
In this paper we investigate the energy-momentum tensor of the most general second-order vector-tensor theory of gravitation and electromagnetism which has field equations which are (i) derivable from a variational principle, (ii) consistent with the notion of conservation of charge, and (iii) compatible with Maxwell's equations in a flat space. This energy-momentum tensor turns out to be quadratic in the first partial derivatives of the electromagnetic field tensor and depends upon the curvature tensor. The asymptotic behavior of this energy-momentum tensor is examined for solutions to Maxwell's equations in Minkowski space, and it is demonstrated that this energy-momentum tensor predicts regions of negative energy density in the vicinity of point sources
Quantum mechanics of Yano tensors: Dirac equation in curved spacetime
International Nuclear Information System (INIS)
Cariglia, Marco
2004-01-01
In spacetimes admitting Yano tensors, the classical theory of the spinning particle possesses enhanced worldline supersymmetry. Quantum mechanically generators of extra supersymmetries correspond to operators that in the classical limit commute with the Dirac operator and generate conserved quantities. We show that the result is preserved in the full quantum theory, that is, Yano symmetries are not anomalous. This was known for Yano tensors of rank 2, but our main result is to show that it extends to Yano tensors of arbitrary rank. We also describe the conformal Yano equation and show that is invariant under Hodge duality. There is a natural relationship between Yano tensors and supergravity theories. As the simplest possible example, we show that when the spacetime admits a Killing spinor then this generates Yano and conformal Yano tensors. As an application, we construct Yano tensors on maximally symmetric spaces: they are spanned by tensor products of Killing vectors
Algebraic and computational aspects of real tensor ranks
Sakata, Toshio; Miyazaki, Mitsuhiro
2016-01-01
This book provides comprehensive summaries of theoretical (algebraic) and computational aspects of tensor ranks, maximal ranks, and typical ranks, over the real number field. Although tensor ranks have been often argued in the complex number field, it should be emphasized that this book treats real tensor ranks, which have direct applications in statistics. The book provides several interesting ideas, including determinant polynomials, determinantal ideals, absolutely nonsingular tensors, absolutely full column rank tensors, and their connection to bilinear maps and Hurwitz-Radon numbers. In addition to reviews of methods to determine real tensor ranks in details, global theories such as the Jacobian method are also reviewed in details. The book includes as well an accessible and comprehensive introduction of mathematical backgrounds, with basics of positive polynomials and calculations by using the Groebner basis. Furthermore, this book provides insights into numerical methods of finding tensor ranks through...
International Nuclear Information System (INIS)
Veneziano, S.; Paulica, P.; Querze', R.; Viglietta, G.; Trenta, A.
1991-01-01
US-guided biopsy was performed in 94 patients with suspected lesions at transerectal US. Histology demonstrated carcinoma in 43 cases, benign hyperplasia in 44, and prostatis in 7. In all cases the prostate specific antigen (PSA) was calculated, by means of US, together with prostatic volume (v). PSA was related to the corresponding gland volume, which resulted in PSA/V ratio. Our study showed PSA/V ration to have higher sensitivity and specificity than absolulute PSA value in the diagnosis of prostatic carcinoma. The authors believe prostate US-guided biopsy to be: a) necessary when the suspected area has PSA/V ratio >0.15, and especially when PSA/V >0.30; b) not indicated when echo-structural alterations are associated with PSA/V <0.15, because they are most frequently due to benign lesions. The combined use of PSA/V ratio and US is therefore suggested to select the patients in whom biopsy is to be performed
Energy Technology Data Exchange (ETDEWEB)
Adams, S.M.; Cunningham, P.A.; Gray, D.D.; Kumar, K.D.
1976-08-10
A comprehensive study of the data collected as part of the environmental Technical Specifications program for Unit 1 of the San Onofre Nuclear Generating Station (SONGS 1) was conducted for the Office of Nuclear Regulatory Research of the U.S. Nuclear Regulatory Commission. The program included an analysis of the hydrothermal and ecological monitoring data collected during 1975. The hydrothermal analysis includes a discussion of models used in plume predictions prior to plant operation and an evaluation of the present hydrothermal monitoring program. The ecological evaluation was directed toward reviewing the strengths and weaknesses of the various sampling programs designed to monitor the planktonic, benthic, and nektonic communities inhabiting the inshore coastal area in the vicinity of San Onofre.
International Nuclear Information System (INIS)
Adams, S.M.; Cunningham, P.A.; Gray, D.D.; Kumar, K.D.
1976-01-01
A comprehensive study of the data collected as part of the environmental Technical Specifications program for Unit 1 of the San Onofre Nuclear Generating Station (SONGS 1) was conducted for the Office of Nuclear Regulatory Research of the U.S. Nuclear Regulatory Commission. The program included an analysis of the hydrothermal and ecological monitoring data collected during 1975. The hydrothermal analysis includes a discussion of models used in plume predictions prior to plant operation and an evaluation of the present hydrothermal monitoring program. The ecological evaluation was directed toward reviewing the strengths and weaknesses of the various sampling programs designed to monitor the planktonic, benthic, and nektonic communities inhabiting the inshore coastal area in the vicinity of San Onofre
Kennedy, J. R.; Fitzpatrick, W. S.
1971-01-01
The computer executive functional system design concepts derived from study of the Space Station/Base are presented. Information Management System hardware configuration as directly influencing the executive design is reviewed. The hardware configuration and generic executive design requirements are considered in detail in a previous report (System Configuration and Executive Requirements Specifications for Reusable Shuttle and Space Station/Base, 9/25/70). This report defines basic system primitives and delineates processes and process control. Supervisor states are considered for describing basic multiprogramming and multiprocessing systems. A high-level computer executive including control of scheduling, allocation of resources, system interactions, and real-time supervisory functions is defined. The description is oriented to provide a baseline for a functional simulation of the computer executive system.
Comparison of quality control software tools for diffusion tensor imaging.
Liu, Bilan; Zhu, Tong; Zhong, Jianhui
2015-04-01
Image quality of diffusion tensor imaging (DTI) is critical for image interpretation, diagnostic accuracy and efficiency. However, DTI is susceptible to numerous detrimental artifacts that may impair the reliability and validity of the obtained data. Although many quality control (QC) software tools are being developed and are widely used and each has its different tradeoffs, there is still no general agreement on an image quality control routine for DTIs, and the practical impact of these tradeoffs is not well studied. An objective comparison that identifies the pros and cons of each of the QC tools will be helpful for the users to make the best choice among tools for specific DTI applications. This study aims to quantitatively compare the effectiveness of three popular QC tools including DTI studio (Johns Hopkins University), DTIprep (University of North Carolina at Chapel Hill, University of Iowa and University of Utah) and TORTOISE (National Institute of Health). Both synthetic and in vivo human brain data were used to quantify adverse effects of major DTI artifacts to tensor calculation as well as the effectiveness of different QC tools in identifying and correcting these artifacts. The technical basis of each tool was discussed, and the ways in which particular techniques affect the output of each of the tools were analyzed. The different functions and I/O formats that three QC tools provide for building a general DTI processing pipeline and integration with other popular image processing tools were also discussed. Copyright © 2015 Elsevier Inc. All rights reserved.
Entanglement entropy from the holographic stress tensor
International Nuclear Information System (INIS)
Bhattacharyya, Arpan; Sinha, Aninda
2013-01-01
We consider entanglement entropy in the context of gauge/gravity duality for conformal field theories in even dimensions. The holographic prescription due to Ryu and Takayanagi (RT) leads to an equation describing how the entangling surface extends into the bulk geometry. We show that setting to zero, the time–time component of the Brown–York stress tensor evaluated on the co-dimension 1 entangling surface, leads to the same equation. By considering a spherical entangling surface as an example, we observe that the Euclidean action methods in AdS/CFT will lead to the RT area functional arising as a counterterm needed to regularize the stress tensor. We present arguments leading to a justification for the minimal area prescription. (paper)
Tensor modes on the string theory landscape
International Nuclear Information System (INIS)
Westphal, Alexander
2012-06-01
We attempt an estimate for the distribution of the tensor mode fraction r over the landscape of vacua in string theory. The dynamics of eternal inflation and quantum tunneling lead to a kind of democracy on the landscape, providing no bias towards large-field or small-field inflation regardless of the class of measure. The tensor mode fraction then follows the number frequency distributions of inflationary mechanisms of string theory over the landscape. We show that an estimate of the relative number frequencies for small-field vs large-field inflation, while unattainable on the whole landscape, may be within reach as a regional answer for warped Calabi-Yau flux compactifications of type IIB string theory.
