On higher order geometric and renormalization group flows
Prabhu, Kartik; Das, Sanjit; Kar, Sayan
2011-10-01
Renormalization group (RG) flows of the bosonic nonlinear σ-model are governed, perturbatively, at different orders of α', by perturbatively evaluated β-functions. In regions where {α'}/{Rc2}≪1 ( {1}/{Rc2} represents the curvature scale), the flow equations at various orders in α' can be thought of as approximating the full, non-perturbative RG flow. On the other hand, taking a different viewpoint, we may consider the above-mentioned RG flow equations as viable geometric flows in their own right, without any reference to the RG aspect. Looked at as purely geometric flows where higher order terms appear, we no longer have the perturbative restrictions (small curvatures). In this paper, we perform our analysis from both these perspectives using specific target manifolds such as S2, H2, unwarped S2×H2 and simple warped products. We analyse and solve the higher order RG flow equations within the appropriate perturbative domains and find the corrections arising due to the inclusion of higher order terms. Such corrections, within the perturbative regime, are shown to be small and they provide an estimate of the error that arises when higher orders are ignored. We also investigate higher order geometric flows on the same manifolds and figure out generic features of geometric evolution, the appearance of singularities and solitons. The aim, in this context, is to demonstrate the role of higher order terms in modifying the flow. One interesting aspect of our analysis is that, separable solutions of the higher order flow equations for simple warped spacetimes (of the kind used in bulk-brane models with a single extra dimension), correspond to constant curvature anti de Sitter (AdS) spacetimes, modulo an overall flow parameter dependent scale factor. The functional form of this scale factor (that we obtain) changes on the inclusion of successive higher order terms in the flow.
Higher-order gravity in higher dimensions: geometrical origins of four-dimensional cosmology?
Energy Technology Data Exchange (ETDEWEB)
Troisi, Antonio [Universita degli Studi di Salerno, Dipartimento di Fisica ' ' E.R. Caianiello' ' , Salerno (Italy)
2017-03-15
Determining the cosmological field equations is still very much debated and led to a wide discussion around different theoretical proposals. A suitable conceptual scheme could be represented by gravity models that naturally generalize Einstein theory like higher-order gravity theories and higher-dimensional ones. Both of these two different approaches allow one to define, at the effective level, Einstein field equations equipped with source-like energy-momentum tensors of geometrical origin. In this paper, the possibility is discussed to develop a five-dimensional fourth-order gravity model whose lower-dimensional reduction could provide an interpretation of cosmological four-dimensional matter-energy components. We describe the basic concepts of the model, the complete field equations formalism and the 5-D to 4-D reduction procedure. Five-dimensional f(R) field equations turn out to be equivalent, on the four-dimensional hypersurfaces orthogonal to the extra coordinate, to an Einstein-like cosmological model with three matter-energy tensors related with higher derivative and higher-dimensional counter-terms. By considering the gravity model with f(R) = f{sub 0}R{sup n} the possibility is investigated to obtain five-dimensional power law solutions. The effective four-dimensional picture and the behaviour of the geometrically induced sources are finally outlined in correspondence to simple cases of such higher-dimensional solutions. (orig.)
Do Lumped-Parameter Models Provide the Correct Geometrical Damping?
DEFF Research Database (Denmark)
Andersen, Lars
response during excitation and the geometrical damping related to free vibrations of a hexagonal footing. The optimal order of a lumped-parameter model is determined for each degree of freedom, i.e. horizontal and vertical translation as well as torsion and rocking. In particular, the necessity of coupling...
Do Lumped-Parameter Models Provide the Correct Geometrical Damping?
DEFF Research Database (Denmark)
Andersen, Lars
2007-01-01
This paper concerns the formulation of lumped-parameter models for rigid footings on homogenous or stratified soil with focus on the horizontal sliding and rocking. Such models only contain a few degrees of freedom, which makes them ideal for inclusion in aero-elastic codes for wind turbines and ......-parameter models with respect to the prediction of the maximum response during excitation and the geometrical damping related to free vibrations of a footing....
National Research Council Canada - National Science Library
Notaros, Branislav M; Ilic, Milan M; Djordjevic, Miroslav
2004-01-01
...), method of moments (MoM), and physical optics (PO). The simulations combine higher order geometrical modeling and higher order field/current modeling, which is referred to as double-higher-order modeling...
Geometrical structures of higher-order dynamical systems and field theories
Prieto-Martínez, Pedro D.
2014-01-01
Geometrical physics is a relatively young branch of applied mathematics that was initiated by the 60's and the 70's when A. Lichnerowicz, W.M. Tulczyjew and J.M. Souriau, among many others, began to study various topics in physics using methods of differential geometry. This "geometrization" provides a way to analyze the features of the physical systems from a global viewpoint, thus obtaining qualitative properties that help us in the integration of the equations that describe them. Since the...
Statistics Report on TEQSA Registered Higher Education Providers, 2016
Australian Government Tertiary Education Quality and Standards Agency, 2016
2016-01-01
This Statistics Report is the third release of selected higher education sector data held by the Australian Government Tertiary Education Quality and Standards Agency (TEQSA) for its quality assurance activities. It provides a snapshot of national statistics on all parts of the sector by bringing together data collected directly by TEQSA with data…
Statistics Report on TEQSA Registered Higher Education Providers
Australian Government Tertiary Education Quality and Standards Agency, 2015
2015-01-01
This statistics report provides a comprehensive snapshot of national statistics on all parts of the sector for the year 2013, by bringing together data collected directly by TEQSA with data sourced from the main higher education statistics collections managed by the Australian Government Department of Education and Training. The report provides…
Directory of Open Access Journals (Sweden)
Tomoyasu Takahiro
2008-10-01
Full Text Available Abstract Objective We examined the hypothesis that higher cerebral oxygen saturation (rSO2 during RCP is correlated with urinary output. Methods Between December 2002 and August 2006, 12 patients aged 3 to 61 days and weighing 2.6 to 3.4 kg underwent aortic arch repair with RCP. Urinary output and rSO2 were analyzed retrospectively. Data were assigned to either of 2 groups according to their corresponding rSO2: Group A (rSO2 ≦ 75% and Group B (rSO2 Results Seven and 5 patients were assigned to Group A and Group B, respectively. Group A was characterized by mean radial arterial pressure (37.9 ± 9.6 vs 45.8 ± 7.8 mmHg; P = 0.14 and femoral arterial pressure (6.7 ± 6.1 vs 20.8 ± 14.6 mmHg; P = 0.09 compared to Group B. However, higher urinary output during CPB (1.03 ± 1.18 vs 0.10 ± 0.15 ml·kg-1·h-1; P = 0.03. Furthermore our results indicate that a higher dose of Chlorpromazine was used in Group A (2.9 ± 1.4 vs 1.7 ± 1.0 mg/kg; P = 0.03. Conclusion Higher cerebral oxygenation may provide higher urinary output due to higher renal blood flow through collateral circulation.
Winblad, Ulrika; Blomqvist, Paula; Karlsson, Andreas
2017-07-14
Swedish nursing home care has undergone a transformation, where the previous virtual public monopoly on providing such services has been replaced by a system of mixed provision. This has led to a rapidly growing share of private actors, the majority of which are large, for-profit firms. In the wake of this development, concerns have been voiced regarding the implications for care quality. In this article, we investigate the relationship between ownership and care quality in nursing homes for the elderly by comparing quality levels between public, for-profit, and non-profit nursing home care providers. We also look at a special category of for-profit providers; private equity companies. The source of data is a national survey conducted by the Swedish National Board of Health and Welfare in 2011 at 2710 nursing homes. Data from 14 quality indicators are analyzed, including structure and process measures such as staff levels, staff competence, resident participation, and screening for pressure ulcers, nutrition status, and risk of falling. The main statistical method employed is multiple OLS regression analysis. We differentiate in the analysis between structural and processual quality measures. The results indicate that public nursing homes have higher quality than privately operated homes with regard to two structural quality measures: staffing levels and individual accommodation. Privately operated nursing homes, on the other hand, tend to score higher on process-based quality indicators such as medication review and screening for falls and malnutrition. No significant differences were found between different ownership categories of privately operated nursing homes. Ownership does appear to be related to quality outcomes in Swedish nursing home care, but the results are mixed and inconclusive. That staffing levels, which has been regarded as a key quality indicator in previous research, are higher in publicly operated homes than private is consistent with earlier
Geometric numerical integration applied to the elastic pendulum at higher order resonance
Tuwankotta, J.M.; Quispel, G.R.W.
2000-01-01
In this paper we study the performance of a symplectic numerical integrator based on the splitting method This method is applied to a subtle problem ie higher order resonance of the elastic pendulum In order to numerically study the phase space of the elastic pendulum at higher order resonance a
Sahmani, S.; Bahrami, M.; Ansari, R.
2014-12-01
This investigation deals with the free vibration characteristics of circular higher-order shear deformable nanoplates around the postbuckling configuration incorporating surface effects. Using the Gurtin-Murdoch elasticity theory, a size-dependent higher-order shear deformable plate model is developed which takes account all surface effects including surface elasticity, surface stress and surface density. Geometrical nonlinearity is considered based on the von Karman type nonlinear strain-displacement relationships. Also, in order to satisfy the balance conditions between bulk and surfaces of nanoplate, it is assumed that the normal stress is distributed cubically through the thickness of nanoplate. Hamilton's principle is utilized to derive non-classical governing differential equations of motion and related boundary conditions. Afterwards, an efficient numerical methodology based on a generalized differential quadrature (GDQ) method is employed to solve numerically the problem so as to discretize the governing partial differential equations along various edge supports using Chebyshev-Gauss-Lobatto grid points and pseudo arc-length continuation technique. A comparison between the results of present non-classical model and those of the classical plate theory is conducted. It is demonstrated that in contrast to the prebuckling domain, for a specified value of axial load in the postbuckling domain, increasing the plate thickness leads to higher frequencies.
Kasmaee, Roya Babaee; Nadi, Mohammad Ali; Shahtalebi, Badri
2016-01-01
Purpose: The purpose of this paper is to study and identify the effective components of higher education marketing and providing a marketing model for Iranian higher education private sector institutions. Design/methodology/approach: This study is a qualitative research. For identifying the effective components of higher education marketing and…
Coley, Alan A.; McNutt, David D.; Shoom, Andrey A.
