Rodríguez-Vázquez, Jose Francisco; Honkura, Yohei; Katori, Yukio; Murakami, Gen; Abe, Hiroshi
2017-01-01
The existence of hard tissue pulleys that act to change the direction of a muscle insertion tendon is well known in the human body. These include (1) the trochlea for the extraocular obliquus superior muscle, (2) the pterygoid hamulus for the tensor veli palatini muscle, (3) the deep sulcus on the plantar aspect of the cuboid bone for the peroneus longus tendon, (4) the lesser sciatic notch for the obturator internus muscle, and (5) the bony trochleariformis process for the tensor tympani muscle tendon. In addition, (6) the stapedius muscle tendon shows a lesser or greater angulation at the pyramidal eminence of the temporal bone. Our recent studies have shown that the development of pulleys Nos. 1 and 2 can be explained by a change in the topographical relationship between the pulley and the tendon, that of pulley No. 3 by the rapidly growing calcaneus pushing the tendon, and that of pulley No. 4 by migration of the insertion along the sciatic nerve and gluteus medius tendon. Therefore, in Nos. 1-4, an initially direct tendon curves secondarily and obtains an attachment to the pulley. In case No. 6, the terminal part of the stapedius tendon originates secondarily from the interzone mesenchymal tissue of the incudostapedial joint. In the case of pulley No. 5, we newly demonstrated that its initial phase of development was similar to No. 6, but the tensor tympani tendon achieved a right-angled turn under guidance by a specific fibrous tissue and it migrated along the growing malleus manubrium. Copyright Â© 2016 Elsevier GmbH. All rights reserved.
Rodríguez-Vázquez, José Francisco; Sakiyama, Koji; Abe, Hiroshi; Amano, Osamu; Murakami, Gen
2016-04-01
Some researchers contend that in adults the tensor tympani muscle (TT) connects with the tensor veli palatini muscle (TVP) by an intermediate tendon, in disagreement with the other researchers. To resolve this controversy, we examined serial sections of 50 human embryos and fetuses at 6-17 weeks of development. At 6 weeks, in the first pharyngeal arch, a mesenchymal connection was found first to divide a single anlage into the TT and TVP. At and after 7 weeks, the TT was connected continuously with the TVP by a definite tendinous tissue mediolaterally crossing the pharyngotympanic tube. At 11 weeks another fascia was visible covering the cranial and lateral sides of the tube. This "gonial fascia" had two thickened borders: the superior one corresponded to a part of the connecting tendon between the TT and TVP; the inferior one was a fibrous band ending at the os goniale near the lateral end of the TVP. In association with the gonial fascia, the fetal TT and TVP seemed to provide a functional complex. The TT-TVP complex might first help elevate the palatal shelves in association with the developing tongue. Next, the tubal passage, maintained by contraction of the muscle complex, seems to facilitate the removal of loose mesenchymal tissues from the tympanic cavity. Third, the muscle complex most likely determined the final morphology of the pterygoid process. Consequently, despite the controversial morphologies in adults, the TT and TVP seemed to make a single digastric muscle acting for the morphogenesis of the cranial base. © 2016 Wiley Periodicals, Inc.
Albu, Silviu; Babighian, Gregorio; Amadori, Maurizio; Trabalzini, Franco
2015-12-01
This study aims to compare the outcomes of patients with Meniere's disease submitted to either endolymphatic mastoid shunt (ES) or tenotomy of the stapedius and tensor tympani muscles (TSTM). This is a retrospective chart review of patients treated with ES or TSTM between 2000 and 2010 and followed up for at least 12 months. The main outcomes were represented by: (1) vertigo class, hearing stage and functional level according to the American Academy of Otolaryngology-Head and Neck Surgery criteria; (2) adjustment of dizziness handicap inventory (DHI) and (3) complete and substantial vertigo control using the Kaplan-Meier survival method. Sixty-three patients met the inclusion criteria: 34 underwent ES and 29 TSTM. The baseline demographic characteristics, the hearing stage, the functional level, the DHI and hearing levels were not different between the two groups. No significant difference in vertigo class was demonstrated: 66 % of TSTM patients attained class A compared to 44 % in the ES group (p = 0.14). Kaplan-Meier survival curves specific to class A showed significant differences, favoring TSTM (log-rank test, p = 0.022). TSTM patients demonstrated significantly improved functional level (p = 0.0004) and improved DHI scores (p = 0.001). Eight ES patients (25 %) demanded a second surgical attempt compared to none in the TSTM. Aural fullness was significantly improved in TSTM group (p = 0.01), while the difference in tinnitus improvement was non-significant. Hearing preservation was significantly better in TSTM group (p = 0.001). TSTM is a safe surgical procedure, with significant vertigo control rates, and important hearing preservation rates. More patients and longer follow-up are needed to support our preliminary findings.
Tonic tensor tympani syndrome in tinnitus and hyperacusis patients: A multi-clinic prevalence study
Directory of Open Access Journals (Sweden)
Myriam Westcott
2013-01-01
Full Text Available Tonic tensor tympani syndrome (TTTS is an involuntary, anxiety-based condition where the reflex threshold for tensor tympani muscle activity is reduced, causing a frequent spasm. This can trigger aural symptoms from tympanic membrane tension, middle ear ventilation alterations and trigeminal nerve irritability. TTTS is considered to cause the distinctive symptoms of acoustic shock (AS, which can develop after exposure to an unexpected loud sound perceived as highly threatening. Hyperacusis is a dominant AS symptom. Aural pain/blockage without underlying pathology has been noted in tinnitus and hyperacusis patients, without wide acknowledgment. This multiclinic study investigated the prevalence of TTTS symptoms and AS in tinnitus and hyperacusis patients. This study included consecutive patients with tinnitus and/or hyperacusis seen in multiple clinics. Data collected: Symptoms consistent with TTTS (pain/numbness/burning in and around the ear; aural "blockage"; mild vertigo/nausea; "muffled" hearing; tympanic flutter; headache; onset or exacerbation from exposure to loud/intolerable sounds; tinnitus/hyperacusis severity. All patients were medically cleared of underlying pathology, which could cause these symptoms. 60.0% of the total sample (345 patients, 40.6% of tinnitus only patients, 81.1% of hyperacusis patients had ≥1 symptoms (P < 0.001. 68% of severe tinnitus patients, 91.3% of severe hyperacusis patients had ≥1 symptoms (P < 0.001. 19.7% (68/345 of patients in the total sample had AS. 83.8% of AS patients had hyperacusis, 41.2% of non-AS patients had hyperacusis (P < 0.001. The high prevalence of TTTS symptoms suggests they readily develop in tinnitus patients, more particularly with hyperacusis. Along with AS, they should be routinely investigated in history-taking.
Directory of Open Access Journals (Sweden)
Logan S. W. Bale
2017-01-01
Full Text Available Muscle variants are routinely encountered in the dissection laboratory and in clinical practice and therefore anatomists and clinicians need to be aware of their existence. Here we describe two different accessory muscles identified while performing educational dissection of a 51-year-old male cadaver. Tensor fasciae suralis, a rare muscle variant, was identified bilaterally and accessory flexor digitorum longus, a more common muscle variant, was present unilaterally. Tensor fasciae suralis and accessory flexor digitorum longus are clinically relevant muscle variants. To our knowledge, the coexistence of tensor fasciae suralis and accessory flexor digitorum longus in the same individual has not been reported in either cadaveric or imaging studies.
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.
Diffusion tensor tractography reveals muscle reconnection during axolotl limb regeneration.
Directory of Open Access Journals (Sweden)
Cheng-Han Wu
Full Text Available Axolotls have amazing ability to regenerate their lost limbs. Our previous works showed that after amputation the remnant muscle ends remained at their original location whilst sending satellite cells into the regenerating parts to develop into early muscle fibers in the late differentiation stage. The parental and the newly formed muscle fibers were not connected until very late stage. The present study used non-invasive diffusion tensor imaging (DTI to monitor weekly axolotl upper arm muscles after amputation of their upper arms. DTI tractography showed that the regenerating muscle fibers became visible at 9-wpa (weeks post amputation, but a gap was observed between the regenerating and parental muscles. The gap was filled at 10-wpa, indicating reconnection of the fibers of both muscles. This was confirmed by histology. The DTI results indicate that 23% of the muscle fibers were reconnected at 10-wpa. In conclusion, DTI can be used to visualize axolotls' skeletal muscles and the results of muscle reconnection were in accordance with our previous findings. This non-invasive technique will allow researchers to identify the timeframe in which muscle fiber reconnection takes place and thus enable the study of the mechanisms underlying this reconnection.
MR imaging and ultrasonographic findings of tensor fasciae suralis muscle: A case report
Energy Technology Data Exchange (ETDEWEB)
Kim, Keun Ho; Shim, Jae Chan; Lee, Ghi Jai; Lee, Kyoung Eun; Kim, Ho Kyun; Suh, Jung Ho [Dept. of Radiology, Seoul Paik Hospital, Inje University College of Medicine, Seoul (Korea, Republic of)
2015-10-15
The tensor fasciae suralis muscle is a very rare anomalous muscle located in the popliteal region. This anatomic variation has been reported often through cadaver studies. However, there are only a few radiologic reports of this entity. We presented a case of tensor fasciae suralis muscle detected as an incidental finding in magnetic resonance imaging and ultrasound.
Walby, A P
1985-01-01
The length and cross-sectional height of the scala tympani are relevant to the design of cochlear implants. The lengths and heights of the scalae tympani in ten pairs of serially sectioned temporal bones were measured by an adaptation of the serial section method of cochlear reconstruction. The study found the middle segments of individual pairs of scalae tympani to be very similar in height, but each pair varied slightly from other pairs. The height decreased overall from the base to the apex, but there was a small expansion at the junction of the basal and middle turns where the interscalar septum originated. The theoretical relationships of different diameter electrodes to the organ of Corti were plotted for one cochlea. The size of the electrode and the path it followed were shown in theory to alter considerably its position in relation to the organ of Corti.
Determination of mouse skeletal muscle architecture using three dimensional diffusion tensor imaging
Heemskerk, A.M.; Strijkers, G.J.; Vilanova, A.; Drost, M.R.; Nicolaij, K.
2005-01-01
Muscle architecture is the main determinant of the mechanical behavior of skeletal muscles. This study explored the feasibility of diffusion tensor imaging (DTI) and fiber tracking to noninvasively determine the in vivo three-dimensional (3D) architecture of skeletal muscle in mouse hind leg. In six
Determination of mouse skeletal muscle architecture using three-dimensional diffusion tensor imaging
Heemskerk, Anneriet M.; Strijkers, Gustav J.; Vilanova, Anna; Drost, Maarten R.; Nicolay, Klaas
2005-01-01
Muscle architecture is the main determinant of the mechanical behavior of skeletal muscles. This study explored the feasibility of diffusion tensor imaging (DTI) and fiber tracking to noninvasively determine the in vivo three-dimensional (3D) architecture of skeletal muscle in mouse hind leg. In six
International Nuclear Information System (INIS)
Montet, Xavier; Mauget, Denis; Sandoz, Alain; Martinoli, Carlo; Bianchi, Stefano
2002-01-01
A 20-year-old white man presented with a localized unilateral swelling in the popliteal fossa. Ultrasound (US) showed the presence of an accessory muscle, the tensor fasciae suralis. The muscle was located in the proximal portion of the popliteal fossa, superficial to the medial head of the gastrocnemius. Its long tendon extended inferiorly to join the Achilles tendon. Magnetic resonance images correlated well with the US findings, confirming the diagnosis. Tensor fasciae suralis muscle is a rare cause of popliteal swelling and must be differentiated from other masses. Both US and magnetic resonance imaging can diagnose it but we suggest US as the first-line technique in its evaluation. (orig.)
Diffusion tensor imaging of the human skeletal muscle: contributions and applications
International Nuclear Information System (INIS)
Neji, Radhouene
2010-01-01
In this thesis, we present several techniques for the processing of diffusion tensor images. They span a wide range of tasks such as estimation and regularization, clustering and segmentation, as well as registration. The variational framework proposed for recovering a tensor field from noisy diffusion weighted images exploits the fact that diffusion data represent populations of fibers and therefore each tensor can be reconstructed using a weighted combination of tensors lying in its neighborhood. The segmentation approach operates both at the voxel and the fiber tract levels. It is based on the use of Mercer kernels over Gaussian diffusion probabilities to model tensor similarity and spatial interactions, allowing the definition of fiber metrics that combine information from spatial localization and diffusion tensors. Several clustering techniques can be subsequently used to segment tensor fields and fiber tractographies. Moreover, we show how to develop supervised extensions of these algorithms. The registration algorithm uses probability kernels in order to match moving and target images. The deformation consistency is assessed using the distortion induced in the distances between neighboring probabilities. Discrete optimization is used to seek an optimum of the defined objective function. The experimental validation is done over a dataset of manually segmented diffusion images of the lower leg muscle for healthy and diseased subjects. The results of the techniques developed throughout this thesis are promising. (author)
Heidsieck, David S P; Smarius, Bram J A; Oomen, Karin P Q; Breugem, Corstiaan C
2016-09-01
Otitis media with effusion is common in infants with an unrepaired cleft palate. Although its prevalence is reduced after cleft surgery, many children continue to suffer from middle ear problems during childhood. While the tensor veli palatini muscle is thought to be involved in middle ear ventilation, evidence about its exact anatomy, function, and role in cleft palate surgery is limited. This study aimed to perform a thorough review of the literature on (1) the role of the tensor veli palatini muscle in the Eustachian tube opening and middle ear ventilation, (2) anatomical anomalies in cleft palate infants related to middle ear disease, and (3) their implications for surgical techniques used in cleft palate repair. A literature search on the MEDLINE database was performed using a combination of the keywords "tensor veli palatini muscle," "Eustachian tube," "otitis media with effusion," and "cleft palate." Several studies confirm the important role of the tensor veli palatini muscle in the Eustachian tube opening mechanism. Maintaining the integrity of the tensor veli palatini muscle during cleft palate surgery seems to improve long-term otological outcome. However, anatomical variations in cleft palate children may alter the effect of the tensor veli palatini muscle on the Eustachian tube's dilatation mechanism. More research is warranted to clarify the role of the tensor veli palatini muscle in cleft palate-associated Eustachian tube dysfunction and development of middle ear problems. Optimized surgical management of cleft palate could potentially reduce associated middle ear problems.
Abductor tendon tears are associated with hypertrophy of the tensor fasciae latae muscle.
Sutter, Reto; Kalberer, Fabian; Binkert, Christoph A; Graf, Nicole; Pfirrmann, Christian W A; Gutzeit, Andreas
2013-05-01
To evaluate the association between hypertrophy of the tensor fasciae latae muscle and abductor tendon tears. Thirty-five patients who underwent MRI of the abductor tendons of the hip were included in this retrospective study. A subgroup of 18 patients was examined bilaterally. The area of the tensor fasciae latae muscle and the area of the sartorius muscle (size reference) were quantified at the level of the femoral head, and a ratio was calculated. Two radiologists assessed the integrity of the gluteus medius and minimus tendon in consensus. Data were analyzed with a Mann-Whitney U test. Sixteen out of 35 patients (46 %) had a tear of the gluteus medius or minimus tendon. The ratio of the area of the tensor fasciae latae to the sartorius muscle was significantly higher (p = .028) in the group with an abductor tendon tear (median 2.25; Interquartile Range [IQR] = 1.97-3.21) compared to the group without any tears (median 1.91; IQR = 1.52-2.26). The bilateral subanalysis showed that in patients without a tear, the ratio of the two areas did not differ between each side (p = .966), with a median of 1.54 (primary side) and 1.76 (contralateral side). In patients with an abductor tendon tear the ratio was significantly higher (p = .031) on the side with a tear (median 2.81) compared to the contralateral healthy side (1.67). Patients with abductor tendon tears showed hypertrophy of the tensor fasciae latae muscle when compared to the contralateral healthy side and to patients without a tear.
Muscle changes detected with diffusion-tensor imaging after long-distance running.
Froeling, Martijn; Oudeman, Jos; Strijkers, Gustav J; Maas, Mario; Drost, Maarten R; Nicolay, Klaas; Nederveen, Aart J
2015-02-01
To develop a protocol for diffusion-tensor imaging (DTI) of the complete upper legs and to demonstrate feasibility of detection of subclinical sports-related muscle changes in athletes after strenuous exercise, which remain undetected by using conventional T2-weighted magnetic resonance (MR) imaging with fat suppression. The research was approved by the institutional ethics committee review board, and the volunteers provided written consent before the study. Five male amateur long-distance runners underwent an MR examination (DTI, T1-weighted MR imaging, and T2-weighted MR imaging with fat suppression) of both upper legs 1 week before, 2 days after, and 3 weeks after they participated in a marathon. The tensor eigenvalues (λ1, λ2, and λ3), the mean diffusivity, and the fractional anisotropy (FA) were derived from the DTI data. Data per muscle from the three time-points were compared by using a two-way mixed-design analysis of variance with a Bonferroni posthoc test. The DTI protocol allowed imaging of both complete upper legs with adequate signal-to-noise ratio and within a 20-minute imaging time. After the marathon, T2-weighted MR imaging revealed grade 1 muscle strains in nine of the 180 investigated muscles. The three eigenvalues, mean diffusivity, and FA were significantly increased (P DTI measurements of the upper legs was developed that fully included frequently injured muscles, such as hamstrings, in one single imaging session. This study also revealed changes in DTI parameters that over time were not revealed by qualitative T2-weighted MR imaging with fat suppression. © RSNA, 2014.
Heemskerk, Anneriet M; Strijkers, Gustav J; Vilanova, Anna; Drost, Maarten R; Nicolay, Klaas
2005-06-01
Muscle architecture is the main determinant of the mechanical behavior of skeletal muscles. This study explored the feasibility of diffusion tensor imaging (DTI) and fiber tracking to noninvasively determine the in vivo three-dimensional (3D) architecture of skeletal muscle in mouse hind leg. In six mice, the hindlimb was imaged with a diffusion-weighted (DW) 3D fast spin-echo (FSE) sequence followed by the acquisition of an exercise-induced, T(2)-enhanced data set. The data showed the expected fiber organization, from which the physiological cross-sectional area (PCSA), fiber length, and pennation angle for the tibialis anterior (TA) were obtained. The values of these parameters ranged from 5.4-9.1 mm(2), 5.8-7.8 mm, and 21-24 degrees , respectively, which is in agreement with values obtained previously with the use of invasive methods. This study shows that 3D DT acquisition and fiber tracking is feasible for the skeletal muscle of mice, and thus enables the quantitative determination of muscle architecture.
An exploration of diffusion tensor eigenvector variability within human calf muscles.
Rockel, Conrad; Noseworthy, Michael D
2016-01-01
To explore the effect of diffusion tensor imaging (DTI) acquisition parameters on principal and minor eigenvector stability within human lower leg skeletal muscles. Lower leg muscles were evaluated in seven healthy subjects at 3T using an 8-channel transmit/receive coil. Diffusion-encoding was performed with nine signal averages (NSA) using 6, 15, and 25 directions (NDD). Individual DTI volumes were combined into aggregate volumes of 3, 2, and 1 NSA according to number of directions. Tensor eigenvalues (λ1 , λ2 , λ3 ), eigenvectors (ε1 , ε2 , ε3 ), and DTI metrics (fractional anisotropy [FA] and mean diffusivity [MD]) were calculated for each combination of NSA and NDD. Spatial maps of signal-to-noise ratio (SNR), λ3 :λ2 ratio, and zenith angle were also calculated for region of interest (ROI) analysis of vector orientation consistency. ε1 variability was only moderately related to ε2 variability (r = 0.4045). Variation of ε1 was affected by NDD, not NSA (P < 0.0002), while variation of ε2 was affected by NSA, not NDD (P < 0.0003). In terms of tensor shape, vector variability was weakly related to FA (ε1 :r = -0.1854, ε2 : ns), but had a stronger relation to the λ3 :λ2 ratio (ε1 :r = -0.5221, ε2 :r = -0.1771). Vector variability was also weakly related to SNR (ε1 :r = -0.2873, ε2 :r = -0.3483). Zenith angle was found to be strongly associated with variability of ε1 (r = 0.8048) but only weakly with that of ε2 (r = 0.2135). The second eigenvector (ε2 ) displayed higher directional variability relative to ε1 , and was only marginally affected by experimental conditions that impacted ε1 variability. © 2015 Wiley Periodicals, Inc.
Hypertrophy of the tensor fascia lata muscle as a complication of total hip arthroplasty.
Rodríguez-Roiz, Juan Miguel; Bori, Guillem; Tomas, Xavier; Fernández-Valencia, Jenaro A; García-Díez, Ana Isabel; Pomés, Jaume; Garcia, Sebastián
2017-02-01
Hypertrophy of the tensor fascia lata muscle (HTFLM) is a rare complication after total hip arthroplasty (THA) and is a potential source of pain, palpable mass, or both. We retrospectively analyzed 1285 primary THAs and 482 THA revisions (THAR) performed at our center from 2008 to 2014. Among these, five patients had HTFLM (average age 68.8 years). The type of surgery and symptoms were evaluated, as were imaging studies (CT or MRI) of both hips (10 hips), and functional outcomes with the Merle d'Aubigné score. The suspected diagnosis was established at an average of 30.2 months after surgery. Four cases occurred after THA and one case after THAR. A modified Hardinge approach was used in four cases and a Röttinger approach in one case. Two cases had pain and palpable mass in the trochanteric region and three cases only pain. The asymmetric HTFLM of the THA side against the nonsurgical side was confirmed by measuring the cross section of the tensor fascia lata muscle on imaging. The sartorius muscle was measured for reference in each case. The Merle d'Aubigne scale had a mean value of 16.6 (range 13-18) at 38 months after the procedure. HTFLM after THA is a benign condition that could be mistaken for a tumor when presenting as a palpable mass. We propose that it should be considered in the differential diagnosis of pain in the lateral aspect of hips that have previously undergone THA.
Diffusion tensor imaging and T2 mapping in early denervated skeletal muscle in rats.
Ha, Dong-Ho; Choi, Sunseob; Kang, Eun-Ju; Park, Hwan Tae
2015-09-01
To evaluate the temporal changes of diffusion tensor imaging (DTI) indices, T2 values, and visual signal intensity on various fat suppression techniques in the early state of denervated skeletal muscle in a rat model. Institutional Animal Care and Use Committee approval was obtained. Sciatic nerves of eight rats were transected for irreversible neurotmesis model. We examined normal lower leg and denervated muscles at 3 days, 1 week, and 2 weeks on a 3 Tesla MR. fractional anisotropy (FA), mean apparent diffusion coefficient (mADC), and T2 values were measured by using DTI and T2 mapping scan. We subjectively classified the signal intensity change on various fat suppression images into the following three grades: negative, suspicious, and definite change. Wilcoxon-sign rank test and Kruskal-Wallis test were used for the comparison of FA, mADC, T2 values. McNemar's test was used for comparing signal intensity change among fat suppression techniques. FA values of denervated muscles at 3 days (0.35 ± 0.06), 1 week (0.29 ± 0.04), and 2 weeks (0.34 ± 0.05) were significantly (P 0.05) change. T2 values were significantly increased at 1 week (38.11 ± 6.42 ms, P = 0.017) and markedly increased at 2 weeks (46.53 ± 5.17 ms, P = 0.012). The grade of visual signal intensity change on chemical shift selective fat saturation, STIR and IDEAL images were identical in all cases (P = 1.000). FA and T2 values can demonstrate the early temporal changes in denervated rat skeletal muscle. © 2014 Wiley Periodicals, Inc.
Giraudo, Chiara; Motyka, Stanislav; Weber, Michael; Karner, Manuela; Resinger, Christoph; Feiweier, Thorsten; Trattnig, Siegfried; Bogner, Wolfgang
2018-02-08
To assess acute muscle tears in professional football players by diffusion tensor imaging (DTI) and evaluate the impact of normalization of data. Eight football players with acute lower limb muscle tears were examined. DTI metrics of the injured muscle and corresponding healthy contralateral muscle and of ROIs drawn in muscle tears (ROI tear ) in the corresponding healthy contralateral muscle (ROI hc_t ) in a healthy area ipsilateral to the injury (ROI hi ) and in a corresponding contralateral area (ROI hc_i ) were compared. The same comparison was performed for ratios of the injured (ROI tear /ROI hi ) and contralateral sides (ROI hc_t /ROI hc_i ). ANOVA, Bonferroni-corrected post-hoc and Student's t-tests were used. Analyses of the entire muscle did not show any differences (p>0.05 each) except for axial diffusivity (AD; p=0.048). ROI tear showed higher mean diffusivity (MD) and AD than ROI hc_t (ptear than in ROI hi and ROI hc_t (ptear than in any other ROI (pmuscle tears in athletes especially after normalization to healthy muscle tissue. • STEAM-based DTI allows the investigation of muscle tears affecting professional football players. • Fractional anisotropy and mean diffusivity differ between injured and healthy muscle areas. • Only normalized data show differences of fibre tracking metrics in muscle tears. • The normalization of DTI-metrics enables a more robust characterization of muscle tears.
Improvement of Reliability of Diffusion Tensor Metrics in Thigh Skeletal Muscles.
Keller, Sarah; Chhabra, Avneesh; Ahmed, Shaheen; Kim, Anne C; Chia, Jonathan M; Yamamura, Jin; Wang, Zhiyue J
2018-05-01
Quantitative diffusion tensor imaging (DTI) of skeletal muscles is challenging due to the bias in DTI metrics, such as fractional anisotropy (FA) and mean diffusivity (MD), related to insufficient signal-to-noise ratio (SNR). This study compares the bias of DTI metrics in skeletal muscles via pixel-based and region-of-interest (ROI)-based analysis. DTI of the thigh muscles was conducted on a 3.0-T system in N = 11 volunteers using a fat-suppressed single-shot spin-echo echo planar imaging (SS SE-EPI) sequence with eight repetitions (number of signal averages (NSA) = 4 or 8 for each repeat). The SNR was calculated for different NSAs and estimated for the composite images combining all data (effective NSA = 48) as standard reference. The bias of MD and FA derived by pixel-based and ROI-based quantification were compared at different NSAs. An "intra-ROI diffusion direction dispersion angle (IRDDDA)" was calculated to assess the uniformity of diffusion within the ROI. Using our standard reference image with NSA = 48, the ROI-based and pixel-based measurements agreed for FA and MD. Larger disagreements were observed for the pixel-based quantification at NSA = 4. MD was less sensitive than FA to the noise level. The IRDDDA decreased with higher NSA. At NSA = 4, ROI-based FA showed a lower average bias (0.9% vs. 37.4%) and narrower 95% limits of agreement compared to the pixel-based method. The ROI-based estimation of FA is less prone to bias than the pixel-based estimations when SNR is low. The IRDDDA can be applied as a quantitative quality measure to assess reliability of ROI-based DTI metrics. Copyright © 2018 Elsevier B.V. All rights reserved.
Flack, Natasha Amy May Sparks; Nicholson, Helen D; Woodley, Stephanie Jane
2012-09-01
The hip abductor muscles have the capability to contribute to numerous actions, including pelvic stabilization during gait, and abduction and rotation at the hip joint. To fully understand the role of these muscles, as well as their involvement in hip joint dysfunction, knowledge of their anatomical structure is essential. The clinical literature suggests anatomical diversity within these muscles, and that gluteus medius (GMed) and gluteus minimus (GMin), in particular, may be comprised of compartments. This systematic review of the English literature focuses on the gross anatomy of GMed, GMin, and tensor fascia lata (TFL) muscles. Although studies of this muscle group have generated useful descriptions, comparison of results is hindered by methodological limitations. Furthermore, there is no single comprehensive anatomical investigation of all three muscles. Several aspects of the morphology of attachment sites are unknown or unclear. There is little data on fascicle orientation, the interface between fascicles and tendons, and the specific patterning of the superior gluteal nerve. Consequently, the existence of anatomical compartmentalization within the hip abductor muscles is difficult to assess. Further research of the architecture and innervation of the hip abductor muscle group is required; a better understanding of the precise anatomy of these muscles should improve our understanding of their specific functions and their contribution to the pathogenesis of disorders affecting the hip joint. Copyright © 2011 Wiley Periodicals, Inc.