Tensor modes on the string theory landscape
Energy Technology Data Exchange (ETDEWEB)
Westphal, Alexander
2012-06-15
We attempt an estimate for the distribution of the tensor mode fraction r over the landscape of vacua in string theory. The dynamics of eternal inflation and quantum tunneling lead to a kind of democracy on the landscape, providing no bias towards large-field or small-field inflation regardless of the class of measure. The tensor mode fraction then follows the number frequency distributions of inflationary mechanisms of string theory over the landscape. We show that an estimate of the relative number frequencies for small-field vs large-field inflation, while unattainable on the whole landscape, may be within reach as a regional answer for warped Calabi-Yau flux compactifications of type IIB string theory.
International Nuclear Information System (INIS)
Kibler, M.; Grenet, G.
1979-07-01
The SU 2 unit tensor operators tsub(k,α) are studied. In the case where the spinor point group G* coincides with U 1 , then tsub(k α) reduces up to a constant to the Wigner-Racah-Schwinger tensor operator tsub(kqα), an operator which produces an angular momentum state. One first investigates those general properties of tsub(kα) which are independent of their realization. The tsub(kα) in terms of two pairs of boson creation and annihilation operators are realized. This leads to look at the Schwinger calculus relative to one angular momentum of two coupled angular momenta. As a by-product, a procedure is given for producing recursion relationships between SU 2 Wigner coefficients. Finally, some of the properties of the Wigner and Racah operators for an arbitrary compact group and the SU 2 coupling coefficients are studied
Tensor Networks and Quantum Error Correction
Ferris, Andrew J.; Poulin, David
2014-07-01
We establish several relations between quantum error correction (QEC) and tensor network (TN) methods of quantum many-body physics. We exhibit correspondences between well-known families of QEC codes and TNs, and demonstrate a formal equivalence between decoding a QEC code and contracting a TN. We build on this equivalence to propose a new family of quantum codes and decoding algorithms that generalize and improve upon quantum polar codes and successive cancellation decoding in a natural way.
Old tensor mesons in QCD sum rules
International Nuclear Information System (INIS)
Aliev, T.M.; Shifman, M.A.
1981-01-01
Tensor mesons f, A 2 and A 3 are analyzed within the framework of QCD sum rules. The effects of gluon and quark condensate is accounted for phenomenologically. Accurate estimates of meson masses and coupling constants of the lowest-lying states are obtained. It is shown that the masses are reproduced within theoretical uncertainty of about 80 MeV. The coupling of f meson to the corresponding quark current is determined. The results are in good aqreement with experimental data [ru
Energy-momentum-tensor in quantumelectrodynamics
Energy Technology Data Exchange (ETDEWEB)
Schott, T
1974-01-01
This work deals with the operator properties of the energy-momentum-tensor (ET) in the framework of quantum electrodynamics. The principles of construction of the ET are discussed for quantized fields in the Schwinger variation principle. Dealing with the conserved quantities for quantized fields operator problems are coming up in the Coulomb gauge because Dirac- and Maxwellfield do not commute completely. Further on contemporary commutators of the ET components are investigated mutually. Finally non-canonical methods are developed.
Embryo Cell Membranes Reconstruction by Tensor Voting
Michelin , Gaël; Guignard , Léo; Fiuza , Ulla-Maj; Malandain , Grégoire
2014-01-01
International audience; Image-based studies of developing organs or embryos produce a huge quantity of data. To handle such high-throughput experimental protocols, automated computer-assisted methods are highly desirable. This article aims at designing an efficient cell segmentation method from microscopic images. The proposed approach is twofold: first, cell membranes are enhanced or extracted by the means of structure-based filters, and then perceptual grouping (i.e. tensor voting) allows t...
Sasakian manifolds with purely transversal Bach tensor
Ghosh, Amalendu; Sharma, Ramesh
2017-10-01
We show that a (2n + 1)-dimensional Sasakian manifold (M, g) with a purely transversal Bach tensor has constant scalar curvature ≥2 n (2 n +1 ) , equality holding if and only if (M, g) is Einstein. For dimension 3, M is locally isometric to the unit sphere S3. For dimension 5, if in addition (M, g) is complete, then it has positive Ricci curvature and is compact with finite fundamental group π1(M).
Vector-tensor interaction of gravitation
Energy Technology Data Exchange (ETDEWEB)
Zhang Yuan-zhong; Guo han-ying
1982-11-01
In the paper, by using the equation of motion a particle, we show that the antigravity exist in the vector-tensor model of gravitation. Thus the motion of a particle deviates from the geodesic equation. In Newtonian approximation and weak gravitational field, acceleration of a particle in a spherically symmetric and astatic gravitation field is zero. The result is obviously not in agreement with gravitational phenomena.
Numerical CP Decomposition of Some Difficult Tensors
Czech Academy of Sciences Publication Activity Database
Tichavský, Petr; Phan, A. H.; Cichocki, A.
2017-01-01
Roč. 317, č. 1 (2017), s. 362-370 ISSN 0377-0427 R&D Projects: GA ČR(CZ) GA14-13713S Institutional support: RVO:67985556 Keywords : Small matrix multiplication * Canonical polyadic tensor decomposition * Levenberg-Marquardt method Subject RIV: BB - Applied Statistics, Operational Research OBOR OECD: Applied mathematics Impact factor: 1.357, year: 2016 http://library.utia.cas.cz/separaty/2017/SI/tichavsky-0468385. pdf
Experimental status of scalar and tensor mesons
International Nuclear Information System (INIS)
Von Dombrowski, S.
1997-01-01
The recent discoveries of a 0 (1450) and f 0 (1370)/f 0 (1500) in antiproton-proton annihilation at rest shed new light on the interpretation of light scalar mesons. The properties of f 0 (1500) match the expectations of a scalar glueball mixed with nearby qq states. New decay modes of the ξ(2230) are reported in radiative J/Ψ decays, pointing also towards a (tensor) glueball nature of this state. Results from different experiments are discussed and compared. (orig.)
Bayesian approach to magnetotelluric tensor decomposition
Czech Academy of Sciences Publication Activity Database
Červ, Václav; Pek, Josef; Menvielle, M.
2010-01-01
Roč. 53, č. 2 (2010), s. 21-32 ISSN 1593-5213 R&D Projects: GA AV ČR IAA200120701; GA ČR GA205/04/0746; GA ČR GA205/07/0292 Institutional research plan: CEZ:AV0Z30120515 Keywords : galvanic distortion * telluric distortion * impedance tensor * basic procedure * inversion * noise Subject RIV: DE - Earth Magnetism, Geodesy, Geography Impact factor: 0.336, year: 2010
Monte Carlo Volcano Seismic Moment Tensors
Waite, G. P.; Brill, K. A.; Lanza, F.
2015-12-01
Inverse modeling of volcano seismic sources can provide insight into the geometry and dynamics of volcanic conduits. But given the logistical challenges of working on an active volcano, seismic networks are typically deficient in spatial and temporal coverage; this potentially leads to large errors in source models. In addition, uncertainties in the centroid location and moment-tensor components, including volumetric components, are difficult to constrain from the linear inversion results, which leads to a poor understanding of the model space. In this study, we employ a nonlinear inversion using a Monte Carlo scheme with the objective of defining robustly resolved elements of model space. The model space is randomized by centroid location and moment tensor eigenvectors. Point sources densely sample the summit area and moment tensors are constrained to a randomly chosen geometry within the inversion; Green's functions for the random moment tensors are all calculated from modeled single forces, making the nonlinear inversion computationally reasonable. We apply this method to very-long-period (VLP) seismic events that accompany minor eruptions at Fuego volcano, Guatemala. The library of single force Green's functions is computed with a 3D finite-difference modeling algorithm through a homogeneous velocity-density model that includes topography, for a 3D grid of nodes, spaced 40 m apart, within the summit region. The homogenous velocity and density model is justified by long wavelength of VLP data. The nonlinear inversion reveals well resolved model features and informs the interpretation through a better understanding of the possible models. This approach can also be used to evaluate possible station geometries in order to optimize networks prior to deployment.
Electrical tensor Green functions for cylindrical waveguides
International Nuclear Information System (INIS)
Prijmenko, S.D.; Papkovich, V.G.; Khizhnyak, N.A.