2017-08-01
We discuss black hole spacetimes with a geometrically defined quasi-local horizon on which the curvature tensor is algebraically special relative to the alignment classification. Based on many examples and analytical results, we conjecture that a spacetime horizon is always more algebraically special (in all of the orders of specialization) than other regions of spacetime. Using recent results in invariant theory, such geometric black hole horizons can be identified by the alignment type II or D discriminant conditions in terms of scalar curvature invariants, which are not dependent on spacetime foliations. The above conjecture is, in fact, a suite of conjectures (isolated vs dynamical horizon; four vs higher dimensions; zeroth order invariants vs higher order differential invariants). However, we are particularly interested in applications in four dimensions and especially the location of a black hole in numerical computations.
Teacher's Attitude into Different Approach to Providing Feedback to Students in Higher Education
Chaqmaqchee, Zina Adil
2015-01-01
Feedback within higher education has an effective role in teaching staffs mode. The treatise on teachers' methods of feedback is represented to demonstrate how the novel feedback can help the academic staffs to provide an effective feedback for students in their assignments and written draft. The study investigates the academic staff's methods of…
Geometrization of Quantum Mechanics
Carinena, J. F.; Clemente-Gallardo, J.; Marmo, G.
2007-01-01
We show that it is possible to represent various descriptions of Quantum Mechanics in geometrical terms. In particular we start with the space of observables and use the momentum map associated with the unitary group to provide an unified geometrical description for the different pictures of Quantum Mechanics. This construction provides an alternative to the usual GNS construction for pure states.
Plastic spatula with narrow long tip provides higher satisfactory smears for Pap test
Directory of Open Access Journals (Sweden)
Pervinder Kaur
2013-01-01
Full Text Available Background: Ayre spatula for cervical smear collection is being used despite the suggestion that different modified spatulas provide more satisfactory sampling. Aims: To see whether the cytological pickup improves with the use of long tipped spatula. Setting and Design: Rurally based University Hospital; crossover study. Materials and Methods: Pap smear using Ayre spatula in 500 and with plastic narrow long tip (Szalay spatula in 500 clinic attending women was taken and analyzed. Crossover smears were taken with modified spatula in 163 and using Ayre spatula in 187 women after 2 weeks of initial smears. The same pathologist made cytological reporting for all smears and was unaware of the type of spatula used. Results: Smears from Ayre spatula had significantly higher reports of inadequate smears (94 of 500 vs. 68 of 500 for Ayre and Szalay, respectively; P = 0.032 and it remained so even after crossover (94 of 187 vs. 70 of 163 for Ayre and Szalay, respectively; P = 0.2. Cellular quality appeared better with smears taken using Szalay spatula, but the overall abnormal smear detection rate remained similar with either collection tool (χ2 = 1.5; P = 0.2. Conclusions: Proportion of satisfactory smears is higher when long tip plastic spatula is used for collection of sample.
Bray, Hubert L; Mazzeo, Rafe; Sesum, Natasa
2015-01-01
This volume includes expanded versions of the lectures delivered in the Graduate Minicourse portion of the 2013 Park City Mathematics Institute session on Geometric Analysis. The papers give excellent high-level introductions, suitable for graduate students wishing to enter the field and experienced researchers alike, to a range of the most important areas of geometric analysis. These include: the general issue of geometric evolution, with more detailed lectures on Ricci flow and Kähler-Ricci flow, new progress on the analytic aspects of the Willmore equation as well as an introduction to the recent proof of the Willmore conjecture and new directions in min-max theory for geometric variational problems, the current state of the art regarding minimal surfaces in R^3, the role of critical metrics in Riemannian geometry, and the modern perspective on the study of eigenfunctions and eigenvalues for Laplace-Beltrami operators.
The Charrette Design Model Provides a Means to Promote Collaborative Design in Higher Education
Directory of Open Access Journals (Sweden)
Webber Steven B.
2016-02-01
Full Text Available Higher education is typically compartmentalized by field and expertise level leading to a lack of collaboration across disciplines and reduced interaction among students of the same discipline that possess varying levels of expertise. The divisions between disciplines and expertise levels can be perforated through the use of a concentrated, short-term design problem called a charrette. The charrette is commonly used in architecture and interior design, and applications in other disciplines are possible. The use of the charrette in an educational context provides design students the opportunity to collaborate in teams where members have varying levels of expertise and consult with experts in allied disciplines in preparation for a profession that will expect the same. In the context of a competitive charrette, this study examines the effectiveness of forming teams of design students that possess a diversity of expertise. This study also looks at the effectiveness of integrating input from professional experts in design-allied disciplines (urban planning, architecture, mechanical and electrical engineering and a design-scenario-specific discipline (medicine into the students' design process. Using a chi-square test of goodness-of-fit, it is possible to determine student preferences in terms of the team configurations as well as their preferences on the experts. In this charrette context, the students indicated that the cross-expertise student team make-up had a positive effect for both the more experienced students and the less experienced students. Overall, the students placed high value on the input from experts in design-allied fields for the charrette. They also perceived a preference of input from external experts that had an immediate and practical implication to their design process. This article will also show student work examples as additional evidence of the successful cross-expertise collaboration among the design students and evidence
Muniz Oliva, Waldyr
2002-01-01
Geometric Mechanics here means mechanics on a pseudo-riemannian manifold and the main goal is the study of some mechanical models and concepts, with emphasis on the intrinsic and geometric aspects arising in classical problems. The first seven chapters are written in the spirit of Newtonian Mechanics while the last two ones as well as two of the four appendices describe the foundations and some aspects of Special and General Relativity. All the material has a coordinate free presentation but, for the sake of motivation, many examples and exercises are included in order to exhibit the desirable flavor of physical applications.
Students with intellectual disability in higher education: adult service provider perspectives.
Sheppard-Jones, Kathleen; Kleinert, Harold Lawrence; Druckemiller, Wendy; Ray, Megan Kovacevich
2015-04-01
Postsecondary education (PSE) is increasingly becoming an option for students with intellectual disability (ID; Grigal & Hart, 2012 ). Postsecondary education offers the promise of pursuing a valued social role (that of college student), enhanced social networks, and, most significantly, increased employment options. To date, research and practice in the area of transition to PSE for students with ID has focused primarily upon the sending (public school systems) and receiving (colleges or universities) agencies ( Oertle & Bragg, 2014 ; Thoma et al., 2011 ). Yet adults with ID often require ongoing supports through state and federally funded developmental disability waivers, and agency providers of waiver services have, for the most part, not been part of this vital conversation. This study represents an exploratory study of directors of developmental disability provider agencies in one midwestern state to assess their knowledge of PSE for individuals with ID. A total of 87 directors responded; quantitative results are presented and, based on these findings, we provide implications for the future.
Academic Governance Provided by Academic Boards within the Australian Higher Education Sector
Vilkinas, Tricia; Peters, Margaret
2014-01-01
Academic boards play a key role in the maintenance of quality standards and the provision of strategic leadership on academic issues. The current research investigated the role provided at present to Australian universities through their academic boards. All universities described their academic boards as their principal academic body. The…
Lightweight Innovative Solar Array (LISA): Providing Higher Power to Small Spacecraft
Johnson, Les; Carr, John; Fabisinski, Leo; Russell,Tiffany; Smith, Leigh
2015-01-01
Affordable and convenient access to electrical power is essential for all spacecraft and is a critical design driver for the next generation of smallsats, including cubesats, which are currently extremely power limited. The Lightweight Innovative Solar Array (LISA), a concept designed, prototyped, and tested at the NASA Marshall Space Flight Center (MSFC) in Huntsville, Alabama provides an affordable, lightweight, scalable, and easily manufactured approach for power generation in space. This flexible technology has many wide-ranging applications from serving small satellites to providing abundant power to large spacecraft in GEO and beyond. By using very thin, ultra-flexible solar arrays adhered to an inflatable structure, a large area (and thus large amount of power) can be folded and packaged into a relatively small volume. The LISA array comprises a launch-stowed, orbit-deployed structure on which lightweight photovoltaic devices and, potentially, transceiver elements are embedded. The system will provide a 2.5 to 5 fold increase in specific power generation (Watts/kilogram) coupled with a >2x enhancement of stowed volume (Watts/cubic-meter) and a decrease in cost (dollars/Watt) when compared to state-of-the-art solar arrays.
Hierarchies of geometric entanglement
Blasone, M.; Dell'Anno, F.; de Siena, S.; Illuminati, F.
2008-06-01
We introduce a class of generalized geometric measures of entanglement. For pure quantum states of N elementary subsystems, they are defined as the distances from the sets of K -separable states (K=2,…,N) . The entire set of generalized geometric measures provides a quantification and hierarchical ordering of the different bipartite and multipartite components of the global geometric entanglement, and allows discrimination among the different contributions. The extended measures are applied to the study of entanglement in different classes of N -qubit pure states. These classes include W and Greenberger-Horne-Zeilinger (GHZ) states, and their symmetric superpositions; symmetric multimagnon states; cluster states; and, finally, asymmetric generalized W -like superposition states. We discuss in detail a general method for the explicit evaluation of the multipartite components of geometric entanglement, and we show that the entire set of geometric measures establishes an ordering among the different types of bipartite and multipartite entanglement. In particular, it determines a consistent hierarchy between GHZ and W states, clarifying the original result of Wei and Goldbart that W states possess a larger global entanglement than GHZ states. Furthermore, we show that all multipartite components of geometric entanglement in symmetric states obey a property of self-similarity and scale invariance with the total number of qubits and the number of qubits per party.
Hashemi, M. S.; Baleanu, D.
2016-07-01
We propose a simple and accurate numerical scheme for solving the time fractional telegraph (TFT) equation within Caputo type fractional derivative. A fictitious coordinate ϑ is imposed onto the problem in order to transform the dependent variable u (x , t) into a new variable with an extra dimension. In the new space with the added fictitious dimension, a combination of method of line and group preserving scheme (GPS) is proposed to find the approximate solutions. This method preserves the geometric structure of the problem. Power and accuracy of this method has been illustrated through some examples of TFT equation.