Okamoto, Yoshikazu; Okamoto, Toru; Yuka, Kujiraoka; Hirano, Yuji; Isobe, Tomonori; Minami, Manabu
2012-12-01
The aim of this study was to ascertain whether a correlation existed between muscle pennation angle and the ability to successfully perform tractography of the lower leg muscle fibres with deterministic diffusion tensor imaging (DTI) in normal volunteers. Fourteen volunteers aged 20-39 (mean 28.2 years old) were recruited. All volunteers were scanned using DTI, and six fibre tractographs were constructed from one lower leg of each volunteer, and the 'fibre density' was calculated in each of the tractographs. The pennation angle is the angle formed by the muscle fibre and the aponeurosis. The average pennation angle (AVPA) and standard deviation of the pennation angle (SDPA) were also measured for each muscle by ultrasonography in the same region as the MRI scan. For all 84 tractography images, the correlation coefficient between the fibre density and AVPA or SDPA was calculated. Fibre density and AVPA showed a moderate negative correlation (R = -0.72), and fibre density and SDPA showed a weak negative correlation (R = -0.47). With respect to comparisons within each muscle, AVPA and fibre density showed a moderate negative correlation in the gastrocnemius lateralis muscle (R = -0.57). Our data suggest that a larger, more variable pennation angle resulted in worse skeletal muscle tractography using deterministic DTI. © 2012 The Authors. Journal of Medical Imaging and Radiation Oncology © 2012 The Royal Australian and New Zealand College of Radiologists.
[Impedance between modiolus and different walls of scala tympani].
Du, Qiang; Wang, Zhengmin
2008-10-01
To compare the impedance between the modiolus and the inner wall of scala tympani with that between the modiolus and the outer wall of scala tympani. The impedances between the modiolus and the inner wall of scala tympani and the impedance between the modiolus and the outer wall of scala tympani were measured, calculated and compared under different stimulating rates 0.1, 1.0, 10.0 kHz. The impedance between the modiolus and the inner wall of scala tympani is less than that between the modiolus and the outer wall of scala tympani (P < 0.05). To effectively stimulate the residual neurons in the spiral ganglion, the electrodes should be kept close to the inner wall of scale tympani.
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.
Filli, Lukas; Piccirelli, Marco; Kenkel, David; Guggenberger, Roman; Andreisek, Gustav; Beck, Thomas; Runge, Val M; Boss, Andreas
2015-01-01
PURPOSE The aim of this study was to investigate the feasibility of accelerated diffusion tensor imaging (DTI) of skeletal muscle using echo planar imaging (EPI) applying simultaneous multislice excitation with a blipped controlled aliasing in parallel imaging results in higher acceleration unaliasing technique. MATERIALS AND METHODS After federal ethics board approval, the lower leg muscles of 8 healthy volunteers (mean [SD] age, 29.4 [2.9] years) were examined in a clinical 3-T magnetic ...
Scala tympani cochleostomy II: topography and histology.
Adunka, Oliver F; Radeloff, Andreas; Gstoettner, Wolfgang K; Pillsbury, Harold C; Buchman, Craig A
2007-12-01
To assess intracochlear trauma using two different round window-related cochleostomy techniques in human temporal bones. Twenty-eight human temporal bones were included in this study. In 21 specimens, cochleostomies were initiated inferior to the round window (RW) annulus. In seven bones, cochleostomies were drilled anterior-inferior to the RW annulus. Limited cochlear implant electrode insertions were performed in 19 bones. In each specimen, promontory anatomy and cochleostomy drilling were photographically documented. Basal cochlear damage was assessed histologically and electrode insertion properties were documented in implanted bones. All implanted specimens showed clear scala tympani electrode placements regardless of cochleostomy technique. All 21 inferior cochleostomies were atraumatic. Anterior-inferior cochleostomies resulted in various degrees of intracochlear trauma in all seven bones. For atraumatic opening of the scala tympani using a cochleostomy approach, initiation of drilling should proceed from inferior to the round window annulus, with gradual progression toward the undersurface of the lumen. While cochleostomies initiated anterior-inferior to the round window annulus resulted in scala tympani opening, many of these bones displayed varying degrees of intracochlear trauma that may result in hearing loss. When intracochlear drilling is avoided, the anterior bony margin of the cochleostomy remains a significant intracochlear impediment to in-line electrode insertion.
Energy Technology Data Exchange (ETDEWEB)
Wada, Keizo; Goto, Tomohiro; Takasago, Tomoya; Hamada, Daisuke; Sairyo, Koichi [The University of Tokushima Graduate School, Department of Orthopedics, Institute of Health Biosciences, Tokushima (Japan)
2017-10-15
Piriformis muscle syndrome (PMS) is difficult to diagnose by objective evaluation of sciatic nerve injury. Here we report a case of PMS diagnosed by diffusion tensor imaging (DTI) and tractography of the sciatic nerve, which can assess and visualize the extent of nerve injury. The patient was a 53-year-old man with a 2-year history of continuous pain and numbness in the left leg. His symptoms worsened when sitting. Physical examination, including sensorimotor neurologic tests, the deep tendon reflex test, and the straight leg raise test, revealed no specific findings. The hip flexion adduction and internal rotation test and resisted contraction maneuvers for the piriformis muscle were positive. There were no abnormal findings on magnetic resonance imaging (MRI) of the lumbar spine. The transverse diameter of piriformis muscle was slightly thicker in affected side on MRI of the pelvis. A single DTI sequence was performed during MRI of the pelvis. Fractional anisotropy (FA) and the apparent diffusion coefficient (ADC) of the sciatic nerve were quantified at three levels using the fiber-tracking method. FA values were significantly lower and ADC values were significantly higher distal to the piriformis muscle. We performed endoscopic-assisted resection of the piriformis tendon. Intraoperatively, the motor-evoked potentials in the left gastrocnemius were improved by resection of the piriformis tendon. The patient's symptoms improved immediately after surgery. There was no significant difference in FA or ADC at any level between the affected side and the unaffected side 3 months postoperatively. MRI-DTI may aid the diagnosis of PMS. (orig.)
Wada, Keizo; Goto, Tomohiro; Takasago, Tomoya; Hamada, Daisuke; Sairyo, Koichi
2017-10-01
Piriformis muscle syndrome (PMS) is difficult to diagnose by objective evaluation of sciatic nerve injury. Here we report a case of PMS diagnosed by diffusion tensor imaging (DTI) and tractography of the sciatic nerve, which can assess and visualize the extent of nerve injury. The patient was a 53-year-old man with a 2-year history of continuous pain and numbness in the left leg. His symptoms worsened when sitting. Physical examination, including sensorimotor neurologic tests, the deep tendon reflex test, and the straight leg raise test, revealed no specific findings. The hip flexion adduction and internal rotation test and resisted contraction maneuvers for the piriformis muscle were positive. There were no abnormal findings on magnetic resonance imaging (MRI) of the lumbar spine. The transverse diameter of piriformis muscle was slightly thicker in affected side on MRI of the pelvis. A single DTI sequence was performed during MRI of the pelvis. Fractional anisotropy (FA) and the apparent diffusion coefficient (ADC) of the sciatic nerve were quantified at three levels using the fiber-tracking method. FA values were significantly lower and ADC values were significantly higher distal to the piriformis muscle. We performed endoscopic-assisted resection of the piriformis tendon. Intraoperatively, the motor-evoked potentials in the left gastrocnemius were improved by resection of the piriformis tendon. The patient's symptoms improved immediately after surgery. There was no significant difference in FA or ADC at any level between the affected side and the unaffected side 3 months postoperatively. MRI-DTI may aid the diagnosis of PMS.
International Nuclear Information System (INIS)
Wada, Keizo; Goto, Tomohiro; Takasago, Tomoya; Hamada, Daisuke; Sairyo, Koichi
2017-01-01
Piriformis muscle syndrome (PMS) is difficult to diagnose by objective evaluation of sciatic nerve injury. Here we report a case of PMS diagnosed by diffusion tensor imaging (DTI) and tractography of the sciatic nerve, which can assess and visualize the extent of nerve injury. The patient was a 53-year-old man with a 2-year history of continuous pain and numbness in the left leg. His symptoms worsened when sitting. Physical examination, including sensorimotor neurologic tests, the deep tendon reflex test, and the straight leg raise test, revealed no specific findings. The hip flexion adduction and internal rotation test and resisted contraction maneuvers for the piriformis muscle were positive. There were no abnormal findings on magnetic resonance imaging (MRI) of the lumbar spine. The transverse diameter of piriformis muscle was slightly thicker in affected side on MRI of the pelvis. A single DTI sequence was performed during MRI of the pelvis. Fractional anisotropy (FA) and the apparent diffusion coefficient (ADC) of the sciatic nerve were quantified at three levels using the fiber-tracking method. FA values were significantly lower and ADC values were significantly higher distal to the piriformis muscle. We performed endoscopic-assisted resection of the piriformis tendon. Intraoperatively, the motor-evoked potentials in the left gastrocnemius were improved by resection of the piriformis tendon. The patient's symptoms improved immediately after surgery. There was no significant difference in FA or ADC at any level between the affected side and the unaffected side 3 months postoperatively. MRI-DTI may aid the diagnosis of PMS. (orig.)
Garbe, Christoph S; Buttgereit, Andreas; Schürmann, Sebastian; Friedrich, Oliver
2012-01-01
Practically, all chronic diseases are characterized by tissue remodeling that alters organ and cellular function through changes to normal organ architecture. Some morphometric alterations become irreversible and account for disease progression even on cellular levels. Early diagnostics to categorize tissue alterations, as well as monitoring progression or remission of disturbed cytoarchitecture upon treatment in the same individual, are a new emerging field. They strongly challenge spatial resolution and require advanced imaging techniques and strategies for detecting morphological changes. We use a combined second harmonic generation (SHG) microscopy and automated image processing approach to quantify morphology in an animal model of inherited Duchenne muscular dystrophy (mdx mouse) with age. Multiphoton XYZ image stacks from tissue slices reveal vast morphological deviation in muscles from old mdx mice at different scales of cytoskeleton architecture: cell calibers are irregular, myofibrils within cells are twisted, and sarcomere lattice disruptions (detected as "verniers") are larger in number compared to samples from healthy mice. In young mdx mice, such alterations are only minor. The boundary-tensor approach, adapted and optimized for SHG data, is a suitable approach to allow quick quantitative morphometry in whole tissue slices. The overall detection performance of the automated algorithm compares very well with manual "by eye" detection, the latter being time consuming and prone to subjective errors. Our algorithm outperfoms manual detection by time with similar reliability. This approach will be an important prerequisite for the implementation of a clinical image databases to diagnose and monitor specific morphological alterations in chronic (muscle) diseases. © 2011 IEEE
Valaparla, Sunil K; Gao, Feng; Daniele, Giuseppe; Abdul-Ghani, Muhammad; Clarke, Geoffrey D
2015-04-01
Twelve healthy subjects underwent hydrogen-1 magnetic resonance spectroscopy ([Formula: see text]) acquisition ([Formula: see text]), diffusion tensor imaging (DTI) with a [Formula: see text]-value of [Formula: see text], and fat-water magnetic resonance imaging (MRI) using the Dixon method. Subject-specific muscle fiber orientation, derived from DTI, was used to estimate the lipid proton spectral chemical shift. Pennation angles were measured as 23.78 deg in vastus lateralis (VL), 17.06 deg in soleus (SO), and 8.49 deg in tibialis anterior (TA) resulting in a chemical shift between extramyocellular lipids (EMCL) and intramyocellular lipids (IMCL) of 0.15, 0.17, and 0.19 ppm, respectively. IMCL concentrations were [Formula: see text], [Formula: see text], and [Formula: see text] in SO, VL, and TA, respectively. Significant differences were observed in IMCL and EMCL pairwise comparisons in SO, VL, and TA ([Formula: see text]). Strong correlations were observed between total fat fractions from [Formula: see text] and Dixon MRI for VL ([Formula: see text]), SO ([Formula: see text]), and TA ([Formula: see text]). Bland-Altman analysis between fat fractions (FFMRS and FFMRI) showed good agreement with small limits of agreement (LoA): [Formula: see text] (LoA: [Formula: see text] to 0.69%) in VL, [Formula: see text] (LoA: [Formula: see text] to 1.33%) in SO, and [Formula: see text] (LoA: [Formula: see text] to 0.47%) in TA. The results of this study demonstrate the variation in muscle fiber orientation and lipid concentrations in these three skeletal muscle types.
Valaparla, Sunil K.; Gao, Feng; Abdul-Ghani, Muhammad; Clarke, Geoffrey D.
2014-03-01
When muscle fibers are aligned with the B0 field, intramyocellular lipids (IMCL), important for providing energy during physical activity, can be resolved in proton magnetic resonance spectra (1H-MRS). Various muscles of the leg differ significantly in their proportion of fibers and angular distribution. This study determined the influence of muscle fiber type and orientation on IMCL using 1H-MRS and diffusion tensor imaging (DTI). Muscle fiber orientation relative to B0 was estimated by pennation angle (PA) measurements from DTI, providing orientation-specific extramyocellular lipid (EMCL) chemical shift data that were used for subject-specific IMCL quantification. Vastus lateralis (VL), tibialis anterior (TA) and soleus (SO) muscles of 6 healthy subjects (21-40 yrs) were studied on a Siemens 3T MRI system with a flex 4-channel coil. 1H-MRS were acquired using stimulated echo acquisition mode (STEAM, TR=3s, TE=270ms). DTI was performed using single shot EPI (b=600s/mm2, 30 directions, TR=4.5s, TE=82ms, and ten×5mm slices) with center slice indexed to the MRS voxel. The average PA's measured from ROI analysis of primary eigenvectors were PA=19.46+/-5.43 for unipennate VL, 15.65+/-3.73 for multipennate SO, and 7.04+/-3.34 for bipennate TA. Chemical shift (CS) was calculated using [3cos2θ-1] dependence: 0.17+/-0.02 for VL, 0.18+/-0.01 for SO and 0.19+/-0.004 ppm for TA. IMCL-CH2 concentrations from spectral analysis were 12.77+/-6.3 for VL, 3.07+/-1.63 for SO and 0.27+/-0.08 mmol/kg ww for TA. Small PA's were measured in TA and large CS with clear separation between EMCL and IMCL peaks were observed. Larger variations in PA were measured VL and SO resulting in an increased overlap of the EMCL on IMCL peaks.
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...
Bernard, J; Beldame, J; Van Driessche, S; Brunel, H; Poirier, T; Guiffault, P; Matsoukis, J; Billuart, F
2017-11-01
Minimally invasive total hip arthroplasty (THA) is presumed to provide functional and clinical benefits, whereas in fact the literature reveals that gait and posturographic parameters following THA do not recover values found in the general population. There is a significant disturbance of postural sway in THA patients, regardless of the surgical approach, although with some differences between approaches compared to controls: the anterior and anterolateral minimally invasive approaches seem to be more disruptive of postural parameters than the posterior approach. Electromyographic (EMG) study of the hip muscles involved in surgery [gluteus maximus (GMax), gluteus medius (GMed), tensor fasciae latae (TFL), and sartorius (S)] could shed light, the relevant literature involves discordant methodologies. We developed a methodology to assess EMG activity during maximal voluntary contraction (MVC) of the GMax, GMed, TFL and sartorius muscles as a reference for normalization. A prospective study aimed to assess whether hip joint positioning and the learning curve on an MVC test affect the EMG signal during a maximal voluntary contraction. Hip positioning and the learning curve on an MVC test affect EMG signal during MVC of GMax, GMed, TFL and S. Thirty young asymptomatic subjects participated in the study. Each performed 8 hip muscle MVCs in various joint positions recorded with surface EMG sensors. Each MVC was performed 3 times in 1 week, with the same schedule every day, controlling for activity levels in the preceding 24h. EMG activity during MVC was expressed as a ratio of EMG activity during unipedal stance. Non-parametric tests were applied. Statistical analysis showed no difference according to hip position for abductors or flexors in assessing EMG signal during MVC over the 3 sessions. Hip abductors showed no difference between abduction in lateral decubitus with hip straight versus hip flexed: GMax (19.8±13.7 vs. 14.5±7.8, P=0.78), GMed (13.4±9.0 vs. 9.9±6
ATP-gamma-S shifts the operating point of outer hair cell transduction towards scala tympani.
Bobbin, Richard P; Salt, Alec N
2005-07-01
ATP receptor agonists and antagonists alter cochlear mechanics as measured by changes in distortion product otoacoustic emissions (DPOAE). Some of the effects on DPOAEs are consistent with the hypothesis that ATP affects mechano-electrical transduction and the operating point of the outer hair cells (OHCs). This hypothesis was tested by monitoring the effect of ATP-gamma-S on the operating point of the OHCs. Guinea pigs anesthetized with urethane and with sectioned middle ear muscles were used. The cochlear microphonic (CM) was recorded differentially (scala vestibuli referenced to scala tympani) across the basal turn before and after perfusion (20 min) of the perilymph compartment with artificial perilymph (AP) and ATP-gamma-S dissolved in AP. The operating point was derived from the cochlear microphonics (CM) recorded in response low frequency (200 Hz) tones at high level (106, 112 and 118 dB SPL). The analysis procedure used a Boltzmann function to simulate the CM waveform and the Boltzmann parameters were adjusted to best-fit the calculated waveform to the CM. Compared to the initial perfusion with AP, ATP-gamma-S (333 microM) enhanced peak clipping of the positive peak of the CM (that occurs during organ of Corti displacements towards scala tympani), which was in keeping with ATP-induced displacement of the transducer towards scala tympani. CM waveform analysis quantified the degree of displacement and showed that the changes were consistent with the stimulus being centered on a different region of the transducer curve. The change of operating point meant that the stimulus was applied to a region of the transducer curve where there was greater saturation of the output on excursions towards scala tympani and less saturation towards scala vestibuli. A significant degree of recovery of the operating point was observed after washing with AP. Dose response curves generated by perfusing ATP-gamma-S (333 microM) in a cumulative manner yielded an EC(50) of 19.8 micro
International Nuclear Information System (INIS)
Wang Fengzhe; Pan Shinong; An Qi; Shu Hong; Li Qi; Sun He; Zhang Guangxin; Guo Qiyong
2010-01-01
Objective: To evaluate the value of ice-compression therapy in mice skeletal muscle after acute crush injuries and correlate treatment effect with different compression time by MR DTI. Methods: Forty Weistar mice were randomly divided into 4 groups by random number table method: control group (A), 5 min compression time group (B), 15 min compression time group (C) and 30 min compression time group (D). Diffusion tensor imaging examinations were performed before, immediately after, 24, 48 and 72 hours after injuries. ADC and FA values were calculated by fiber tracking tool. The morphological changes were confirmed by histopathology, and immunohistochemical methods were used for the assessment of Desmin expression with mean of A value. Statistical analysis by LSD-t test and Spearman rank correlation. Results: (1) For every group before injuries, ADC values were (1.38±0.04) × 10 -3 , (1.38±0.08) × 10 -3 , (1.34±0.05) × 10 -3 , (1.36±0.09) × 10 -3 mm 2 /s respectively, FA value were 0.46±0.05, 0.45±0.03, 0.45±0.05, 0.48±0.04 respectively. ADC values increased significantly and FA values reduced in each group immediately after injuries compared with pre-injury values. ADC values were (1.84± 0.10) × 10 -3 (1.79±0.09) × 10 -3 , (1.55±0.07) × 10 -3 , (1.57±0.04) × 10 -3 mm 2 /s respectively, FA value were 0.21±0.04, 0.26±0.03, 0.31±0.02, 0.30±0.04 respectively. ADC values were still higher and FA values lower than pre-injury values at 24 hours after injury in A, B groups. ADC values were (1.54±0.13) × 10 -3 , (1.57±0.13) × 10 -3 mm 2 /s, FA value were 0.25±0.03, 0.26±0.02. (2) DTT showed fibers distorted and the number of fiber bundles reduced, some separation and displacement in each group immediately after injury. C, D groups improved more than A, B groups over time. (3) The disorder arrangement of skeletal muscle cells with edema and filaments separation were found in HE staining after injury, but the degree mitigated in C, D groups. Desmin
Li, Gui Dian; Liang, Ying Yin; Xu, Ping; Ling, Jian; Chen, Ying Ming
2016-04-01
The purpose of this study is to investigate the correlation of apparent diffusion coefficient (ADC) and fractional anisotropy (FA) values with fatty infiltration in the thigh muscles of patients with Duchenne muscular dystrophy (DMD) using diffusion-tensor imaging (DTI). Twenty-one boys with DMD were recruited. The grade of fatty infiltration and the ADC and FA values of four thigh muscles (rectus femoris, semitendinosus, sartorius, and gracilis) were measured, and the FA and ADC values were compared with the grade of fatty infiltration. Twenty age-matched healthy boys were enrolled as the control group. The differences in the ADC and FA values of the thigh muscles between patients with DMD and the control group were compared. The patients with DMD showed lower FA values and higher ADC values in all measured muscles when compared with the control group. The FA and ADC values were correlated with the grade of fatty infiltration. For the rectus femoris muscle, r = -0.753 and p = 0.007 for FA, and r = 0.685 and p = 0.001 for ADC. For the semitendinosus muscle, r = -0.621 and p = 0.041 for FA, and r = 0.705 and p = 0.021 for ADC. For the sartorius muscle, r = -0.662 and p = 0.027 for FA, and r = 0.701 and p = 0.017 for ADC. For the gracilis muscle, r = -0.618 and p = 0.043 for FA, and r = 0.695 and p = 0.022 for ADC. Damage to the thigh muscles in patients with DMD can be detected by ADC and FA values using DTI. DTI can be used to assess the severity of the disease.
Directory of Open Access Journals (Sweden)
Pankaj Kumar Mishra
2014-01-01
Full Text Available Background: Femoral neck fractures are notorious for complications like avascular necrosis and nonunion. In developing countries, various factors such as illiteracy, low socioeconomic status, ignorance are responsible for the delay in surgery. Neglected fracture neck femur always poses a formidable challenge. The purpose of this study was to evaluate the results of triple muscle pedicle bone grafting using sartorius, tensor fasciae latae and part of gluteus medius in neglected femoral neck fracture. Materials and Methods: This is a retrospective study with medical record of 50 patients, who were operated by open reduction, internal fixation along with muscle pedicle bone grafting by the anterior approach. After open reduction, two to three cancellous screws (6.5 mm were used for internal fixation in all cases. A bony chunk of the whole anterior superior iliac spine of 1 cm thickness, 1 cm width and 4.5 cm length, taken from the iliac crest comprised of muscle pedicle of sartorius, tensor fascia latae and part of gluteus medius. Then the graft with all three muscles mobilized and put in the trough made over the anterior or anterosuperior aspect of the femoral head. The graft was fixed with one or two 4.5 mm self-tapping cortical screw in anterior to posterior direction. Results: 14 patients were lost to followup. The results were based on 36 patients. We observed that in our series, there was union in 34, out of 36 (94.4% patients. All patients were within the age group of 15-51 years (average 38 years with displaced neglected femoral neck fracture of ≥30 days. Mean time taken for full clinicoradiological union was 14 weeks (range-10-24 weeks. Conclusion: Triple muscle pedicle bone grafting gives satisfactory results for neglected femoral neck fracture in physiologically active patients.
Directory of Open Access Journals (Sweden)
Shozo Yoshida
2018-01-01
Full Text Available We herein report a case of clear cell carcinoma arising from endometriosis in the groin in a 53-year-old woman. The findings of MRI and FDG/PET-CT indicated a malignant tumor, and surgical biopsy confirmed adenocarcinoma of the female genital tract. The tumor including a part of the abdominal rectus muscle and rectus sheath, subcutaneous fat, skin, and the right inguinal ligament was resected en bloc. The defect in the abdominal wall was reconstructed with a fascia lata tensor muscle skin flap. The tumor was composed of clear cell adenocarcinoma arising from extrapelvic endometriosis. The patient received chemotherapy with gemcitabine and carboplatin for 6 cycles and had no evidence of recurrence 7 months after the treatment. We herein described the diagnosis and surgical management of endometriosis-associated carcinoma in the groin.
Ponrartana, Skorn; Andrade, Kristine E; Wren, Tishya A L; Ramos-Platt, Leigh; Hu, Houchun H; Bluml, Stefan; Gilsanz, Vicente
2014-06-01
The purpose of this study was to assess the repeatability of water-fat MRI and diffusion-tensor imaging (DTI) as quantitative biomarkers of pediatric lower extremity skeletal muscle. MRI at 3 T of a randomly selected thigh and lower leg of seven healthy children was studied using water-fat separation and DTI techniques. Muscle-fat fraction, apparent diffusion coefficient (ADC), and fractional anisotropy (FA) values were calculated. Test-retest and interrater repeatability were assessed by calculating the Pearson correlation coefficient, intraclass correlation coefficient, and Bland-Altman analysis. Bland-Altman plots show that the mean difference between test-retest and interrater measurements of muscle-fat fraction, ADC, and FA was near 0. The correlation coefficients and intraclass correlation coefficients were all between 0.88 and 0.99 (p DTI measurements in lower extremity skeletal muscles are objective repeatable biomarkers in children. This knowledge should aid in the understanding of the number of participants needed in clinical trials when using these determinations as an outcome measure to noninvasively monitor neuromuscular disease.
Dimensions of the scala tympani in the human and cat with reference to cochlear implants.
Hatsushika, S; Shepherd, R K; Tong, Y C; Clark, G M; Funasaka, S
1990-11-01
The width, height, and cross-sectional area of the scala tympani in both the human and cat were measured to provide dimensional information relevant to the design of scala tympani electrode arrays. Both the height and width of the human scala tympani decreased rapidly within the first 1.5 mm from the round window. Thereafter, they exhibit a gradual reduction in their dimension with increasing distance from the round window. The cross-sectional area of the human scala tympani reflects the changes observed in both the height and width. In contrast, the cat scala tympani exhibits a rapid decrease in its dimensions over the first 6 to 8 mm from the round window. However, beyond this point the cat scala tympani also exhibits a more gradual decrease in its dimensions. Finally, the width of the scala tympani, in both human and cat, is consistently greater than the height.
Endoscopic Anatomy of the Tensor Fold and Anterior Attic.
Li, Bin; Doan, Phi; Gruhl, Robert R; Rubini, Alessia; Marchioni, Daniele; Fina, Manuela
2018-02-01
Objectives The objectives of the study were to (1) study the anatomical variations of the tensor fold and its anatomic relation with transverse crest, supratubal recess, and anterior epitympanic space and (2) explore the most appropriate endoscopic surgical approach to each type of the tensor fold variants. Study Design Cadaver dissection study. Setting Temporal bone dissection laboratory. Subjects and Methods Twenty-eight human temporal bones (26 preserved and 2 fresh) were dissected through an endoscopic transcanal approach between September 2016 and June 2017. The anatomical variations of the tensor fold, transverse crest, supratubal recess, and anterior epitympanic space were studied before and after removing ossicles. Results Three different tensor fold orientations were observed: vertical (type A, 11/28, 39.3%) with attachment to the transverse crest, oblique (type B, 13/28, 46.4%) with attachment to the anterior tegmen tympani, and horizontal (type C, 4/28, 14.3%) with attachment to the tensor tympani canal. The tensor fold was a complete membrane in 20 of 28 (71.4%) specimens, preventing direct ventilation between the supratubal recess and anterior epitympanic space. We identified 3 surgical endoscopic approaches, which allowed visualization of the tensor fold without removing the ossicles. Conclusions The orientation of the tensor fold is the determining structure that dictates the conformation and limits of the epitympanic space. We propose a classification of the tensor fold based on 3 anatomical variants. We also describe 3 different minimally invasive endoscopic approaches to identify the orientation of the tensor fold while maintaining ossicular chain continuity.
A transparent model of the human scala tympani cavity.