1988-01-01
Formation of electrical tensor Green functions for cylindrical waveguides is considered. Behaviour of these functions in the source region is studied. Cases of electrical tensor Green functions for vector potential G E (r-vector, r'-vector) and electric field G e (r-vector, r'-vector) are analysed. When forming G E (r-vector, r'-vector), its dependence on lateral coordinates is taken into account by means of two-dimensional fundamental vector Hansen functions, several methods are used to take into account the dependence on transverse coordinate. When forming G e (r-vector, r'-vector) we use the fact that G E (r-vector, r'-vector) and G e (r-vector, r'-vector) are the generalized functions. It is shown that G e (r-vector, r'-vector) behaviour in the source region is defined by a singular term, which properties are described by the delta-function. Two variants of solving the problem of defining singular and regular sides of tensor function G E (r-vector, r'-vector) are presented. 23 refs
Tensor integrand reduction via Laurent expansion
Energy Technology Data Exchange (ETDEWEB)
Hirschi, Valentin [SLAC, National Accelerator Laboratory,2575 Sand Hill Road, Menlo Park, CA 94025-7090 (United States); Peraro, Tiziano [Higgs Centre for Theoretical Physics, School of Physics and Astronomy,The University of Edinburgh,Edinburgh EH9 3JZ, Scotland (United Kingdom)
2016-06-09
We introduce a new method for the application of one-loop integrand reduction via the Laurent expansion algorithm, as implemented in the public C++ library Ninja. We show how the coefficients of the Laurent expansion can be computed by suitable contractions of the loop numerator tensor with cut-dependent projectors, making it possible to interface Ninja to any one-loop matrix element generator that can provide the components of this tensor. We implemented this technique in the Ninja library and interfaced it to MADLOOP, which is part of the public MADGRAPH5{sub A}MC@NLO framework. We performed a detailed performance study, comparing against other public reduction tools, namely CUTTOOLS, SAMURAI, IREGI, PJFRY++ and GOLEM95. We find that Ninja outperforms traditional integrand reduction in both speed and numerical stability, the latter being on par with that of the tensor integral reduction tool GOLEM95 which is however more limited and slower than Ninja. We considered many benchmark multi-scale processes of increasing complexity, involving QCD and electro-weak corrections as well as effective non-renormalizable couplings, showing that Ninja’s performance scales well with both the rank and multiplicity of the considered process.
Liu, Chunlei; Murphy, Nicole E.; Li, Wei
2012-01-01
Diffusion MRI has become an invaluable tool for studying white matter microstructure and brain connectivity. The emergence of quantitative susceptibility mapping and susceptibility tensor imaging (STI) has provided another unique tool for assessing the structure of white matter. In the highly ordered white matter structure, diffusion MRI measures hindered water mobility induced by various tissue and cell membranes, while susceptibility sensitizes to the molecular composition and axonal arrangement. Integrating these two methods may produce new insights into the complex physiology of white matter. In this study, we investigated the relationship between diffusion and magnetic susceptibility in the white matter. Experiments were conducted on phantoms and human brains in vivo. Diffusion properties were quantified with the diffusion tensor model and also with the higher order tensor model based on the cumulant expansion. Frequency shift and susceptibility tensor were measured with quantitative susceptibility mapping and susceptibility tensor imaging. These diffusion and susceptibility quantities were compared and correlated in regions of single fiber bundles and regions of multiple fiber orientations. Relationships were established with similarities and differences identified. It is believed that diffusion MRI and susceptibility MRI provide complementary information of the microstructure of white matter. Together, they allow a more complete assessment of healthy and diseased brains. PMID:23507987
Non-Newtonian stress tensor and thermal conductivity tensor in granular plane shear flow
Alam, Meheboob; Saha, Saikat
2014-11-01
The non-Newtonian stress tensor and the heat flux in the plane shear flow of smooth inelastic disks are analysed from the Grad-level moment equations using the anisotropic Gaussian as a reference. Closed-form expressions for shear viscosity, pressure, first normal stress difference (N1) and the dissipation rate are given as functions of (i) the density or the area fraction (ν), (ii) the restitution coefficient (e), (iii) the dimensionless shear rate (R), (iv) the temperature anisotropy [ η, the difference between the principal eigenvalues of the second moment tensor] and (v) the angle (ϕ) between the principal directions of the shear tensor and the second moment tensor. Particle simulation data for a sheared hard-disk system is compared with theoretical results, with good agreement for p, μ and N1 over a large range of density. In contrast, the predictions from a Navier-Stokes order constitutive model are found to deviate significantly from both the simulation and the moment theory even at moderate values of e. We show that the gradient of the deviatoric part of the kinetic stress drives a heat current and the thermal conductivity is characterized by an anisotropic 2nd rank tensor for which explicit expressions are derived.
International Nuclear Information System (INIS)
Adams, S.M.; Cunningham, P.A.; Gray, D.D.; Kumar, K.D.
1976-01-01
A comprehensive study of the data collected as part of the environmental Technical Specifications program for Units 1 and 2 of the Surry Nuclear Power Plant was carried out for the Office of Regulatory Research of the U.S. Nuclear Regulatory Commission. The program included an analysis of the hydrothermal and ecological monitoring data collected from 1973 through 1975. The hydrothermal analysis includes a discussion of models used in plume predictions prior to plant operation and an evaluation of the present hydrothermal monitoring program. The two primary methods used for temperature monitoring employ a fixed thermographs network and boat measurements. Review of data indicates that both the application and formulation of the hydrothermal monitoring program are inadequate to fully characterize the operation of the plant and the behavior of the thermal plume. Furthermore, there are no existing data that can be used to adequately verify or disprove the validity of the various Surry plume predictions. The ecological analysis includes validation of impacts predicted in the Final Environmental Statement using the operational monitoring data. Phytoplankton cell concentrations, chlorophyll a, and carbon-14 measurements were used to monitor changes in the primary producers. Densities of consumers (i.e., zooplankton, benthos, and fish) were sed to monitor changes in the primary producers. Models based on operating data were constructed to determine whether changes were occurring at each trophic level. Analysis of the monitoring data suggests that the thermal discharges at Surry are having a negative effect on the phytoplankton and zooplankton but are enhancing the benthic and nekton populations in the discharge area
Detection of antisymmetric tensor contribution to the magnetic screening of 13C nuclei
International Nuclear Information System (INIS)
Kuhn, W.
1983-01-01
In the present thesis for the first time a practicable way for the detection of antisymmetric contributions to the tensor of the magnetic screening of atomic nuclei is indicated. The detection is based on the relaxation efficiency of the antisymmetric screening. The measurements were performed on the 13 C nuclei of phthalic acid anhydride. Measured were the spin-lattice relaxation times of all 13 C nuclei of the molecule at field strengths between 4.69 T and 11.74 T, this corresponds to 1 H resonance frequencies in the range from 200 MHz to 500 MHz. From this the interaction-specific relaxation rates could be determined without problems. The space-group of the crystal and the molecule geometry were determined by X-ray structure analysis. For the accurate determination of the hydrogen position on a deuterated monocrystal by means of deuterium nuclear resonance measurements the electric field gradient tensors were measured and from the orientation of the main axes of these tensors the bonding angles calculated. On a monocrystal enriched in the C(7) respectively C(8) position with 13 C the symmetric part of the tensor of the magnetic screening of these two nuclei was measured. With these values and the relaxation rates of the 13 C nuclei by an iterative procedure from the equations for the theoretical relaxation rates of all 13 C nuclei of the molecule the main values of the rotation-diffusion tensor could be determined. On the base of the plane molecule geometry from this the tensor element sigmasub(xz)sup(A) could be explicety detected according to an amount of 11.7 ppm. (orig.) [de
Graña, M; Termenon, M; Savio, A; Gonzalez-Pinto, A; Echeveste, J; Pérez, J M; Besga, A
2011-09-20
The aim of this paper is to obtain discriminant features from two scalar measures of Diffusion Tensor Imaging (DTI) data, Fractional Anisotropy (FA) and Mean Diffusivity (MD), and to train and test classifiers able to discriminate Alzheimer's Disease (AD) patients from controls on the basis of features extracted from the FA or MD volumes. In this study, support vector machine (SVM) classifier was trained and tested on FA and MD data. Feature selection is done computing the Pearson's correlation between FA or MD values at voxel site across subjects and the indicative variable specifying the subject class. Voxel sites with high absolute correlation are selected for feature extraction. Results are obtained over an on-going study in Hospital de Santiago Apostol collecting anatomical T1-weighted MRI volumes and DTI data from healthy control subjects and AD patients. FA features and a linear SVM classifier achieve perfect accuracy, sensitivity and specificity in several cross-validation studies, supporting the usefulness of DTI-derived features as an image-marker for AD and to the feasibility of building Computer Aided Diagnosis systems for AD based on them. Copyright © 2011 Elsevier Ireland Ltd. All rights reserved.