Hamshire, Claire; Cullen, W. Rod
2014-01-01
The transition to higher education can be problematic for some students as they adapt to institutional procedures and degree level working at the same time as developing new social networks. To help facilitate these complex transitions institutions are increasingly turning towards digital technologies to provide both flexible access to resources…
Geometric Modeling for Computer Vision
1974-10-01
The main contribution of this thesis is the development of a three dimensional geometric modeling system for application to computer vision . In... computer vision geometric models provide a goal for descriptive image analysis, an origin for verification image synthesis, and a context for spatial
Geometric inequalities methods of proving
Sedrakyan, Hayk
2017-01-01
This unique collection of new and classical problems provides full coverage of geometric inequalities. Many of the 1,000 exercises are presented with detailed author-prepared-solutions, developing creativity and an arsenal of new approaches for solving mathematical problems. This book can serve teachers, high-school students, and mathematical competitors. It may also be used as supplemental reading, providing readers with new and classical methods for proving geometric inequalities. .
Aldrich, Heather Troxell; Salandanan, Karen; Kendall, Patricia; Bunning, Marisa; Stonaker, Frank; Külen, Oktay; Stushnoff, Cecil
2010-12-01
Tomatoes (Solanum lycopersicum L.) are widely consumed and well known for their health benefits, many of which have been associated with the high levels of antioxidants present in tomatoes. With a growing interest in local and organic foods, it would be helpful to determine whether farmers could naturally improve the quality and antioxidant content of tomatoes for sale in local markets. This study evaluated antioxidant properties, quality attributes, and yield for 10 tomato cultivars grown for 2 years using certified organic and conventional practices. Cultivar and year effects impacted (P < 0.05) all tests conducted, while growing method influenced (P < 0.05) yield, soluble solids content, ascorbic acid, and antioxidant radical scavenging capacity. Even when accounting for year-to-year variability, cultivars in the highest groups had 1.35- to 1.67-fold higher antioxidant levels than cultivars in the lowest groups. 'New Girl', 'Jet Star', 'Fantastic', and 'First Lady' were always in the highest groups, while 'Roma' and 'Early Girl' consistently had the lowest antioxidant content. Compared to production practices and environmental effects of years that are generally beyond the control of small-scale producers, choice of cultivar provides the simplest and most effective means of increasing antioxidant properties. Knowledge of tomato cultivars with naturally higher antioxidant levels could assist smaller-scale producers to grow fruit that may provide a competitive advantage and the opportunity to capitalize on the increasing popularity of locally grown, high-quality fresh produce. Copyright © 2010 Society of Chemical Industry.
Bestvina, Mladen; Vogtmann, Karen
2014-01-01
Geometric group theory refers to the study of discrete groups using tools from topology, geometry, dynamics and analysis. The field is evolving very rapidly and the present volume provides an introduction to and overview of various topics which have played critical roles in this evolution. The book contains lecture notes from courses given at the Park City Math Institute on Geometric Group Theory. The institute consists of a set of intensive short courses offered by leaders in the field, designed to introduce students to exciting, current research in mathematics. These lectures do not duplicate standard courses available elsewhere. The courses begin at an introductory level suitable for graduate students and lead up to currently active topics of research. The articles in this volume include introductions to CAT(0) cube complexes and groups, to modern small cancellation theory, to isometry groups of general CAT(0) spaces, and a discussion of nilpotent genus in the context of mapping class groups and CAT(0) gro...
DEFF Research Database (Denmark)
Andersen, Jørgen Ellegaard; Borot, Gaëtan; Orantin, Nicolas
We propose a general theory whose main component are functorial assignments ∑→Ω∑ ∈ E (∑), for a large class of functors E from a certain category of bordered surfaces (∑'s) to a suitable a target category of topological vector spaces. The construction is done by summing appropriate compositions o...... by integration of the GR amplitudes over the moduli space of bordered Riemann surfaces and Laplace transform with respect the boundary lengths. In this regard, the structure of the Mirzakhani-McShane identities served as a prototype of GR.......We propose a general theory whose main component are functorial assignments ∑→Ω∑ ∈ E (∑), for a large class of functors E from a certain category of bordered surfaces (∑'s) to a suitable a target category of topological vector spaces. The construction is done by summing appropriate compositions...... of the initial data over all homotopy classes of successive excisions of embedded pair of pants. We provide sufficient conditions to guarantee these infinite sums converge and as a result, we can generate mapping class group invariant vectors Ω∑ which we call amplitudes. The initial data encode the amplitude...
The geometric Hopf invariant and surgery theory
Crabb, Michael
2017-01-01
Written by leading experts in the field, this monograph provides homotopy theoretic foundations for surgery theory on higher-dimensional manifolds. Presenting classical ideas in a modern framework, the authors carefully highlight how their results relate to (and generalize) existing results in the literature. The central result of the book expresses algebraic surgery theory in terms of the geometric Hopf invariant, a construction in stable homotopy theory which captures the double points of immersions. Many illustrative examples and applications of the abstract results are included in the book, making it of wide interest to topologists. Serving as a valuable reference, this work is aimed at graduate students and researchers interested in understanding how the algebraic and geometric topology fit together in the surgery theory of manifolds. It is the only book providing such a wide-ranging historical approach to the Hopf invariant, double points and surgery theory, with many results old and new. .
Murray, James L.; Hu, Peixu; Shafer, David A.
2015-01-01
We have developed novel probe systems for real-time PCR that provide higher specificity, greater sensitivity, and lower cost relative to dual-labeled probes. The seven DNA Detection Switch (DDS)-probe systems reported here employ two interacting polynucleotide components: a fluorescently labeled probe and a quencher antiprobe. High-fidelity detection is achieved with three DDS designs: two internal probes (internal DDS and Flip probes) and a primer probe (ZIPR probe), wherein each probe is combined with a carefully engineered, slightly mismatched, error-checking antiprobe. The antiprobe blocks off-target detection over a wide range of temperatures and facilitates multiplexing. Other designs (Universal probe, Half-Universal probe, and MacMan probe) use generic components that enable low-cost detection. Finally, single-molecule G-Force probes employ guanine-mediated fluorescent quenching by forming a hairpin between adjacent C-rich and G-rich sequences. Examples provided show how these probe technologies discriminate drug-resistant Mycobacterium tuberculosis mutants, Escherichia coli O157:H7, oncogenic EGFR deletion mutations, hepatitis B virus, influenza A/B strains, and single-nucleotide polymorphisms in the human VKORC1 gene. PMID:25307756
Crinnion, Walter J
2010-04-01
The multi-billion dollar organic food industry is fueled by consumer perception that organic food is healthier (greater nutritional value and fewer toxic chemicals). Studies of the nutrient content in organic foods vary in results due to differences in the ground cover and maturity of the organic farming operation. Nutrient content also varies from farmer to farmer and year to year. However, reviews of multiple studies show that organic varieties do provide significantly greater levels of vitamin C, iron, magnesium, and phosphorus than non-organic varieties of the same foods. While being higher in these nutrients, they are also significantly lower in nitrates and pesticide residues. In addition, with the exception of wheat, oats, and wine, organic foods typically provide greater levels of a number of important antioxidant phytochemicals (anthocyanins, flavonoids, and carotenoids). Although in vitro studies of organic fruits and vegetables consistently demonstrate that organic foods have greater antioxidant activity, are more potent suppressors of the mutagenic action of toxic compounds, and inhibit the proliferation of certain cancer cell lines, in vivo studies of antioxidant activity in humans have failed to demonstrate additional benefit. Clear health benefits from consuming organic dairy products have been demonstrated in regard to allergic dermatitis.
Przylog, Adam; Stroka, Magdalena A; Engel, Susanne; Linder, Roland
2016-06-01
In 2009 a new system for the objective evaluation of nursing homes was introduced in Germany. The so-called nursing transparency agreement (Pflege-Transparenzvereinbarungen) was introduced to provide a reliable tool for an objective comparison of inpatient (PTVS) and outpatient (PTVA) care; however, the new regulations have been the subject of a broad discussion regarding reliability, efficiency and objectivity. To overcome the lack of objective health outcomes, this study used administrative data from Germany's largest health insurance fund, the Techniker Krankenkasse, in order to analyze the association between the quality ratings and objective quality measures on an individual level. This is the first study that provides empirical evidence on this topic using administrative data. The administrative dataset contained information on several individual characteristics as well as data on injuries, poisoning and other extrinsic effects on care-dependent individuals over the age of 64 years who were living in a nursing home in 2009. Based on these data an objective measure was constructed to test whether higher quality ratings of nursing homes led to a better quality of care of the respective patients using non-linear regression models. The results of the estimated models showed no significant evidence of such a relationship, neither considering the probability nor the number of injuries, poisoning and other extrinsic effects. Significant effects were only observed for gender and specific diseases. The results of this study support the argument that the current rating procedure for nursing homes has to be refined. Using quality indicators in combination with the administrative data could possibly contribute to such an enhancement.
Corrochano, Eduardo Bayro
2010-01-01
This book presents contributions from a global selection of experts in the field. This useful text offers new insights and solutions for the development of theorems, algorithms and advanced methods for real-time applications across a range of disciplines. Written in an accessible style, the discussion of all applications is enhanced by the inclusion of numerous examples, figures and experimental analysis. Features: provides a thorough discussion of several tasks for image processing, pattern recognition, computer vision, robotics and computer graphics using the geometric algebra framework; int
Federal Laboratory Consortium — Purpose: The mission of the Geometric Design Laboratory (GDL) is to support the Office of Safety Research and Development in research related to the geometric design...
Bathmaker, Ann-Marie
2016-01-01
This paper examines changing policy orientations to widening participation through college-based higher education in England. After more than 30 years of increasing and diversifying participation in higher education (HE) in a wide range of countries, such policy goals are coming under increasing scrutiny in countries such as the United States and…
Upadhyay, Sanjay K
2014-05-01
To determine the bioactive conformation required to bind with receptor aIIbb3, the peptide sequence RIPRGDMP from Kistrin was inserted into CDR 1 loop region of REI protein, resulting in REI-RGD34. The activity of REI-RGD34 was observed to increase at higher temperature towards the receptor aIIbb3. It could be justified in either way: the modified complex forces the restricted peptide to adapt bioactive conformation or it unfolds the peptide in a way that opens its binding surface with high affinity for receptor. Here, we model the conformational preference of RGD sequence in RIPRGDMP at 25 and 42 °C using multiple MD simulations. Further, we model the peptide sequence RGD, PRGD and PRGDMP from kistrin to observe the effect of flanking residues on conformational sampling of RGD. The presence of flanking residues around RGD peptide greatly influenced the conformational sampling. A transition from bend to turn conformation was observed for RGD sequence at 42 °C. The turn conformation shows pharmacophoric parameters required to recognize the receptor aIIbb3. Thus, the temperaturedependent activity of RIPRGDMP when inserted into the loop region of REI can be explained by the presence of the turn conformation. This study will help in designing potential antagonist for the receptor aIIbb3.