Rebscher, S J; Talbot, N; Bruszewski, W; Heilmann, M; Brasell, J; Merzenich, M M
1996-01-01
A dimensionally accurate clear model of the human scala tympani has been produced to evaluate the insertion and position of clinically applied intracochlear electrodes for electrical stimulation. Replicates of the human scala tympani were made from low melting point metal alloy (LMA) and from polymethylmeth-acrylate (PMMA) resin. The LMA metal casts were embedded in blocks of epoxy and in clear silicone rubber. After removal of the metal alloy, a cavity was produced that accurately models the human scala tympani. Investment casting molds were made from the PMMA scala tympani casts to enable production of multiple LMA casts from which identical models were fabricated. Total dimensional distortion of the LMA casting process was less than 1% in length and 2% in diameter. The models have been successfully integrated into the design process for the iterative development of advanced intracochlear electrode arrays at UCSF. These fabrication techniques are applicable to a wide range of biomedical design problems that require modelling of visually obscured cavities.
Filli, Lukas; Piccirelli, Marco; Kenkel, David; Guggenberger, Roman; Andreisek, Gustav; Beck, Thomas; Runge, Val M; Boss, Andreas
2015-07-01
The aim of this study was to investigate the feasibility of accelerated diffusion tensor imaging (DTI) of skeletal muscle using echo planar imaging (EPI) applying simultaneous multislice excitation with a blipped controlled aliasing in parallel imaging results in higher acceleration unaliasing technique. After federal ethics board approval, the lower leg muscles of 8 healthy volunteers (mean [SD] age, 29.4 [2.9] years) were examined in a clinical 3-T magnetic resonance scanner using a 15-channel knee coil. The EPI was performed at a b value of 500 s/mm2 without slice acceleration (conventional DTI) as well as with 2-fold and 3-fold acceleration. Fractional anisotropy (FA) and mean diffusivity (MD) were measured in all 3 acquisitions. Fiber tracking performance was compared between the acquisitions regarding the number of tracks, average track length, and anatomical precision using multivariate analysis of variance and Mann-Whitney U tests. Acquisition time was 7:24 minutes for conventional DTI, 3:53 minutes for 2-fold acceleration, and 2:38 minutes for 3-fold acceleration. Overall FA and MD values ranged from 0.220 to 0.378 and 1.595 to 1.829 mm2/s, respectively. Two-fold acceleration yielded similar FA and MD values (P ≥ 0.901) and similar fiber tracking performance compared with conventional DTI. Three-fold acceleration resulted in comparable MD (P = 0.199) but higher FA values (P = 0.006) and significantly impaired fiber tracking in the soleus and tibialis anterior muscles (number of tracks, P DTI of skeletal muscle with similar image quality and quantification accuracy of diffusion parameters. This may increase the clinical applicability of muscle anisotropy measurements.
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
Scala tympani cochleostomy I: results of a survey.
Adunka, Oliver F; Buchman, Craig A
2007-12-01
To assess current surgical techniques for scala tympani cochlear implantation among North American surgeons. A survey was distributed to all cochlear implant surgeons participating in the 2006 William House Cochlear Implant Study Group in Toronto, Canada. Participants were asked to anonymously identify their routine surgical practices. Images of trans-facial recess approaches to the round window and cochlear promontory were used in a multiple-choice fashion to assess the surgeon's typical exposure and cochleostomy location. Returned questionnaires were electronically processed and evaluated. Fifty-five (75%) of 73 returned surveys had adequate data validity and availability. Landmark identification and preferred cochleostomy locations varied greatly. About 20% of surgeons selected cochleostomy locations superior to the round window membrane. Cochleostomy size and location appeared to be influenced by surgical experience and whether or not the round window overhang was drilled off. This survey clearly documents marked variations in surgical techniques for scala tympani cochlear implantation. Future studies should more clearly define the surgical anatomy of this region for appropriate placement of a scala tympani cochleostomy. These findings may ultimately have an impact on hearing and neural preservation cochlear implant surgeries.
Sigmund, Eric E; Sui, Dabang; Ukpebor, Obehi; Baete, Steven; Fieremans, Els; Babb, James S; Mechlin, Michael; Liu, Kecheng; Kwon, Jane; McGorty, KellyAnne; Hodnett, Philip A; Bencardino, Jenny
2013-11-01
To evaluate the performance of diffusion tensor imaging (DTI) in the evaluation of chronic exertional compartment syndrome (CECS) as compared to T2 -weighted (T2w) imaging. Using an Institutional Review Board (IRB)-approved, Health Insurance Portability and Accountability Act (HIPAA)-compliant protocol, spectral adiabatic inversion recovery (SPAIR) T2w imaging and stimulated echo DTI were applied to eight healthy volunteers and 14 suspected CECS patients before and after exertion. Longitudinal and transverse diffusion eigenvalues, mean diffusivity (MD), and fractional anisotropy (FA) were measured in seven calf muscle compartments, which in patients were classified by their response on T2w: normal (20% change). Mixed model analysis of variance compared subject groups and compartments in terms of response factors (post/pre-exercise ratios) of DTI parameters. All diffusivities significantly increased (P DTI shows promise as an ancillary imaging method in the diagnosis and understanding of the pathophysiology in CECS. Future studies may explore its utility in predicting response to treatment. Copyright © 2013 Wiley Periodicals, Inc.
Fouré, Alexandre; Ogier, Augustin C; Le Troter, Arnaud; Vilmen, Christophe; Feiweier, Thorsten; Guye, Maxime; Gondin, Julien; Besson, Pierre; Bendahan, David
2018-05-01
Purpose To demonstrate the reproducibility of the diffusion properties and three-dimensional structural organization measurements of the lower leg muscles by using diffusion-tensor imaging (DTI) assessed with ultra-high-field-strength (7.0-T) magnetic resonance (MR) imaging and tractography of skeletal muscle fibers. On the basis of robust statistical mapping analyses, this study also aimed at determining the sensitivity of the measurements to sex difference and intramuscular variability. Materials and Methods All examinations were performed with ethical review board approval; written informed consent was obtained from all volunteers. Reproducibility of diffusion tensor indexes assessment including eigenvalues, mean diffusivity, and fractional anisotropy (FA) as well as muscle volume and architecture (ie, fiber length and pennation angle) were characterized in lower leg muscles (n = 8). Intramuscular variability and sex differences were characterized in young healthy men and women (n = 10 in each group). Student t test, statistical parametric mapping, correlation coefficients (Spearman rho and Pearson product-moment) and coefficient of variation (CV) were used for statistical data analysis. Results High reproducibility of measurements (mean CV ± standard deviation, 4.6% ± 3.8) was determined in diffusion properties and architectural parameters. Significant sex differences were detected in FA (4.2% in women for the entire lower leg; P = .001) and muscle volume (21.7% in men for the entire lower leg; P = .008), whereas architecture parameters were almost identical across sex. Additional differences were found independently of sex in diffusion properties and architecture along several muscles of the lower leg. Conclusion The high-spatial-resolution DTI assessed with 7.0-T MR imaging allows a reproducible assessment of structural organization of superficial and deep muscles, giving indirect information on muscle function. © RSNA, 2018 Online supplemental material is
Scala tympani cochleostomy survey: a follow-up study.
Iseli, Claire; Adunka, Oliver F; Buchman, Craig A
2014-08-01
To reassess cochleostomy techniques among North American cochlear implant surgeons after a 6-year period of widespread education and research on the topic. Prospective cohort study. A multiple-choice survey of cochlear implant techniques was distributed to surgeons attending the William House Cochlear Implant Study Group in 2006 and 2012. This survey contained questions regarding routine surgical access and cochleostomy techniques. Responses were anonymous, and >50% were repeat respondents. Statistical analysis sought changes in technique in the past 6 years. Comparisons between 2006 and 2012 responses revealed no significant changes in the proportion of surgeons identifying the facial nerve or chorda tympani. By contrast, respondents in 2012 were more likely to drill off the round window niche overhang (P < .001), use a round window insertion (P < .001), or make a smaller cochleostomy (P = .003). In two images of a transfacial recess approach, there was a significant increase in the proportion choosing an inferior or anterior cochleostomy site over a superior location (image 1, 76% in 2006 to 92% in 2012, P = .003; image 3, 78% to 90%, respectively, P = .044). This repeat survey documents a change in practice among cochlear implant surgeons. Specifically, scala tympani access techniques now appear to be more consistent with known anatomical relationships in the round window region. These findings may have resulted from the concerted education and research efforts over the past 6 years. © 2014 The American Laryngological, Rhinological and Otological Society, Inc.
Round window electrode insertion potentiates retention in the scala tympani.
Connor, Stephen E J; Holland, N Julian; Agger, Andreas; Leong, Annabelle C; Varghese, Re Ajay; Jiang, Dan; Fitzgerald O'Connor, Alec
2012-09-01
The round window membrane (RWM)-intentioned approach is superior to the traditional bony cochleostomy (BC) approach in obtaining electrode placement within the scala tympani (ST). Cochlear implant outcome is influenced by several factors, including optimal placement and retention of the electrode array within the ST. The present study aimed to assess whether the RWM route is superior to a traditional BC for placement and retention of the electrode array in the ST. This was a prospective consecutive non-randomized comparison study. All patients were implanted with the Advanced Bionics 1J electrode array. The RWM approach (n = 32) was compared with a traditional BC group (n = 33). The outcome measure was the electrode position as judged within the scalar chambers at four points along the basal turn using postoperative computed tomography (CT). When the mean position scores were compared, the RWM-intentioned group had significantly more electrodes directed towards the ST compartment than the BC group (p scala vestibuli.
Kiefer, J; Weber, A; Pfennigdorff, T; von Ilberg, C
2000-01-01
Insertion of a sufficient number of electrodes is important for a successful use of cochlear implants. We investigated the results of scala vestibuli insertion for cochlear implantation in cases of obstructed scala tympani. In a series of 200 cochlear implantations, scala vestibuli insertion was successfully performed in 4 cases with obstruction of the scala tympani. Etiologies included a temporal bone fracture, severe otosclerosis and malformations of the cochlea. The maximum insertion depth obtained via the scala vestibuli was 30 mm. Postoperative results were comparable to patients in whom conventional scala tympani insertion was performed. No adverse effects related to the site of insertion were observed. Scala vestibuli insertion offers a valuable alternative in cases of obstructed scala tympani that can be employed for a variety of etiologies. Copyright 2000 S. Karger AG, Basel
[Applied anatomy of scala tympani inlet related to cochlear implantation].
Zou, Tuanming; Guo, Menghe; Zhang, Hongzheng; Shu, Fan; Xie, Nanping
2012-06-01
To investigate the related parameters of the temporal bone structure for determining the position of implanting electrode into the scala tympani in cochlear implantation surgery through the facial recess and epitympanum approach. In a surgical simulation experiment, 20 human temporal bones were studied and measured to determine the related parameters of the temporal bone structure. The distance 5.91∓0.29 mm between the short process of the incus and the round window niche, 2.11∓0.18 mm between the stapes and the round window niche, 6.70∓0.19 mm between the facial nerve in the perpendicular paragraph and the round window niche, 2.22∓0.21 mm from the pyramidal eminence to the round window, and 2.16∓0.14 mm between the stapes and the round window. The minimal distance between the implanting electrode and the vestibular window was 2.12∓0.19 mm. The distance between the cochleariform process and the round window niche was 3.79∓0.17 mm. The position of the cochlear electrode array insertion into the second cochlear turn was 2.25∓0.13 mm under the stapes. The location of the cochlear electrode array insertion into the second cochlear turn was 2.28∓0.20 mm inferior to the pyramidal eminence. These parameters provide a reference value to determine the different positions of cochlear electrode array insertion into the scale tympani in different patients.
Shepherd, Robert K; Xu, Jin
2002-10-01
We have developed a novel scala tympani electrode array suitable for use in experimental animals. A unique feature of this array is its ability to chronically deliver pharmacological agents to the scala tympani. The design of the electrode array is described in detail. Experimental studies performed in guinea pigs confirm that this array can successfully deliver various drugs to the cochlea while chronically stimulating the auditory nerve.
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.
Sweeney, Alex D; Hunter, Jacob B; Carlson, Matthew L; Rivas, Alejandro; Bennett, Marc L; Gifford, Rene H; Noble, Jack H; Haynes, David S; Labadie, Robert F; Wanna, George B
2016-05-01
To analyze factors that influence hearing preservation over time in cochlear implant recipients with conventional-length electrode arrays located entirely within the scala tympani. Case series with planned chart review. Single tertiary academic referral center. A retrospective review was performed to analyze a subgroup of cochlear implant recipients with residual acoustic hearing. Patients were included in the study only if their electrode arrays remained fully in the scala tympani after insertion and serviceable acoustic hearing (≤80 dB at 250 Hz) was preserved. Electrode array location was verified through a validated radiographic assessment tool. Patients with scala tympani. In this group, the style of electrode array may influence residual hearing preservation over time. © American Academy of Otolaryngology—Head and Neck Surgery Foundation 2016.
Parametric model of the scala tympani for haptic-rendered cochlear implantation.
Todd, Catherine; Naghdy, Fazel
2005-01-01
A parametric model of the human scala tympani has been designed for use in a haptic-rendered computer simulation of cochlear implant surgery. It will be the first surgical simulator of this kind. A geometric model of the Scala Tympani has been derived from measured data for this purpose. The model is compared with two existing descriptions of the cochlear spiral. A first approximation of the basilar membrane is also produced. The structures are imported into a force-rendering software application for system development.
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
Gentamicin concentration gradients in scala tympani perilymph following systemic applications.
Hahn, Hartmut; Salt, Alec N; Schumacher, Ulrike; Plontke, Stefan K
2013-01-01
It has been shown in prior studies that round window membrane (RWM) application of gentamicin produced a robust basal-apical concentration gradient in the perilymph of scala tympani (ST) with peak concentrations in the basal turn of ST. These gradients potentially contribute to the clinical efficacy and safety of intratympanic gentamicin applications for the treatment of Ménière's disease. The present study aimed to establish the distribution of gentamicin along ST perilymph after systemic applications. Gentamicin sulfate was applied intravenously in the amounts of 100, 300 and 600 mg/kg body weight (BW) over a period of 3 h or as a 300 mg/kg BW subcutaneous bolus injection. At 3 and 5 h after the start of the application perilymph of ST was aspirated from the cochlea apex of the right and left cochlea, respectively, and 10 sequential 1-µl perilymph samples from the apex of each cochlea were quantitatively analyzed using a fluorescence polarization immunoassay. In contrast to local RWM delivery, systemic application of gentamicin resulted in the highest perilymph levels in the apex of the cochlea with decreasing concentrations towards the basal regions of ST. The absolute gentamicin concentrations increased with the amount of drug applied and time before sampling. While it is likely that the basal-apical gradient measured after local drug applications to the round window niche is the result of the direct uptake of drugs into the perilymph of the ST, distribution by diffusion and a very low perilymph flow towards the cochlear apex, computer simulations suggested that the apical-basal gradient observed with these systemic applications can be explained by higher entry rates of gentamicin in the apex compared to the basal turns of the cochlea. It is also possible that gentamicin enters perilymph indirectly from the blood via the endolymph. In this case the faster kinetics in apical turns could be due to the smaller cross-sectional area of ST relative to endolymph in
Cartee, Lianne A; Miller, Charles A; van den Honert, Chris
2006-05-01
To determine the site of excitation on the spiral ganglion cell in response to electrical stimulation similar to that from a cochlear implant, single-fiber responses to electrical stimuli delivered by an electrode positioned in the scala tympani were compared to responses from stimuli delivered by an electrode placed in the internal auditory meatus. The response to intrameatal stimulation provided a control set of data with a known excitation site, the central axon of the spiral ganglion cell. For both intrameatal and scala tympani stimuli, the responses to single-pulse, summation, and refractory stimulus protocols were recorded. The data demonstrated that summation pulses, as opposed to single pulses, are likely to give the most insightful measures for determination of the site of excitation. Single-fiber summation data for both scala tympani and intrameatally stimulated fibers were analyzed with a clustering algorithm. Combining cluster analysis and additional numerical modeling data, it was hypothesized that the scala tympani responses corresponded to central excitation, peripheral excitation adjacent to the cell body, and peripheral excitation at a site distant from the cell body. Fibers stimulated by an intrameatal electrode demonstrated the greatest range of jitter measurements indicating that greater fiber independence may be achieved with intrameatal stimulation.
Kobayashi, T; Rokugo, M; Takasaka, T; Thalmann, R
1993-07-01
The effectiveness of perilymphatic perfusion with oxygenated artificial media upon the endocochlear potential (EP) was measured during systemic ischemia in the guinea pig. Differences in the effects of perfusion of the two perilymphatic scalae were determined. Perfusion of scala vestibuli with oxygenated artificial perilymph at a high flow rate resulted in complete recovery of the EP to the pre-ischemic level, whereas perfusion of scala tympani with the same medium was unable to effect complete recovery. The recovery obtained by perfusion of scala tympani was about half that obtained of scala vestibuli. The pO2 in scala media was measured during perfusion by means of oxygen-sensitive microelectrodes. perfusion of scala vestibuli led to an approximately two-fold higher pO2 in scala media than perfusion of scala tympani. During perfusion, the pO2 in scala media varied dependent upon depth of electrode insertion, with a gradient decreasing toward the stria vascularis, a direction opposite to that seen under normal metabolic conditions. These findings suggest that, in the ischemic cochlea, oxygen enters scala media more easily from scala vestibuli across Reissner's membrane than from scala tympani via the basilar membrane/organ of Corti complex.
Li, Yi-Ke; Yang, Juan-Mei; Huang, Yi-Bo; Ren, Dong-Dong; Chi, Fang-Lu
2015-06-01
The morphological changes that occur in the taste buds after denervation are not well understood in rats, especially in the contralateral tongue epithelium. In this study, we investigated the time course of morphological changes in the taste buds following unilateral nerve transection. The role of the trigeminal component of the lingual nerve in maintaining the structural integrity of the taste buds was also examined. Twenty-four Sprague-Dawley rats were randomly divided into three groups: control, unilateral chorda tympani nerve transection and unilateral chorda tympani nerve transection + lingual nerve transection. Rats were allowed up to 42 days of recovery before being euthanized. The taste buds were visualized using a cytokeratin 8 antibody. Taste bud counts, volumes and taste receptor cell numbers were quantified and compared among groups. No significant difference was detected between the chorda tympani nerve transection and chorda tympani nerve transection + lingual nerve transection groups. Taste bud counts, volumes and taste receptor cell numbers on the ipsilateral side all decreased significantly compared with control. On the contralateral side, the number of taste buds remained unchanged over time, but they were larger, and taste receptor cells were more numerous postoperatively. There was no evidence for a role of the trigeminal branch of the lingual nerve in maintaining the structural integrity of the anterior taste buds.
Directory of Open Access Journals (Sweden)
Yi-ke Li
2015-01-01
Full Text Available The morphological changes that occur in the taste buds after denervation are not well understood in rats, especially in the contralateral tongue epithelium. In this study, we investigated the time course of morphological changes in the taste buds following unilateral nerve transection. The role of the trigeminal component of the lingual nerve in maintaining the structural integrity of the taste buds was also examined. Twenty-four Sprague-Dawley rats were randomly divided into three groups: control, unilateral chorda tympani nerve transection and unilateral chorda tympani nerve transection + lingual nerve transection. Rats were allowed up to 42 days of recovery before being euthanized. The taste buds were visualized using a cytokeratin 8 antibody. Taste bud counts, volumes and taste receptor cell numbers were quantified and compared among groups. No significant difference was detected between the chorda tympani nerve transection and chorda tympani nerve transection + lingual nerve transection groups. Taste bud counts, volumes and taste receptor cell numbers on the ipsilateral side all decreased significantly compared with control. On the contralateral side, the number of taste buds remained unchanged over time, but they were larger, and taste receptor cells were more numerous postoperatively. There was no evidence for a role of the trigeminal branch of the lingual nerve in maintaining the structural integrity of the anterior taste buds.
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...
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.
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.
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
Sone, M
1998-10-01
The inner layer of the round window membrane is composed of mesothelial cells and this mesothelial cell layer extends to the scala tympani. This study describes the histopathologic findings of temporal bone analysis from a patient with bilateral perilymphatic fistula of the round window membrane. The left ear showed proliferation of mesothelial cells in the scala tympani of the basal turn adjoining the round window membrane. This cell proliferation is thought to be a reaction to the rupture of the round window membrane.
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
Changes in immunostaining of inner ears after antigen challenge into the scala tympani.
Ichimiya, I; Kurono, Y; Hirano, T; Mogi, G
1998-04-01
To study the mechanisms of immune responses and immune injuries in inner ears, labyrinthitis was induced by inoculation of keyhole limpet hemocyanin (KLH) into the scala tympani of systemically sensitized guinea pigs. Inner ears were then immunostained for KLH, immunoglobulin G (IgG), albumin, connexin26 (Cx26), and sodium-potassium adenosine triphosphate (Na,K-ATPase). Inflammatory cells containing KLH were observed in the scala tympani and in the collecting venule of the spiral modiolar vein (SMV). Spiral ligament, spiral limbus, and blood vessels including the SMV were diffusely positive for IgG and albumin. Immunoreactivity for Cx26 and Na,K-ATPase was decreased compared with the normal ears in the fibrocytes of the spiral ligament. These results suggest that inflammatory cells and blood constituents could extravasate into the cochlea from blood vessels and that fibrocyte damage in the spiral ligament could cause cochlear dysfunction.
Visualization of spiral ganglion neurites within the scala tympani with a cochlear implant in situ.
Chikar, Jennifer A; Batts, Shelley A; Pfingst, Bryan E; Raphael, Yehoash
2009-05-15
Current cochlear histology methods do not allow in situ processing of cochlear implants. The metal components of the implant preclude standard embedding and mid-modiolar sectioning, and whole mounts do not have the spatial resolution needed to view the implant within the scala tympani. One focus of recent auditory research is the regeneration of structures within the cochlea, particularly the ganglion cells and their processes, and there are multiple potential benefits to cochlear implant users from this work. To facilitate experimental investigations of auditory nerve regeneration performed in conjunction with cochlear implantation, it is critical to visualize the cochlear tissue and the implant together to determine if the nerve has made contact with the implant. This paper presents a novel histological technique that enables simultaneous visualization of the in situ cochlear implant and neurofilament-labeled nerve processes within the scala tympani, and the spatial relationship between them.
In vitro modifications of the scala tympani environment and the cochlear implant array surface.
Kontorinis, Georgios; Scheper, Verena; Wissel, Kirsten; Stöver, Timo; Lenarz, Thomas; Paasche, Gerrit
2012-09-01
To investigate the influence of alterations of the scala tympani environment and modifications of the surface of cochlear implant electrode arrays on insertion forces in vitro. Research experimental study. Fibroblasts producing neurotrophic factors were cultivated on the surface of Nucleus 24 Contour Advance electrodes. Forces were recorded by an Instron 5542 Force Measurement System as three modified arrays were inserted into an artificial scala tympani model filled with phosphate-buffered saline (PBS). The recorded forces were compared to control groups including three unmodified electrodes inserted into a model filled with PBS (unmodified environment) or Healon (current practice). Fluorescence microscopy was used before and after the insertions to identify any remaining fibroblasts. Additionally, three Contour Advance electrodes were inserted into an artificial model, filled with alginate/barium chloride solution at different concentrations, while insertion forces were recorded. Modification of the scala tympani environment with 50% to 75% alginate gel resulted in a significant decrease in the insertion forces. The fibroblast-coated arrays also led to decreased forces comparable to those recorded with Healon. Fluorescence microscopy revealed fully cell-covered arrays before and partially covered arrays after the insertion; the fibroblasts on the arrays' modiolar surface remained intact. Modifications of the scala tympani's environment with 50% to 75% alginate/barium chloride and of the cochlear implant electrode surface with neurotrophic factor-producing fibroblasts drastically reduce the insertion forces. As both modifications may serve future intracochlear therapies, it is expected that these might additionally reduce possible insertion trauma. Copyright © 2012 The American Laryngological, Rhinological, and Otological Society, Inc.
Perilymph composition in scala tympani of the cochlea: influence of cerebrospinal fluid.
Hara, A; Salt, A N; Thalmann, R
1989-11-01
A commonly used technique to obtain cochlear perilymph for analysis has been the aspiration of samples through the round window membrane. The present study has investigated the influence of the volume withdrawn on sample composition in the guinea pig. Samples of less than 200 nl in volume taken through the round window showed relatively high glycine content, comparable to the level found in samples taken from scala vestibuli. If larger volumes are withdrawn, lower glycine levels are observed. This is consistent with cerebrospinal fluid (having a low glycine content) being drawn into scala tympani through the cochlear aqueduct and contaminating the sample. The existence of a concentration difference for glycine between scala tympani perilymph and cerebrospinal fluid suggests the physiologic communication across the cochlear aqueduct is relatively small in this species. The observation of considerable exchange between cerebrospinal fluid and perilymph, as reported in some studies, is more likely to be an artifact of the experimental procedures, rather than of physiologic significance. Alternative sampling procedures have been evaluated which allow larger volumes of uncontaminated scala tympani perilymph to be collected.
Pierre, Pernilla Videhult; Engmér, Cecilia; Wallin, Inger; Laurell, Göran; Ehrsson, Hans
2009-02-01
High concentrations of the antioxidant thiosulfate reach scala tympani perilymph after i.v. administration in the guinea pig. Thiosulfate concentrations in perilymph remain elevated longer than in blood. This warrants further studies on the possibility of obtaining otoprotection by thiosulfate administration several hours before that of cisplatin without compromising the anticancer effect caused by cisplatin inactivation in the blood compartment. Thiosulfate may reduce cisplatin-induced ototoxicity, presumably by oxidative stress relief and formation of inactivate platinum complexes. This study aimed to explore to what extent thiosulfate reaches scala tympani perilymph after systemic administration in the guinea pig. Scala tympani perilymph (1 microl) was aspirated from the basal turn of each cochlea up to 3 h after thiosulfate administration (103 mg/kg b.w., i.v.). Blood samples were also taken. Thiosulfate was quantified by HPLC and fluorescence detection. Substantial thiosulfate concentrations were found in perilymph. The area under the concentration-time curve for thiosulfate in perilymph and blood was 3100 microMxmin and 6300 microMxmin, respectively. The highest thiosulfate concentrations in perilymph were found at the first sampling at about 10 min. Due to a more rapid elimination from blood, perilymph concentrations exceeded those of blood towards the end of the experiment.
BDNF is required for taste axon regeneration following unilateral chorda tympani nerve section.
Meng, Lingbin; Huang, Tao; Sun, Chengsan; Hill, David L; Krimm, Robin
2017-07-01
Taste nerves readily regenerate to reinnervate denervated taste buds; however, factors required for regeneration have not yet been identified. When the chorda tympani nerve is sectioned, expression of brain-derived neurotrophic factor (BDNF) remains high in the geniculate ganglion and lingual epithelium, despite the loss of taste buds. These observations suggest that BDNF is present in the taste system after nerve section and may support taste nerve regeneration. To test this hypothesis, we inducibly deleted Bdnf during adulthood in mice. Shortly after Bdnf gene recombination, the chorda tympani nerve was unilaterally sectioned causing a loss of both taste buds and neurons, irrespective of BDNF levels. Eight weeks after nerve section, however, regeneration was differentially affected by Bdnf deletion. In control mice, there was regeneration of the chorda tympani nerve and taste buds reappeared with innervation. In contrast, few taste buds were reinnervated in mice lacking normal Bdnf expression such that taste bud number remained low. In all genotypes, taste buds that were reinnervated were normal-sized, but non-innervated taste buds remained small and atrophic. On the side of the tongue contralateral to the nerve section, taste buds for some genotypes became larger and all taste buds remained innervated. Our findings suggest that BDNF is required for nerve regeneration following gustatory nerve section. Copyright © 2017 Elsevier Inc. All rights reserved.
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.