Directory of Open Access Journals (Sweden)
Yayoi K. Hayakawa
2014-01-01
Full Text Available Depressive symptoms, even at a subclinical level, have been associated with structural brain abnormalities. However, previous studies have used regions of interest or small sample sizes, limiting the ability to generalize the results. In this study, we examined neuroanatomical structures of both gray matter and white matter associated with depressive symptoms across the whole brain in a large sample. A total of 810 community-dwelling adult participants underwent measurement of depressive symptoms with the Center for Epidemiologic Studies Depression Scale (CES-D. The participants were not demented and had no neurological or psychiatric history. To examine the gray and white matter volume, we used structural MRI scans and voxel-based morphometry (VBM; to examine the white matter integrity, we used diffusion tensor imaging with tract-based spatial statistics (TBSS. In female participants, VBM revealed a negative correlation between bilateral anterior cingulate gray matter volume and the CES-D score. TBSS showed a CES-D-related decrease in fractional anisotropy and increase in radial and mean diffusivity in several white matter regions, including the right anterior cingulum. In male participants, there was no significant correlation between gray or white matter volume or white matter integrity and the CES-D score. Our results indicate that the reduction in gray matter volume and differences in white matter integrity in specific brain regions, including the anterior cingulate, are associated with depressive symptoms in women.
Hayakawa, Yayoi K; Sasaki, Hiroki; Takao, Hidemasa; Hayashi, Naoto; Kunimatsu, Akira; Ohtomo, Kuni; Aoki, Shigeki
2014-01-01
Depressive symptoms, even at a subclinical level, have been associated with structural brain abnormalities. However, previous studies have used regions of interest or small sample sizes, limiting the ability to generalize the results. In this study, we examined neuroanatomical structures of both gray matter and white matter associated with depressive symptoms across the whole brain in a large sample. A total of 810 community-dwelling adult participants underwent measurement of depressive symptoms with the Center for Epidemiologic Studies Depression Scale (CES-D). The participants were not demented and had no neurological or psychiatric history. To examine the gray and white matter volume, we used structural MRI scans and voxel-based morphometry (VBM); to examine the white matter integrity, we used diffusion tensor imaging with tract-based spatial statistics (TBSS). In female participants, VBM revealed a negative correlation between bilateral anterior cingulate gray matter volume and the CES-D score. TBSS showed a CES-D-related decrease in fractional anisotropy and increase in radial and mean diffusivity in several white matter regions, including the right anterior cingulum. In male participants, there was no significant correlation between gray or white matter volume or white matter integrity and the CES-D score. Our results indicate that the reduction in gray matter volume and differences in white matter integrity in specific brain regions, including the anterior cingulate, are associated with depressive symptoms in women.
Tensor interaction in heavy-ion scattering. Pt. 1
International Nuclear Information System (INIS)
Nishioka, H.; Johnson, R.C.
1985-01-01
The Heidelberg shape-effect model for heavy-ion tensor interactions is reformulated and generalized using the Hooton-Johnson formulation. The generalized semiclassical model (the turning-point model) predicts that the components of the tensor analysing power anti Tsub(2q) have certain relations with each other for each type of tensor interaction (Tsub(R), Tsub(P) and Tsub(L) types). The predicted relations between the anti Tsub(2q) are very simple and have a direct connection with the properties of the tensor interaction at the turning point. The model predictions are satisfied in quantum-mechanical calculations for 7 Li and 23 Na elastic scattering from 58 Ni in the Fresnel-diffraction energy region. As a consequence of this model, it becomes possible to single out effects from a Tsub(P)- or Tsub(L)-type tensor interaction in polarized heavy-ion scattering. The presence of a Tsub(P)-type tensor interaction is suggested by measured anti T 20 /anti T 22 ratios for 7 Li + 58 Ni scattering. In the turning-point model the three types of tensor operator are not independent, and this is found to be true also in a quantum-mechanical calculation. The model also predicts relations between the components of higher-rank tensor analysing power in the presence of a higher-rank tensor interaction. The rank-3 tensor case is discussed in detail. (orig.)
Rossi, Marcel M; Alderson, Jacqueline; El-Sallam, Amar; Dowling, James; Reinbolt, Jeffrey; Donnelly, Cyril J
2016-12-08
The aims of this study were to: (i) establish a new criterion method to validate inertia tensor estimates by setting the experimental angular velocity data of an airborne objects as ground truth against simulations run with the estimated tensors, and (ii) test the sensitivity of the simulations to changes in the inertia tensor components. A rigid steel cylinder was covered with reflective kinematic markers and projected through a calibrated motion capture volume. Simulations of the airborne motion were run with two models, using inertia tensor estimated with geometric formula or the compound pendulum technique. The deviation angles between experimental (ground truth) and simulated angular velocity vectors and the root mean squared deviation angle were computed for every simulation. Monte Carlo analyses were performed to assess the sensitivity of simulations to changes in magnitude of principal moments of inertia within ±10% and to changes in orientation of principal axes of inertia within ±10° (of the geometric-based inertia tensor). Root mean squared deviation angles ranged between 2.9° and 4.3° for the inertia tensor estimated geometrically, and between 11.7° and 15.2° for the compound pendulum values. Errors up to 10% in magnitude of principal moments of inertia yielded root mean squared deviation angles ranging between 3.2° and 6.6°, and between 5.5° and 7.9° when lumped with errors of 10° in principal axes of inertia orientation. The proposed technique can effectively validate inertia tensors from novel estimation methods of body segment inertial parameter. Principal axes of inertia orientation should not be neglected when modelling human/animal mechanics. Copyright © 2016 Elsevier Ltd. All rights reserved.
Diffusion tensor imaging tensor shape analysis for assessment of regional white matter differences.
Middleton, Dana M; Li, Jonathan Y; Lee, Hui J; Chen, Steven; Dickson, Patricia I; Ellinwood, N Matthew; White, Leonard E; Provenzale, James M
2017-08-01
Purpose The purpose of this study was to investigate a novel tensor shape plot analysis technique of diffusion tensor imaging data as a means to assess microstructural differences in brain tissue. We hypothesized that this technique could distinguish white matter regions with different microstructural compositions. Methods Three normal canines were euthanized at seven weeks old. Their brains were imaged using identical diffusion tensor imaging protocols on a 7T small-animal magnetic resonance imaging system. We examined two white matter regions, the internal capsule and the centrum semiovale, each subdivided into an anterior and posterior region. We placed 100 regions of interest in each of the four brain regions. Eigenvalues for each region of interest triangulated onto tensor shape plots as the weighted average of three shape metrics at the plot's vertices: CS, CL, and CP. Results The distribution of data on the plots for the internal capsule differed markedly from the centrum semiovale data, thus confirming our hypothesis. Furthermore, data for the internal capsule were distributed in a relatively tight cluster, possibly reflecting the compact and parallel nature of its fibers, while data for the centrum semiovale were more widely distributed, consistent with the less compact and often crossing pattern of its fibers. This indicates that the tensor shape plot technique can depict data in similar regions as being alike. Conclusion Tensor shape plots successfully depicted differences in tissue microstructure and reflected the microstructure of individual brain regions. This proof of principle study suggests that if our findings are reproduced in larger samples, including abnormal white matter states, the technique may be useful in assessment of white matter diseases.
Asselmeyer-Maluga, Torsten
2016-01-01
In this book, leading theorists present new contributions and reviews addressing longstanding challenges and ongoing progress in spacetime physics. In the anniversary year of Einstein's General Theory of Relativity, developed 100 years ago, this collection reflects the subsequent and continuing fruitful development of spacetime theories. The volume is published in honour of Carl Brans on the occasion of his 80th birthday. Carl H. Brans, who also contributes personally, is a creative and independent researcher and one of the founders of the scalar-tensor theory, also known as Jordan-Brans-Dicke theory. In the present book, much space is devoted to scalar-tensor theories. Since the beginning of the 1990s, Brans has worked on new models of spacetime, collectively known as exotic smoothness, a field largely established by him. In this Festschrift, one finds an outstanding and unique collection of articles about exotic smoothness. Also featured are Bell's inequality and Mach's principle. Personal memories and hist...