Geometric procedures for civil engineers
Tonias, Elias C
2016-01-01
This book provides a multitude of geometric constructions usually encountered in civil engineering and surveying practice. A detailed geometric solution is provided to each construction as well as a step-by-step set of programming instructions for incorporation into a computing system. The volume is comprised of 12 chapters and appendices that may be grouped in three major parts: the first is intended for those who love geometry for its own sake and its evolution through the ages, in general, and, more specifically, with the introduction of the computer. The second section addresses geometric features used in the book and provides support procedures used by the constructions presented. The remaining chapters and the appendices contain the various constructions. The volume is ideal for engineering practitioners in civil and construction engineering and allied areas.
Vergence, Vision, and Geometric Optics
Keating, Michael P.
1975-01-01
Provides a definition of vergence in terms of the curvature of the wave fronts, and gives examples to illustrate the advantages of this approach. The vergence treatment of geometrical optics provides both conceptual and algebraic advantages, particularly for the life science student, over the traditional object distance-image distance-focal length…
Geometric group theory an introduction
Löh, Clara
2017-01-01
Inspired by classical geometry, geometric group theory has in turn provided a variety of applications to geometry, topology, group theory, number theory and graph theory. This carefully written textbook provides a rigorous introduction to this rapidly evolving field whose methods have proven to be powerful tools in neighbouring fields such as geometric topology. Geometric group theory is the study of finitely generated groups via the geometry of their associated Cayley graphs. It turns out that the essence of the geometry of such groups is captured in the key notion of quasi-isometry, a large-scale version of isometry whose invariants include growth types, curvature conditions, boundary constructions, and amenability. This book covers the foundations of quasi-geometry of groups at an advanced undergraduate level. The subject is illustrated by many elementary examples, outlooks on applications, as well as an extensive collection of exercises.
Vilkinas, Tricia
2014-01-01
This study seeks to identify the leadership behaviours displayed by non-academic middle-level managers in the Australian higher education sector. The study also identifies the importance of these leadership behaviours and the leadership effectiveness of these managers. The integrated competing values framework was used to measure leadership…
2010-07-01
... an institution of higher education to assist designated State agencies? 386.35 Section 386.35... grantee that is an institution of higher education to assist designated State agencies? A grantee that is an institution of higher education provided assistance under this part shall cooperate with the...
Guide to Geometric Algebra in Practice
Dorst, Leo
2011-01-01
This highly practical "Guide to Geometric Algebra in Practice" reviews algebraic techniques for geometrical problems in computer science and engineering, and the relationships between them. The topics covered range from powerful new theoretical developments, to successful applications, and the development of new software and hardware tools. This title: provides hands-on review exercises throughout the book, together with helpful chapter summaries; presents a concise introductory tutorial to conformal geometric algebra (CGA) in the appendices; examines the application of CGA for the d
Geometric magnetism in open quantum systems
Campisi, Michele; Denisov, Sergey; Hänggi, Peter
2012-01-01
An isolated classical chaotic system, when driven by the slow change of several parameters, responds with two reaction forces: geometric friction and geometric magnetism. By using the theory of quantum fluctuation relations we show that this holds true also for open quantum systems, and provide explicit expressions for those forces in this case. This extends the concept of Berry curvature to the realm of open quantum systems. We illustrate our findings by calculating the geometric magnetism o...
Katirci, Hakan
2016-01-01
Considering various themes, this study aims to examine the content of web sites of universities that provide sports management education in higher education level in Turkey and in England. Within this framework, the websites of the higher education institutions that provide sports management education are analyzed by using the content analysis…
Directory of Open Access Journals (Sweden)
RANJIT SINGH GHUMAN
2013-12-01
Full Text Available The paper highlights a case study of a rural girls college located in a remote village of Gurdaspur district in Indian Punjab. The idea of this unique college was conceptualised by one Baba Aya Singh, a social and religious activist, from a village near the college way back in 1925. It was really a revolutionary idea because female education in India, particularly higher education, was a distant dream at that time. The college was, however, started with only 14 rural girls after about half-a-century when the great visionary Baba Aya Singh had a dream to educate the rural girls. Access to and affordability of higher education is the uniqueness of this college. The student has to pay only Rs. 5800 (about US $ 65 per annum, which includes both the tuition fee and boarding and lodging. It is equally significant to note that the entire expenses of the college are met by this and the produce of agricultural land of the college. The college does not take any outside help. The meritorious senior class students teach the junior class students. The college in its own humble, but significant, way made a revolutionary contribution to the education of poor rural girls who, otherwise, would not have dreamt of college education. Apart from, class-room teaching and bookish knowledge, the students are taught social, ethical and management skills in a most natural manner. The product of the college has proved to be the agents of change and rural transformation.
Sexton, J Bryan; Adair, Kathryn C; Leonard, Michael W; Frankel, Terri Christensen; Proulx, Joshua; Watson, Sam R; Magnus, Brooke; Bogan, Brittany; Jamal, Maleek; Schwendimann, Rene; Frankel, Allan S
2017-10-09
There is a poorly understood relationship between Leadership WalkRounds (WR) and domains such as safety culture, employee engagement, burnout and work-life balance. This cross-sectional survey study evaluated associations between receiving feedback about actions taken as a result of WR and healthcare worker assessments of patient safety culture, employee engagement, burnout and work-life balance, across 829 work settings. 16 797 of 23 853 administered surveys were returned (70.4%). 5497 (32.7% of total) reported that they had participated in WR, and 4074 (24.3%) reported that they participated in WR with feedback. Work settings reporting more WR with feedback had substantially higher safety culture domain scores (first vs fourth quartile Cohen's d range: 0.34-0.84; % increase range: 15-27) and significantly higher engagement scores for four of its six domains (first vs fourth quartile Cohen's d range: 0.02-0.76; % increase range: 0.48-0.70). This WR study of patient safety and organisational outcomes tested relationships with a comprehensive set of safety culture and engagement metrics in the largest sample of hospitals and respondents to date. Beyond measuring simply whether WRs occur, we examine WR with feedback, as WR being done well. We suggest that when WRs are conducted, acted on, and the results are fed back to those involved, the work setting is a better place to deliver and receive care as assessed across a broad range of metrics, including teamwork, safety, leadership, growth opportunities, participation in decision-making and the emotional exhaustion component of burnout. Whether WR with feedback is a manifestation of better norms, or a cause of these norms, is unknown, but the link is demonstrably potent. © Article author(s) (or their employer(s) unless otherwise stated in the text of the article) 2017. All rights reserved. No commercial use is permitted unless otherwise expressly granted.
Chen, Xiao-Jing; Gao, Xi-Lian; You, Gui-Ying; Jiang, Jing; Sun, Xiao-Lin; Li, Xiao; Chen, Yu-Cheng; Liang, Yu-Jia; Zhang, Qing; Zeng, Zhi
2014-01-01
Background Community health service center (CHSC) in China is always regarded as a good facility of primary care, which plays an important role in chronic non-communicable disease management. This study aimed to investigate the blood pressure (BP) control rate in a real life CHSC-based management program and its determinants. Methods The study enrolled 3191 patients (mean age of 70 ± 10 years, 43% males) in a hypertension management program provided by the Yulin CHSC (Chengdu, China), which h...
Liu, Lei; Bartke, Nana; Van Daele, Hans; Lawrence, Peter; Qin, Xia; Park, Hui Gyu; Kothapalli, Kumar; Windust, Anthony; Bindels, Jacques; Wang, Zhe; Brenna, J. Thomas
2014-01-01
Long-chain PUFAs (LCPUFAs) occur in foods primarily in the natural lipid classes, triacylglycerols (TAGs) or phospholipids (PLs). We studied the relative efficacy of the neural omega-3 DHA provided in formula to growing piglets as a dose of 13C-DHA bound to either TAG or phosphatidylcholine (PC). Piglets were assigned to identical formula-based diets from early life and provided with TAG-13C-DHA or PC-13C-DHA orally at 16 days. Days later, piglet organs were analyzed for 13C-DHA and other FA metabolites. PC-13C-DHA was 1.9-fold more efficacious for brain gray matter DHA accretion than TAG-13C-DHA, and was similarly more efficacious in gray matter synaptosomes, retina, liver, and red blood cells (RBCs). Liver labeling was greatest, implying initial processing in that organ followed by export to other organs, and suggesting that transfer from gut to bloodstream to liver in part drove the difference in relative efficacy for tissue accretion. Apparent retroconversion to 22:5n-3 was more than double for PC-13C-DHA and was more prominent in neural tissue than in liver or RBCs. These data directly support greater efficacy for PC as a carrier for LCPUFAs compared with TAG, consistent with previous studies of arachidonic acid and DHA measured in other species. PMID:24470588
Eisenhart lift for higher derivative systems
Energy Technology Data Exchange (ETDEWEB)
Galajinsky, Anton, E-mail: galajin@tpu.ru; Masterov, Ivan, E-mail: masterov@tpu.ru
2017-02-10
The Eisenhart lift provides an elegant geometric description of a dynamical system of second order in terms of null geodesics of the Brinkmann-type metric. In this work, we attempt to generalize the Eisenhart method so as to encompass higher derivative models. The analysis relies upon Ostrogradsky's Hamiltonian. A consistent geometric description seems feasible only for a particular class of potentials. The scheme is exemplified by the Pais–Uhlenbeck oscillator.
Eisenhart lift for higher derivative systems
Directory of Open Access Journals (Sweden)
Anton Galajinsky
2017-02-01
Full Text Available The Eisenhart lift provides an elegant geometric description of a dynamical system of second order in terms of null geodesics of the Brinkmann-type metric. In this work, we attempt to generalize the Eisenhart method so as to encompass higher derivative models. The analysis relies upon Ostrogradsky's Hamiltonian. A consistent geometric description seems feasible only for a particular class of potentials. The scheme is exemplified by the Pais–Uhlenbeck oscillator.