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
Saito, Takehisa; Ito, Tetsufumi; Kato, Yuji; Yamada, Takechiyo; Manabe, Yasuhiro; Narita, Norihiko
2014-03-01
To evaluate whether regenerated fungiform taste buds after severing the chorda tympani nerve can be detected by confocal laser scanning microscopy in vivo. Retrospective study. University hospital. Six patients with a normal gustatory function (Group 1), 9 patients with taste function recovery after severing the CTN (Group 2), and 5 patients without taste function recovery (Group 3) were included. In Groups 2 and 3, canal wall up (closed) tympanoplasty or canal wall down with canal reconstruction tympanoplasty was performed in all patients. Diagnostic. The severed nerves were readapted or approximated on the temporalis muscle fascia used to reconstruct the eardrum during surgery. Preoperative and postoperative gustatory functions were assessed using electrogustometry. Twelve to 260 months after severing the CTN, the surface of the midlateral region of the tongue was observed with a confocal laser microscope. EGM thresholds showed no response 1 month after surgery in all patients of Groups 2 and 3. In Group 2, EGM thresholds showed recovery 1 to 2 years after surgery and before confocal microscopy (-1.3 ± 6.5 dB). There was a significant difference between Group 1 (-5.7 ± 2.0 dB; p taste buds were observed in each FP, and 55 (79.7%) of 69 FP contained at least 1 taste bud. The mean number of taste bud per papilla was 3.7 ± 3.6. In patients with a recovered taste function (Group 2), 0 to 8 taste buds were observed in each FP. In this group, 54 (56.2%) of 94 FP contained at least 1 taste bud. The mean number of taste bud per papilla was 2.0 ± 2.2 (p taste bud was observed. Regenerated fungiform taste bud could be observed in vivo using confocal laser scanning microscopy, indicating that regenerated taste bud can be detected without biopsy.
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.)
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...
Animal model of cochlear third window in the scala vestibuli or scala tympani.
Attias, Joseph; Preis, Michal; Shemesh, Rafi; Hadar, Tuvia; Nageris, Ben I
2010-08-01
The auditory impact of a cochlear third window differs by its location in the scala vestibuli or scala tympani. Pathologic third window has been investigated primarily in the vestibular apparatus of animals and humans. Dehiscence of the superior semicircular canal is the clinical model. Fat sand rats (n = 11) have a unique inner-ear anatomy that allows easy surgical access. A window was drilled in the bony labyrinth over the scala vestibuli in 1 group (12 ears) and over the scala tympani in another (7 ears) while preserving the membranous labyrinth. Auditory brain stem responses to high- and low-frequency stimuli delivered by air and bone conduction were recorded before and after the procedure. Scala vestibuli group: preoperative air-conduction thresholds to clicks and tone-bursts averaged 8.3 and 9.6 dB, respectively, and bone-conduction thresholds, 4.6 and 3.3 dB, respectively; after fenestration, air-conduction thresholds averaged 40.4 and 41.8 dB, respectively, and bone-conduction thresholds, -1 and 5.6 dB, respectively. Scala tympani group: preoperative air-conduction thresholds to clicks and tone-bursts averaged 8.6 dB each, and bone-conduction thresholds, 7.9 dB and 7.1 dB, respectively; after fenestration, air-conduction thresholds averaged 11.4 and 9.3 dB, respectively, and bone-conduction thresholds, 9.3 and 4.2 dB, respectively. The changes in air- (p = 0.0001) and bone-conduction (p = 0.04) thresholds were statistically significant only in the scala vestibuli group. The presence of a cochlear third window over the scala vestibuli, but not over the scala tympani, causes a significant increase in air-conduction auditory thresholds. These results agree with the theoretic model and clinical findings and contribute to our understanding of vestibular dehiscence.
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
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.)
Plontke, Stefan K; Mynatt, Robert; Gill, Ruth M; Borgmann, Stefan; Salt, Alec N
2007-07-01
The distribution of gentamicin along the fluid spaces of the cochlea after local applications has never previously been demonstrated. Computer simulations have predicted that significant basal-apical concentration gradients might be expected, and histologic studies indicate that hair cell damage is greater at the base than at the apex after local gentamicin application. In the present study, gradients of gentamicin along the cochlea were measured. A recently developed method of sampling perilymph from the cochlear apex of guinea pigs was used in which the samples represent fluid originating from different regions along the scala tympani. Gentamicin concentration was determined in sequential apical samples that were taken after up to 3 hours of local application to the round window niche. Substantial gradients of gentamicin along the length of the scala tympani were demonstrated and quantified, averaging more than 4,000 times greater concentration at the base compared with the apex at the time of sampling. Peak concentrations and gradients for gentamicin varied considerably between animals, likely resulting from variations in round window membrane permeability and rates of perilymph flow. The large gradients for gentamicin demonstrated here in guinea pigs account for how it is possible to suppress vestibular function in some patients with a local application of gentamicin without damaging auditory function. Variations in round window membrane permeability and in perilymph flow could account for why hearing losses are observed in some patients.
Plontke, Stefan K.; Mynatt, Robert; Gill, Ruth M.; Borgmann, Stefan; Salt, Alec N.
2008-01-01
Objectives The distribution of gentamicin along the fluid spaces of the cochlea following local applications has never previously been demonstrated. Computer simulations have predicted that significant basal-apical concentration gradients might be expected and histological studies indicate that hair cell damage is greater at the base than at the apex following local gentamicin application. In the present study, gradients of gentamicin along the cochlea were measured. Methods A recently-developed method of sampling perilymph from the cochlear apex of guinea pigs was used, in which the samples represent fluid originating from different regions along scala tympani. Gentamicin concentration was determined in sequential apical samples which were taken following up to three hours of local application to the round window niche. Results Substantial gradients of gentamicin along the length of scala tympani were demonstrated and quantified, averaging more than 4000 times greater concentration at the base compared to the apex at the time of sampling. Peak concentrations and gradients for gentamicin varied considerably between animals, likely resulting from variations in round window membrane permeability and rates of perilymph flow. Conclusions The large gradients for gentamicin demonstrated here in guinea pigs account for how it is possible to suppress vestibular function in some patients with a local application of gentamicin without damaging auditory function. Variations in round window membrane permeability and in perilymph flow could account for why hearing losses are observed in some patients. PMID:17603318
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.
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.
Assessment of Middle Ear Function during the Acoustic Reflex Using Laser-Doppler Vibrometry
2017-08-07
gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any...Keefe 1999, Silman 2012); whereas the acoustic reflex activates both stapedius and tensor tympani MEMCs in many animals (Forbes & Sherrington 1914...stapedius) and one muscle that attaches the neck of the malleus (i.e., the tensor tympani). These muscles are innervated by branches of the facial (CN
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.
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...
Briaire, Jeroen J; Frijns, Johan H M
2006-04-01
Cochlear implant research endeavors to optimize the spatial selectivity, threshold and dynamic range with the objective of improving the speech perception performance of the implant user. One of the ways to achieve some of these goals is by electrode design. New cochlear implant electrode designs strive to bring the electrode contacts into close proximity to the nerve fibers in the modiolus: this is done by placing the contacts on the medial side of the array and positioning the implant against the medial wall of scala tympani. The question remains whether this is the optimal position for a cochlea with intact neural fibers and, if so, whether it is also true for a cochlea with degenerated neural fibers. In this study a computational model of the implanted human cochlea is used to investigate the optimal position of the array with respect to threshold, dynamic range and spatial selectivity for a cochlea with intact nerve fibers and for degenerated nerve fibers. In addition, the model is used to evaluate the predictive value of eCAP measurements for obtaining peri-operative information on the neural status. The model predicts improved threshold, dynamic range and spatial selectivity for the peri-modiolar position at the basal end of the cochlea, with minimal influence of neural degeneration. At the apical end of the array (1.5 cochlear turns), the dynamic range and the spatial selectivity are limited due to the occurrence of cross-turn stimulation, with the exception of the condition without neural degeneration and with the electrode array along the lateral wall of scala tympani. The eCAP simulations indicate that a large P(0) peak occurs before the N(1)P(1) complex when the fibers are not degenerated. The absence of this peak might be used as an indicator for neural degeneration.
Tensor veli palatini electromyography for monitoring Eustachian tube rehabilitation in otitis media.
Picciotti, P M; Della Marca, G; D'Alatri, L; Lucidi, D; Rigante, M; Scarano, E
2017-05-01
The pathogenesis of otitis media is related to Eustachian tube dysfunction. The tensor veli palatini muscle actively opens the Eustachian tube and promotes middle-ear ventilation. This study describes a technique for paratubal electromyography that uses a surface, non-invasive electrode able to record tensor veli palatini muscle activity during swallowing. Twenty otitis media patients and 10 healthy patients underwent tensor veli palatini electromyography. Activity of this muscle before and after Eustachian tube rehabilitation was also assessed. In 78.5 per cent of patients, the electromyography duration phase and/or amplitude were reduced in the affected side. The muscle action potential was impaired in all patients who underwent Eustachian tube rehabilitation. This study confirmed that Eustachian tube muscle dysfunction has a role in otitis media pathogenesis and showed that muscle activity increases after Eustachian tube rehabilitation therapy.
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.
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...
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…
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.
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...
Lesinski, S George; Prewitt, Jessica; Bray, Victor; Aravamudhan, Radhika; Bermeo Blanco, Oscar A; Farmer-Fedor, Brenda L; Ward, Jonette A
2014-04-01
The safety of implanting a titanium microactuator into the lateral wall of cat scala tympani was assessed by comparing preoperative and postoperative auditory brainstem response (ABR) thresholds for 1 to 3 months. The safety of directly stimulating cochlear perilymph with an implantable hearing system requires maintaining preoperative hearing levels. This cat study is an essential step in the development of the next generation of fully implantable hearing devices for humans. Following GLP surgical standards, a 1-mm cochleostomy was drilled into the lateral wall of the scala tympani, and a nonfunctioning titanium anchor/microactuator assembly was inserted in 8 cats. The scala media was damaged in the 1 cat. ABR thresholds with click and 4- and 8-kHz stimuli were measured preoperatively and compared with postoperative thresholds at 1, 2, and 3 months. Nonimplanted ear thresholds were also measured to establish statistical significance for threshold shifts (>28.4 dB). Two audiologists independently interpreted thresholds. Postoperatively, 7 cats implanted in the scala tympani demonstrated no significant ABR threshold shift for click stimulus; one shifted ABR thresholds to 4- and 8-kHz stimuli. The eighth cat, with surgical damage to the scala media, maintained stable click threshold but had a significant shift to 4- and 8-kHz stimuli. This cat study provides no evidence of worsening hearing thresholds after fenestration of the scala tympani and insertion of a titanium anchor/microactuator, provided there is no surgical trauma to the scala media and the implanted device is securely anchored in the cochleostomy. These 2 issues have been resolved in the development of a fully implantable hearing system for humans. The long-term hearing stability (combined with histologic studies) reaffirm that the microactuator is well tolerated by the cat cochlea.
Trudel, Mathieu; Côté, Mathieu; Philippon, Daniel; Simonyan, David; Villemure-Poliquin, Noémie; Bussières, Richard
2018-07-01
To compare scala vestibuli versus scala tympani cochlear implantation in terms of postoperative auditory performances and programming parameters in patients with severe scala tympani ossification. Retrospective case-control study. Tertiary referral center. One hundred three pediatric and adult patients who underwent cochlear implant surgery between 2000 and 2016. Three groups were formed: a scala vestibuli group, a scala tympani with ossification group, and a scala tympani without ossification group. Patients were matched based on their age, sex, duration of deafness, and side of implantation (ratio of 1:2:2). Postoperative evaluation of auditory performances and programming parameters following intensive functional rehabilitation program completion. Multimedia adaptive test (MAT), hearing in noise test (HINT SNR +10 dB, HINT SNR +5 dB, and HINT SNR +0 dB), impedances, neural response telemetry thresholds (NRT), neural response imaging thresholds (NRI), comfortable levels (C-levels), and threshold levels (T-levels) were compared between groups. Twenty-one patients underwent scala vestibuli cochlear implantation: 19 adults and two children. Auditory performances were similar between groups, although sentence recognition in a noisy environment was slightly higher in the scala vestibuli group. Impedance values were also higher in the scala vestibuli group, but all other programming parameters were similar between groups. We present the largest series of patients with scala vestibuli cochlear implantation. This approach provides at least comparable auditory performances without having any deleterious effects on programming parameters. This viable and useful insertion route might be the primary surgical alternative when facing partial cochlear ossification.
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
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...
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 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...
Shepherd, R K; Clark, G M; Xu, S A; Pyman, B C
1995-03-01
result in more extensive neural degeneration compared with electrodes located within the scala tympani. In conclusion, the present study has shown that the reimplantation of a multichannel scala, tympani electrode array can be achieved with minimal damage to the majority of cochlear structures. Increased insertion trauma, resulting in new bone formation and spiral ganglion cell loss, can occur in the lower basal turn in cases where the electrode entry point is difficult to identify due to proliferation of granulation and fibrous tissue.
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.
Effect of Chorda Tympani Nerve Transection on Salt Taste Perception in Mice
Ishiwatari, Yutaka; Theodorides, Maria L.; Bachmanov, Alexander A.
2011-01-01
Effects of gustatory nerve transection on salt taste have been studied extensively in rats and hamsters but have not been well explored in the mouse. We examined the effects of chorda tympani (CT) nerve transection on NaCl taste preferences and thresholds in outbred CD-1 mice using a high-throughput phenotyping method developed in our laboratory. To measure taste thresholds, mice were conditioned by oral self-administration of LiCl or NaCl and then presented with NaCl concentration series in 2-bottle preference tests. LiCl-conditioned and control NaCl-exposed mice were given bilateral transections of the CT nerve (LiCl-CTX, NaCl-CTX) or were left intact as controls (LiCl-CNT, NaCl-CNT). After recovery from surgery, mice received a concentration series of NaCl (0–300 mM) in 48-h 2-bottle tests. CT transection increased NaCl taste thresholds in LiCl-conditioned mice and eliminated avoidance of concentrated NaCl in control NaCl-exposed mice. This demonstrates that in mice, the CT nerve is important for detection and recognition of NaCl taste and is necessary for the normal avoidance of high concentrations of NaCl. The results of this experiment also show that the method of high-throughput phenotyping of salt taste thresholds is suitable for detecting changes in the taste periphery in mouse genetic studies. PMID:21743094
Ni, D
1992-12-01
A physiological investigation of cochlear electrical stimulation was undertaken in six two-month-old kittens. The scala tympani electrodes were implanted and electrically stimulated using biphasic balanced electrical pulses for periods of 1000-1500h in four ears. Four ears received implants for same period but without electrical stimulation. The other two ears served as normal control. The results indicated: 1) Chronic electrical stimulation of the cochlea within electrochemically safe limits did not influence the hearing of kittens and the normal delivery of impulses evoked by acoustic and electrical signals on the auditory brainstem pathway. 2) The wave shapes of EABRs were similar to those of ABRs. The amplitudes of EABRs showed a significant increase following chronic electrical stimulation, resulting in a leftward shift in the input/output function. The absolute latencies and interwave latencies of waves II-III, III-IV and II-IV were significantly shorter than those of ABRs. These results imply that there was no adverse effect of chronic electrical stimulation on the maturing auditory systems of kittens using these electrical parameters and the mechanism of electrical hearing should be further studied.
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
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.)
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
Verberne, Juul; Risi, Frank; Campbell, Luke; Chambers, Scott; O'Leary, Stephen
2017-01-01
Scala tympani morphology influences the insertion dynamics and intra-scalar position of straight electrode arrays. Hearing preservation is the goal of cochlear implantation with current thin straight electrode arrays. These hug the lateral wall, facilitating full, atraumatic insertions. However, most studies still report some postoperative hearing loss. This study explores the influence of scala tympani morphology on array position relative to the basilar membrane and its possible contribution to postoperative hearing loss. Twenty-six fresh-frozen human temporal bones implanted with a straight electrode array were three-dimensionally reconstructed from micro-photographic histological sections. Insertion depth and the proximity between the array and basilar membrane were recorded. Lateral wall shape was quantified as a curvature ratio. Insertion depths ranged from 233 to 470 degrees. The mean first point of contact between the array and basilar membrane was 185 degrees; arrays tended to remain in contact with the membrane after first contacting it. Eighty-nine and 93% of arrays that reached the upper basal (>240-360 degrees) and second (>360-720 degrees) turns respectively contacted the basilar membrane in these regions. Scalar wall curvature ratio decreased significantly (the wall became steeper) from the basal to second turns. This shift correlated with a reduced distance between the array and basilar membrane. Scala tympani morphology influences the insertion dynamics and intra-scalar position of a straight electrode array. In addition to gross trauma of cochlear structures, contact between the array and basilar membrane and how this impacts membrane function should be considered in hearing preservation cases.
Hans, P; Grant, A J; Laitt, R D; Ramsden, R T; Kassner, A; Jackson, A
1999-08-01
Cochlear implantation requires introduction of a stimulating electrode array into the scala vestibuli or scala tympani. Although these structures can be separately identified on many high-resolution scans, it is often difficult to ascertain whether these channels are patent throughout their length. The aim of this study was to determine whether an optimized combination of an imaging protocol and a visualization technique allows routine 3D rendering of the scala vestibuli and scala tympani. A submillimeter T2 fast spin-echo imaging sequence was designed to optimize the performance of 3D visualization methods. The spatial resolution was determined experimentally using primary images and 3D surface and volume renderings from eight healthy subjects. These data were used to develop the imaging sequence and to compare the quality and signal-to-noise dependency of four data visualization algorithms: maximum intensity projection, ray casting with transparent voxels, ray casting with opaque voxels, and isosurface rendering. The ability of these methods to produce 3D renderings of the scala tympani and scala vestibuli was also examined. The imaging technique was used in five patients with sensorineural deafness. Visualization techniques produced optimal results in combination with an isotropic volume imaging sequence. Clinicians preferred the isosurface-rendered images to other 3D visualizations. Both isosurface and ray casting displayed the scala vestibuli and scala tympani throughout their length. Abnormalities were shown in three patients, and in one of these, a focal occlusion of the scala tympani was confirmed at surgery. Three-dimensional images of the scala vestibuli and scala tympani can be routinely produced. The combination of an MR sequence optimized for use with isosurface rendering or ray-casting algorithms can produce 3D images with greater spatial resolution and anatomic detail than has been possible previously.
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.
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
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.
Plontke, Stefan K; Biegner, Thorsten; Kammerer, Bernd; Delabar, Ursular; Salt, Alec N
2008-04-01
Local application of dexamethasone-21-dihydrogen-phosphate (Dex-P) to the round window (RW) membrane of guinea pigs produces a substantial basal-apical concentration gradient in scala tympani (ST) perilymph. In recent years, intratympanically applied glucocorticoids are increasingly being used for the treatment of inner ear disease. Although measurements of intracochlear concentrations after RW application exist, there is limited information on the distribution of these drugs in the inner ear fluids. It has been predicted from computer simulations that substantial concentration gradients will occur after RW application, with lower concentrations expected in apical turns. Concentration gradients of other substances along the cochlea have recently been confirmed using a sequential apical sampling method to obtain perilymph. Dexamethasone-21-dihydrogen-phosphate (10 mg/ml) was administered to the RW membrane of guinea pigs (n = 9) in vivo for 2 to 3 hours. Perilymph was then collected using a protocol in which 10 samples, each of approximately 1 mul, were taken sequentially from the cochlear apex into capillary tubes. Dexamethasone-21-dihydrogen-phosphate concentration of the samples was analyzed by high-performance liquid chromatography. Interpretation of sample data using a finite element model allowed the longitudinal gradients of Dex-P in ST to be quantified. The Dex-P content of the first sample in each experiment (dominated by perilymph from apical regions) was substantially lower than that of the third and fourth sample (dominated by basal turn perilymph). These findings qualitatively demonstrated the existence of a concentration gradient along ST. After detailed analysis of the measured sample concentrations using an established finite element computer model, the mean basal-apical concentration gradient was estimated to be 17,000. Both absolute concentrations of Dex-P in ST and the basal-apical gradients were found to vary substantially. The existence of
Hahn, Hartmut; Kammerer, Bernd; DiMauro, Andre; Salt, Alec N; Plontke, Stefan K
2006-02-01
Before new drugs for the treatment of inner ear disorders can be studied in controlled clinical trials, it is important that their pharmacokinetics be established in inner ear fluids. Microdialysis allows drug levels to be measured in perilymph without the volume disturbances and potential cerebrospinal fluid contamination associated with fluid sampling. The aims of this study were to show: (i) that despite low recovery rates from miniature dialysis probes, significant amounts of drug are removed from small fluid compartments, (ii) that dialysis sampling artifacts can be accounted for using computer simulations and (iii) that microdialysis allows quantification of the entry rates through the round window membrane (RWM) into scala tympani (ST). Initial experiments used microdialysis probes in small compartments in vitro containing sodium fluorescein. Stable concentrations were observed in large compartments (1000 microl) but significant concentration declines were observed in smaller compartments (100, 10 and 5.6 microl) comparable to the size of the inner ear. Computer simulations of these experiments closely approximated the experimental data. In in vivo experiments, sodium fluorescein 10 mg/ml and dexamethasone-dihydrogen-phosphate disodium salt 8 mg/ml were simultaneously applied to the RWM of guinea pigs. Perilymph concentration in the basal turn of ST was monitored using microdialysis. The fluorescein concentration reached after 200 min application (585+/-527 microg/ml) was approximately twice that of dexamethasone phosphate (291+/-369 microg/ml). Substantial variation in concentrations was found between animals by approximately a factor of 34 for fluorescein and at least 41 for dexamethasone phosphate. This is, to a large extent, thought to be the result of the RWM permeability varying in different animals. It was not caused by substance analysis variations, because two different analytic methods were used and the concentration ratio between the two
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...
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.
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.
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.
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.
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....
Angeli, Roberto D; Lavinsky, Joel; Setogutti, Enio T; Lavinsky, Luiz
2017-01-01
The aim of this work was to describe the dimensions of the crista fenestra and determine its presence by means of high-resolution computed tomography (CT) for the purpose of cochlear implantation via the round window approach. A series of 10 adult human temporal bones underwent high-resolution CT scanning and were further dissected for microscopic study of the round window niche. In all of the specimens, the round window membrane was fully visualized after the complete removal of bony overhangs. The crista fenestra was identified as a sharp bony crest located in the anterior and inferior borders of the niche; its area ranged from 0.28 to 0.80 mm2 (mean 0.51 ± 0.18). The proportion of the area occupied by the crista fenestra in the whole circumference of the round window ranged from 23 to 50% (mean 36%). We found a moderate positive correlation between the area of the niche and the dimensions of the crista fenestra (Spearman rho: 0.491). In every case, high-resolution CT scanning was unable to determine the presence of the crista fenestra. The crista fenestra occupies a variable but expressive area within the bony round window niche. Narrower round window niches tended to house smaller crests. The presence of the crista fenestra is an important obstacle to adequate access to the scala tympani. Nevertheless, a high-resolution CT scan provides no additional preoperative information with regard to its presence for the purpose of surgical access to the scala tympani via the round window niche. © 2017 S. Karger AG, Basel.
Hahn, Hartmut; Salt, Alec N.; Biegner, Thorsten; Kammerer, Bernd; Delabar, Ursular; Hartsock, Jared; Plontke, Stefan K.
2012-01-01
Hypothesis To determine whether intracochlearly applied dexamethasone will lead to better control of drug levels, higher peak concentrations and lower base-to apex concentration gradients in scala tympani (ST) of the guinea pig than after intratympanic (round window, RW) application. Background Local application of drugs to the RW results in substantial variation of intracochlear drug levels and significant base-to apex concentration gradients in ST. Methods Two μL of dexamethasone-phosphate (10 mg/mL) were injected into ST either through the RW membrane which was covered with 1% sodium hyaluronate gel or through a cochleostomy with a fluid tight seal of the micropipette. Perilymph was sequentially sampled from the apex at a single time point for each animal, at 20, 80, or 200 min after the injection ended. Results were mathematically interpreted by the means of an established computer model and compared with prior experiments performed by our group with the same experimental techniques but using intratympanic applications. Results Single intracochlear injections over 20 min resulted in approximately ten times higher peak concentrations (on average) than 2-3 hours of intratympanic application to the round window niche. Intracochlear drug levels were less variable and could be measured for at least up to 220 min. Concentration gradients along scala tympani were less pronounced. The remaining variability in intracochlear drug levels was attributable to perilymph and drug leak from the injection site. Conclusion With significantly higher, less variable drug levels and smaller base-to apex concentration gradients, intracochlear applications have advantages to intratympanic injections. For further development of this technique, it is of importance to control leaks of perilymph and drug from the injection site and to evaluate its clinical feasibility and associated risks. PMID:22588238
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.
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.
Pyomyositis of tensor fascia lata: a case report
Ozkan, Korhan; Unay, Koray; Ugutmen, Ender; Eren, Abdullah; Eceviz, Engin; Saygý, Baransel
2008-01-01
Introduction Pyomyositis is a disease in which an abscess is formed deep within large striated muscles. Case presentation We report the case of a 10-year-old boy who presented with fever and a painful hip and was subsequently diagnosed with pyomyositis of the tensor fascia lata. In children with clinical and laboratory findings of inflammation in the vicinity of the hip joint, the differential diagnosis includes transient synovitis, an early stage of Legg-Calvé-Perthes disease, infectious arthritis of the hip, rheumatologic diseases and extracapsular infection such as osteomyelitis. Conclusion To the best of the authors' knowledge, this is the first report of pyomyositis of the tensor fascia lata. Although pyomyositis is a rare disease and the differential diagnosis includes a variety of other commonly observed diseases, pyomyositis should be considered in cases where children present with fever, leukocytosis and localized pain. PMID:18652647
Pyomyositis of tensor fascia lata: a case report
Directory of Open Access Journals (Sweden)
Ozkan Korhan
2008-07-01
Full Text Available Abstract Introduction Pyomyositis is a disease in which an abscess is formed deep within large striated muscles. Case presentation We report the case of a 10-year-old boy who presented with fever and a painful hip and was subsequently diagnosed with pyomyositis of the tensor fascia lata. In children with clinical and laboratory findings of inflammation in the vicinity of the hip joint, the differential diagnosis includes transient synovitis, an early stage of Legg-Calvé-Perthes disease, infectious arthritis of the hip, rheumatologic diseases and extracapsular infection such as osteomyelitis. Conclusion To the best of the authors' knowledge, this is the first report of pyomyositis of the tensor fascia lata. Although pyomyositis is a rare disease and the differential diagnosis includes a variety of other commonly observed diseases, pyomyositis should be considered in cases where children present with fever, leukocytosis and localized pain.
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.
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.
An introduction to visualization of diffusion tensor imaging and its applications
Vilanova, A.; Zhang, S.; Kindlmann, G.; Laidlaw, D.H.; Weickert, J.; Hagen, H.
2005-01-01
Summary. Water diffusion is anisotropic in organized tissues such as white matter and muscle. Diffusion tensor imaging (DTI), a non-invasive MR technique, measures water self-diffusion rates and thus gives an indication of the underlying tissue microstructure. The diffusion rate is often expressed
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.
Z. Bani Ismail; A. Al-Majali; K. Al-Qudah
2007-01-01
Medical records of 31 adult dairy cows suffering from recurrent rumen tympany for at least 1 month duration that underwent exploratory laparotomy and rumenotomy were reviewed and information was obtained on signalment, history, physical examination findings, laboratory findings and surgical findings. Cases were categorized according to surgical findings into 3 groups. Group 1 (n = 10) included cattle with reticuloruminal, metallic foreign bodies and perireticular adhesions/inflammation, group...
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 ...
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...
Li, Yong-he; Chen, Hao; Guo, Meng-he
2008-02-01
To study the therapeutic effect of insulin-like growth factor-1 (IGF-1) injection into the inner ears through a scala tympani fenestration on sensorineural deafness in a guinea pig model of gentamicin-induced hearing loss. Twenty guinea pigs with gentamicin-induced hearing loss were randomized equally into IGF-1 group and control group. In both groups, scala tympani fenestration was performed for injection of IGF-1 (10 microl) or artificial perilymphatic fluid (10 microl). Auditory brainstem responses (ABR) test was performed before and 7 and 14 days after surgery, respectively, and the cochlea was removed by decollation of 3 guinea pigs from each group after ABR test for observing the changes in the hair cells using scanning electron microscope. Significant reduction in the ABR response threshold (RT) occurred in IGF-1 group 7 and 14 days after the surgery, and on day 14, ABR RT showed significant difference between IGF-1 group and the control group. Scanning electron microscopy revealed severer damages of the hair cells in the control group, and in the IGF-1 group, finger-like microvilli was detected on the surface of the damaged hair cells. IGF-1 injection in the inner ear through the scala tympani fenestration may ameliorate the damages of the auditory function and relieve sustained toxicity of gentamicin in guinea pigs possibly by protection and partial repair of the damaged cochlea hair cells as well as protection of the afferent nerves.