A MAPLE Package for Energy-Momentum Tensor Assessment in Curved Space-Time
International Nuclear Information System (INIS)
Murariu, Gabriel; Praisler, Mirela
2010-01-01
One of the most interesting problem which remain unsolved, since the birth of the General Theory of Relativity (GR), is the energy-momentum localization. All our reflections are within the Lagrange formalism of the field theory. The concept of the energy-momentum tensor for gravitational interactions has a long history. To find a generally accepted expression, there have been different attempts. This paper is dedicated to the investigation of the energy-momentum problem in the theory of General Relativity. We use Einstein [1], Landau-Lifshitz [2], Bergmann-Thomson [3] and Moller's [4] prescriptions to evaluate energy-momentum distribution. In order to cover the huge volume of computation and, bearing in mind to make a general approaching for different space-time configurations, a MAPLE application to succeed in studying the energy momentum tensor was built. In the second part of the paper for two space-time configuration, the comparative results were presented.
Xu, Ding; Yu, Yongjiang; Zhu, Yunkai; Huang, Tao; Chen, Yaqing; Qi, Jun
2014-04-01
The Prostate-specific antigen (PSA) level is largely used to diagnose prostate cancer (PCa) in last decades. However, its specificity is low in patients with a PSA level ranging from 4.0 to 10.0 ng/ml. This study aims to define the correlation between intravesical prostatic protrusion (IPP) and PSA and to establish a new model to predict PCa. A total of 339 patients order than 45 years examined between October 2010 and June 2012 were enrolled. Eligible patients were recommended for transrectal ultrasonography (TRUS)-guided prostate biopsies after measuring total prostate volume (TPV), tranzisional zone volume (TZV) and IPP. The levels of total PSA (tPSA), free PSA (fPSA) were analyzed by using Hybritech calibrated Access tPSA and fPSA assays. A new mathematical model, named IPP removed PCa predicting score (IRPPS), consists of tPSA, TZV and IPP was established. The predictive accuracy of IRPPS, PSA density (PSAD), %PSA and tPSA were compared using receiver-operator characteristic (ROC) analysis. Eighty-six patients had PSA levels of 4.0-10.0 ng/ml. Twenty of them were diagnosed as PCa. Using ROC curves, the areas under the curve for IRPPS, PSAD and %PSA and tPSA were 0.786, 0.768 and 0.664 and 0.585, respectively. We suggested IPP grade had a significant relationship with serum tPSA levels. The predictive accuracy of IRPPS was higher than the other 3 indictors.
An introduction to tensors and group theory for physicists
Jeevanjee, Nadir
2011-01-01
An Introduction to Tensors and Group Theory for Physicists provides both an intuitive and rigorous approach to tensors and groups and their role in theoretical physics and applied mathematics. A particular aim is to demystify tensors and provide a unified framework for understanding them in the context of classical and quantum physics. Connecting the component formalism prevalent in physics calculations with the abstract but more conceptual formulation found in many mathematical texts, the work will be a welcome addition to the literature on tensors and group theory. Part I of the text begins with linear algebraic foundations, follows with the modern component-free definition of tensors, and concludes with applications to classical and quantum physics through the use of tensor products. Part II introduces abstract groups along with matrix Lie groups and Lie algebras, then intertwines this material with that of Part I by introducing representation theory. Exercises and examples are provided throughout for go...
Theoretical study of lithium clusters by electronic stress tensor
International Nuclear Information System (INIS)
Ichikawa, Kazuhide; Nozaki, Hiroo; Komazawa, Naoya; Tachibana, Akitomo
2012-01-01
We study the electronic structure of small lithium clusters Li_n (n = 2 ∼ 8) using the electronic stress tensor. We find that the three eigenvalues of the electronic stress tensor of the Li clusters are negative and degenerate, just like the stress tensor of liquid. This leads us to propose that we may characterize a metallic bond in terms of the electronic stress tensor. Our proposal is that in addition to the negativity of the three eigenvalues of the electronic stress tensor, their degeneracy characterizes some aspects of the metallic nature of chemical bonding. To quantify the degree of degeneracy, we use the differential eigenvalues of the electronic stress tensor. By comparing the Li clusters and hydrocarbon molecules, we show that the sign of the largest eigenvalue and the differential eigenvalues could be useful indices to evaluate the metallicity or covalency of a chemical bond.
Radiative corrections in a vector-tensor model
International Nuclear Information System (INIS)
Chishtie, F.; Gagne-Portelance, M.; Hanif, T.; Homayouni, S.; McKeon, D.G.C.
2006-01-01
In a recently proposed model in which a vector non-Abelian gauge field interacts with an antisymmetric tensor field, it has been shown that the tensor field possesses no physical degrees of freedom. This formal demonstration is tested by computing the one-loop contributions of the tensor field to the self-energy of the vector field. It is shown that despite the large number of Feynman diagrams in which the tensor field contributes, the sum of these diagrams vanishes, confirming that it is not physical. Furthermore, if the tensor field were to couple with a spinor field, it is shown at one-loop order that the spinor self-energy is not renormalizable, and hence this coupling must be excluded. In principle though, this tensor field does couple to the gravitational field
Generalization of binary tensor product schemes depends upon four parameters
International Nuclear Information System (INIS)
Bashir, R.; Bari, M.; Mustafa, G.
2018-01-01
This article deals with general formulae of parametric and non parametric bivariate subdivision scheme with four parameters. By assigning specific values to those parameters we get some special cases of existing tensor product schemes as well as a new proposed scheme. The behavior of schemes produced by the general formulae is interpolating, approximating and relaxed. Approximating bivariate subdivision schemes produce some other surfaces as compared to interpolating bivariate subdivision schemes. Polynomial reproduction and polynomial generation are desirable properties of subdivision schemes. Capability of polynomial reproduction and polynomial generation is strongly connected with smoothness, sum rules, convergence and approximation order. We also calculate the polynomial generation and polynomial reproduction of 9-point bivariate approximating subdivision scheme. Comparison of polynomial reproduction, polynomial generation and continuity of existing and proposed schemes has also been established. Some numerical examples are also presented to show the behavior of bivariate schemes. (author)
Supergravity tensor calculus in 5D from 6D
International Nuclear Information System (INIS)
Kugo, Taichiro; Ohashi, Keisuke
2000-01-01
Supergravity tensor calculus in five spacetime dimensions is derived by dimensional reduction from the d=6 superconformal tensor calculus. In particular, we obtain an off-shell hypermultiplet in 5D from the on-shell hypermultiplet in 6D. Our tensor calculus retains the dilatation gauge symmetry, so that it is a trivial gauge fixing to make the Einstein term canonical in a general matter-Yang-Mills-supergravity coupled system. (author)
Mesh Denoising based on Normal Voting Tensor and Binary Optimization
Yadav, S. K.; Reitebuch, U.; Polthier, K.
2016-01-01
This paper presents a tensor multiplication based smoothing algorithm that follows a two step denoising method. Unlike other traditional averaging approaches, our approach uses an element based normal voting tensor to compute smooth surfaces. By introducing a binary optimization on the proposed tensor together with a local binary neighborhood concept, our algorithm better retains sharp features and produces smoother umbilical regions than previous approaches. On top of that, we provide a stoc...
Comparison of two global digital algorithms for Minkowski tensor estimation
DEFF Research Database (Denmark)
The geometry of real world objects can be described by Minkowski tensors. Algorithms have been suggested to approximate Minkowski tensors if only a binary image of the object is available. This paper presents implementations of two such algorithms. The theoretical convergence properties...... are confirmed by simulations on test sets, and recommendations for input arguments of the algorithms are given. For increasing resolutions, we obtain more accurate estimators for the Minkowski tensors. Digitisations of more complicated objects are shown to require higher resolutions....
A General Expression for the Quartic Lovelock Tensor
Briggs, C. C.
1997-01-01
A general expression is given for the quartic Lovelock tensor in terms of the Riemann-Christoffel and Ricci curvature tensors and the Riemann curvature scalar for n-dimensional differentiable manifolds having a general linear connection. In addition, expressions are given (in the appendix) for the coefficient of the quartic Lovelock Lagrangian as well as for lower-order Lovelock tensors and Lovelock Lagrangian coefficients.
Energy-momentum tensor in the quantum field theory
International Nuclear Information System (INIS)
Azakov, S.I.
1977-01-01
An energy-momentum tensor in the scalar field theory is built. The tensor must satisfy the finiteness requirement of the Green function. The Green functions can always be made finite by renormalizations in the S-matrix by introducing counter terms into the Hamiltonian (or Lagrangian) of the interaction. Such a renormalization leads to divergencies in the Green functions. Elimination of these divergencies requires the introduction of new counter terms, which must be taken into account in the energy-momentum tensor
Joint Tensor Feature Analysis For Visual Object Recognition.