Enhancing geometric reasoning.
Mistretta, R M
2000-01-01
Geometry is an important part of the mathematics curriculum. However, students are not demonstrating strong conceptual knowledge of this subject. The research of Van Hiele and Van Hiele-Geldof has focused on the concept of thinking levels in geometry and the role of instruction in raising levels of thinking. This paper describes a field trial of a supplemental geometry unit intended to raise Van Hiele thinking levels in a group of 23 eighth-grade students by having them become more adept at using higher order thinking skills. Sample questions assessing particular Van Hiele thinking levels and attitudes toward geometry, as well as field-tested activities yielding the most positive results, are presented. Educators can benefit from this application of the Van Hiele model of geometric thinking, since the thought processes involved in learning geometry are explained, along with teaching techniques and tools for assessment. By having teachers become more aware of their students' cognitive skills, attitudes, and misconceptions, teaching practices and student achievement can be enhanced.
Energy Technology Data Exchange (ETDEWEB)
Balderson, Michael, E-mail: michael.balderson@rmp.uhn.ca; Brown, Derek; Johnson, Patricia; Kirkby, Charles
2016-07-01
The purpose of this work was to compare static gantry intensity-modulated radiation therapy (IMRT) with volume-modulated arc therapy (VMAT) in terms of tumor control probability (TCP) under scenarios involving large geometric misses, i.e., those beyond what are accounted for when margin expansion is determined. Using a planning approach typical for these treatments, a linear-quadratic–based model for TCP was used to compare mean TCP values for a population of patients who experiences a geometric miss (i.e., systematic and random shifts of the clinical target volume within the planning target dose distribution). A Monte Carlo approach was used to account for the different biological sensitivities of a population of patients. Interestingly, for errors consisting of coplanar systematic target volume offsets and three-dimensional random offsets, static gantry IMRT appears to offer an advantage over VMAT in that larger shift errors are tolerated for the same mean TCP. For example, under the conditions simulated, erroneous systematic shifts of 15 mm directly between or directly into static gantry IMRT fields result in mean TCP values between 96% and 98%, whereas the same errors on VMAT plans result in mean TCP values between 45% and 74%. Random geometric shifts of the target volume were characterized using normal distributions in each Cartesian dimension. When the standard deviations were doubled from those values assumed in the derivation of the treatment margins, our model showed a 7% drop in mean TCP for the static gantry IMRT plans but a 20% drop in TCP for the VMAT plans. Although adding a margin for error to a clinical target volume is perhaps the best approach to account for expected geometric misses, this work suggests that static gantry IMRT may offer a treatment that is more tolerant to geometric miss errors than VMAT.
A Babylonian Geometrical Algebra.
Bidwell, James K.
1986-01-01
A possible method of derivation of prescriptions for solving problems, found in Babylonian cuneiform texts, is presented. It is a kind of "geometric algebra" based mainly on one figure and the manipulation of or within various areas and segments. (MNS)
Geometric and engineering drawing
Morling, K
2010-01-01
The new edition of this successful text describes all the geometric instructions and engineering drawing information that are likely to be needed by anyone preparing or interpreting drawings or designs with plenty of exercises to practice these principles.
Differential geometric structures
Poor, Walter A
2007-01-01
This introductory text defines geometric structure by specifying parallel transport in an appropriate fiber bundle and focusing on simplest cases of linear parallel transport in a vector bundle. 1981 edition.
Further improving geometric fitting
Kanatani, Kenichi
2005-01-01
We give a formal definition of geometric fitting in a way that suits computer vision applications. We point out that the performance of geometric fitting should be evaluated in the limit of small noise rather than in the limit of a large number of data as recommended in the statistical literature. Taking the KCR lower bound as an optimality requirement and focusing on the linearized constraint case, we compare the accuracy of Kanatani's renormalization with maximum likelihood (ML) approaches ...
Transition curves for highway geometric design
Kobryń, Andrzej
2017-01-01
This book provides concise descriptions of the various solutions of transition curves, which can be used in geometric design of roads and highways. It presents mathematical methods and curvature functions for defining transition curves. .
Directory of Open Access Journals (Sweden)
Ilham Rizkianto
2013-07-01
Full Text Available Previous studies have provided that when learning shapes for the first time, young children tend to use the prototype as the reference point for comparisons, but often fail when doing so since they do not yet think about the defining attributes or the geometric properties of the shapes. Most of the time, elementary students learn geometric properties of shapes only as empty verbal statements to be memorized, without any chance to experience the contepts meaningfully. In the light of it, a sequence of instructional activities along with computer manipulative was designed to support Indonesian third graders in constructing geometric properties of square, rectangle, and triangle. The aim of the present study is to develop a loval instructional theory to support third graders in constructing geometric properties of rectangle, square, and triangle. Thirty seven students of one third grade classes in SD Pupuk Sriwijaya Palembang, along with their class teacher, were involved in the study. Our findings suggest that the combination of computer and non-computer activities suppots third graders in constructing geometric properties of square, rectangle, and triangle in that it provides opportunities to the students to experience and to develop the concepts meaningfully while using their real experiences as the bases to attain a higher geometric thinking level.Key concepts: Geometric properties, rectangle, square, triangle, design research, realistic mathematics education DOI: http://dx.doi.org/10.22342/jme.4.2.414.160-171
Height and Tilt Geometric Texture
DEFF Research Database (Denmark)
Andersen, Vedrana; Desbrun, Mathieu; Bærentzen, Jakob Andreas
2009-01-01
We propose a new intrinsic representation of geometric texture over triangle meshes. Our approach extends the conventional height field texture representation by incorporating displacements in the tangential plane in the form of a normal tilt. This texture representation offers a good practical...... compromise between functionality and simplicity: it can efficiently handle and process geometric texture too complex to be represented as a height field, without having recourse to full blown mesh editing algorithms. The height-and-tilt representation proposed here is fully intrinsic to the mesh, making...... texture editing and animation (such as bending or waving) intuitively controllable over arbitrary base mesh. We also provide simple methods for texture extraction and transfer using our height-and-field representation....
Hidden geometric character of relativistic quantum mechanics
Almeida, José B.
2007-01-01
Geometry can be an unsuspected source of equations with physical relevance, as everybody is aware since Einstein formulated the general theory of relativity. However, efforts to extend a similar type of reasoning to other areas of physics, namely, electrodynamics, quantum mechanics, and particle physics, usually had very limited success; particularly in quantum mechanics the standard formalism is such that any possible relation to geometry is impossible to detect; other authors have previously trod the geometric path to quantum mechanics, some of that work being referred to in the text. In this presentation we will follow an alternate route to show that quantum mechanics has indeed a strong geometric character. The paper makes use of geometric algebra, also known as Clifford algebra, in five-dimensional space-time. The choice of this space is given the character of first principle, justified solely by the consequences that can be derived from such choice and their consistency with experimental results. Given a metric space of any dimension, one can define monogenic functions, the natural extension of analytic functions to higher dimensions; such functions have null vector derivative and have previously been shown by other authors to play a decisive role in lower dimensional spaces. All monogenic functions have null Laplacian by consequence; in a hyperbolic space this fact leads inevitably to a wave equation with planelike solutions. This is also true for five-dimensional space-time and we will explore those solutions, establishing a parallel with the solutions of the free particle Dirac equation. For this purpose we will invoke the isomorphism between the complex algebra of 4×4 matrices, also known as Dirac's matrices. There is one problem with this isomorphism, because the solutions to Dirac's equation are usually known as spinors (column matrices) that do not belong to the 4×4 matrix algebra and as such are excluded from the isomorphism. We will show that a
Shahshahani, M.
1991-01-01
The performance characteristics are discussed of certain algebraic geometric codes. Algebraic geometric codes have good minimum distance properties. On many channels they outperform other comparable block codes; therefore, one would expect them eventually to replace some of the block codes used in communications systems. It is suggested that it is unlikely that they will become useful substitutes for the Reed-Solomon codes used by the Deep Space Network in the near future. However, they may be applicable to systems where the signal to noise ratio is sufficiently high so that block codes would be more suitable than convolutional or concatenated codes.
Riemannian geometry and geometric analysis
Jost, Jürgen
2017-01-01
This established reference work continues to provide its readers with a gateway to some of the most interesting developments in contemporary geometry. It offers insight into a wide range of topics, including fundamental concepts of Riemannian geometry, such as geodesics, connections and curvature; the basic models and tools of geometric analysis, such as harmonic functions, forms, mappings, eigenvalues, the Dirac operator and the heat flow method; as well as the most important variational principles of theoretical physics, such as Yang-Mills, Ginzburg-Landau or the nonlinear sigma model of quantum field theory. The present volume connects all these topics in a systematic geometric framework. At the same time, it equips the reader with the working tools of the field and enables her or him to delve into geometric research. The 7th edition has been systematically reorganized and updated. Almost no page has been left unchanged. It also includes new material, for instance on symplectic geometry, as well as the B...
Mahavira's Geometrical Problems
DEFF Research Database (Denmark)
Høyrup, Jens
2004-01-01
Analysis of the geometrical chapters Mahavira's 9th-century Ganita-sara-sangraha reveals inspiration from several chronological levels of Near-Eastern and Mediterranean mathematics: (1)that known from Old Babylonian tablets, c. 1800-1600 BCE; (2)a Late Babylonian but pre-Seleucid Stratum, probabl...
The geometric semantics of algebraic quantum mechanics.
Cruz Morales, John Alexander; Zilber, Boris
2015-08-06
In this paper, we will present an ongoing project that aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We argue that this approach provides a geometric semantics for such a formalism by means of establishing a (non-commutative) duality between certain algebraic and geometric objects. © 2015 The Author(s) Published by the Royal Society. All rights reserved.
Graphene geometric diodes for terahertz rectennas
Zhu, Zixu; Joshi, Saumil; Grover, Sachit; Moddel, Garret
2013-05-01
We demonstrate a new thin-film graphene diode called a geometric diode that relies on geometric asymmetry to provide rectification at 28 THz. The geometric diode is coupled to an optical antenna to form a rectenna that rectifies incoming radiation. This is the first reported graphene-based antenna-coupled diode working at 28 THz, and potentially at optical frequencies. The planar structure of the geometric diode provides a low RC time constant, on the order of 10-15 s, required for operation at optical frequencies, and a low impedance for efficient power transfer from the antenna. Fabricated geometric diodes show asymmetric current-voltage characteristics consistent with Monte Carlo simulations for the devices. Rectennas employing the geometric diode coupled to metal and graphene antennas rectify 10.6 µm radiation, corresponding to an operating frequency of 28 THz. The graphene bowtie antenna is the first demonstrated functional antenna made using graphene. Its response indicates that graphene is a suitable terahertz resonator material. Applications for this terahertz diode include terahertz-wave and optical detection, ultra-high-speed electronics and optical power conversion.