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.
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.
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.
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...
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.
Roeder, B L; Chengappa, M M; Nagaraja, T G; Avery, T B; Kennedy, G A
1988-02-01
The etiologic role of Clostridum perfringens type A in the acute abdominal syndrome characterized by abomasal and rumen tympany, abomasitis, and abomasal ulceration was investigated in neonatal calves. Eight calves, 4 to 12 days old, were inoculated intraruminally with toxigenic C perfringens type A. Before and after C perfringens inoculation, blood samples were collected from all calves for blood gas and serum biochemical analysis and for determination of serum copper concentration; ruminal fluid was obtained for isolation of C perfringens. Calves were monitored daily for clinical signs of the syndrome and, depending on the severity of clinical signs, they were either euthanatized or redosed within 4 to 7 days. After necropsy, specimens obtained from the abomasum and rumen for macroscopic and microscopic examination and for anaerobic bacteriologic culture were processed in routine manner. Intraruminal inoculation of C perfringens type A into healthy calves induced anorexia, depression, bloat, diarrhea, and in some calves, death. Serum copper concentration was within normal range. Necropsy revealed variable degrees of abomasitis, petechial and ecchymotic hemorrhages, and ulcers (ranging from pinpoint to nearly perforate) in the abomasum. Seven of those calves also had multiple trichobezoars in the rumen. These necropsy findings were not seen in calves (controls) given distilled H2O only. In affected calves, acute abdominal syndrome was unrelated to copper deficiency, and C perfringens type A given intraruminally was able to induce clinical signs similar to those of the naturally acquired disease.
Shi, Xunbei; Wu, Nan; Zhang, Yue; Guo, Weiwei; Lin, Chang; Yang, Shiming
2017-09-01
To investigate the expression of the miniature pig cochlea after AAV1 transfect into the cochlea via round window membrane (RWM). Twenty miniature pigs are equally divided into four experimental groups. Twelve miniature pigs are equally divided into four control groups. Each pig was transfected with the AAV1 in the experimental group via RWM and each pig was transduced with the artificial perilymph in the control group. The expression of green fluorescent protein (GFP) was observed at 2 weeks, 3 weeks and 4 weeks, respectively. Likewise, AAV1 was delivered into the guinea pigs cochleas using the same method, and the results were compared with that of the miniature pigs. The expression was mainly in the inner hair cells of the miniature pig. The expression of GFP began to appear at 2 weeks, reached the peak at 3 weeks. It also expressed in Hensen's cells, inner pillar cells, outer pillar cells, spiral limbus, and spiral ligament. In the meanwhile, AAV1 was delivered into guinea pig cochlea via the same method, and AAV1 was also expressed in the inner hair cells. But the expression peaked at 2 weeks, and the efficiency of the inner hair cell transfection was higher than that of the pig. AAV1 can be transformed into miniature pig cochlea via scala tympani by the RWM method efficiently.
Saito, Takehisa; Ito, Tetsufumi; Ito, Yumi; Kato, Yuji; Manabe, Yasuhiro; Narita, Norihiko
2015-03-01
To elucidate the degeneration process of fungiform taste buds after severing the chorda tympani nerve (CTN) by confocal laser scanning microscopy in vivo. Prospective study. University hospital. Seven consecutive patients whose CTN was severed during tympanoplasty for middle ear cholesteatoma. Diagnostic. Preoperative and postoperative gustatory functions were assessed by electrogustometry (EGM). An average of 10 fungiform papillae (FP) in the midlateral region of the tongue were periodically observed, and the number of taste buds was counted using a confocal laser microscope. Among them, 2 to 3 reference FPs were selected based on the typical form of the FP or characteristic arrangements of taste pores. Observation was performed before surgery, 1 or 2 days after surgery, 2 or 3 times a week until 2 weeks after surgery, once a week between 2 and 4 weeks, and every 2 to 4 weeks thereafter until all taste buds had disappeared. EGM thresholds showed no response within 1 month after surgery in all patients. The initial change in the degeneration process was the disappearance of taste pores. The surface of taste buds became covered with epithelium. Finally, taste buds themselves atrofied and disappeared. The time course of degeneration differed depending upon individuals, each FP, and each taste bud. By employing the generalized linear mixed model under the Poisson distribution, it was calculated that all taste buds would disappear at around 50 days after surgery. Confocal laser scanning microscopy was useful for clarifying the degeneration process of fungiform taste buds.
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...
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.
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.)
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
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).
Umehara, Jun; Ikezoe, Tome; Nishishita, Satoru; Nakamura, Masatoshi; Umegaki, Hiroki; Kobayashi, Takuya; Fujita, Kosuke; Ichihashi, Noriaki
2015-12-01
Decreased flexibility of the tensor fasciae latae is one factor that causes iliotibial band syndrome. Stretching has been used to improve flexibility or tightness of the muscle. However, no studies have investigated the effective stretching position for the tensor fasciae latae using an index to quantify muscle elongation in vivo. The aim of this study was to investigate the effects of hip rotation and knee angle on tensor fasciae latae elongation during stretching in vivo using ultrasonic shear wave elastography. Twenty healthy men participated in this study. The shear elastic modulus of the tensor fasciae latae was calculated using ultrasonic shear wave elastography. Stretching was performed at maximal hip adduction and maximal hip extension in 12 different positions with three hip rotation conditions (neutral, internal, and external rotations) and four knee angles (0°, 45°, 90°, and 135°). Two-way analysis of variance showed a significant main effect for knee angle, but not for hip rotation. The post-hoc test for knee angle indicated that the shear elastic modulus at 90° and 135° were significantly greater than those at 0° and 45°. Our results suggest that adding hip rotation to the stretching position with hip adduction and extension may have less effect on tensor fasciae latae elongation, and that stretching at >90° of knee flexion may effectively elongate the tensor fasciae latae. Copyright © 2015 Elsevier Ltd. All rights reserved.
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)
Lamm, K; Lamm, C; Lamm, H; Schumann, K
1988-09-01
In 14 guinea pigs the pO2 in the perilymph of the scala tympani fell to 50%-80% of the original value during exposure to noise consisting of 4,000 Hz clicks with a repetition rate of 20/s, 100 dB CHL = 120 dB SPL p.e., repeated twice over a period of 24 minutes each time. For the measurements of the pO2 we used the thin 0.5 micron micro-coaxial needle electrode described by Baumgärtl and Luebbers, which was placed through the round-window membrane in the scala tympani to a depth of 600 micron. The simultaneously recorded CAP latency times were prolonged by 0.8 ms at a test loudness of 60 and 80 dB CHL. The amplitudes of the CM had declined by 60%-70% of the original values at a test loudness of 80 dB SPL p.e. The intra-arterial blood pressure in the common carotid artery of all animals remained constant. As the cortilymph spaces communicate with the perilymph of the scala tympani, our measured decline of pO2 in the perilymph could indicate a cortilymph hypoxia. During exposure to noise the oxygen-dependent Na+ and K+ pumps, which maintain the ion balance and function of the organ of Corti, can decompensate due to lack of oxygen. That would lead to a K+ contamination of the cortilymph and to an intracellular Na+ accumulation, which can cause microstructural damage (hair cell-cilia fusion, hair cell, synaptic and dendritic swelling, hair cell contraction and sustained depolarization), which would be reflected in the CMs and CAPs.
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.
Holden, Laura K; Firszt, Jill B; Reeder, Ruth M; Uchanski, Rosalie M; Dwyer, Noël Y; Holden, Timothy A
2016-12-01
To identify primary biographic and audiologic factors contributing to cochlear implant (CI) performance variability in quiet and noise by controlling electrode array type and electrode position within the cochlea. Although CI outcomes have improved over time, considerable outcome variability still exists. Biographic, audiologic, and device-related factors have been shown to influence performance. Examining CI recipients with consistent array type and electrode position may allow focused investigation into outcome variability resulting from biographic and audiologic factors. Thirty-nine adults (40 ears) implanted for at least 6 months with a perimodiolar electrode array known (via computed tomography [CT] imaging) to be in scala tympani participated. Test materials, administered CI only, included monosyllabic words, sentences in quiet and noise, and spectral ripple discrimination. In quiet, scores were high with mean word and sentence scores of 76 and 87%, respectively; however, sentence scores decreased by an average of 35 percentage points when noise was added. A principal components (PC) analysis of biographic and audiologic factors found three distinct factors, PC1 Age, PC2 Duration, and PC3 Pre-op Hearing. PC1 Age was the only factor that correlated, albeit modestly, with speech recognition in quiet and noise. Spectral ripple discrimination strongly correlated with speech measures. For these recipients with consistent electrode position, PC1 Age was related to speech recognition performance. Consistent electrode position may have contributed to high speech understanding in quiet. Inter-subject variability in noise may have been influenced by auditory/cognitive processing, known to decline with age, and mechanisms that underlie spectral resolution ability.
Nguyen, Yann; Bernardeschi, Daniele; Kazmitcheff, Guillaume; Miroir, Mathieu; Vauchel, Thomas; Ferrary, Evelyne; Sterkers, Olivier
2015-02-01
Loading otoprotective drug into cochlear implant might change its mechanical properties, thus compromising atraumatic insertion. This study evaluated the effect of incorporation of dexamethasone (DXM) in the silicone of cochlear implant arrays on insertion forces. Local administration of DXM with embedded array can potentially reduce inflammation and fibrosis after cochlear implantation procedure to improve hearing preservation and reduce long-term impedances. Four models of arrays have been tested: 0.5-mm distal diameter array (n = 5) used as a control, drug-free 0.4-mm distal diameter array (n = 5), 0.4-mm distal diameter array with 1% eluded DXM silicone (n = 5), and 0.4-mm distal diameter array with 10% eluded DXM silicone (n = 5). Via a motorized insertion bench, each array has been inserted into an artificial scala tympani model. The forces were recorded by a 6-axis force sensor. Each array was tested seven times for a total number of 140 insertions. During the first 10-mm insertion, no difference between the four models was observed. From 10- to 24-mm insertion, the 0.5-mm distal diameter array presented higher insertion forces than the drug-free 0.4-mm distal diameter arrays, with or without DXM. Friction forces for drug-free 0.4-mm distal diameter array and 0.4-mm distal diameter DXM eluded arrays were similar on all insertion lengths. Incorporation of DXM in silicone for cochlear implant design does not change electrode array insertion forces. It does not raise the risk of trauma during array insertion, making it suitable for long-term in situ administration to the cochlea.
Mynatt, Robert; Hale, Shane A; Gill, Ruth M; Plontke, Stefan K; Salt, Alec N
2006-06-01
Local applications of drugs to the inner ear are increasingly being used to treat patients' inner ear disorders. Knowledge of the pharmacokinetics of drugs in the inner ear fluids is essential for a scientific basis for such treatments. When auditory function is of primary interest, the drug's kinetics in scala tympani (ST) must be established. Measurement of drug levels in ST is technically difficult because of the known contamination of perilymph samples taken from the basal cochlear turn with cerebrospinal fluid (CSF). Recently, we reported a technique in which perilymph was sampled from the cochlear apex to minimize the influence of CSF contamination (J. Neurosci. Methods, doi: 10.1016/j.jneumeth.2005.10.008 ). This technique has now been extended by taking smaller fluid samples sequentially from the cochlear apex, which can be used to quantify drug gradients along ST. The sampling and analysis methods were evaluated using an ionic marker, trimethylphenylammonium (TMPA), that was applied to the round window membrane. After loading perilymph with TMPA, 10 1-muL samples were taken from the cochlear apex. The TMPA content of the samples was consistent with the first sample containing perilymph from apical regions and the fourth or fifth sample containing perilymph from the basal turn. TMPA concentration decreased in subsequent samples, as they increasingly contained CSF that had passed through ST. Sample concentration curves were interpreted quantitatively by simulation of the experiment with a finite element model and by an automated curve-fitting method by which the apical-basal gradient was estimated. The study demonstrates that sequential apical sampling provides drug gradient data for ST perilymph while avoiding the major distortions of sample composition associated with basal turn sampling. The method can be used for any substance for which a sensitive assay is available and is therefore of high relevance for the development of preclinical and clinical
Lamm, K; Lamm, C; Lamm, H; Schumann, K
1989-02-01
Nineteen guinea pigs were exposed to impulse noise from gunfire (G3 of the Federal German Army, 156 dB peak SPL), 6+6 shots or 12+6 shots, with a 3-s pulse interval. For simultaneous measurements of pO2, cochlea microphonics (CM) and compound action potentials of the auditory nerve (CAP), we used the thin 0.5 microns microcoaxial needle electrode described by Baumgaertl and Luebbers, which was placed through the roundwindow membrane into the scala tympani to a depth of 1000 microns. After exposure to the first 6 or 12 gunshots, the pO2 increased by about 20% of the original values in 12 guinea pigs (63%). In the following 30 min of recovery time the pO2 decreased, stabilized or showed a further decline. There were only 3 animals with a pO2 loss of 70% of the original values. Most animals showed a decline of 25% at the end of the recovery period. In all animals after 6 additional shots, the pO2 only decreased by another 5% of the original values. Amplitudes of CM and CAP were reduced by about 40% of the original values after 6 or 12 shots and by another 20%-24% (CM) and 5%-15% (CAP) after 6 additional shots. The intra-arterial blood pressure in the common carotid artery remained constant. The results are discussed with respect to the well-known morphological damage, subsequent ion imbalance and hypoxia within the cortilymph after exposure to gunfire. These changes are reflected in the loss of CMs and CAPs.
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
Ikeno, K
1990-09-01
Characteristic nystagmus similar to the Meniere's attack could be observed after introducing KCl solution into the tympanic cavity of guinea pigs. To confirm the fact that this nystagmus was provoked by the high perilymphatic potassium ion concentration, the K+ activity of perilymph was recorded serially through the K+ specific microelectrode inserted into the scala tympani. The rapid increment of K+ activity reached maximum at 120 minutes after introducing KCl solution, and then it decreased gradually to a half of the maximum activity. However, such change of perilymphatic potassium ion concentration was not observed by introducing sucrose solution as control.
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
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.
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.
Zhu, Yanjie; Peng, Xi; Wu, Yin; Wu, Ed X; Ying, Leslie; Liu, Xin; Zheng, Hairong; Liang, Dong
2017-02-01
To develop a new model-based method with spatial and parametric constraints (MB-SPC) aimed at accelerating diffusion tensor imaging (DTI) by directly estimating the diffusion tensor from highly undersampled k-space data. The MB-SPC method effectively incorporates the prior information on the joint sparsity of different diffusion-weighted images using an L1-L2 norm and the smoothness of the diffusion tensor using a total variation seminorm. The undersampled k-space datasets were obtained from fully sampled DTI datasets of a simulated phantom and an ex-vivo experimental rat heart with acceleration factors ranging from 2 to 4. The diffusion tensor was directly reconstructed by solving a minimization problem with a nonlinear conjugate gradient descent algorithm. The reconstruction performance was quantitatively assessed using the normalized root mean square error (nRMSE) of the DTI indices. The MB-SPC method achieves acceptable DTI measures at an acceleration factor up to 4. Experimental results demonstrate that the proposed method can estimate the diffusion tensor more accurately than most existing methods operating at higher net acceleration factors. The proposed method can significantly reduce artifact, particularly at higher acceleration factors or lower SNRs. This method can easily be adapted to MR relaxometry parameter mapping and is thus useful in the characterization of biological tissue such as nerves, muscle, and heart tissue. © 2016 American Association of Physicists in Medicine.
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.
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.
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.
Muscle Deoxygenation Causes Muscle Fatigue
Murthy, G.; Hargens, A. R.; Lehman, S.; Rempel, D.
1999-01-01
Muscle fatigue is a common musculoskeletal disorder in the work place, and may be a harbinger for more disabling cumulative trauma disorders. Although the cause of fatigue is multifactorial, reduced blood flow and muscle oxygenation may be the primary factor in causing muscle fatigue during low intensity muscle exertion. Muscle fatigue is defined as a reduction in muscle force production, and also occurs among astronauts who are subjected to postural constraints while performing lengthy, repetitive tasks. The objectives of this research are to: 1) develop an objective tool to study the role of decreased muscle oxygenation on muscle force production, and 2) to evaluate muscle fatigue during prolonged glovebox work.
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...
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....
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...
... Talk to your provider about the risks and benefits of medicines. How can I prevent muscle cramps? To prevent muscle cramps, you can Stretch your muscles, especially before exercising. If you often get leg cramps at night, ...
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....
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-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.
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...
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)
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.
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
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…
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.
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)
Salt, Alec N; Hale, Shane A; Plonkte, Stefan K R
2006-05-15
Measurements of drug levels in the fluids of the inner ear are required to establish kinetic parameters and to determine the influence of specific local delivery protocols. For most substances, this requires cochlear fluids samples to be obtained for analysis. When auditory function is of primary interest, the drug level in the perilymph of scala tympani (ST) is most relevant, since drug in this scala has ready access to the auditory sensory cells. In many prior studies, ST perilymph samples have been obtained from the basal turn, either by aspiration through the round window membrane (RWM) or through an opening in the bony wall. A number of studies have demonstrated that such samples are likely to be contaminated with cerebrospinal fluid (CSF). CSF enters the basal turn of ST through the cochlear aqueduct when the bony capsule is perforated or when fluid is aspirated. The degree of sample contamination has, however, not been widely appreciated. Recent studies have shown that perilymph samples taken through the round window membrane are highly contaminated with CSF, with samples greater than 2microL in volume containing more CSF than perilymph. In spite of this knowledge, many groups continue to sample from the base of the cochlea, as it is a well-established method. We have developed an alternative, technically simple method to increase the proportion of ST perilymph in a fluid sample. The sample is taken from the apex of the cochlea, a site that is distant from the cochlear aqueduct. A previous problem with sampling through a perforation in the bone was that the native perilymph rapidly leaked out driven by CSF pressure and was lost to the middle ear space. We therefore developed a procedure to collect all the fluid that emerged from the perforated apex after perforation. We evaluated the method using a marker ion trimethylphenylammonium (TMPA). TMPA was applied to the perilymph of guinea pigs either by RW irrigation or by microinjection into the apical turn. The
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
Hahn, Hartmut; Salt, Alec N; Biegner, Thorsten; Kammerer, Bernd; Delabar, Ursular; Hartsock, Jared J; Plontke, Stefan K
2012-06-01
To determine whether intracochlearly applied dexamethasone will lead to better control of drug levels, higher peak concentrations, and lower base-to-apex concentration gradients in the scala tympani (ST) of the guinea pig than after intratympanic (round window [RW]) application. Local application of drugs to the RW results in substantial variation of intracochlear drug levels and significant base-to-apex concentration gradients in ST. Two microliters of dexamethasone-phosphate (10 mg/ml) were injected into ST either through the RW membrane, which was covered with 1% sodium hyaluronate gel or through a cochleostomy with a fluid tight seal of the micropipette. Perilymph was sequentially sampled from the apex at a single time point for each animal, at 20, 80, or 200 min after the injection ended. Results were mathematically interpreted by means of an established computer model and compared with previous experiments performed by our group with the same experimental techniques but using intratympanic applications. Single intracochlear injections of 20 minutes resulted in approximately 10 times higher peak concentrations (on average) than 2 to 3 hours of intratympanic application to the RW niche. Intracochlear drug levels were less variable and could be measured for over 220 minutes. Concentration gradients along the scala tympani were less pronounced. The remaining variability in intracochlear drug levels was attributable to perilymph and drug leak from the injection site. With significantly higher, less variable drug levels and smaller base-to-apex concentration gradients, intracochlear applications have advantages to intratympanic injections. For further development of this technique, it is of importance to control leaks of perilymph and drug from the injection site and to evaluate its clinical feasibility and associated risks.
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
Grob, Karl; Manestar, Mirjana; Gascho, Dominic; Ackland, Timothy; Gilbey, Helen; Fretz, Christian; Kuster, Markus S
2017-11-01
The tensor of the vastus intermedius (TVI) is a newly described component of the extensor apparatus of the knee joint. The objective of this study was to evaluate the appearance of the TVI on magnetic resonance (MR) imaging and its association with the adjacent vastus lateralis (VL) and vastus intermedius (VI) muscles and to compare these findings with the corresponding anatomy. MR images were analyzed from a cadaveric thigh where the TVI, as part of the extensor apparatus of the knee joint, had been dissected. The course of the TVI in relation to the adjacent VL and VI was studied. The anatomic dissection and MR imaging revealed a multilayered organization of the lateral extensor apparatus of the knee joint. The TVI is an intervening muscle between the VL and VI that combined into a broad flat aponeurosis in the midthigh and merged into the quadriceps tendon. Dorsally, the muscle fibers of the TVI joined those of the VL and VI and blended into the attachment at the lateral lip of the linea aspera. In this area, distinguishing between these three muscles was not possible macroscopically or virtually by MR imaging. In the dorsal aspect, the onion-like muscle layers of the VL, TVI, and VI fuse to a hardly separable muscle mass indicating that these muscles work in conjunction to produce knee extension torque when knee joint action is performed. Clin. Anat. 30:1096-1102, 2017. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.
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
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.
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...
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.
Unilateral hypertrophy of tensor fascia lata: a soft tissue tumor simulator
Energy Technology Data Exchange (ETDEWEB)
Ilaslan, H. [Department of Radiology, Mayo Clinic, 200 First Street, 55905, SW Rochester, MN (United States); Department of Radiology A21, Cleveland Clinic, Cleveland, OH (United States); Wenger, D.E. [Department of Radiology, Mayo Clinic, 200 First Street, 55905, SW Rochester, MN (United States); Shives, T.C. [Department of Orthopedic Surgery, Mayo Clinic, Rochester, MN (United States); Unni, K.K. [Department of Laboratory Medicine and Pathology, Mayo Clinic, Rochester, MN (United States)
2003-11-01
To describe the imaging findings in eight cases of unilateral tensor fascia lata (TFL) hypertrophy presenting as soft tissue masses. Imaging studies and medical charts of eight patients were reviewed retrospectively. The imaging studies included five radiographs, five computed tomography (CT) and six magnetic resonance imaging (MRI) examinations. The majority of patients (seven of eight) presented with a palpable proximal anterior thigh mass. One patient was asymptomatic and incidentally diagnosed. There were six females and two males. Ages ranged from 27 to 86 years old (mean 61). MRI and CT showed unilateral enlargement of the TFL muscle in all cases. TFL muscle hypertrophy is an uncommon clinical entity, which can simulate a soft tissue tumor. The characteristic appearance on CT or MRI allows a confident diagnosis of muscle hypertrophy to be made, avoiding unnecessary biopsy or surgical intervention. (orig.)
Unilateral hypertrophy of tensor fascia lata: a soft tissue tumor simulator
International Nuclear Information System (INIS)
Ilaslan, H.; Wenger, D.E.; Shives, T.C.; Unni, K.K.
2003-01-01
To describe the imaging findings in eight cases of unilateral tensor fascia lata (TFL) hypertrophy presenting as soft tissue masses. Imaging studies and medical charts of eight patients were reviewed retrospectively. The imaging studies included five radiographs, five computed tomography (CT) and six magnetic resonance imaging (MRI) examinations. The majority of patients (seven of eight) presented with a palpable proximal anterior thigh mass. One patient was asymptomatic and incidentally diagnosed. There were six females and two males. Ages ranged from 27 to 86 years old (mean 61). MRI and CT showed unilateral enlargement of the TFL muscle in all cases. TFL muscle hypertrophy is an uncommon clinical entity, which can simulate a soft tissue tumor. The characteristic appearance on CT or MRI allows a confident diagnosis of muscle hypertrophy to be made, avoiding unnecessary biopsy or surgical intervention. (orig.)
International Nuclear Information System (INIS)
Ponrartana, Skorn; Hu, Houchun Harry; Ramos-Platt, Leigh; Wren, Tishya Anne Leong; Gilsanz, Vicente; Perkins, Thomas Gardner; Chia, Jonathan Mawlin
2015-01-01
There is currently a lack of suitable objective endpoints to measure disease progression in Duchenne muscular dystrophy (DMD). Emerging research suggests that diffusion tensor imaging (DTI) has potential as an outcome measure for the evaluation of skeletal muscle injury. The objective of this study was to evaluate the potential of DTI as quantitative magnetic resonance imaging (MRI) markers of disease severity in DMD. Thirteen consecutive boys (8.9 years ± 3.0 years) with DMD were evaluated using DTI. Fractional anisotropy (FA) and apparent diffusion coefficient (ADC) were compared with clinical outcome measures of manual muscle testing and MRI determinations of muscle fat fraction (MFF) in the right lower extremity. Both MRI measures of FA and ADC strongly correlated with age and muscle strength. Values for FA positively correlated with age and negatively correlated with muscle strength (r = 0.78 and -0.96; both P ≤ 0.002) while measures of ADC negatively correlated age, but positively correlated with muscle strength (r = -0.87 and 0.83; both P ≤ 0.0004). Additionally, ADC and FA strongly correlated with MFF (r = -0.891 and 0.894, respectively; both P ≤ 0.0001). Mean MMF was negatively correlated with muscle strength (r = -0.89, P = 0.0001). DTI measures of muscle structure strongly correlated with muscle strength and adiposity in boys with DMD in this pilot study, although these markers may be more reflective of fat replacement rather than muscle damage in later stages of the disease. Further studies in presymptomatic younger children are needed to assess the ability of DTI to detect early changes in DMD. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Ponrartana, Skorn; Hu, Houchun Harry [Children' s Hospital Los Angeles, Department of Radiology, Los Angeles, CA (United States); Ramos-Platt, Leigh [Children' s Hospital Los Angeles, Department of Neurology, Los Angeles, CA (United States); Wren, Tishya Anne Leong; Gilsanz, Vicente [Children' s Hospital Los Angeles, Department of Radiology, Los Angeles, CA (United States); Children' s Hospital Los Angeles, Department of Orthopaedic Surgery, Los Angeles, CA (United States); Perkins, Thomas Gardner; Chia, Jonathan Mawlin [Philips Healthcare North America, Cleveland, OH (United States)
2015-04-01
There is currently a lack of suitable objective endpoints to measure disease progression in Duchenne muscular dystrophy (DMD). Emerging research suggests that diffusion tensor imaging (DTI) has potential as an outcome measure for the evaluation of skeletal muscle injury. The objective of this study was to evaluate the potential of DTI as quantitative magnetic resonance imaging (MRI) markers of disease severity in DMD. Thirteen consecutive boys (8.9 years ± 3.0 years) with DMD were evaluated using DTI. Fractional anisotropy (FA) and apparent diffusion coefficient (ADC) were compared with clinical outcome measures of manual muscle testing and MRI determinations of muscle fat fraction (MFF) in the right lower extremity. Both MRI measures of FA and ADC strongly correlated with age and muscle strength. Values for FA positively correlated with age and negatively correlated with muscle strength (r = 0.78 and -0.96; both P ≤ 0.002) while measures of ADC negatively correlated age, but positively correlated with muscle strength (r = -0.87 and 0.83; both P ≤ 0.0004). Additionally, ADC and FA strongly correlated with MFF (r = -0.891 and 0.894, respectively; both P ≤ 0.0001). Mean MMF was negatively correlated with muscle strength (r = -0.89, P = 0.0001). DTI measures of muscle structure strongly correlated with muscle strength and adiposity in boys with DMD in this pilot study, although these markers may be more reflective of fat replacement rather than muscle damage in later stages of the disease. Further studies in presymptomatic younger children are needed to assess the ability of DTI to detect early changes in DMD. (orig.)
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
Evaluation of skeletal muscle DTI in patients with duchenne muscular dystrophy
Hooijmans, M. T.; Damon, B. M.; Froeling, M.; Versluis, M. J.; Burakiewicz, J.; Verschuuren, J. J G M; Niks, E. H.; Webb, A. G.; Kan, H. E.
2015-01-01
Diffusion tensor imaging (DTI) is a popular method to assess differences in fiber organization in diseased and healthy muscle tissue. Previous work has shown that muscle DTI measurements depend on signal-to-noise ratio (SNR), %fat, and tissue T2. The goal of this study was to evaluate the potential
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,...