Wong, Wai Keung; Lai, Zhihui; Xu, Yong; Wen, Jiajun; Ho, Chu Po
2015-11-01
Tensor-based object recognition has been widely studied in the past several years. This paper focuses on the issue of joint feature selection from the tensor data and proposes a novel method called joint tensor feature analysis (JTFA) for tensor feature extraction and recognition. In order to obtain a set of jointly sparse projections for tensor feature extraction, we define the modified within-class tensor scatter value and the modified between-class tensor scatter value for regression. The k-mode optimization technique and the L(2,1)-norm jointly sparse regression are combined together to compute the optimal solutions. The convergent analysis, computational complexity analysis and the essence of the proposed method/model are also presented. It is interesting to show that the proposed method is very similar to singular value decomposition on the scatter matrix but with sparsity constraint on the right singular value matrix or eigen-decomposition on the scatter matrix with sparse manner. Experimental results on some tensor datasets indicate that JTFA outperforms some well-known tensor feature extraction and selection algorithms.
The Topology of Three-Dimensional Symmetric Tensor Fields
Lavin, Yingmei; Levy, Yuval; Hesselink, Lambertus
1994-01-01
We study the topology of 3-D symmetric tensor fields. The goal is to represent their complex structure by a simple set of carefully chosen points and lines analogous to vector field topology. The basic constituents of tensor topology are the degenerate points, or points where eigenvalues are equal to each other. First, we introduce a new method for locating 3-D degenerate points. We then extract the topological skeletons of the eigenvector fields and use them for a compact, comprehensive description of the tensor field. Finally, we demonstrate the use of tensor field topology for the interpretation of the two-force Boussinesq problem.
QCD vacuum tensor susceptibility and properties of transversely polarized mesons
International Nuclear Information System (INIS)
Bakulev, A.P.; Mikhajlov, S.V.
1999-01-01
We re-estimate the tensor susceptibility of QCD vacuum, χ, and to this end, we re-estimate the leptonic decay constants for transversely polarized ρ-, ρ'- and b 1 -mesons. The origin of the susceptibility is analyzed using duality between ρ- and b 1 -channels in a 2-point correlator of tensor currents and disagree with [2] on both OPE expansion and the value of QCD vacuum tensor susceptibility. Using our value for the latter we determine new estimations of nucleon tensor charges related to the first moment of the transverse structure functions h 1 of a nucleon
3D Inversion of SQUID Magnetic Tensor Data
DEFF Research Database (Denmark)
Zhdanov, Michael; Cai, Hongzhu; Wilson, Glenn
2012-01-01
Developments in SQUID-based technology have enabled direct measurement of magnetic tensor data for geophysical exploration. For quantitative interpretation, we introduce 3D regularized inversion for magnetic tensor data. For mineral exploration-scale targets, our model studies show that magnetic...... tensor data have significantly improved resolution compared to magnetic vector data for the same model. We present a case study for the 3D regularized inversion of magnetic tensor data acquired over a magnetite skarn at Tallawang, Australia. The results obtained from our 3D regularized inversion agree...
Superconformal tensor calculus and matter couplings in six dimensions
International Nuclear Information System (INIS)
Bergshoeff, E.; Sezgin, E.; van Proeyen, A.
1989-01-01
Using superconformal tensor calculus the authors construct general interactions of N = 2, d = 6 supergravity with a tensor multiplet and a number of scalar, vector and linear multiplets. They start from the superconformal algebra which they realize on a 40 + 40 Weyl multiplet and on several matter multiplets. A special role is played by the tensor multiplet, which cannot be treated as an ordinary matter multiplet, but leads to a second 40 + 40 version of the Weyl multiplet. The authors also obtain a 48 + 48 off-shell formulation of Poincare supergravity coupled to a tensor multiplet
Superconformal tensor calculus and matter couplings in six dimensions
International Nuclear Information System (INIS)
Bergshoeff, E.; Sezgin, E.; Proeyen, A. van
1986-01-01
Using superconformal tensor calculus we construct general interactions of N = 2, d = 6 supergravity with a tensor multiplet and a number of scalar, vector and linear multiplets. We start from the superconformal algebra which we realize on a 40 + 40 Weyl multiplet and on several matter multiplets. A special role is played by the tensor multiplet, which cannot be treated as an ordinary matter multiplet, but leads to a second 40 + 40 version of the Weyl multiplet. We also obtain a 48 + 48 off-shell formulation of Poincare supergravity coupled to a tensor multiplet. (orig.)
TENSOR MODELING BASED FOR AIRBORNE LiDAR DATA CLASSIFICATION
Directory of Open Access Journals (Sweden)
N. Li
2016-06-01
Full Text Available Feature selection and description is a key factor in classification of Earth observation data. In this paper a classification method based on tensor decomposition is proposed. First, multiple features are extracted from raw LiDAR point cloud, and raster LiDAR images are derived by accumulating features or the “raw” data attributes. Then, the feature rasters of LiDAR data are stored as a tensor, and tensor decomposition is used to select component features. This tensor representation could keep the initial spatial structure and insure the consideration of the neighborhood. Based on a small number of component features a k nearest neighborhood classification is applied.
p-Norm SDD tensors and eigenvalue localization
Directory of Open Access Journals (Sweden)
Qilong Liu
2016-07-01
Full Text Available Abstract We present a new class of nonsingular tensors (p-norm strictly diagonally dominant tensors, which is a subclass of strong H $\\mathcal{H}$ -tensors. As applications of the results, we give a new eigenvalue inclusion set, which is tighter than those provided by Li et al. (Linear Multilinear Algebra 64:727-736, 2016 in some case. Based on this set, we give a checkable sufficient condition for the positive (semidefiniteness of an even-order symmetric tensor.
Prescribed curvature tensor in locally conformally flat manifolds
Pina, Romildo; Pieterzack, Mauricio
2018-01-01
A global existence theorem for the prescribed curvature tensor problem in locally conformally flat manifolds is proved for a special class of tensors R. Necessary and sufficient conditions for the existence of a metric g ¯ , conformal to Euclidean g, are determined such that R ¯ = R, where R ¯ is the Riemannian curvature tensor of the metric g ¯ . The solution to this problem is given explicitly for special cases of the tensor R, including the case where the metric g ¯ is complete on Rn. Similar problems are considered for locally conformally flat manifolds.
The classification of the Ricci tensor in the general theory of relativity
International Nuclear Information System (INIS)
Cormack, W.J.
1979-10-01
A comprehensive classification of the Ricci tensor in General Relativity using several techniques is given and their connection with existing classification studied under the headings; canonical forms for the Ricci tensor, invariant 2-spaces in the classification of the Ricci tensor, Riemannian curvature and the classification of the Riemann and Ricci tensors, and spinor classifications of the Ricci tensor. (U.K.)
A diffusion tensor imaging tractography algorithm based on Navier-Stokes fluid mechanics.
Hageman, Nathan S; Toga, Arthur W; Narr, Katherine L; Shattuck, David W
2009-03-01
We introduce a fluid mechanics based tractography method for estimating the most likely connection paths between points in diffusion tensor imaging (DTI) volumes. We customize the Navier-Stokes equations to include information from the diffusion tensor and simulate an artificial fluid flow through the DTI image volume. We then estimate the most likely connection paths between points in the DTI volume using a metric derived from the fluid velocity vector field. We validate our algorithm using digital DTI phantoms based on a helical shape. Our method segmented the structure of the phantom with less distortion than was produced using implementations of heat-based partial differential equation (PDE) and streamline based methods. In addition, our method was able to successfully segment divergent and crossing fiber geometries, closely following the ideal path through a digital helical phantom in the presence of multiple crossing tracts. To assess the performance of our algorithm on anatomical data, we applied our method to DTI volumes from normal human subjects. Our method produced paths that were consistent with both known anatomy and directionally encoded color images of the DTI dataset.
Symmetric Topological Phases and Tensor Network States
Jiang, Shenghan
Classification and simulation of quantum phases are one of main themes in condensed matter physics. Quantum phases can be distinguished by their symmetrical and topological properties. The interplay between symmetry and topology in condensed matter physics often leads to exotic quantum phases and rich phase diagrams. Famous examples include quantum Hall phases, spin liquids and topological insulators. In this thesis, I present our works toward a more systematically understanding of symmetric topological quantum phases in bosonic systems. In the absence of global symmetries, gapped quantum phases are characterized by topological orders. Topological orders in 2+1D are well studied, while a systematically understanding of topological orders in 3+1D is still lacking. By studying a family of exact solvable models, we find at least some topological orders in 3+1D can be distinguished by braiding phases of loop excitations. In the presence of both global symmetries and topological orders, the interplay between them leads to new phases termed as symmetry enriched topological (SET) phases. We develop a framework to classify a large class of SET phases using tensor networks. For each tensor class, we can write down generic variational wavefunctions. We apply our method to study gapped spin liquids on the kagome lattice, which can be viewed as SET phases of on-site symmetries as well as lattice symmetries. In the absence of topological order, symmetry could protect different topological phases, which are often referred to as symmetry protected topological (SPT) phases. We present systematic constructions of tensor network wavefunctions for bosonic symmetry protected topological (SPT) phases respecting both onsite and spatial symmetries.