Field guide to geometrical optics
Greivenkamp, John E
2004-01-01
This Field Guide derives from the treatment of geometrical optics that has evolved from both the undergraduate and graduate programs at the Optical Sciences Center at the University of Arizona. The development is both rigorous and complete, and it features a consistent notation and sign convention. This volume covers Gaussian imagery, paraxial optics, first-order optical system design, system examples, illumination, chromatic effects, and an introduction to aberrations. The appendices provide supplemental material on radiometry and photometry, the human eye, and several other topics.
Directory of Open Access Journals (Sweden)
Ilham Rizkianto
2013-07-01
Full Text Available Previous studies have provided that when learning shapes for the first time, young children tend to use the prototype as the reference point for comparisons, but often fail when doing so since they do not yet think about the defining attributes or the geometric properties of the shapes. Most of the time, elementary students learn geometric properties of shapes only as empty verbal statements to be memorized, without any chance to experience the concepts meaningfully. In the light of it, a sequence of instructional activities along with computer manipulative was designed to support Indonesian third graders in constructing geometric properties of square, rectangle, and triangle. The aim of the present study is to develop a localinstructional theory to support third graders in constructing geometric properties of rectangle, square and triangle. Thirty seven students of one third grade classes in SD Pupuk Sriwijaya Palembang, along with their class teacher, were involved in the study. Our findings suggest that the combination of computer and non computer activities supports third graders in constructing geometric properties of square, rectangle, and triangle in that it provides opportunities to the students to experience and to develop the concepts meaningfully while using their real experiences as the bases to attain a higher geometric thinking level.
Dynamics in geometrical confinement
Kremer, Friedrich
2014-01-01
This book describes the dynamics of low molecular weight and polymeric molecules when they are constrained under conditions of geometrical confinement. It covers geometrical confinement in different dimensionalities: (i) in nanometer thin layers or self supporting films (1-dimensional confinement) (ii) in pores or tubes with nanometric diameters (2-dimensional confinement) (iii) as micelles embedded in matrices (3-dimensional) or as nanodroplets.The dynamics under such conditions have been a much discussed and central topic in the focus of intense worldwide research activities within the last two decades. The present book discusses how the resulting molecular mobility is influenced by the subtle counterbalance between surface effects (typically slowing down molecular dynamics through attractive guest/host interactions) and confinement effects (typically increasing the mobility). It also explains how these influences can be modified and tuned, e.g. through appropriate surface coatings, film thicknesses or pore...
Frè, Pietro Giuseppe
2013-01-01
‘Gravity, a Geometrical Course’ presents general relativity (GR) in a systematic and exhaustive way, covering three aspects that are homogenized into a single texture: i) the mathematical, geometrical foundations, exposed in a self consistent contemporary formalism, ii) the main physical, astrophysical and cosmological applications, updated to the issues of contemporary research and observations, with glimpses on supergravity and superstring theory, iii) the historical development of scientific ideas underlying both the birth of general relativity and its subsequent evolution. The book is divided in two volumes. Volume One is dedicated to the development of the theory and basic physical applications. It guides the reader from the foundation of special relativity to Einstein field equations, illustrating some basic applications in astrophysics. A detailed account of the historical and conceptual development of the theory is combined with the presentation of its mathematical foundations. Differe...
Geometric theory of information
2014-01-01
This book brings together geometric tools and their applications for Information analysis. It collects current and many uses of in the interdisciplinary fields of Information Geometry Manifolds in Advanced Signal, Image & Video Processing, Complex Data Modeling and Analysis, Information Ranking and Retrieval, Coding, Cognitive Systems, Optimal Control, Statistics on Manifolds, Machine Learning, Speech/sound recognition, and natural language treatment which are also substantially relevant for the industry.
Geometrically Consistent Mesh Modification
Bonito, A.
2010-01-01
A new paradigm of adaptivity is to execute refinement, coarsening, and smoothing of meshes on manifolds with incomplete information about their geometry and yet preserve position and curvature accuracy. We refer to this collectively as geometrically consistent (GC) mesh modification. We discuss the concept of discrete GC, show the failure of naive approaches, and propose and analyze a simple algorithm that is GC and accuracy preserving. © 2010 Society for Industrial and Applied Mathematics.
Waerden, B
1996-01-01
From the reviews: "... Federer's timely and beautiful book indeed fills the need for a comprehensive treatise on geometric measure theory, and his detailed exposition leads from the foundations of the theory to the most recent discoveries. ... The author writes with a distinctive style which is both natural and powerfully economical in treating a complicated subject. This book is a major treatise in mathematics and is essential in the working library of the modern analyst." Bulletin of the London Mathematical Society.
Geometric diffusion of quantum trajectories
Yang, Fan; Liu, Ren-Bao
2015-07-01
A quantum object can acquire a geometric phase (such as Berry phases and Aharonov-Bohm phases) when evolving along a path in a parameter space with non-trivial gauge structures. Inherent to quantum evolutions of wavepackets, quantum diffusion occurs along quantum trajectories. Here we show that quantum diffusion can also be geometric as characterized by the imaginary part of a geometric phase. The geometric quantum diffusion results from interference between different instantaneous eigenstate pathways which have different geometric phases during the adiabatic evolution. As a specific example, we study the quantum trajectories of optically excited electron-hole pairs in time-reversal symmetric insulators, driven by an elliptically polarized terahertz field. The imaginary geometric phase manifests itself as elliptical polarization in the terahertz sideband generation. The geometric quantum diffusion adds a new dimension to geometric phases and may have applications in many fields of physics, e.g., transport in topological insulators and novel electro-optical effects.
Shapere, Alfred D
1989-01-01
During the last few years, considerable interest has been focused on the phase that waves accumulate when the equations governing the waves vary slowly. The recent flurry of activity was set off by a paper by Michael Berry, where it was found that the adiabatic evolution of energy eigenfunctions in quantum mechanics contains a phase of geometric origin (now known as 'Berry's phase') in addition to the usual dynamical phase derived from Schrödinger's equation. This observation, though basically elementary, seems to be quite profound. Phases with similar mathematical origins have been identified
Geometrizing adiabatic quantum computation
Rezakhani, Ali; Kuo, Wan-Jung; Hamma, Alioscia; Lidar, Daniel; Zanardi, Paolo
2010-03-01
A time-optimal approach to adiabatic quantum computation (AQC) is formulated. The corresponding natural Riemannian metric is also derived, through which AQC can be understood as the problem of finding a geodesic on the manifold of control parameters. We demonstrate this geometrization through some examples, where we show that it leads to improved performance of AQC, and sheds light on the roles of entanglement and curvature of the control manifold in algorithmic performance. The underlying connection with quantum phase transitions is also explored.
Geometric Rationalization for Freeform Architecture
Jiang, Caigui
2016-06-20
The emergence of freeform architecture provides interesting geometric challenges with regards to the design and manufacturing of large-scale structures. To design these architectural structures, we have to consider two types of constraints. First, aesthetic constraints are important because the buildings have to be visually impressive. Sec- ond, functional constraints are important for the performance of a building and its e cient construction. This thesis contributes to the area of architectural geometry. Specifically, we are interested in the geometric rationalization of freeform architec- ture with the goal of combining aesthetic and functional constraints and construction requirements. Aesthetic requirements typically come from designers and architects. To obtain visually pleasing structures, they favor smoothness of the building shape, but also smoothness of the visible patterns on the surface. Functional requirements typically come from the engineers involved in the construction process. For exam- ple, covering freeform structures using planar panels is much cheaper than using non-planar ones. Further, constructed buildings have to be stable and should not collapse. In this thesis, we explore the geometric rationalization of freeform archi- tecture using four specific example problems inspired by real life applications. We achieve our results by developing optimization algorithms and a theoretical study of the underlying geometrical structure of the problems. The four example problems are the following: (1) The design of shading and lighting systems which are torsion-free structures with planar beams based on quad meshes. They satisfy the functionality requirements of preventing light from going inside a building as shad- ing systems or reflecting light into a building as lighting systems. (2) The Design of freeform honeycomb structures that are constructed based on hex-dominant meshes with a planar beam mounted along each edge. The beams intersect without
Geometric decompositions of collective motion
Mischiati, Matteo; Krishnaprasad, P. S.
2017-04-01
Collective motion in nature is a captivating phenomenon. Revealing the underlying mechanisms, which are of biological and theoretical interest, will require empirical data, modelling and analysis techniques. Here, we contribute a geometric viewpoint, yielding a novel method of analysing movement. Snapshots of collective motion are portrayed as tangent vectors on configuration space, with length determined by the total kinetic energy. Using the geometry of fibre bundles and connections, this portrait is split into orthogonal components each tangential to a lower dimensional manifold derived from configuration space. The resulting decomposition, when interleaved with classical shape space construction, is categorized into a family of kinematic modes-including rigid translations, rigid rotations, inertia tensor transformations, expansions and compressions. Snapshots of empirical data from natural collectives can be allocated to these modes and weighted by fractions of total kinetic energy. Such quantitative measures can provide insight into the variation of the driving goals of a collective, as illustrated by applying these methods to a publicly available dataset of pigeon flocking. The geometric framework may also be profitably employed in the control of artificial systems of interacting agents such as robots.
Geometric spin echo under zero field
Sekiguchi, Yuhei; Komura, Yusuke; Mishima, Shota; Tanaka, Touta; Niikura, Naeko; Kosaka, Hideo
2016-05-01
Spin echo is a fundamental tool for quantum registers and biomedical imaging. It is believed that a strong magnetic field is needed for the spin echo to provide long memory and high resolution, since a degenerate spin cannot be controlled or addressed under a zero magnetic field. While a degenerate spin is never subject to dynamic control, it is still subject to geometric control. Here we show the spin echo of a degenerate spin subsystem, which is geometrically controlled via a mediating state split by the crystal field, in a nitrogen vacancy centre in diamond. The demonstration reveals that the degenerate spin is protected by inherent symmetry breaking called zero-field splitting. The geometric spin echo under zero field provides an ideal way to maintain the coherence without any dynamics, thus opening the way to pseudo-static quantum random access memory and non-invasive biosensors.