Pixel-based meshfree modelling of skeletal muscles
Chen, Jiun-Shyan; Basava, Ramya Rao; Zhang, Yantao; Csapo, Robert; Malis, Vadim; Sinha, Usha; Hodgson, John; Sinha, Shantanu
2015-01-01
This paper introduces the meshfree Reproducing Kernel Particle Method (RKPM) for 3D image-based modeling of skeletal muscles. This approach allows for construction of simulation model based on pixel data obtained from medical images. The material properties and muscle fiber direction obtained from Diffusion Tensor Imaging (DTI) are input at each pixel point. The reproducing kernel (RK) approximation allows a representation of material heterogeneity with smooth transition. A ...
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 ...
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.
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.
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.
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.)
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.
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
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.)
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.
Kim, Youn Hwan; Kim, Sang Wha; Kim, Jeong Tae; Kim, Chang Yeon
2013-06-01
Tensor fascia lata (TFL) musculocutaneous flaps often require a donor site graft when harvesting a large flap. However, a major drawback is that it also sacrifices the muscle. To overcome this disadvantage, we designed a TFL perforator-based island flap that was harvested from a site near the defect and involved transposition within 90 degrees without full isolation of the pedicles. We performed procedures on 17 musculocutaneous flaps and 23 perforator-based island flaps, and compared the outcomes of these surgeries. The overall complication rate was 27.5% (11 regions). There were 7 complications related to the musculocutaneous flaps and 4 complications related to the perforator flaps. Although there were no statistical differences between those groups, lower complication rates were associated with procedures involving perforator flaps. The TFL perforator procedure is a simple and fast operation that avoids sacrificing muscle. This decreases complication rates compared to true perforator flap techniques that require dissection around the perforator or pedicle.
Sweeney, H Lee; Hammers, David W
2018-02-01
SUMMARYMuscle cells are designed to generate force and movement. There are three types of mammalian muscles-skeletal, cardiac, and smooth. Skeletal muscles are attached to bones and move them relative to each other. Cardiac muscle comprises the heart, which pumps blood through the vasculature. Skeletal and cardiac muscles are known as striated muscles, because the filaments of actin and myosin that power their contraction are organized into repeating arrays, called sarcomeres, that have a striated microscopic appearance. Smooth muscle does not contain sarcomeres but uses the contraction of filaments of actin and myosin to constrict blood vessels and move the contents of hollow organs in the body. Here, we review the principal molecular organization of the three types of muscle and their contractile regulation through signaling mechanisms and discuss their major structural and functional similarities that hint at the possible evolutionary relationships between the cell types. Copyright © 2018 Cold Spring Harbor Laboratory Press; all rights reserved.
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.)
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...
Sinha, Usha; Csapo, Robert; Malis, Vadim; Xue, Yanjie; Sinha, Shantanu
2014-01-01
Purpose To investigate age related changes in diffusion tensor indices and fiber architecture of the medial and lateral gastrocnemius (MG and LG) muscles using diffusion tensor imaging (DTI). Materials and Methods The lower leg of five young and five senior subjects was scanned at 3T and DTI indices extracted using three methods: ROI, histogram and tract based. Tracked fibers were automatically edited to ensure physiologically relevant tracks. Pennation angles were measured with respect to the deep and superficial aponeuroses of both muscles. Results The three methods provided internally consistent measures of the DTI indices (correlation coefficient in the range of 0.90-0.99). The primary, secondary and tertiary eigenvalues in the MG and LG increased significantly in the senior cohort (p<0.05), while the small increase in fractional anisotropy (FA) with age was not significant (MG/LG: p=0.39/0.85; 95% CI:[ −0.059/-0.056, 0.116/0.064]). Fiber lengths of MG fibers originating distally were significantly decreased in seniors (p<0.05) while pennation angles decreased with age in the MG and LG but this was not significant. Conclusion Fiber atrophy and increased fibrosis have opposing effects on the diffusion indices resulting in a complicated dependence with aging. Fiber architectural changes could play a role in determining aging muscle function. PMID:24771672
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)
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.
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...
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.
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...
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.
... and you need to throw up. The muscles push the food back out of the stomach so it comes up ... body the power it needs to lift and push things. Muscles in your neck and the top part of your back aren't as large, but they are capable ...
Metzger, Julia; Ohnesorge, Bernhard; Distl, Ottmar
2012-01-01
Equine guttural pouch tympany (GPT) is a hereditary condition affecting foals in their first months of life. Complex segregation analyses in Arabian and German warmblood horses showed the involvement of a major gene as very likely. Genome-wide linkage and association analyses including a high density marker set of single nucleotide polymorphisms (SNPs) were performed to map the genomic region harbouring the potential major gene for GPT. A total of 85 Arabian and 373 German warmblood horses were genotyped on the Illumina equine SNP50 beadchip. Non-parametric multipoint linkage analyses showed genome-wide significance on horse chromosomes (ECA) 3 for German warmblood at 16–26 Mb and 34–55 Mb and for Arabian on ECA15 at 64–65 Mb. Genome-wide association analyses confirmed the linked regions for both breeds. In Arabian, genome-wide association was detected at 64 Mb within the region with the highest linkage peak on ECA15. For German warmblood, signals for genome-wide association were close to the peak region of linkage at 52 Mb on ECA3. The odds ratio for the SNP with the highest genome-wide association was 0.12 for the Arabian. In conclusion, the refinement of the regions with the Illumina equine SNP50 beadchip is an important step to unravel the responsible mutations for GPT. PMID:22848553
Ihler, Friedrich; Pelz, Sabrina; Coors, Melanie; Matthias, Christoph; Canis, Martin
2014-11-01
Cochlear implantation trauma causes both macroscopic and inflammatory trauma. The aim of the present study was to evaluate the effectiveness of the TNF-alpha inhibitor etanercept applied after cochlear implantation trauma on the preservation of acoustic hearing. Guinea pigs were randomly assigned to three groups receiving cochlear implantation trauma by cochleostomy. In one group, the site was sealed by bone cement with no further treatment. A second group was additionally implanted with an osmotic minipump delivering artificial perilymph into the scala tympani for seven days. In the third group, etanercept 1 mg/ml was added to artificial perilymph. Hearing was assessed by auditory brainstem responses at 2, 4, 6, and 8 kHz prior to and after surgery and on days 3, 5, 7, 14, 28. Fifteen healthy guinea pigs. The trauma led to threshold shifts from 50.3 dB ± 16.3 dB to 68.0 dB ± 19.3 dB. Hearing thresholds were significantly lower in etanercept-treated animals compared to controls on day 28 at 8 kHz and from day 3 onwards at 4 and 2 kHz (p < 0.01; two-way RM ANOVA / Bonferroni t-test). The application of etanercept led to preservation of acoustic hearing after cochlear implantation trauma.
Saito, Takehisa; Ito, Tetsufumi; Ito, Yumi; Manabe, Yasuhiro
2016-05-01
To elucidate the regeneration process of fungiform taste buds after severing the chorda tympani nerve (CTN) by confocal laser scanning microscopy in vivo. In 7 consecutive patients whose CTN was severed during tympanoplasty, an average of 10 fungiform papillae in the midlateral region of the tongue were periodically observed, and the number of taste buds was counted until 12 to 24 months after surgery. Gustatory function was assessed by EGM. EGM thresholds showed no response within 1 month after surgery in any patient. All taste buds had disappeared until 13 to 71 days after surgery. Regenerated taste buds were first detected 5 to 8 months after surgery in 5 of the 7 patients. EGM thresholds recovered to their preoperative values in 2 patients. In these 2 patients, the number of regenerated taste buds gradually increased in combination with a recovered taste function. However, a time lag existed between taste bud regeneration and taste function recovery. EGM thresholds did not recover in the other 3 patients with regenerated taste buds, suggesting that these taste buds were immature without gustatory function. The long-term regeneration process of fungiform taste buds could be clarified using confocal laser scanning microscopy. © The Author(s) 2015.
Saito, Takehisa; Ito, Tetsufumi; Narita, Norihiko; Yamada, Takechiyo; Manabe, Yasuhiro
2011-11-01
The aim of this study was to evaluate the mean number of regenerated fungiform taste buds per papilla and perform light and electron microscopic observation of taste buds in patients with recovered taste function after severing the chorda tympani nerve during middle ear surgery. We performed a biopsy on the fungiform papillae (FP) in the midlateral region of the dorsal surface of the tongue from 5 control volunteers (33 total FP) and from 7 and 5 patients with and without taste recovery (34 and 29 FP, respectively) 3 years 6 months to 18 years after surgery. The specimens were observed by light and transmission electron microscopy. The taste function was evaluated by electrogustometry. The mean number of taste buds in the FP of patients with completely recovered taste function was significantly smaller (1.9 +/- 1.4 per papilla; p taste buds. Nerve fibers and nerve terminals were also found in the taste buds. It was clarified that taste buds containing taste cells and nerve endings do regenerate in the FP of patients with recovered taste function.
Khwairakpam Zhimina Devi; Sai Kumar. N; Vinod Babu. K; V.R. Ayyappan
2014-01-01
Background and Objective: Stretching of Lower Back Muscle, Hamstring and Tensor Fasciae Latae have an immediate effect on Chronic Lower Back Pain. Hence the purpose is to find the short term effect of stretching of Lower Back Muscle, Hamstring and Tensor Fasciae Latae on intensity of low back pain, flexibility and functional disability in occupation related Chronic Mechanical Low Back Pain in Community Nurses. Method: Single blind experimental study design, 40 subjects with Chronic mechani...
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.)
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.
Pixel-based meshfree modelling of skeletal muscles.
Chen, Jiun-Shyan; Basava, Ramya Rao; Zhang, Yantao; Csapo, Robert; Malis, Vadim; Sinha, Usha; Hodgson, John; Sinha, Shantanu
2016-01-01
This paper introduces the meshfree Reproducing Kernel Particle Method (RKPM) for 3D image-based modeling of skeletal muscles. This approach allows for construction of simulation model based on pixel data obtained from medical images. The material properties and muscle fiber direction obtained from Diffusion Tensor Imaging (DTI) are input at each pixel point. The reproducing kernel (RK) approximation allows a representation of material heterogeneity with smooth transition. A multiphase multichannel level set based segmentation framework is adopted for individual muscle segmentation using Magnetic Resonance Images (MRI) and DTI. The application of the proposed methods for modeling the human lower leg is demonstrated.
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.
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
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....
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
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.)
... the lower leg/calf Back of the thigh (hamstrings) Front of the thigh (quadriceps) Cramps in the ... Names Cramps - muscle Images Chest stretch Groin stretch Hamstring stretch Hip stretch Thigh stretch Triceps stretch References ...
... People who cannot actively move one or more joints can do exercises using braces or splints . When ... A.M. Editorial team. Muscle Disorders Read more Neuromuscular Disorders Read more NIH MedlinePlus Magazine Read more ...
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.
Directory of Open Access Journals (Sweden)
Hellekant Göran
2003-03-01
Full Text Available Abstract Background Recent progress in discernment of molecular pathways of taste transduction underscores the need for comprehensive phenotypic information for the understanding of the influence of genetic factors in taste. To obtain information that can be used as a base line for assessment of effects of genetic manipulations in mice taste, we have recorded the whole-nerve integrated responses to a wide array of taste stimuli in the chorda tympani (CT and glossopharyngeal (NG nerves, the two major taste nerves from the tongue. Results In C57BL/6J mice the responses in the two nerves were not the same. In general sweeteners gave larger responses in the CT than in the NG, while responses to bitter taste in the NG were larger. Thus the CT responses to cyanosuosan, fructose, NC00174, D-phenylalanline and sucrose at all concentrations were significantly larger than in the NG, whereas for acesulfame-K, L-proline, saccharin and SC45647 the differences were not significant. Among bitter compounds amiloride, atropine, cycloheximide, denatonium benzoate, L-phenylalanine, 6-n-propyl-2-thiouracil (PROP and tetraethyl ammonium chloride (TEA gave larger responses in the NG, while the responses to brucine, chloroquine, quinacrine, quinine hydrochloride (QHCl, sparteine and strychnine, known to be very bitter to humans, were not significantly larger in the NG than in the CT. Conclusion These data provide a comprehensive survey and comparison of the taste sensitivity of the normal C57BL/6J mouse against which the effects of manipulations of its gustatory system can be better assessed.
Ganchrow, Donald; Ganchrow, Judith R; Cicchini, Vanessa; Bartel, Dianna L; Kaufman, Daniel; Girard, David; Whitehead, Mark C
2014-05-01
The nucleus of the solitary tract (NST) processes gustatory and related somatosensory information rostrally and general viscerosensory information caudally. To compare its connections with those of other rodents, this study in the C57BL/6J mouse provides a subnuclear cytoarchitectonic parcellation (Nissl stain) of the NST into rostral, intermediate, and caudal divisions. Subnuclei are further characterized by NADPH staining and P2X2 immunoreactivity (IR). Cholera toxin subunit B (CTb) labeling revealed those NST subnuclei receiving chorda tympani nerve (CT) afferents, those connecting with the parabrachial nucleus (PBN) and reticular formation (RF), and those interconnecting NST subnuclei. CT terminals are densest in the rostral central (RC) and medial (M) subnuclei; less dense in the rostral lateral (RL) subnucleus; and sparse in the ventral (V), ventral lateral (VL), and central lateral (CL) subnuclei. CTb injection into the PBN retrogradely labels cells in the aforementioned subnuclei; RC and M providing the largest source of PBN projection neurons. Pontine efferent axons terminate mainly in V and rostral medial (RM) subnuclei. CTb injection into the medullary RF labels cells and axonal endings predominantly in V at rostral and intermediate NST levels. Small CTb injections within the NST label extensive projections from the rostral division to caudal subnuclei. Projections from the caudal division primarily interconnect subnuclei confined to the caudal division of the NST; they also connect with the area postrema. P2X2 -IR identifies probable vagal nerve terminals in the central (Ce) subnucleus in the intermediate/caudal NST. Ce also shows intense NADPH staining and does not project to the PBN. Copyright © 2013 Wiley Periodicals, Inc.
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].
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.
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.
Preliminary diffusion tensor imaging studies in limb-girdle muscular dystrophies
Hidalgo-Tobon, S.; Hernandez-Salazar, G.; Vargas-Cañas, S.; Marrufo-Melendez, O.; Solis-Najera, S.; Taboada-Barajas, J.; Rodriguez, A. O.; Delgado-Hernandez, R.
2012-10-01
Limb-girdle muscular dystrophies (LGMD) are a group of autosomal dominantly or recessively inherited muscular dystrophies that also present with primary proximal (limb-girdle) muscle weakness. This type of dystrophy involves the shoulder and pelvic girdles, distinct phenotypic or clinical characteristics are recognized. Imaging experiments were conducted on a 1.5T GE scanner (General Electric Medical Systems. Milwaukee. USA), using a combination of two eight-channel coil array. Diffusion Tensor Imaging (DTI) data were acquired using a SE-EPI sequence, diffusion weighted gradients were applied along 30 non-collinear directions with a b-value=550 s/mm2. The connective tissue content does not appear to have a significant effect on the directionality of the diffusion, as assessed by fractional anisotropy. The fibers of the Sartorius muscle and gracilis showed decreased number of tracts, secondary to fatty infiltration and replacement of connective tissue and muscle mass loss characteristic of the underlying pathology. Our results demonstrated the utility of non-invasive MRI techniques to characterize the muscle pathology, through quantitative and qualitative methods such as the FA values and tractrography.
Tensor estimation for double-pulsed diffusional kurtosis imaging.
Shaw, Calvin B; Hui, Edward S; Helpern, Joseph A; Jensen, Jens H
2017-07-01
Double-pulsed diffusional kurtosis imaging (DP-DKI) represents the double diffusion encoding (DDE) MRI signal in terms of six-dimensional (6D) diffusion and kurtosis tensors. Here a method for estimating these tensors from experimental data is described. A standard numerical algorithm for tensor estimation from conventional (i.e. single diffusion encoding) diffusional kurtosis imaging (DKI) data is generalized to DP-DKI. This algorithm is based on a weighted least squares (WLS) fit of the signal model to the data combined with constraints designed to minimize unphysical parameter estimates. The numerical algorithm then takes the form of a quadratic programming problem. The principal change required to adapt the conventional DKI fitting algorithm to DP-DKI is replacing the three-dimensional diffusion and kurtosis tensors with the 6D tensors needed for DP-DKI. In this way, the 6D diffusion and kurtosis tensors for DP-DKI can be conveniently estimated from DDE data by using constrained WLS, providing a practical means for condensing DDE measurements into well-defined mathematical constructs that may be useful for interpreting and applying DDE MRI. Data from healthy volunteers for brain are used to demonstrate the DP-DKI tensor estimation algorithm. In particular, representative parametric maps of selected tensor-derived rotational invariants are presented. Copyright © 2017 John Wiley & Sons, Ltd.
Secoond order parallel tensors on some paracontact manifolds | Liu ...
African Journals Online (AJOL)
The object of the present paper is to study the symmetric and skewsymmetric properties of a second order parallel tensor on paracontact metric (k;μ)- spaces and almost β-para-Kenmotsu (k;μ)-spaces. In this paper, we prove that if there exists a second order symmetric parallel tensor on a paracontact metric (k;μ)- space M, ...
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.
A tensor approach to the estimation of hydraulic conductivities in ...
African Journals Online (AJOL)
Based on the field measurements of the physical properties of fractured rocks, the anisotropic properties of hydraulic conductivity (HC) of the fractured rock aquifer can be assessed and presented using a tensor approach called hydraulic conductivity tensor. Three types of HC values, namely point value, axial value and flow ...
Tensor meson dominance and e+e--physics
International Nuclear Information System (INIS)
Genz, H.; Karlsruhe Univ.; Mallik, S.
1983-01-01
The phenomenological status of tensor meson dominance is reported. Some new results concerning hadronic decays of the 2 ++ -meson chi 2 (3.55) and the heavy lepton tau are also included. Considering experimental errors, tensor meson dominance is in agreement with experiment. (author)
Tensor Excitations in Nambu - Jona-Lasinio Model
Chizhov, M V
1996-01-01
It is shown that in the one-flavour NJL model the vector and axial-vector quasiparticles described by the antisymmetric tensor field are generated. These excitations have tensor interactions with quarks in contrast to usual vector ones. Phenomenological applications are discussed.
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.
Energy momentum tensor in local causal perturbation theory
International Nuclear Information System (INIS)
Prange, D.
2001-01-01
We study the energy momentum tensor in the Bogolyubov-Epstein-Glaser approach to perturbation theory. It is found to be locally conserved for a class of theories containing to derivated fields in the interaction. For the massless φ 4 -theory we derive the trace anomaly of the improved tensor. (orig.)
Exploring the tensor networks/AdS correspondence
Energy Technology Data Exchange (ETDEWEB)
Bhattacharyya, Arpan [Department of Physics and Center for Field Theory and Particle Physics, Fudan University,220 Handan Road, 200433 Shanghai (China); Centre For High Energy Physics, Indian Institute of Science,560012 Bangalore (India); Gao, Zhe-Shen [Department of Physics and Center for Field Theory and Particle Physics, Fudan University,220 Handan Road, 200433 Shanghai (China); Hung, Ling-Yan [Department of Physics and Center for Field Theory and Particle Physics, Fudan University,220 Handan Road, 200433 Shanghai (China); State Key Laboratory of Surface Physics and Department of Physics, Fudan University,220 Handan Road, 200433 Shanghai (China); Collaborative Innovation Center of Advanced Microstructures, Nanjing University,Nanjing, 210093 (China); Liu, Si-Nong [Department of Physics and Center for Field Theory and Particle Physics, Fudan University,220 Handan Road, 200433 Shanghai (China)
2016-08-11
In this paper we study the recently proposed tensor networks/AdS correspondence. We found that the Coxeter group is a useful tool to describe tensor networks in a negatively curved space. Studying generic tensor network populated by perfect tensors, we find that the physical wave function generically do not admit any connected correlation functions of local operators. To remedy the problem, we assume that wavefunctions admitting such semi-classical gravitational interpretation are composed of tensors close to, but not exactly perfect tensors. Computing corrections to the connected two point correlation functions, we find that the leading contribution is given by structures related to geodesics connecting the operators inserted at the boundary physical dofs. Such considerations admit generalizations at least to three point functions. This is highly suggestive of the emergence of the analogues of Witten diagrams in the tensor network. The perturbations alone however do not give the right entanglement spectrum. Using the Coxeter construction, we also constructed the tensor network counterpart of the BTZ black hole, by orbifolding the discrete lattice on which the network resides. We found that the construction naturally reproduces some of the salient features of the BTZ black hole, such as the appearance of RT surfaces that could wrap the horizon, depending on the size of the entanglement region A.
Black holes with surrounding matter in scalar-tensor theories.
Cardoso, Vitor; Carucci, Isabella P; Pani, Paolo; Sotiriou, Thomas P
2013-09-13
We uncover two mechanisms that can render Kerr black holes unstable in scalar-tensor gravity, both associated with the presence of matter in the vicinity of the black hole and the fact that this introduces an effective mass for the scalar. Our results highlight the importance of understanding the structure of spacetime in realistic, astrophysical black holes in scalar-tensor theories.
A Gradient Based Iterative Solutions for Sylvester Tensor Equations
Directory of Open Access Journals (Sweden)
Zhen Chen
2013-01-01
proposed by Ding and Chen, 2005, and by using tensor arithmetic concepts, an iterative algorithm and its modification are established to solve the Sylvester tensor equation. Convergence analysis indicates that the iterative solutions always converge to the exact solution for arbitrary initial value. Finally, some examples are provided to show that the proposed algorithms are effective.
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)
Parity and isospin in pion condensation and tensor binding
International Nuclear Information System (INIS)
Pace, E.; Palumbo, F.
1978-01-01
In infinite nuclear matter with pion condensates or tensor binding both parity and isospin symmetries are broken. Finite nuclei with pion condensates or tensor binding, however, can have definite parity. They cannot have a definite value of isospin, whose average value is of the order of the number of nucleons. (Auth.)
Superspace actions and duality transformations for N=2 tensor multiplets
International Nuclear Information System (INIS)
Galperin, A.; Ivanov, E.; Ogievetsky, V.
1985-01-01
General actions for self-interacting N=2 tensor multiplets are considered in the harmonic superspace approach. All of them are shown to be equivalent, by superfield duality transformations, to some restricted class of the hypermultiplets actions. In particular, the improved tensor multiplet theory is dual to a free hypermultiplet one. Superspace couplings of these improved matter multiplets against conformal supergravity are also constructed
Multiple M2-branes and the embedding tensor
Bergshoeff, Eric A.; de Roo, Mees; Hohm, Olaf
2008-01-01
We show that the Bagger-Lambert theory of multiple M2-branes fits into the general construction of maximally supersymmetric gauge theories using the embedding tensor technique. We apply the embedding tensor technique in order to systematically obtain the consistent gaugings of N = 8 superconformal
Subtracting a best rank-1 approximation may increase tensor rank
Stegeman, Alwin; Comon, Pierre
2010-01-01
It has been shown that a best rank-R approximation of an order-k tensor may not exist when R >= 2 and k >= 3. This poses a serious problem to data analysts using tensor decompositions it has been observed numerically that, generally, this issue cannot be solved by consecutively computing and
Couplings of self-dual tensor multiplet in six dimensions
Bergshoeff, E.; Sezgin, E.; Sokatchev, E.
1996-01-01
The (1, 0) supersymmetry in six dimensions admits a tensor multiplet which contains a second-rank antisymmetric tensor field with a self-dual field strength and a dilaton. We describe the fully supersymmetric coupling of this multiplet to a Yangâ€“Mills multiplet, in the absence of supergravity. The
Superconformal tensor calculus and matter couplings in six dimensions
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
Data fusion in metabolomics using coupled matrix and tensor factorizations
DEFF Research Database (Denmark)
Evrim, Acar Ataman; Bro, Rasmus; Smilde, Age Klaas
2015-01-01
of heterogeneous (i.e., in the form of higher order tensors and matrices) data sets with shared/unshared factors. In order to jointly analyze such heterogeneous data sets, we formulate data fusion as a coupled matrix and tensor factorization (CMTF) problem, which has already proved useful in many data mining...
Fast evaluation of nonlinear functionals of tensor product wavelet expansions
Schwab, C.; Stevenson, R.
2011-01-01
Abstract For a nonlinear functional f, and a function u from the span of a set of tensor product interpolets, it is shown how to compute the interpolant of f (u) from the span of this set of tensor product interpolets in linear complexity, assuming that the index set has a certain multiple tree
Gauge theories, duality relations and the tensor hierarchy
Bergshoeff, Eric A.; Hartong, Jelle; Hohm, Olaf; Huebscher, Mechthild; Ortin, Tomas; Hübscher, Mechthild
We compute the complete 3- and 4-dimensional tensor hierarchies, i.e. sets of p-form fields, with 1 We construct gauge-invariant actions that include all the fields in the tensor hierarchies. We elucidate the relation between the gauge transformations of the p-form fields in the action and those of
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.
The Twist Tensor Nuclear Norm for Video Completion.
Hu, Wenrui; Tao, Dacheng; Zhang, Wensheng; Xie, Yuan; Yang, Yehui
2017-12-01
In this paper, we propose a new low-rank tensor model based on the circulant algebra, namely, twist tensor nuclear norm (t-TNN). The twist tensor denotes a three-way tensor representation to laterally store 2-D data slices in order. On one hand, t-TNN convexly relaxes the tensor multirank of the twist tensor in the Fourier domain, which allows an efficient computation using fast Fourier transform. On the other, t-TNN is equal to the nuclear norm of block circulant matricization of the twist tensor in the original domain, which extends the traditional matrix nuclear norm in a block circulant way. We test the t-TNN model on a video completion application that aims to fill missing values and the experiment results validate its effectiveness, especially when dealing with video recorded by a nonstationary panning camera. The block circulant matricization of the twist tensor can be transformed into a circulant block representation with nuclear norm invariance. This representation, after transformation, exploits the horizontal translation relationship between the frames in a video, and endows the t-TNN model with a more powerful ability to reconstruct panning videos than the existing state-of-the-art low-rank models.
The superspace-translation tensor and linearized N = 1 supergravities
International Nuclear Information System (INIS)
Bedding, S.P.; Lang, W.
1982-01-01
The recently proposed superspace-translation tensor is considered as the source of supergravities in the context of N = 1 supersymmetry. It is shown how the structure of this tensor leads to a complete evaluation of the linearized supervielbein in terms of unconstrained prepotentials with derived transformation laws. Connection with formulations using torsion constraints is made. (orig.)
(2, 0) tensor multiplets and conformal supergravity in D = 6
Bergshoeff, Eric; Sezgin, Ergin; Proeyen, Antoine Van
1999-01-01
We construct the supercurrent multiplet that contains the energyâ€“momentum tensor of the (2, 0) tensor multiplet. By coupling this multiplet of currents to the fields of conformal supergravity, we first construct the linearized superconformal transformations rules of the (2, 0) Weyl multiplet.
A General Expression for the Quintic Lovelock Tensor
Briggs, C. C.
1996-01-01
A general expression is given for the quintic Lovelock tensor as well as for the coefficient of the quintic Lovelock Lagrangian 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.
Decomposition of a symmetric second-order tensor
Heras, José A.
2018-05-01
In the three-dimensional space there are different definitions for the dot and cross products of a vector with a second-order tensor. In this paper we show how these products can uniquely be defined for the case of symmetric tensors. We then decompose a symmetric second-order tensor into its ‘dot’ part, which involves the dot product, and the ‘cross’ part, which involves the cross product. For some physical applications, this decomposition can be interpreted as one in which the dot part identifies with the ‘parallel’ part of the tensor and the cross part identifies with the ‘perpendicular’ part. This decomposition of a symmetric second-order tensor may be suitable for undergraduate courses of vector calculus, mechanics and electrodynamics.
On energy-momentum tensors of gravitational field
International Nuclear Information System (INIS)
Nikishov, A.I.