Holographic duality from random tensor networks
Energy Technology Data Exchange (ETDEWEB)
Hayden, Patrick; Nezami, Sepehr; Qi, Xiao-Liang; Thomas, Nathaniel; Walter, Michael; Yang, Zhao [Stanford Institute for Theoretical Physics, Department of Physics, Stanford University,382 Via Pueblo, Stanford, CA 94305 (United States)
2016-11-02
Tensor networks provide a natural framework for exploring holographic duality because they obey entanglement area laws. They have been used to construct explicit toy models realizing many of the interesting structural features of the AdS/CFT correspondence, including the non-uniqueness of bulk operator reconstruction in the boundary theory. In this article, we explore the holographic properties of networks of random tensors. We find that our models naturally incorporate many features that are analogous to those of the AdS/CFT correspondence. When the bond dimension of the tensors is large, we show that the entanglement entropy of all boundary regions, whether connected or not, obey the Ryu-Takayanagi entropy formula, a fact closely related to known properties of the multipartite entanglement of assistance. We also discuss the behavior of Rényi entropies in our models and contrast it with AdS/CFT. Moreover, we find that each boundary region faithfully encodes the physics of the entire bulk entanglement wedge, i.e., the bulk region enclosed by the boundary region and the minimal surface. Our method is to interpret the average over random tensors as the partition function of a classical ferromagnetic Ising model, so that the minimal surfaces of Ryu-Takayanagi appear as domain walls. Upon including the analog of a bulk field, we find that our model reproduces the expected corrections to the Ryu-Takayanagi formula: the bulk minimal surface is displaced and the entropy is augmented by the entanglement of the bulk field. Increasing the entanglement of the bulk field ultimately changes the minimal surface behavior topologically, in a way similar to the effect of creating a black hole. Extrapolating bulk correlation functions to the boundary permits the calculation of the scaling dimensions of boundary operators, which exhibit a large gap between a small number of low-dimension operators and the rest. While we are primarily motivated by the AdS/CFT duality, the main
A supersymmetric SYK-like tensor model
Energy Technology Data Exchange (ETDEWEB)
Peng, Cheng; Spradlin, Marcus; Volovich, Anastasia [Department of Physics, Brown University,Providence, RI, 02912 (United States)
2017-05-11
We consider a supersymmetric SYK-like model without quenched disorder that is built by coupling two kinds of fermionic N=1 tensor-valued superfields, “quarks” and “mesons”. We prove that the model has a well-defined large-N limit in which the (s)quark 2-point functions are dominated by mesonic “melon” diagrams. We sum these diagrams to obtain the Schwinger-Dyson equations and show that in the IR, the solution agrees with that of the supersymmetric SYK model.
Tensor glueball-meson mixing phenomenology
International Nuclear Information System (INIS)
Burakovsky, L.; Page, P.R.
2000-01-01
The overpopulated isoscalar tensor states are sifted using Schwinger-type mass relations. Two solutions are found: one where the glueball is the f J (2220), and one where the glueball is more distributed, with f 2 (1820) having the largest component. The f 2 (1565) and f J (1710) cannot be accommodated as glueball-(hybrid) meson mixtures in the absence of significant coupling to decay channels. f 2 '(1525)→ππ is in agreement with experiment. The f J (2220) decays neither flavour democratically nor is narrow. (orig.)
Tensor Network Wavefunctions for Topological Phases
Ware, Brayden Alexander
The combination of quantum effects and interactions in quantum many-body systems can result in exotic phases with fundamentally entangled ground state wavefunctions--topological phases. Topological phases come in two types, both of which will be studied in this thesis. In topologically ordered phases, the pattern of entanglement in the ground state wavefunction encodes the statistics of exotic emergent excitations, a universal indicator of a phase that is robust to all types of perturbations. In symmetry protected topological phases, the entanglement instead encodes a universal response of the system to symmetry defects, an indicator that is robust only to perturbations respecting the protecting symmetry. Finding and creating these phases in physical systems is a motivating challenge that tests all aspects--analytical, numerical, and experimental--of our understanding of the quantum many-body problem. Nearly three decades ago, the creation of simple ansatz wavefunctions--such as the Laughlin fractional quantum hall state, the AKLT state, and the resonating valence bond state--spurred analytical understanding of both the role of entanglement in topological physics and physical mechanisms by which it can arise. However, quantitative understanding of the relevant phase diagrams is still challenging. For this purpose, tensor networks provide a toolbox for systematically improving wavefunction ansatz while still capturing the relevant entanglement properties. In this thesis, we use the tools of entanglement and tensor networks to analyze ansatz states for several proposed new phases. In the first part, we study a featureless phase of bosons on the honeycomb lattice and argue that this phase can be topologically protected under any one of several distinct subsets of the crystalline lattice symmetries. We discuss methods of detecting such phases with entanglement and without. In the second part, we consider the problem of constructing fixed-point wavefunctions for
Scalar-tensor cosmology with cosmological constant
International Nuclear Information System (INIS)
Maslanka, K.
1983-01-01
The equations of scalar-tensor theory of gravitation with cosmological constant in the case of homogeneous and isotropic cosmological model can be reduced to dynamical system of three differential equations with unknown functions H=R/R, THETA=phi/phi, S=e/phi. When new variables are introduced the system becomes more symmetrical and cosmological solutions R(t), phi(t), e(t) are found. It is shown that when cosmological constant is introduced large class of solutions which depend also on Dicke-Brans parameter can be obtained. Investigations of these solutions give general limits for cosmological constant and mean density of matter in plane model. (author)
Tensor Decompositions for Learning Latent Variable Models
2012-12-08
and eigenvectors of tensors is generally significantly more complicated than their matrix counterpart (both algebraically [Qi05, CS11, Lim05] and...The reduction First, let W ∈ Rd×k be a linear transformation such that M2(W,W ) = W M2W = I where I is the k × k identity matrix (i.e., W whitens ...approximate the whitening matrix W ∈ Rd×k from second-moment matrix M2 ∈ Rd×d. To do this, one first multiplies M2 by a random matrix R ∈ Rd×k′ for some k′ ≥ k
Electrical conductivity tensor of an irradiated metal
International Nuclear Information System (INIS)
Corciovei, A.; Dumitru, R.D.
1979-01-01
A method to calculate the electrical conductivity tensor of an irradiated metal is presented. The proposed method relies on the use of the Kubo formula, evaluated by a perturbation method. The one electron Hamiltonian is written as a sum of two terms: the Hamiltonian of the conduction electrons moving in a periodic lattice and the perturbation, namely, the scattering potential due to the irradiation defects of the ideal crystal. Then, the lowest order of the conductivity is determined by the lowest order of the Laplace transform of the current. An integral equation is written for this last quantity. (author)
A supersymmetric SYK-like tensor model
International Nuclear Information System (INIS)
Peng, Cheng; Spradlin, Marcus; Volovich, Anastasia
2017-01-01
We consider a supersymmetric SYK-like model without quenched disorder that is built by coupling two kinds of fermionic N=1 tensor-valued superfields, “quarks” and “mesons”. We prove that the model has a well-defined large-N limit in which the (s)quark 2-point functions are dominated by mesonic “melon” diagrams. We sum these diagrams to obtain the Schwinger-Dyson equations and show that in the IR, the solution agrees with that of the supersymmetric SYK model.