Fitting a geometric graph to a protein-protein interaction network.
Higham, Desmond J; Rasajski, Marija; Przulj, Natasa
2008-04-15
Finding a good network null model for protein-protein interaction (PPI) networks is a fundamental issue. Such a model would provide insights into the interplay between network structure and biological function as well as into evolution. Also, network (graph) models are used to guide biological experiments and discover new biological features. It has been proposed that geometric random graphs are a good model for PPI networks. In a geometric random graph, nodes correspond to uniformly randomly distributed points in a metric space and edges (links) exist between pairs of nodes for which the corresponding points in the metric space are close enough according to some distance norm. Computational experiments have revealed close matches between key topological properties of PPI networks and geometric random graph models. In this work, we push the comparison further by exploiting the fact that the geometric property can be tested for directly. To this end, we develop an algorithm that takes PPI interaction data and embeds proteins into a low-dimensional Euclidean space, under the premise that connectivity information corresponds to Euclidean proximity, as in geometric-random graphs. We judge the sensitivity and specificity of the fit by computing the area under the Receiver Operator Characteristic (ROC) curve. The network embedding algorithm is based on multi-dimensional scaling, with the square root of the path length in a network playing the role of the Euclidean distance in the Euclidean space. The algorithm exploits sparsity for computational efficiency, and requires only a few sparse matrix multiplications, giving a complexity of O(N(2)) where N is the number of proteins. The algorithm has been verified in the sense that it successfully rediscovers the geometric structure in artificially constructed geometric networks, even when noise is added by re-wiring some links. Applying the algorithm to 19 publicly available PPI networks of various organisms indicated that: (a
Dean, M; Levis, A
2016-12-01
To establish the rationale for using a lecturer as a visiting tutor, and to identify the activities undertaken during clinical placements to support student learning and assessment in practice. A secure electronic survey was used to incorporate qualitative and quantitative data collection procedures. Thirty-three higher education institution (HEI) providers of physiotherapy education in the UK, registered with the Chartered Society of Physiotherapy. UK HEI physiotherapy placement coordinators. A questionnaire was used to examine HEI perceptions. A pilot focus group consultation informed the questionnaire content. Surveys were analysed based on the proportion of responses to closed questions on an adapted Likert scale, with further thematic analysis of open questions. All 25 respondents (25/33, 76%) indicated their provision of support for students and clinical educators throughout their clinical placements. 'Face-to-face' engagement during the placement visit was viewed as essential to guide the clinical educator to provide a consistent approach to learning and assessment strategies; ensuring cohesion between theoretical and clinical components of the curriculum was viewed as a core objective by visiting academic tutors. However, the emergent themes highlighted key differences between HEIs' perspectives of what this support for clinical placement learning should entail. The majority of HEIs endorse the use of a lecturer as a visiting tutor to inform and maintain the standard of learning and assessment within the clinical placement. However, the value of this interaction requires confirmation via other stakeholders, and exploration of other forms of non-face-to-face support processes warrant further investigation. Copyright © 2015 Chartered Society of Physiotherapy. Published by Elsevier Ltd. All rights reserved.
Geometric phase around exceptional points
Mailybaev, Alexei; Kirillov, Oleg; Seyranian, Alexander,
2005-01-01
A wave function picks up, in addition to the dynamic phase, the geometric (Berry) phase when traversing adiabatically a closed cycle in parameter space. We develop a general multidimensional theory of the geometric phase for (double) cycles around exceptional degeneracies in non-Hermitian Hamiltonians. We show that the geometric phase is exactly $\\pi$ for symmetric complex Hamiltonians of arbitrary dimension and for nonsymmetric non-Hermitian Hamiltonians of dimension 2. For nonsymmetric non-...
Andersen, Nils; Lauterbach, Stefan; Erlenkeuser, Helmut; Danielopol, Dan L.; Namiotko, Tadeusz; Hüls, Matthias; Belmecheri, Soumaya; Dulski, Peter; Nantke, Carla; Meyer, Hanno; Chapligin, Bernhard; von Grafenstein, Ulrich; Brauer, Achim
2017-09-01
The so-called 8.2 ka event represents one of the most prominent cold climate anomalies during the Holocene warm period. Accordingly, several studies have addressed its trigger mechanisms, absolute dating and regional characteristics so far. However, knowledge about subsequent climate recovery is still limited although this might be essential for the understanding of rapid climatic changes. Here we present a new sub-decadally resolved and precisely dated oxygen isotope (δ18O) record for the interval between 7.7 and 8.7 ka BP (103 calendar years before AD 1950), derived from the calcareous valves of benthic ostracods preserved in the varved lake sediments of pre-Alpine Mondsee (Austria). Besides a clear reflection of the 8.2 ka event, showing a good agreement in timing, duration and magnitude with other regional stable isotope records, the high-resolution Mondsee lake sediment record provides evidence for a 75-year-long interval of higher-than-average δ18O values directly after the 8.2 ka event, possibly reflecting increased air temperatures in Central Europe. This observation is consistent with evidence from other proxy records in the North Atlantic realm, thus most probably reflecting a hemispheric-scale climate signal rather than a local phenomenon. As a possible trigger we suggest an enhanced resumption of the Atlantic meridional overturning circulation (AMOC), supporting assumptions from climate model simulations.
Geometric inequalities in spherically symmetric spacetimes
Csukás, Károly Z.
2017-07-01
In geometric inequalities ADM mass plays more fundamental role than the concept of quasi-local mass. This paper is to demonstrate that using the quasi-local mass some new insights can be acquired. In spherically symmetric spacetimes the Misner-Sharp mass and the concept of the Kodama vector field provides an ideal setting to the investigations of geometric inequalities. We applying the proposed new techniques to investigate the spacetimes containing black hole or cosmological horizons but we shall also apply them in context of normal bodies. Most of the previous investigations applied only the quasi-local charges and the area. Our main point is to include the quasi-local mass in the corresponding geometrical inequalities. This way we recover some known relations but new inequalities are also derived.
Understanding geometric algebra for electromagnetic theory
Arthur, John W
2011-01-01
"This book aims to disseminate geometric algebra as a straightforward mathematical tool set for working with and understanding classical electromagnetic theory. It's target readership is anyone who has some knowledge of electromagnetic theory, predominantly ordinary scientists and engineers who use it in the course of their work, or postgraduate students and senior undergraduates who are seeking to broaden their knowledge and increase their understanding of the subject. It is assumed that the reader is not a mathematical specialist and is neither familiar with geometric algebra or its application to electromagnetic theory. The modern approach, geometric algebra, is the mathematical tool set we should all have started out with and once the reader has a grasp of the subject, he or she cannot fail to realize that traditional vector analysis is really awkward and even misleading by comparison"--Provided by publisher.
Modern Geometric Algebra: A (Very Incomplete!) Survey
Suzuki, Jeff
2009-01-01
Geometric algebra is based on two simple ideas. First, the area of a rectangle is equal to the product of the lengths of its sides. Second, if a figure is broken apart into several pieces, the sum of the areas of the pieces equals the area of the original figure. Remarkably, these two ideas provide an elegant way to introduce, connect, and…
Preservation of the geometric quantum discord in noisy environments
Energy Technology Data Exchange (ETDEWEB)
Hu, Ming-Liang, E-mail: mingliang0301@163.com [School of Science, Xi’an Jiaotong University, Xi’an 710049 (China); School of Science, Xi’an University of Posts and Telecommunications, Xi’an 710121 (China); Tian, Dong-Ping [School of Science, Xi’an Jiaotong University, Xi’an 710049 (China)
2014-04-15
Geometric description of quantum correlations is favored for their distinct physical significance. Geometric discords based on the trace distance and the Bures distance are shown to be well-defined quantum correlation measures. Here, we examine their particular dynamical behaviors under independent as well as common structured reservoirs and reveal their robustness against decoherence. We showed that the two well-defined geometric discords may be preserved well or even be improved and generated by the noisy process of the common reservoir. Moreover, we also provided a strategy for the long-time preservation of these two geometric discords in independent reservoirs. -- Highlights: •Inherent robustness of the trace distance and the Bures distance discord. •Generating geometric discord from classical states by the noisy process. •Improvement of the geometric discord in common reservoir. •The robust pathway for preserving discord in independent reservoirs.
Rydberg-atom-based scheme of nonadiabatic geometric quantum computation
Zhao, P. Z.; Cui, Xiao-Dan; Xu, G. F.; Sjöqvist, Erik; Tong, D. M.
2017-11-01
Nonadiabatic geometric quantum computation provides a means to perform fast and robust quantum gates. It has been implemented in various physical systems, such as trapped ions, nuclear magnetic resonance, and superconducting circuits. Another system being adequate for implementation of nonadiabatic geometric quantum computation may be Rydberg atoms, since their internal states have very long coherence time and the Rydberg-mediated interaction facilitates the implementation of a two-qubit gate. Here, we propose a scheme of nonadiabatic geometric quantum computation based on Rydberg atoms, which combines the robustness of nonadiabatic geometric gates with the merits of Rydberg atoms.
Harmonic and geometric analysis
Citti, Giovanna; Pérez, Carlos; Sarti, Alessandro; Zhong, Xiao
2015-01-01
This book presents an expanded version of four series of lectures delivered by the authors at the CRM. Harmonic analysis, understood in a broad sense, has a very wide interplay with partial differential equations and in particular with the theory of quasiconformal mappings and its applications. Some areas in which real analysis has been extremely influential are PDE's and geometric analysis. Their foundations and subsequent developments made extensive use of the Calderón–Zygmund theory, especially the Lp inequalities for Calderón–Zygmund operators (Beurling transform and Riesz transform, among others) and the theory of Muckenhoupt weights. The first chapter is an application of harmonic analysis and the Heisenberg group to understanding human vision, while the second and third chapters cover some of the main topics on linear and multilinear harmonic analysis. The last serves as a comprehensive introduction to a deep result from De Giorgi, Moser and Nash on the regularity of elliptic partial differen...
Geometric phase and quantum potential
Dandoloff, R.