2001-01-01
The phenomenological approach to gravitation is discussed in which the 3-graviton interaction is reduced to the interaction of each graviton with the energy-momentum tensor of two others. If this is so, (and in general relativity this is not so), then the problem of choosing the correct energy-momentum tensor comes to finding the right 3-graviton vertex. Several energy-momentum tensors od gravitational field are considered and compared in the lowest approximation. Each of them together with the energy-momentum tensor of point-like particles satisfies the conservation laws when equations of motion of particles are the same as in general relativity. It is shown that in Newtonian approximation the considered tensors differ one from other in the way their energy density is distributed between energy density of interaction (nonzero only at locations of particles) and energy density of gravitational field. Stating from Lorentz invariance, the Lagrangians for spin-2, mass-0 field are considered [ru
On the energy-momentum tensor in Moyal space
International Nuclear Information System (INIS)
Balasin, Herbert; Schweda, Manfred; Blaschke, Daniel N.; Gieres, Francois
2015-01-01
We study the properties of the energy-momentum tensor of gauge fields coupled to matter in non-commutative (Moyal) space. In general, the non-commutativity affects the usual conservation law of the tensor as well as its transformation properties (gauge covariance instead of gauge invariance). It is well known that the conservation of the energy-momentum tensor can be achieved by a redefinition involving another star-product. Furthermore, for a pure gauge theory it is always possible to define a gauge invariant energy-momentum tensor by means of a Wilson line. We show that the last two procedures are incompatible with each other if couplings of gauge fields to matter fields (scalars or fermions) are considered: The gauge invariant tensor (constructed via Wilson line) does not allow for a redefinition assuring its conservation, and vice versa the introduction of another star-product does not allow for gauge invariance by means of a Wilson line. (orig.)
Gauge theories, duality relations and the tensor hierarchy
International Nuclear Information System (INIS)
Bergshoeff, Eric A.; Hohm, Olaf; Hartong, Jelle; Huebscher, Mechthild; OrtIn, Tomas
2009-01-01
We compute the complete 3- and 4-dimensional tensor hierarchies, i.e. sets of p-form fields, with 1 ≤ p ≤ D, which realize an off-shell algebra of bosonic gauge transformations. We show how these tensor hierarchies can be put on-shell by introducing a set of duality relations, thereby introducing additional scalars and a metric tensor. These so-called duality hierarchies encode the equations of motion of the bosonic part of the most general gauged supergravity theories in those dimensions, including the (projected) scalar equations of motion. We construct gauge-invariant actions that include all the fields in the tensor hierarchies. We elucidate the relation between the gauge transformations of the p-form fields in the action and those of the same fields in the tensor hierarchy.
Coordinate independent expression for transverse trace-free tensors
International Nuclear Information System (INIS)
Conboye, Rory
2016-01-01
The transverse and trace-free (TT) part of the extrinsic curvature represents half of the dynamical degrees of freedom of the gravitational field in the 3 + 1 formalism. As such, it is part of the freely specifiable initial data for numerical relativity. Though TT tensors in three-space possess only two component degrees of freedom, they cannot ordinarily be given solely by two scalar potentials. Such expressions have been derived, however, in coordinate form, for all TT tensors in flat space which are also translationally or axially symmetric (Conboye and Murchadha 2014 Class. Quantum Grav. 31 085019). Since TT tensors are conformally covariant, these also give TT tensors in conformally flat space. In this article, the work above has been extended by giving a coordinate-independent expression for these TT tensors. The translational and axial symmetry conditions have also been generalized to invariance along any hypersurface orthogonal Killing vector. (paper)
The Scalar-Tensor Theory of Gravitation
International Nuclear Information System (INIS)
Ibanez, J
2003-01-01
Since the scalar-tensor theory of gravitation was proposed almost 50 years ago, it has recently become a robust alternative theory to Einstein's general relativity due to the fact that it appears to represent the lower level of a more fundamental theory and can serve both as a phenomenological theory to explain the recently observed acceleration of the universe, and to solve the cosmological constant problem. To my knowledge The Scalar-Tensor Theory of Gravitation by Y Fujii and K Maeda is the first book to develop a modern view on this topic and is one of the latest titles in the well-presented Cambridge Monographs on Mathematical Physics series. This book is an excellent readable introduction and up-to-date review of the subject. The discussion is well organized; after a comprehensible introduction to the Brans-Dicke theory and the important role played by conformal transformations, the authors review cosmologies with the cosmological constant and how the scalar-tensor theory can serve to explain the accelerating universe, including discussions on dark energy, quintessence and braneworld cosmologies. The book ends with a chapter devoted to quantum effects. To make easy the lectures of the book, each chapter starts with a summary of the subject to be dealt with. As the book proceeds, important issues like conformal frames and the weak equivalence principle are fully discussed. As the authors warn in the preface, the book is not encyclopedic (from my point of view the list of references is fairly short, for example, but this is a minor drawback) and the choice of included topics corresponds to the authors' interests. Nevertheless, the book seems to cover a broad range of the most essential aspects of the subject. Long and 'boring' mathematical derivations are left to appendices so as not to interrupt the flow of the reasoning, allowing the reader to focus on the physical aspects of each subject. These appendices are a valuable help in entering into the mathematical
The effects of noise over the complete space of diffusion tensor shape.
Gahm, Jin Kyu; Kindlmann, Gordon; Ennis, Daniel B
2014-01-01
Diffusion tensor magnetic resonance imaging (DT-MRI) is a technique used to quantify the microstructural organization of biological tissues. Multiple images are necessary to reconstruct the tensor data and each acquisition is subject to complex thermal noise. As such, measures of tensor invariants, which characterize components of tensor shape, derived from the tensor data will be biased from their true values. Previous work has examined this bias, but over a narrow range of tensor shape. Herein, we define the mathematics for constructing a tensor from tensor invariants, which permits an intuitive and principled means for building tensors with a complete range of tensor shape and salient microstructural properties. Thereafter, we use this development to evaluate by simulation the effects of noise on characterizing tensor shape over the complete space of tensor shape for three encoding schemes with different SNR and gradient directions. We also define a new framework for determining the distribution of the true values of tensor invariants given their measures, which provides guidance about the confidence the observer should have in the measures. Finally, we present the statistics of tensor invariant estimates over the complete space of tensor shape to demonstrate how the noise sensitivity of tensor invariants varies across the space of tensor shape as well as how the imaging protocol impacts measures of tensor invariants. Copyright © 2013 Elsevier B.V. All rights reserved.
Tensor products of quantized tilting modules
International Nuclear Information System (INIS)
Andersen, H.H.
1992-01-01
Let U k denote the quantized enveloping algebra corresponding to a finite dimensional simple complex Lie algebra L. Assume that the quantum parameter is a root of unity in k of order at least the Coxeter number for pound. Also assume that this order is odd and not divisible by 3 if type G 2 occurs. We demonstrate how one can define a reduced tensor product on the family F consisting of those finite dimensional simple U k -modules which are deformations of simple L-modules and which have non-zero quantum dimension. This together with the work of Reshetikhin-Turaev and Turaev-Wenzl prove that (U k , F) is a modular Hopf algebra and hence produces invariants of 3-manifolds. Also by recent work of Duurhus, Jakobsen and Nest it leads to a general topological quantum field theory. The method of proof explores quantized analogues of tilting modules for algebraic groups. (orig.)
Image denoising using non linear diffusion tensors
International Nuclear Information System (INIS)
Benzarti, F.; Amiri, H.
2011-01-01
Image denoising is an important pre-processing step for many image analysis and computer vision system. It refers to the task of recovering a good estimate of the true image from a degraded observation without altering and changing useful structure in the image such as discontinuities and edges. In this paper, we propose a new approach for image denoising based on the combination of two non linear diffusion tensors. One allows diffusion along the orientation of greatest coherences, while the other allows diffusion along orthogonal directions. The idea is to track perfectly the local geometry of the degraded image and applying anisotropic diffusion mainly along the preferred structure direction. To illustrate the effective performance of our model, we present some experimental results on a test and real photographic color images.
Diffusion tensor in electron swarm transport
International Nuclear Information System (INIS)
Makabe, T.; Mori, T.
1983-01-01
Expression for the diffusion tensor of the electron (or light ion) swarm is presented from the higher-order expansion of the velocity distribution in the Boltzmann equation in hydrodynamic stage. Derived diffusion coefficients for the transverse and longitudinal directions include the additional terms representative of the curvature effect under the action of an electric field with the usual-two-term expressions. Numerical analysis is given for the electron swarm in model gases having the momentum transfer cross section Qsub(m)(epsilon)=Q 0 epsilon sup(beta) (β=0, 1/2, 1) using the present theory. As the result, appreciable degree of discrepancy appears between the transverse diffusion coefficient defined here and the conventional expression with increasing of β in Qsub(m). (Author)
Poisson-Jacobi reduction of homogeneous tensors
International Nuclear Information System (INIS)
Grabowski, J; Iglesias, D; Marrero, J C; Padron, E; Urbanski, P
2004-01-01
The notion of homogeneous tensors is discussed. We show that there is a one-to-one correspondence between multivector fields on a manifold M, homogeneous with respect to a vector field Δ on M, and first-order polydifferential operators on a closed submanifold N of codimension 1 such that Δ is transversal to N. This correspondence relates the Schouten-Nijenhuis bracket of multivector fields on M to the Schouten-Jacobi bracket of first-order polydifferential operators on N and generalizes the Poissonization of Jacobi manifolds. Actually, it can be viewed as a super-Poissonization. This procedure of passing from a homogeneous multivector field to a first-order polydifferential operator can also be understood as a sort of reduction; in the standard case-a half of a Poisson reduction. A dual version of the above correspondence yields in particular the correspondence between Δ-homogeneous symplectic structures on M and contact structures on N
Lectures on tensor categories and modular functors
Bakalov, Bojko
2000-01-01
This book gives an exposition of the relations among the following three topics: monoidal tensor categories (such as a category of representations of a quantum group), 3-dimensional topological quantum field theory, and 2-dimensional modular functors (which naturally arise in 2-dimensional conformal field theory). The following examples are discussed in detail: the category of representations of a quantum group at a root of unity and the Wess-Zumino-Witten modular functor. The idea that these topics are related first appeared in the physics literature in the study of quantum field theory. Pioneering works of Witten and Moore-Seiberg triggered an avalanche of papers, both physical and mathematical, exploring various aspects of these relations. Upon preparing to lecture on the topic at MIT, however, the authors discovered that the existing literature was difficult and that there were gaps to fill. The text is wholly expository and finely succinct. It gathers results, fills existing gaps, and simplifies some pro...
Complete stress tensor determination by microearthquake analysis
Slunga, R.
2010-12-01
Jones 1984 found that half of the shallow strike-slip EQ in California had at least one M>2 foreshock. By the Gutenberg law this means at least 3-20 M>0 (low b-value 0.4-0.8). deformations within the crust. This was confirmed by observations in Iceland after 1990 when anew seismic network in Iceland operated by IMO started. Like the Parkfield project in California the SIL network in Iceland was established in an area predicted (Einarsson et al 1981, Stefansson and Halldorsson 1988) to be struck by major EQs within decades of years. The area of main interest have a detection threshold of M=0. A physical approach was chosen to the earthquake warning problem (Stefansson et al 1993) and therefore all microearthquakes were analyzed for FPS by the spectral amplitude method (Slunga 1981). As the shear slip is caused by the in situ stress it is logical to investigate what bounds the FPS puts on the stress tensor. McKenzie 1969 assumed that the earthquake takes place in a crust containing only one fracture, the fault plane. He found that in s uch a case only very weak constraints could be put on the stress. This was widely accepted t o be valid also for microearthquakes in the real crust and lead to methods (Angelier 1978, G ephart and Forsythe 1984 etc) to put four constraints on the stress tensor by assuming that the same stress tensor is causing the slip on four or more different fractures. Another and more realistic approach is to assume that the crust have frequent fractures with almost all orientations. In such a case one can rely on Coulomb's failure criterion for isotropic mat erial (gives four constraints) instead of the weaker Bolt's criterion (giving only one const raint). One obvious fifth constraint is to require the vertical stress to equal the lithosta tic pressure. A sixth constraint is achieved by requiring that the deviatoric elastic energy is minimized. The water pressure is also needed for the fourth constraint by Coulomb (CFS=0 ). It can be related to
Tensor ghosts in the inflationary cosmology
International Nuclear Information System (INIS)
Clunan, Tim; Sasaki, Misao
2010-01-01
Theories with curvature-squared terms in the action are known to contain ghost modes in general. However, if we regard curvature-squared terms as quantum corrections to the original theory, the emergence of ghosts may be simply due to the perturbative truncation of a full non-perturbative theory. If this is the case, there should be a way to live with ghosts. In this paper, we take the Euclidean path integral approach, in which ghost degrees of freedom can be, and are integrated out in the Euclideanized spacetime. We apply this procedure to Einstein gravity with a Weyl curvature-squared correction in the inflationary background. We find that the amplitude of tensor perturbations is modified by a term of O(α 2 H 2 ) where α 2 is a coupling constant in front of the Weyl-squared term and H is the Hubble parameter during inflation.
Holographic spin networks from tensor network states
Singh, Sukhwinder; McMahon, Nathan A.; Brennen, Gavin K.
2018-01-01
In the holographic correspondence of quantum gravity, a global on-site symmetry at the boundary generally translates to a local gauge symmetry in the bulk. We describe one way how the global boundary on-site symmetries can be gauged within the formalism of the multiscale renormalization ansatz (MERA), in light of the ongoing discussion between tensor networks and holography. We describe how to "lift" the MERA representation of the ground state of a generic one dimensional (1D) local Hamiltonian, which has a global on-site symmetry, to a dual quantum state of a 2D "bulk" lattice on which the symmetry appears gauged. The 2D bulk state decomposes in terms of spin network states, which label a basis in the gauge-invariant sector of the bulk lattice. This decomposition is instrumental to obtain expectation values of gauge-invariant observables in the bulk, and also reveals that the bulk state is generally entangled between the gauge and the remaining ("gravitational") bulk degrees of freedom that are not fixed by the symmetry. We present numerical results for ground states of several 1D critical spin chains to illustrate that the bulk entanglement potentially depends on the central charge of the underlying conformal field theory. We also discuss the possibility of emergent topological order in the bulk using a simple example, and also of emergent symmetries in the nongauge (gravitational) sector in the bulk. More broadly, our holographic model translates the MERA, a tensor network state, to a superposition of spin network states, as they appear in lattice gauge theories in one higher dimension.
Sinha, Usha; Csapo, Robert; Malis, Vadim; Xue, Yanjie; Sinha, Shantanu
2015-04-01
To investigate age related changes in diffusion tensor indices and fiber architecture of the medial and lateral gastrocnemius (MG and LG) muscles using diffusion tensor imaging (DTI). The lower leg of five young and five senior subjects was scanned at 3 Tesla and DTI indices extracted using three methods: region of interest, histogram, and tract based. Tracked fibers were automatically edited to ensure physiologically relevant tracks. Pennation angles were measured with respect to the deep and superficial aponeuroses of both muscles. The three methods provided internally consistent measures of the DTI indices (correlation coefficient in the range of 0.90-0.99). The primary, secondary, and tertiary eigenvalues in the MG and LG increased significantly in the senior cohort (P < 0.05), while the small increase in fractional anisotropy with age was not significant (MG/LG: P = 0.39/0.85; 95% confidence interval: [-0.059/-0.056, 0.116/0.064]). Fiber lengths of MG fibers originating distally were significantly decreased in seniors (P < 0.05) while pennation angles decreased with age in the MG and LG but this was not significant. Fiber atrophy and increased fibrosis have opposing effects on the diffusion indices resulting in a complicated dependence with aging. Fiber architectural changes could play a role in determining aging muscle function. © 2014 Wiley Periodicals, Inc.
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 Rank Preserving Discriminant Analysis for Facial Recognition.
Tao, Dapeng; Guo, Yanan; Li, Yaotang; Gao, Xinbo
2017-10-12
Facial recognition, one of the basic topics in computer vision and pattern recognition, has received substantial attention in recent years. However, for those traditional facial recognition algorithms, the facial images are reshaped to a long vector, thereby losing part of the original spatial constraints of each pixel. In this paper, a new tensor-based feature extraction algorithm termed tensor rank preserving discriminant analysis (TRPDA) for facial image recognition is proposed; the proposed method involves two stages: in the first stage, the low-dimensional tensor subspace of the original input tensor samples was obtained; in the second stage, discriminative locality alignment was utilized to obtain the ultimate vector feature representation for subsequent facial recognition. On the one hand, the proposed TRPDA algorithm fully utilizes the natural structure of the input samples, and it applies an optimization criterion that can directly handle the tensor spectral analysis problem, thereby decreasing the computation cost compared those traditional tensor-based feature selection algorithms. On the other hand, the proposed TRPDA algorithm extracts feature by finding a tensor subspace that preserves most of the rank order information of the intra-class input samples. Experiments on the three facial databases are performed here to determine the effectiveness of the proposed TRPDA algorithm.
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
Exact tensor network ansatz for strongly interacting systems
Zaletel, Michael P.
It appears that the tensor network ansatz, while not quite complete, is an efficient coordinate system for the tiny subset of a many-body Hilbert space which can be realized as a low energy state of a local Hamiltonian. However, we don't fully understand precisely which phases are captured by the tensor network ansatz, how to compute their physical observables (even numerically), or how to compute a tensor network representation for a ground state given a microscopic Hamiltonian. These questions are algorithmic in nature, but their resolution is intimately related to understanding the nature of quantum entanglement in many-body systems. For this reason it is useful to compute the tensor network representation of various `model' wavefunctions representative of different phases of matter; this allows us to understand how the entanglement properties of each phase are expressed in the tensor network ansatz, and can serve as test cases for algorithm development. Condensed matter physics has many illuminating model wavefunctions, such as Laughlin's celebrated wave function for the fractional quantum Hall effect, the Bardeen-Cooper-Schrieffer wave function for superconductivity, and Anderson's resonating valence bond ansatz for spin liquids. This thesis presents some results on exact tensor network representations of these model wavefunctions. In addition, a tensor network representation is given for the time evolution operator of a long-range one-dimensional Hamiltonian, which allows one to numerically simulate the time evolution of power-law interacting spin chains as well as two-dimensional strips and cylinders.
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
Algebraic Rainich conditions for the fourth rank tensor V
International Nuclear Information System (INIS)
So, Lau Loi
2011-01-01
Algebraic conditions on the Ricci tensor in the Rainich-Misner-Wheeler unified field theory are known as the Rainich conditions. Penrose and more recently Bergqvist and Lankinen made an analogy from the Ricci tensor to the Bel-Robinson tensor B αβμν , a certain fourth rank tensor quadratic in the Weyl curvature, which also satisfies algebraic Rainich-like conditions. However, we found that not only does the tensor B αβμν fulfill these conditions, but so also does our recently proposed tensor V αβμν , which has many of the desirable properties of B αβμν . For the quasilocal small sphere limit restriction, we found that there are only two fourth rank tensors, B αβμν and V αβμν , which form a basis for good energy expressions. Both of them have the completely trace free and causal properties, these two form necessary and sufficient conditions. Surprisingly either completely traceless or causal is enough to fulfill the algebraic Rainich conditions.
The tensor bi-spectrum in a matter bounce
Energy Technology Data Exchange (ETDEWEB)
Chowdhury, Debika; Sreenath, V.; Sriramkumar, L., E-mail: debika@physics.iitm.ac.in, E-mail: sreenath@lsu.edu, E-mail: sriram@physics.iitm.ac.in [Department of Physics, Indian Institute of Technology Madras, Chennai 600036 (India)
2015-11-01
Matter bounces are bouncing scenarios wherein the universe contracts as in a matter dominated phase at early times. Such scenarios are known to lead to a scale invariant spectrum of tensor perturbations, just as de Sitter inflation does. In this work, we examine if the tensor bi-spectrum can discriminate between the inflationary and the bouncing scenarios. Using the Maldacena formalism, we analytically evaluate the tensor bi-spectrum in a matter bounce for an arbitrary triangular configuration of the wavevectors. We show that, over scales of cosmological interest, the non-Gaussianity parameter h{sub NL} that characterizes the amplitude of the tensor bi-spectrum is quite small when compared to the corresponding values in de Sitter inflation. During inflation, the amplitude of the tensor perturbations freeze on super-Hubble scales, a behavior that results in the so-called consistency condition relating the tensor bi-spectrum and the power spectrum in the squeezed limit. In contrast, in the bouncing scenarios, the amplitude of the tensor perturbations grow strongly as one approaches the bounce, which suggests that the consistency condition will not be valid in such situations. We explicitly show that the consistency relation is indeed violated in the matter bounce. We discuss the implications of the results.
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
Effects of Acoustic Impulses on the Middle Ear
2016-10-01
reflexive MEMC measurements, and verification of the integrity of the cranial nerves supplying the stapedius and tensor tympani muscles (CNVII and CNV...of new (or revising existing) damage risk criteria and health hazard assessment methods for exposure to high-level acoustic impulses such as...exposures to acoustic impulses. This information is necessary for the development of new (or revision of existing) damage risk criteria and health hazard
Tensor force and debye screening in quarkonium-type mesons
International Nuclear Information System (INIS)
Kovacs, L.B.; Kovacs, T.G.; Lovas, I.
1990-01-01
We use a non-relativistic quantum-mechanical model to investigate the effect of a screening plasma on two quarkonium-type mesons: the charmonium and bottonium. The stability of these mesons in the plasma is estimated in two cases: including the tensor and spin-orbit term in the potential and without these terms. It turns out that while the bottonium is somewhat stabilized by the tensor force, the charmonium becomes less stabil due to this modification of the potential. Thus the charmonium seems to be a more sensitive probe of the quark-gluon plasma formation than it was thought to be without including the tensor force. (Authors)
Tensor polarized deuteron targets for intermediate energy physics experiments
International Nuclear Information System (INIS)
Meyer, W.; Schilling, E.
1985-03-01
At intermediate energies measurements from a tensor polarized deuteron target are being prepared for the following reactions: the photodisintegration of the deuteron, the elastic pion-deuteron scattering and the elastic electron-deuteron scattering. The experimental situation of the polarization experiments for these reactions is briefly discussed in section 2. In section 3 the definitions of the deuteron polarization and the possibilities to determine the vector and tensor polarization are given. Present tensor polarization values and further improvements in this field are reported in section 4. (orig.)
Extracting the diffusion tensor from molecular dynamics simulation with Milestoning
International Nuclear Information System (INIS)
Mugnai, Mauro L.; Elber, Ron
2015-01-01
We propose an algorithm to extract the diffusion tensor from Molecular Dynamics simulations with Milestoning. A Kramers-Moyal expansion of a discrete master equation, which is the Markovian limit of the Milestoning theory, determines the diffusion tensor. To test the algorithm, we analyze overdamped Langevin trajectories and recover a multidimensional Fokker-Planck equation. The recovery process determines the flux through a mesh and estimates local kinetic parameters. Rate coefficients are converted to the derivatives of the potential of mean force and to coordinate dependent diffusion tensor. We illustrate the computation on simple models and on an atomically detailed system—the diffusion along the backbone torsions of a solvated alanine dipeptide
Some spacetimes with higher rank Killing-Staeckel tensors
International Nuclear Information System (INIS)
Gibbons, G.W.; Houri, T.; Kubiznak, D.; Warnick, C.M.
2011-01-01
By applying the lightlike Eisenhart lift to several known examples of low-dimensional integrable systems admitting integrals of motion of higher-order in momenta, we obtain four- and higher-dimensional Lorentzian spacetimes with irreducible higher-rank Killing tensors. Such metrics, we believe, are first examples of spacetimes admitting higher-rank Killing tensors. Included in our examples is a four-dimensional supersymmetric pp-wave spacetime, whose geodesic flow is superintegrable. The Killing tensors satisfy a non-trivial Poisson-Schouten-Nijenhuis algebra. We discuss the extension to the quantum regime.
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.
A Nonlinear GMRES Optimization Algorithm for Canonical Tensor Decomposition
De Sterck, Hans
2011-01-01
A new algorithm is presented for computing a canonical rank-R tensor approximation that has minimal distance to a given tensor in the Frobenius norm, where the canonical rank-R tensor consists of the sum of R rank-one components. Each iteration of the method consists of three steps. In the first step, a tentative new iterate is generated by a stand-alone one-step process, for which we use alternating least squares (ALS). In the second step, an accelerated iterate is generated by a nonlinear g...
One-loop tensor Feynman integral reduction with signed minors
DEFF Research Database (Denmark)
Fleischer, Jochem; Riemann, Tord; Yundin, Valery
2012-01-01
of the formalism is the immediate evaluation of complete contractions of the tensor integrals with external momenta. This leads to the problem of evaluating sums over products of signed minors with scalar products of chords. Chords are differences of external momenta. These sums may be evaluated analytically......We present an algebraic approach to one-loop tensor integral reduction. The integrals are presented in terms of scalar one- to four-point functions. The reduction is worked out explicitly until five-point functions of rank five. The numerical C++ package PJFry evaluates tensor coefficients in terms...
Scalar-Tensor Black Holes Embedded in an Expanding Universe
Tretyakova, Daria; Latosh, Boris
2018-02-01
In this review we focus our attention on scalar-tensor gravity models and their empirical verification in terms of black hole and wormhole physics. We focus on a black hole, embedded in an expanding universe, describing both cosmological and astrophysical scales. We show that in scalar-tensor gravity it is quite common that the local geometry is isolated from the cosmological expansion, so that it does not backreact on the black hole metric. We try to extract common features of scalar-tensor black holes in an expanding universe and point out the gaps that must be filled.
Scalar-Tensor Black Holes Embedded in an Expanding Universe
Directory of Open Access Journals (Sweden)
Daria Tretyakova
2018-02-01
Full Text Available In this review, we focus our attention on scalar-tensor gravity models and their empirical verification in terms of black hole and wormhole physics. We focus on black holes, embedded in an expanding universe, describing both cosmological and astrophysical scales. We show that in scalar-tensor gravity it is quite common that the local geometry is isolated from the cosmological expansion, so that it does not backreact on the black hole metric. We try to extract common features of scalar-tensor black holes in an expanding universe and point out the issues that are not fully investigated.
Two-perfect fluid interpretation of an energy tensor
International Nuclear Information System (INIS)
Ferrando, J.J.; Morales, J.A.; Portilla, M.
1990-01-01
There are many topics in General Relativity where matter is represented by a mixture of two fluids. In fact, some astrophysical and cosmological situations need to be described by an energy tensor made up of the sum of two or more perfect fluids rather than that with only one. The paper contains the necessary and sufficient conditions for a given energy tensor to be interpreted as a sum of two perfect fluids. Given a tensor of this class, the decomposition in two perfect fluids (which is determined up to a couple of real functions) is obtained
MR muscle tractography study on VX2 soft-tissue tumor in rabbits
International Nuclear Information System (INIS)
Li Yonggang; Guo Liang; Xie Daohai; Hu Chunhogn; Guo Maofeng; Zhu Wei; Chen Jianhua; Xing Jianming; Wang Renfa
2008-01-01
Objective: To determine if diffusion tensor imaging (DTI) and muscle fiber tracts of muscle disease are feasible. Methods: Twenty Newzealand white rabbits were implanted with 0.2 ml VX 2 tumor tissue suspension in the right proximal thighs. MRI and DTI were performed on these rabbits and DTI of muscle fiber tracts in the muscles around the lesions were reconstructed. The fractional anisotropy(FA) and volume ratio anisotropy(VrA) of the tumor and the normal muscle were analyzed. The correlation study between MRI and pathological findings was done. Results: All experimental animal models of rabbit VX 2 soft tissue tumors were successfully established. The difference of FA between the central parenchyma area and the necrosis area, the peripheral area of the tumor, the adjacent and contralateral normal muscle was statistically significant (P 0.05). The difference of FA and VrA between the adjacent and contralateral normal muscle was not statistically significant (P>0.05). The arrangement of normal muscle was regular on DTI of muscle tract. The muscle around the tumor lesions was infiltrated and destructed, which demonstrated irregular and interrupted muscle fiber on muscle tractography. Conclusion: DTI is advantageous to demonstrate the structure of soft tissue tumors and its border, which should be helpful in the structure and function research of muscle, as well as in the diagnosis of muscle diseases. (authors)
Modeling microwave electromagnetic field absorption in muscle tissues
Felbacq, D.; Clerjon, S.; Damez, J. L.; Zolla, F.