Physical states in the canonical tensor model from the perspective of random tensor networks
Energy Technology Data Exchange (ETDEWEB)
Narain, Gaurav [The Institute for Fundamental Study “The Tah Poe Academia Institute”,Naresuan University, Phitsanulok 65000 (Thailand); Sasakura, Naoki [Yukawa Institute for Theoretical Physics,Kyoto University, Kyoto 606-8502 (Japan); Sato, Yuki [National Institute for Theoretical Physics,School of Physics and Centre for Theoretical Physics,University of the Witwartersrand, WITS 2050 (South Africa)
2015-01-07
Tensor models, generalization of matrix models, are studied aiming for quantum gravity in dimensions larger than two. Among them, the canonical tensor model is formulated as a totally constrained system with first-class constraints, the algebra of which resembles the Dirac algebra of general relativity. When quantized, the physical states are defined to be vanished by the quantized constraints. In explicit representations, the constraint equations are a set of partial differential equations for the physical wave-functions, which do not seem straightforward to be solved due to their non-linear character. In this paper, after providing some explicit solutions for N=2,3, we show that certain scale-free integration of partition functions of statistical systems on random networks (or random tensor networks more generally) provides a series of solutions for general N. Then, by generalizing this form, we also obtain various solutions for general N. Moreover, we show that the solutions for the cases with a cosmological constant can be obtained from those with no cosmological constant for increased N. This would imply the interesting possibility that a cosmological constant can always be absorbed into the dynamics and is not an input parameter in the canonical tensor model. We also observe the possibility of symmetry enhancement in N=3, and comment on an extension of Airy function related to the solutions.
Cornu, Jean-Nicolas; Cancel-Tassin, Geraldine; Cox, David G; Roupret, Morgan; Koutlidis, Nicolas; Bigot, Pierre; Valeri, Antoine; Ondet, Valerie; Gaffory, Cécile; Fournier, Georges; Azzouzi, Abdel-Rahmene; Cormier, Luc; Cussenot, Olivier
2016-07-01
Prostate-specific antigen (PSA) is still the cornerstone of prostate cancer (PCa) screening and diagnosis in both research and current clinical practice. Inaccuracy of PSA is partly due to the influence of a number of genetic, clinical, and biological factors modifying PSA blood levels. In the present study, we detailed the respective influence of each factor among age, body mass index (BMI), prostate volume, and five single-nucleotide polymorphisms-rs10788160 (10q26), rs10993994 (10q11), rs11067228 (12q24), rs17632542 (19q13.33), and rs2928679 (8p21)-on PSA values in a cohort of 1374 men without PCa. Our results show that genetic factors, when risk variants are combined, influence PSA levels with an effect size similar to that of BMI. Taken together, the respective correlations of clinical parameters and genetic parameters would make it possible to correct and adjust PSA values more effectively in each individual. These results establish the basis to understand and implement a more personalised approach for the interpretation of PSA blood levels in the context of PCa screening and diagnosis. Prostate-specific antigen (PSA) values in an individual may vary according to genetic predisposition. The effect size of this variation can be significant, comparable with those resulting from clinical characteristics. Personalised PSA testing should take this into account. Copyright © 2016 European Association of Urology. Published by Elsevier B.V. All rights reserved.
International Nuclear Information System (INIS)
Goret, C.
1990-12-01
Several technics of imaging (IRM, image scanners, tomoscintigraphy, echography) give numerical informations presented by means of a stack of parallel cross-sectional images. Since many years, 3-D mathematical tools have been developed and allow the 3 D images synthesis of surfaces. In first part, we give the technics of numerical volume exploitation and their medical applications to diagnosis and therapy. The second part is about a continuous modelling of the volume with a tensor product of cubic splines. We study the characteristics of this representation and its clinical validation. Finally, we treat of the problem of surface visualization of objects contained in the volume. The results show the interest of this model and allow to propose specifications for 3-D workstation realization [fr
Emergent symmetries in the canonical tensor model
Obster, Dennis; Sasakura, Naoki
2018-04-01
The canonical tensor model (CTM) is a tensor model proposing a classically and quantum mechanically consistent description of gravity, formulated as a first-class constraint system with structural similarities to the ADM formalism of general relativity. The classical CTM produces a general relativistic system in a formal continuum limit, the emergence of which should be explained by the quantum CTM. In this paper we study the symmetry properties of a wave function that exactly solves the quantum constraints of the CTM. We have found that it has strong peaks at configurations invariant under some Lie groups, as predicted by a mechanism described in our previous paper. A surprising result is the preference for configurations invariant not only under Lie groups with positive definite signature, but also with Lorentzian signature. Such symmetries could characterize the global structures of spacetimes, and our results are encouraging towards showing spacetime emergence in the CTM. To verify the asymptotic convergence of the wave function we have also analyzed the asymptotic behavior, which for the most part seems to be well under control.
Quantum chaos and holographic tensor models
Energy Technology Data Exchange (ETDEWEB)
Krishnan, Chethan [Center for High Energy Physics, Indian Institute of Science,Bangalore 560012 (India); Sanyal, Sambuddha [International Center for Theoretical Sciences, Tata Institute of Fundamental Research,Bangalore 560089 (India); Subramanian, P.N. Bala [Center for High Energy Physics, Indian Institute of Science,Bangalore 560012 (India)
2017-03-10
A class of tensor models were recently outlined as potentially calculable examples of holography: their perturbative large-N behavior is similar to the Sachdev-Ye-Kitaev (SYK) model, but they are fully quantum mechanical (in the sense that there is no quenched disorder averaging). These facts make them intriguing tentative models for quantum black holes. In this note, we explicitly diagonalize the simplest non-trivial Gurau-Witten tensor model and study its spectral and late-time properties. We find parallels to (a single sample of) SYK where some of these features were recently attributed to random matrix behavior and quantum chaos. In particular, the spectral form factor exhibits a dip-ramp-plateau structure after a running time average, in qualitative agreement with SYK. But we also observe that even though the spectrum has a unique ground state, it has a huge (quasi-?)degeneracy of intermediate energy states, not seen in SYK. If one ignores the delta function due to the degeneracies however, there is level repulsion in the unfolded spacing distribution hinting chaos. Furthermore, there are gaps in the spectrum. The system also has a spectral mirror symmetry which we trace back to the presence of a unitary operator with which the Hamiltonian anticommutes. We use it to argue that to the extent that the model exhibits random matrix behavior, it is controlled not by the Dyson ensembles, but by the BDI (chiral orthogonal) class in the Altland-Zirnbauer classification.
Stress tensor fluctuations in de Sitter spacetime
Energy Technology Data Exchange (ETDEWEB)
Pérez-Nadal, Guillem; Verdaguer, Enric [Departament de Física Fonamental and Institut de Ciències del Cosmos, Universitat de Barcelona, Av. Diagonal 647, 08028 Barcelona (Spain); Roura, Albert, E-mail: guillem@ffn.ub.es, E-mail: albert.roura@aei.mpg.de, E-mail: enric.verdaguer@ub.edu [Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut, Am Mühlenberg 1, 14476 Golm (Germany)
2010-05-01
The two-point function of the stress tensor operator of a quantum field in de Sitter spacetime is calculated for an arbitrary number of dimensions. We assume the field to be in the Bunch-Davies vacuum, and formulate our calculation in terms of de Sitter-invariant bitensors. Explicit results for free minimally coupled scalar fields with arbitrary mass are provided. We find long-range stress tensor correlations for sufficiently light fields (with mass m much smaller than the Hubble scale H), namely, the two-point function decays at large separations like an inverse power of the physical distance with an exponent proportional to m{sup 2}/H{sup 2}. In contrast, we show that for the massless case it decays at large separations like the fourth power of the physical distance. There is thus a discontinuity in the massless limit. As a byproduct of our work, we present a novel and simple geometric interpretation of de Sitter-invariant bitensors for pairs of points which cannot be connected by geodesics.
Quantum chaos and holographic tensor models
International Nuclear Information System (INIS)
Krishnan, Chethan; Sanyal, Sambuddha; Subramanian, P.N. Bala
2017-01-01
A class of tensor models were recently outlined as potentially calculable examples of holography: their perturbative large-N behavior is similar to the Sachdev-Ye-Kitaev (SYK) model, but they are fully quantum mechanical (in the sense that there is no quenched disorder averaging). These facts make them intriguing tentative models for quantum black holes. In this note, we explicitly diagonalize the simplest non-trivial Gurau-Witten tensor model and study its spectral and late-time properties. We find parallels to (a single sample of) SYK where some of these features were recently attributed to random matrix behavior and quantum chaos. In particular, the spectral form factor exhibits a dip-ramp-plateau structure after a running time average, in qualitative agreement with SYK. But we also observe that even though the spectrum has a unique ground state, it has a huge (quasi-?)degeneracy of intermediate energy states, not seen in SYK. If one ignores the delta function due to the degeneracies however, there is level repulsion in the unfolded spacing distribution hinting chaos. Furthermore, there are gaps in the spectrum. The system also has a spectral mirror symmetry which we trace back to the presence of a unitary operator with which the Hamiltonian anticommutes. We use it to argue that to the extent that the model exhibits random matrix behavior, it is controlled not by the Dyson ensembles, but by the BDI (chiral orthogonal) class in the Altland-Zirnbauer classification.