2002-07-01
Absorption of electromagnetic energy in human tissues is an important issue with respect to the safety of low-level exposure. Simulation is a way to a better understanding of electromagnetic dosimetry. This letter presents a comparison between results obtained from a numerical simulation and experimental data of absorbed energy by a muscle. Simulation was done using a bidimensional double-scale homogenization scheme leading to the effective permittivity tensor. Experimental measurements were performed at 10 GHz on bovine muscle, 30 hours after slaughter, thanks to the open-ended rectangular waveguide method. Results show a good agreement between measurements and simulated data.
International Nuclear Information System (INIS)
Zijta, F.M.; Froeling, M.; Paardt, M.P. van der; Bipat, S.; Nederveen, A.J.; Stoker, J.; Lakeman, M.M.E.; Montauban van Swijndregt, A.D.; Strijkers, G.J.
2011-01-01
To prospectively determine the feasibility of diffusion tensor imaging (DTI) with fibre tractography as a tool for the three-dimensional (3D) visualisation of normal pelvic floor anatomy. Five young female nulliparous subjects (mean age 28 ± 3 years) underwent DTI at 3.0T. Two-dimensional diffusion-weighted axial spin-echo echo-planar (SP-EPI) pulse sequence of the pelvic floor was performed, with additional T2-TSE multiplanar sequences for anatomical reference. Fibre tractography for visualisation of predefined pelvic floor and pelvic wall muscles was performed offline by two observers, applying a consensus method. Three eigenvalues (λ1, λ2, λ3), fractional anisotropy (FA) and mean diffusivity (MD) were calculated from the fibre trajectories. In all subjects fibre tractography resulted in a satisfactory anatomical representation of the pubovisceral muscle, perineal body, anal - and urethral sphincter complex and internal obturator muscle. Mean FA values ranged from 0.23 ± 0.02 to 0.30 ± 0.04, MD values from 1.30 ± 0.08 to 1.73 ± 0.12 x 10- 3 mm 2 /s. Muscular structures in the superficial layer of the pelvic floor could not be satisfactorily identified. This study demonstrates the feasibility of visualising the complex three-dimensional pelvic floor architecture using 3T-DTI with fibre tractography. DTI of the deep female pelvic floor may provide new insights into pelvic floor disorders. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Zijta, F.M. [University of Amsterdam, Department of Radiology, Academic Medical Center, Amsterdam (Netherlands); Onze Lieve Vrouwe Gasthuis, Department of Radiology, Amsterdam (Netherlands); Froeling, M. [University of Amsterdam, Department of Radiology, Academic Medical Center, Amsterdam (Netherlands); Eindhoven University of Technology, Biomedical NMR, Department of Biomedical Engineering, Eindhoven (Netherlands); Paardt, M.P. van der; Bipat, S.; Nederveen, A.J.; Stoker, J. [University of Amsterdam, Department of Radiology, Academic Medical Center, Amsterdam (Netherlands); Lakeman, M.M.E. [University of Amsterdam, Department of Gynaecology, Academic Medical Center, Amsterdam (Netherlands); Montauban van Swijndregt, A.D. [Onze Lieve Vrouwe Gasthuis, Department of Radiology, Amsterdam (Netherlands); Strijkers, G.J. [Eindhoven University of Technology, Biomedical NMR, Department of Biomedical Engineering, Eindhoven (Netherlands)
2011-06-15
To prospectively determine the feasibility of diffusion tensor imaging (DTI) with fibre tractography as a tool for the three-dimensional (3D) visualisation of normal pelvic floor anatomy. Five young female nulliparous subjects (mean age 28 {+-} 3 years) underwent DTI at 3.0T. Two-dimensional diffusion-weighted axial spin-echo echo-planar (SP-EPI) pulse sequence of the pelvic floor was performed, with additional T2-TSE multiplanar sequences for anatomical reference. Fibre tractography for visualisation of predefined pelvic floor and pelvic wall muscles was performed offline by two observers, applying a consensus method. Three eigenvalues ({lambda}1, {lambda}2, {lambda}3), fractional anisotropy (FA) and mean diffusivity (MD) were calculated from the fibre trajectories. In all subjects fibre tractography resulted in a satisfactory anatomical representation of the pubovisceral muscle, perineal body, anal - and urethral sphincter complex and internal obturator muscle. Mean FA values ranged from 0.23 {+-} 0.02 to 0.30 {+-} 0.04, MD values from 1.30 {+-} 0.08 to 1.73 {+-} 0.12 x 10-{sup 3} mm{sup 2}/s. Muscular structures in the superficial layer of the pelvic floor could not be satisfactorily identified. This study demonstrates the feasibility of visualising the complex three-dimensional pelvic floor architecture using 3T-DTI with fibre tractography. DTI of the deep female pelvic floor may provide new insights into pelvic floor disorders. (orig.)
Characteristics of acute groin injuries in the hip flexor muscles - a detailed MRI study in athletes
DEFF Research Database (Denmark)
Serner, A; Weir, A; Tol, J L
2018-01-01
acute hip flexor muscle injury were included. A total of 156 athletes presented with acute groin pain of which 33 athletes were included, median age 26 years (range 18-35). There were 16 rectus femoris, 12 iliacus, 7 psoas major, 4 sartorius, and 1 tensor fascia latae injury. Rectus femoris injuries...
On the skew-symmetric character of the couple-stress tensor
Hadjesfandiari, Ali R.
2013-01-01
In this paper, the skew-symmetric character of the couple-stress tensor is established as the result of arguments from tensor analysis. Consequently, the couple-stress pseudo-tensor has a true vectorial character. The fundamental step in this development is that the isotropic couple-stress tensor cannot exist.
International Nuclear Information System (INIS)
Smirnov, Yu.F.; Tolstoi, V.N.; Kharitonov, Yu.I.
1993-01-01
The tree technique for the quantum algebra su q (2) developed in an earlier study is used to construct the q analog of the algebra of irreducible tensor operators. The adjoint action of the algebra su q (2) on irreducible tensor operators is discussed, and the adjoint R matrix is introduced. A set of expressions is obtained for the matrix elements of various irreducible tensor operators and combinations of them. As an application, the recursion relations for the Clebsch-Gordan and Racah coefficients of the algebra su q (2) are derived. 16 refs
Tensor products of process matrices with indefinite causal structure
Jia, Ding; Sakharwade, Nitica
2018-03-01
Theories with indefinite causal structure have been studied from both the fundamental perspective of quantum gravity and the practical perspective of information processing. In this paper we point out a restriction in forming tensor products of objects with indefinite causal structure in certain models: there exist both classical and quantum objects the tensor products of which violate the normalization condition of probabilities, if all local operations are allowed. We obtain a necessary and sufficient condition for when such unrestricted tensor products of multipartite objects are (in)valid. This poses a challenge to extending communication theory to indefinite causal structures, as the tensor product is the fundamental ingredient in the asymptotic setting of communication theory. We discuss a few options to evade this issue. In particular, we show that the sequential asymptotic setting does not suffer the violation of normalization.
Distance Adaptive Tensor Discriminative Geometry Preserving Projection for Face Recognition
Directory of Open Access Journals (Sweden)
Ziqiang Wang
2012-09-01
Full Text Available There is a growing interest in dimensionality reduction techniques for face recognition, however, the traditional dimensionality reduction algorithms often transform the input face image data into vectors before embedding. Such vectorization often ignores the underlying data structure and leads to higher computational complexity. To effectively cope with these problems, a novel dimensionality reduction algorithm termed distance adaptive tensor discriminative geometry preserving projection (DATDGPP is proposed in this paper. The key idea of DATDGPP is as follows: first, the face image data are directly encoded in high-order tensor structure so that the relationships among the face image data can be preserved; second, the data-adaptive tensor distance is adopted to model the correlation among different coordinates of tensor data; third, the transformation matrix which can preserve discrimination and local geometry information is obtained by an iteration algorithm. Experimental results on three face databases show that the proposed algorithm outperforms other representative dimensionality reduction algorithms.
Vectors, tensors and the basic equations of fluid mechanics
Aris, Rutherford
1962-01-01
Introductory text, geared toward advanced undergraduate and graduate students, applies mathematics of Cartesian and general tensors to physical field theories and demonstrates them in terms of the theory of fluid mechanics. 1962 edition.
Ryu-Takayanagi formula for symmetric random tensor networks
Chirco, Goffredo; Oriti, Daniele; Zhang, Mingyi
2018-06-01
We consider the special case of random tensor networks (RTNs) endowed with gauge symmetry constraints on each tensor. We compute the Rényi entropy for such states and recover the Ryu-Takayanagi (RT) formula in the large-bond regime. The result provides first of all an interesting new extension of the existing derivations of the RT formula for RTNs. Moreover, this extension of the RTN formalism brings it in direct relation with (tensorial) group field theories (and spin networks), and thus provides new tools for realizing the tensor network/geometry duality in the context of background-independent quantum gravity, and for importing quantum gravity tools into tensor network research.
On the projective curvature tensor of generalized Sasakian-space ...
African Journals Online (AJOL)
space-forms under some conditions regarding projective curvature tensor. All the results obtained in this paper are in the form of necessary and sufficient conditions. Keywords: Generalized Sasakian-space-forms; projectively flat; ...
An introduction to tensors and group theory for physicists
Jeevanjee, Nadir
2015-01-01
The second edition of this highly praised textbook provides an introduction to tensors, group theory, and their applications in classical and quantum physics. Both intuitive and rigorous, it aims to demystify tensors by giving the slightly more abstract but conceptually much clearer definition found in the math literature, and then connects this formulation to the component formalism of physics calculations. New pedagogical features, such as new illustrations, tables, and boxed sections, as well as additional “invitation” sections that provide accessible introductions to new material, offer increased visual engagement, clarity, and motivation for students. Part I begins with linear algebraic foundations, follows with the modern component-free definition of tensors, and concludes with applications to physics through the use of tensor products. Part II introduces group theory, including abstract groups and Lie groups and their associated Lie algebras, then intertwines this material with that of Part...
Holographic stress tensor for non-relativistic theories
International Nuclear Information System (INIS)
Ross, Simon F.; Saremi, Omid
2009-01-01
We discuss the calculation of the field theory stress tensor from the dual geometry for two recent proposals for gravity duals of non-relativistic conformal field theories. The first of these has a Schroedinger symmetry including Galilean boosts, while the second has just an anisotropic scale invariance (the Lifshitz case). For the Lifshitz case, we construct an appropriate action principle. We propose a definition of the non-relativistic stress tensor complex for the field theory as an appropriate variation of the action in both cases. In the Schroedinger case, we show that this gives physically reasonable results for a simple black hole solution and agrees with an earlier proposal to determine the stress tensor from the familiar AdS prescription. In the Lifshitz case, we solve the linearised equations of motion for a general perturbation around the background, showing that our stress tensor is finite on-shell.
Gauge and non-gauge curvature tensor copies
International Nuclear Information System (INIS)
Srivastava, P.P.
1982-10-01
A procedure for constructing curvature tensor copies is discussed using the anholonomic geometrical framework. The corresponding geometries are compared and the notion of gauge copy is elucidated. An explicit calculation is also made. (author)
Motion Detection in Ultrasound Image-Sequences Using Tensor Voting
Inba, Masafumi; Yanagida, Hirotaka; Tamura, Yasutaka
2008-05-01
Motion detection in ultrasound image sequences using tensor voting is described. We have been developing an ultrasound imaging system adopting a combination of coded excitation and synthetic aperture focusing techniques. In our method, frame rate of the system at distance of 150 mm reaches 5000 frame/s. Sparse array and short duration coded ultrasound signals are used for high-speed data acquisition. However, many artifacts appear in the reconstructed image sequences because of the incompleteness of the transmitted code. To reduce the artifacts, we have examined the application of tensor voting to the imaging method which adopts both coded excitation and synthetic aperture techniques. In this study, the basis of applying tensor voting and the motion detection method to ultrasound images is derived. It was confirmed that velocity detection and feature enhancement are possible using tensor voting in the time and space of simulated ultrasound three-dimensional image sequences.
Renormalization of nonabelian gauge theories with tensor matter fields
International Nuclear Information System (INIS)
Lemes, Vitor; Renan, Ricardo; Sorella, Silvio Paolo
1996-03-01
The renormalizability of a nonabelian model describing the coupling between antisymmetric second rank tensor matter fields and Yang-Mills gauge fields is discussed within the BRS algebraic framework. (author). 12 refs
Tensor analysis and elementary differential geometry for physicists and engineers
Nguyen-Schäfer, Hung
2017-01-01
This book comprehensively presents topics, such as Dirac notation, tensor analysis, elementary differential geometry of moving surfaces, and k-differential forms. Additionally, two new chapters of Cartan differential forms and Dirac and tensor notations in quantum mechanics are added to this second edition. The reader is provided with hands-on calculations and worked-out examples at which he will learn how to handle the bra-ket notation, tensors, differential geometry, and differential forms; and to apply them to the physical and engineering world. Many methods and applications are given in CFD, continuum mechanics, electrodynamics in special relativity, cosmology in the Minkowski four-dimensional spacetime, and relativistic and non-relativistic quantum mechanics. Tensors, differential geometry, differential forms, and Dirac notation are very useful advanced mathematical tools in many fields of modern physics and computational engineering. They are involved in special and general relativity physics, quantum m...
A defect in holographic interpretations of tensor networks
Energy Technology Data Exchange (ETDEWEB)
Czech, Bartłomiej [Institute for Advanced Study,Princeton, NJ 08540 (United States); Nguyen, Phuc H.; Swaminathan, Sivaramakrishnan [Theory Group, Department of Physics and Texas Cosmology Center,The University of Texas at Austin,Austin, TX 78712 (United States)
2017-03-16
We initiate the study of how tensor networks reproduce properties of static holographic space-times, which are not locally pure anti-de Sitter. We consider geometries that are holographically dual to ground states of defect, interface and boundary CFTs and compare them to the structure of the requisite MERA networks predicted by the theory of minimal updates. When the CFT is deformed, certain tensors require updating. On the other hand, even identical tensors can contribute differently to estimates of entanglement entropies. We interpret these facts holographically by associating tensor updates to turning on non-normalizable modes in the bulk. In passing, we also clarify and complement existing arguments in support of the theory of minimal updates, propose a novel ansatz called rayed MERA that applies to a class of generalized interface CFTs, and analyze the kinematic spaces of the thin wall and AdS{sub 3}-Janus geometries.
Two new eigenvalue localization sets for tensors and theirs applications
Directory of Open Access Journals (Sweden)
Zhao Jianxing
2017-10-01
Full Text Available A new eigenvalue localization set for tensors is given and proved to be tighter than those presented by Qi (J. Symbolic Comput., 2005, 40, 1302-1324 and Li et al. (Numer. Linear Algebra Appl., 2014, 21, 39-50. As an application, a weaker checkable sufficient condition for the positive (semi-definiteness of an even-order real symmetric tensor is obtained. Meanwhile, an S-type E-eigenvalue localization set for tensors is given and proved to be tighter than that presented by Wang et al. (Discrete Cont. Dyn.-B, 2017, 22(1, 187-198. As an application, an S-type upper bound for the Z-spectral radius of weakly symmetric nonnegative tensors is obtained. Finally, numerical examples are given to verify the theoretical results.
An eigenvalue localization set for tensors and its applications
Directory of Open Access Journals (Sweden)
Jianxing Zhao
2017-03-01
Full Text Available Abstract A new eigenvalue localization set for tensors is given and proved to be tighter than those presented by Li et al. (Linear Algebra Appl. 481:36-53, 2015 and Huang et al. (J. Inequal. Appl. 2016:254, 2016. As an application of this set, new bounds for the minimum eigenvalue of M $\\mathcal{M}$ -tensors are established and proved to be sharper than some known results. Compared with the results obtained by Huang et al., the advantage of our results is that, without considering the selection of nonempty proper subsets S of N = { 1 , 2 , … , n } $N=\\{1,2,\\ldots,n\\}$ , we can obtain a tighter eigenvalue localization set for tensors and sharper bounds for the minimum eigenvalue of M $\\mathcal{M}$ -tensors. Finally, numerical examples are given to verify the theoretical results.
An eigenvalue localization set for tensors and its applications.
Zhao, Jianxing; Sang, Caili
2017-01-01
A new eigenvalue localization set for tensors is given and proved to be tighter than those presented by Li et al . (Linear Algebra Appl. 481:36-53, 2015) and Huang et al . (J. Inequal. Appl. 2016:254, 2016). As an application of this set, new bounds for the minimum eigenvalue of [Formula: see text]-tensors are established and proved to be sharper than some known results. Compared with the results obtained by Huang et al ., the advantage of our results is that, without considering the selection of nonempty proper subsets S of [Formula: see text], we can obtain a tighter eigenvalue localization set for tensors and sharper bounds for the minimum eigenvalue of [Formula: see text]-tensors. Finally, numerical examples are given to verify the theoretical results.
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.
A General Sparse Tensor Framework for Electronic Structure Theory.
Manzer, Samuel; Epifanovsky, Evgeny; Krylov, Anna I; Head-Gordon, Martin
2017-03-14
Linear-scaling algorithms must be developed in order to extend the domain of applicability of electronic structure theory to molecules of any desired size. However, the increasing complexity of modern linear-scaling methods makes code development and maintenance a significant challenge. A major contributor to this difficulty is the lack of robust software abstractions for handling block-sparse tensor operations. We therefore report the development of a highly efficient symbolic block-sparse tensor library in order to provide access to high-level software constructs to treat such problems. Our implementation supports arbitrary multi-dimensional sparsity in all input and output tensors. We avoid cumbersome machine-generated code by implementing all functionality as a high-level symbolic C++ language library and demonstrate that our implementation attains very high performance for linear-scaling sparse tensor contractions.
A generalization of tensor calculus and its application to physics
International Nuclear Information System (INIS)
Ashtekar, A.
1982-01-01
Penrose's abstract index notation and axiomatic introduction of covariant derivatives in tensor calculus is generalized to fields with internal degrees of freedom. The result provides, in particular, an intrinsic formulation of gauge theories without the use of bundles. (author)
International Nuclear Information System (INIS)
McIntosh, C.B.G.; Foyster, J.M.; Lun, A.W.h.
1981-01-01
A list is given of a canonical set of the Newman--Penrose quantities Phi/sub A/B, the tetrad components of the trace-free Ricci tensor, for each Plebanski class according to Plebanski's classification of this tensor. This comparative list can easily be extended to cover the classification in tetrad language of any second-order, trace-free, symmetric tensor in a space-time. A fourth-order tensor which is the product of two such tensors was defined by Plebanski and used in his classification. This has the same symmetries as the Weyl tensor. The Petrov classification of this tensor, here called the Plebanski tensor, is discussed along with the classification of the Ricci tensor. The use of the Plebanski tensor in a couple of areas of general relativity is also briefly discussed
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 ...
Review of diffusion tensor imaging and its application in children
Energy Technology Data Exchange (ETDEWEB)
Vorona, Gregory A. [Children' s Hospital of Richmond at Virginia Commonwealth University, Department of Radiology, Richmond, VA (United States); Berman, Jeffrey I. [Children' s Hospital of Philadelphia, Department of Radiology, Philadelphia, PA (United States)
2015-09-15
Diffusion MRI is an imaging technique that uses the random motion of water to probe tissue microstructure. Diffusion tensor imaging (DTI) can quantitatively depict the organization and connectivity of white matter. Given the non-invasiveness of the technique, DTI has become a widely used tool for researchers and clinicians to examine the white matter of children. This review covers the basics of diffusion-weighted imaging and diffusion tensor imaging and discusses examples of their clinical application in children. (orig.)
Four dimensional sigma model coupled to the metric tensor field
International Nuclear Information System (INIS)
Ghika, G.; Visinescu, M.
1980-02-01
We discuss the four dimensional nonlinear sigma model with an internal O(n) invariance coupled to the metric tensor field satisfying Einstein equations. We derive a bound on the coupling constant between the sigma field and the metric tensor using the theory of harmonic maps. A special attention is paid to Einstein spaces and some new explicit solutions of the model are constructed. (author)
Optimization via separated representations and the canonical tensor decomposition
Reynolds, Matthew J.; Beylkin, Gregory; Doostan, Alireza
2017-11-01
We introduce a new, quadratically convergent algorithm for finding maximum absolute value entries of tensors represented in the canonical format. The computational complexity of the algorithm is linear in the dimension of the tensor. We show how to use this algorithm to find global maxima of non-convex multivariate functions in separated form. We demonstrate the performance of the new algorithms on several examples.
Optimization via Separated Representations and the Canonical Tensor Decomposition
Reynolds, Matthew J; Beylkin, Gregory; Doostan, Alireza
2016-01-01
We introduce a new, quadratically convergent algorithm for finding maximum absolute value entries of tensors represented in the canonical format. The computational complexity of the algorithm is linear in the dimension of the tensor. We show how to use this algorithm to find global maxima of non-convex multivariate functions in separated form. We demonstrate the performance of the new algorithms on several examples.
Canonical forms of tensor representations and spontaneous symmetry breaking
International Nuclear Information System (INIS)
Cummins, C.J.
1986-01-01
An algorithm for constructing canonical forms for any tensor representation of the classical compact Lie groups is given. This method is used to find a complete list of the symmetry breaking patterns produced by Higgs fields in the third-rank antisymmetric representations of U(n), SU(n) and SO(n) for n<=7. A simple canonical form is also given for kth-rank symmetric tensor representations. (author)
On deformed tensor potential for inelastic deuteron scattering
International Nuclear Information System (INIS)
Raynal, Jacques.
1980-08-01
Tensor analysing powers for inelastic deuteron scattering have been measured around 12 to 15 MeV. There is no problem to use such a tensor potential for the excited states in coupled channel calculations. However, for transition potentials, form factors are very different. A fit has been done with the first order vibrational model for 64 Ni(d,d') 64 Ni*, 2 + at 1,344 MeV
Smartphone dependence classification using tensor factorization
Kim, Yejin; Yook, In Hye; Yu, Hwanjo; Kim, Dai-Jin
2017-01-01
Excessive smartphone use causes personal and social problems. To address this issue, we sought to derive usage patterns that were directly correlated with smartphone dependence based on usage data. This study attempted to classify smartphone dependence using a data-driven prediction algorithm. We developed a mobile application to collect smartphone usage data. A total of 41,683 logs of 48 smartphone users were collected from March 8, 2015, to January 8, 2016. The participants were classified into the control group (SUC) or the addiction group (SUD) using the Korean Smartphone Addiction Proneness Scale for Adults (S-Scale) and a face-to-face offline interview by a psychiatrist and a clinical psychologist (SUC = 23 and SUD = 25). We derived usage patterns using tensor factorization and found the following six optimal usage patterns: 1) social networking services (SNS) during daytime, 2) web surfing, 3) SNS at night, 4) mobile shopping, 5) entertainment, and 6) gaming at night. The membership vectors of the six patterns obtained a significantly better prediction performance than the raw data. For all patterns, the usage times of the SUD were much longer than those of the SUC. From our findings, we concluded that usage patterns and membership vectors were effective tools to assess and predict smartphone dependence and could provide an intervention guideline to predict and treat smartphone dependence based on usage data. PMID:28636614
Mixed symmetry tensors in the worldline formalism
Energy Technology Data Exchange (ETDEWEB)
Corradini, Olindo [Dipartimento di Scienze Fisiche, Informatiche e Matematiche,Università degli Studi di Modena e Reggio Emilia, via Campi 213/A, I-41125 Modena (Italy); INFN - Sezione di Bologna,via Irnerio 46, I-40126 Bologna (Italy); Edwards, James P. [Department of Mathematical Sciences, University of Bath,Claverton Down, Bath BA2 7AY (United Kingdom)
2016-05-10
We consider the first quantised approach to quantum field theory coupled to a non-Abelian gauge field. Representing the colour degrees of freedom with a single family of auxiliary variables the matter field transforms in a reducible representation of the gauge group which — by adding a suitable Chern-Simons term to the particle action — can be projected onto a chosen fully (anti-)symmetric representation. By considering F families of auxiliary variables, we describe how to extend the model to arbitrary tensor products of F reducible representations, which realises a U(F) “flavour” symmetry on the worldline particle model. Gauging this symmetry allows the introduction of constraints on the Hilbert space of the colour fields which can be used to project onto an arbitrary irreducible representation, specified by a certain Young tableau. In particular the occupation numbers of the wavefunction — i.e. the lengths of the columns (rows) of the Young tableau — are fixed through the introduction of Chern-Simons terms. We verify this projection by calculating the number of colour degrees of freedom associated to the matter field. We suggest that, using the worldline approach to quantum field theory, this mechanism will allow the calculation of one-loop scattering amplitudes with the virtual particle in an arbitrary representation of the gauge group.
Diffusion tensor imaging in spinal cord injury
International Nuclear Information System (INIS)
Kamble, Ravindra B; Venkataramana, Neelam K; Naik, Arun L; Rao, Shailesh V
2011-01-01
To assess the feasibility of spinal tractography in patients of spinal cord injury vs a control group and to compare fractional anisotropy (FA) values between the groups. Diffusion tensor imaging (DTI) was performed in the spinal cord of 29 patients (18 patients and 11 controls). DTI was done in the cervical region if the cord injury was at the dorsal or lumbar region and in the conus region if cord injury was in the cervical or dorsal region. FA was calculated for the patients and the controls and the values were compared. The mean FA value was 0.550±0.09 in the control group and 0.367±0.14 in the patients; this difference was statistically significant (P=0.001). Spinal tractography is a feasible technique to assess the extent of spinal cord injury by FA, which is reduced in patients of spinal cord injury, suggesting possible Wallerian degeneration. In future, this technique may become a useful tool for assessing cord injury patients after stem cell therapy, with improvement in FA values indicating axonal regeneration
Diffusion tensor imaging of partial intractable epilepsy
International Nuclear Information System (INIS)
Dumas de la Roque, Anne; Oppenheim, Catherine; Rodrigo, Sebastian; Meder, Jean-Francois; Chassoux, Francine; Devaux, Bertrand; Beuvon, Frederic; Daumas-Duport, Catherine
2005-01-01
Our aim was to assess the value of diffusion tensor imaging (DTI) in patients with partial intractable epilepsy. We used DTI (25 non-collinear directions) in 15 patients with a cortical lesion on conventional MRI. Fractional anisotropy (FA) was measured in the internal capsule, and in the normal-appearing white matter (WM), adjacent tothe lesion, and away from the lesion, at a set distance of 2-3 cm. In each patient, increased or decreased FA measurements were those that varied from mirror values using an arbitrary 10% threshold. Over the whole population, ipsi- and contralateral FA measurements were also compared using a Wilcoxon test (p<0.05). Over the whole population, FA was significantly reduced in the WM adjacent to and away from the lesion, whilst being normal in the internal capsule. FA was reduced by more than 10% in the WM adjacent to and distant from the lesion in 13 and 12 patients respectively. For nine of the ten patients for whom the surgical resection encompassed the limits of the lesion on conventional MRI, histological data showed WM alterations (gliosis, axonal loss, abnormal cells). DTI often reveals WM abnormalities that are undetected on conventional MRI in patients with partial intractable epilepsy. (orig.)
Smartphone dependence classification using tensor factorization.
Directory of Open Access Journals (Sweden)
Jingyun Choi
Full Text Available Excessive smartphone use causes personal and social problems. To address this issue, we sought to derive usage patterns that were directly correlated with smartphone dependence based on usage data. This study attempted to classify smartphone dependence using a data-driven prediction algorithm. We developed a mobile application to collect smartphone usage data. A total of 41,683 logs of 48 smartphone users were collected from March 8, 2015, to January 8, 2016. The participants were classified into the control group (SUC or the addiction group (SUD using the Korean Smartphone Addiction Proneness Scale for Adults (S-Scale and a face-to-face offline interview by a psychiatrist and a clinical psychologist (SUC = 23 and SUD = 25. We derived usage patterns using tensor factorization and found the following six optimal usage patterns: 1 social networking services (SNS during daytime, 2 web surfing, 3 SNS at night, 4 mobile shopping, 5 entertainment, and 6 gaming at night. The membership vectors of the six patterns obtained a significantly better prediction performance than the raw data. For all patterns, the usage times of the SUD were much longer than those of the SUC. From our findings, we concluded that usage patterns and membership vectors were effective tools to assess and predict smartphone dependence and could provide an intervention guideline to predict and treat smartphone dependence based on usage data.