2002-01-01
We show that the geometric phase of Levy-Leblond arises from a low of parallel transport for wave functions and point out that this phase belongs to a new class of geometric phases due to the presence of a quantum potential.
Geometrical approach to fluid models
Kuvshinov, B. N.; Schep, T. J.
1997-01-01
Differential geometry based upon the Cartan calculus of differential forms is applied to investigate invariant properties of equations that describe the motion of continuous media. The main feature of this approach is that physical quantities are treated as geometrical objects. The geometrical
Non-Markovianity of geometrical qudit decoherence
Siudzińska, Katarzyna
2017-12-01
In the following paper, we generalize the geometrical framework of qubit decoherence to higher dimensions. The quantum mixed state is represented by the probability distribution which is the Kähler function on the projective Hilbert space. The Markovian master equation for density operators turns out to be equivalent to the Fokker-Planck equation for quantum probability distributions. Several examples are analyzed, featuring different generalizations of the Pauli channel.
Geometric Algebra Model of Distributed Representations
Patyk, Agnieszka
2010-01-01
Formalism based on GA is an alternative to distributed representation models developed so far --- Smolensky's tensor product, Holographic Reduced Representations (HRR) and Binary Spatter Code (BSC). Convolutions are replaced by geometric products, interpretable in terms of geometry which seems to be the most natural language for visualization of higher concepts. This paper recalls the main ideas behind the GA model and investigates recognition test results using both inner product and a clipp...
Time as a geometric property of space
Directory of Open Access Journals (Sweden)
James Michael Chappell
2016-11-01
Full Text Available The proper description of time remains a key unsolved problem in science. Newton conceived of time as absolute and universal which it `flows equably without relation to anything external'}. In the nineteenth century, the four-dimensional algebraic structure of the quaternions developed by Hamilton, inspired him to suggest that they could provide a unified representation of space and time. With the publishing of Einstein's theory of special relativity these ideas then lead to the generally accepted Minkowski spacetime formulation in 1908. Minkowski, though, rejected the formalism of quaternions suggested by Hamilton and adopted rather an approach using four-vectors. The Minkowski framework is indeed found to provide a versatile formalism for describing the relationship between space and time in accordance with Einstein's relativistic principles, but nevertheless fails to provide more fundamental insights into the nature of time itself. In order to answer this question we begin by exploring the geometric properties of three-dimensional space that we model using Clifford geometric algebra, which is found to contain sufficient complexity to provide a natural description of spacetime. This description using Clifford algebra is found to provide a natural alternative to the Minkowski formulation as well as providing new insights into the nature of time. Our main result is that time is the scalar component of a Clifford space and can be viewed as an intrinsic geometric property of three-dimensional space without the need for the specific addition of a fourth dimension.
Information-geometric measures as robust estimators of connection strengths and external inputs.
Tatsuno, Masami; Fellous, Jean-Marc; Amari, Shun-Ichi
2009-08-01
Information geometry has been suggested to provide a powerful tool for analyzing multineuronal spike trains. Among several advantages of this approach, a significant property is the close link between information-geometric measures and neural network architectures. Previous modeling studies established that the first- and second-order information-geometric measures corresponded to the number of external inputs and the connection strengths of the network, respectively. This relationship was, however, limited to a symmetrically connected network, and the number of neurons used in the parameter estimation of the log-linear model needed to be known. Recently, simulation studies of biophysical model neurons have suggested that information geometry can estimate the relative change of connection strengths and external inputs even with asymmetric connections. Inspired by these studies, we analytically investigated the link between the information-geometric measures and the neural network structure with asymmetrically connected networks of N neurons. We focused on the information-geometric measures of orders one and two, which can be derived from the two-neuron log-linear model, because unlike higher-order measures, they can be easily estimated experimentally. Considering the equilibrium state of a network of binary model neurons that obey stochastic dynamics, we analytically showed that the corrected first- and second-order information-geometric measures provided robust and consistent approximation of the external inputs and connection strengths, respectively. These results suggest that information-geometric measures provide useful insights into the neural network architecture and that they will contribute to the study of system-level neuroscience.
Generalized Geometric Quantum Speed Limits
Directory of Open Access Journals (Sweden)
Diego Paiva Pires
2016-06-01
Full Text Available The attempt to gain a theoretical understanding of the concept of time in quantum mechanics has triggered significant progress towards the search for faster and more efficient quantum technologies. One of such advances consists in the interpretation of the time-energy uncertainty relations as lower bounds for the minimal evolution time between two distinguishable states of a quantum system, also known as quantum speed limits. We investigate how the nonuniqueness of a bona fide measure of distinguishability defined on the quantum-state space affects the quantum speed limits and can be exploited in order to derive improved bounds. Specifically, we establish an infinite family of quantum speed limits valid for unitary and nonunitary evolutions, based on an elegant information geometric formalism. Our work unifies and generalizes existing results on quantum speed limits and provides instances of novel bounds that are tighter than any established one based on the conventional quantum Fisher information. We illustrate our findings with relevant examples, demonstrating the importance of choosing different information metrics for open system dynamics, as well as clarifying the roles of classical populations versus quantum coherences, in the determination and saturation of the speed limits. Our results can find applications in the optimization and control of quantum technologies such as quantum computation and metrology, and might provide new insights in fundamental investigations of quantum thermodynamics.
Geometric Phase Generated Optical Illusion.
Yue, Fuyong; Zang, Xiaofei; Wen, Dandan; Li, Zile; Zhang, Chunmei; Liu, Huigang; Gerardot, Brian D; Wang, Wei; Zheng, Guoxing; Chen, Xianzhong
2017-09-12
An optical illusion, such as "Rubin's vase", is caused by the information gathered by the eye, which is processed in the brain to give a perception that does not tally with a physical measurement of the stimulus source. Metasurfaces are metamaterials of reduced dimensionality which have opened up new avenues for flat optics. The recent advancement in spin-controlled metasurface holograms has attracted considerate attention, providing a new method to realize optical illusions. We propose and experimentally demonstrate a metasurface device to generate an optical illusion. The metasurface device is designed to display two asymmetrically distributed off-axis images of "Rubin faces" with high fidelity, high efficiency and broadband operation that are interchangeable by controlling the helicity of the incident light. Upon the illumination of a linearly polarized light beam, the optical illusion of a 'vase' is perceived. Our result provides an intuitive demonstration of the figure-ground distinction that our brains make during the visual perception. The alliance between geometric metasurface and the optical illusion opens a pathway for new applications related to encryption, optical patterning, and information processing.
Geometrical method of decoupling
Directory of Open Access Journals (Sweden)
C. Baumgarten
2012-12-01
Full Text Available The computation of tunes and matched beam distributions are essential steps in the analysis of circular accelerators. If certain symmetries—like midplane symmetry—are present, then it is possible to treat the betatron motion in the horizontal, the vertical plane, and (under certain circumstances the longitudinal motion separately using the well-known Courant-Snyder theory, or to apply transformations that have been described previously as, for instance, the method of Teng and Edwards. In a preceding paper, it has been shown that this method requires a modification for the treatment of isochronous cyclotrons with non-negligible space charge forces. Unfortunately, the modification was numerically not as stable as desired and it was still unclear, if the extension would work for all conceivable cases. Hence, a systematic derivation of a more general treatment seemed advisable. In a second paper, the author suggested the use of real Dirac matrices as basic tools for coupled linear optics and gave a straightforward recipe to decouple positive definite Hamiltonians with imaginary eigenvalues. In this article this method is generalized and simplified in order to formulate a straightforward method to decouple Hamiltonian matrices with eigenvalues on the real and the imaginary axis. The decoupling of symplectic matrices which are exponentials of such Hamiltonian matrices can be deduced from this in a few steps. It is shown that this algebraic decoupling is closely related to a geometric “decoupling” by the orthogonalization of the vectors E[over →], B[over →], and P[over →], which were introduced with the so-called “electromechanical equivalence.” A mathematical analysis of the problem can be traced down to the task of finding a structure-preserving block diagonalization of symplectic or Hamiltonian matrices. Structure preservation means in this context that the (sequence of transformations must be symplectic and hence canonical. When
Geometric Computing for Freeform Architecture
Wallner, J.
2011-06-03
Geometric computing has recently found a new field of applications, namely the various geometric problems which lie at the heart of rationalization and construction-aware design processes of freeform architecture. We report on our work in this area, dealing with meshes with planar faces and meshes which allow multilayer constructions (which is related to discrete surfaces and their curvatures), triangles meshes with circle-packing properties (which is related to conformal uniformization), and with the paneling problem. We emphasize the combination of numerical optimization and geometric knowledge.
Geometric phase shifting digital holography.
Jackin, Boaz Jessie; Narayanamurthy, C S; Yatagai, Toyohiko
2016-06-01
A new phase shifting digital holographic technique using a purely geometric phase in Michelson interferometric geometry is proposed. The geometric phase in the system does not depend upon either optical path length or wavelength, unlike dynamic phase. The amount of geometric phase generated is controllable through a rotating wave plate. The new approach has unique features and major advantages in holographic measurement of transparent and reflecting three-dimensional (3D) objects. Experimental results on surface shape measurement and imaging of 3D objects are presented using the proposed method.
Geometric technique for the kinematic modeling of a 5 DOF redundant manipulator
CSIR Research Space (South Africa)
Makondo, N
2012-11-01
Full Text Available This paper describes a geometrical method for solving the inverse kinematic (IK) problem of a 5 Degrees of Freedom (DOF) redundant manipulator. A geometric inverse kinematics solution is desirable as it provides complete and simple solutions...
Discrete geometric structures for architecture
Pottmann, Helmut
2010-06-13
The emergence of freeform structures in contemporary architecture raises numerous challenging research problems, most of which are related to the actual fabrication and are a rich source of research topics in geometry and geometric computing. The talk will provide an overview of recent progress in this field, with a particular focus on discrete geometric structures. Most of these result from practical requirements on segmenting a freeform shape into planar panels and on the physical realization of supporting beams and nodes. A study of quadrilateral meshes with planar faces reveals beautiful relations to discrete differential geometry. In particular, we discuss meshes which discretize the network of principal curvature lines. Conical meshes are among these meshes; they possess conical offset meshes at a constant face/face distance, which in turn leads to a supporting beam layout with so-called torsion free nodes. This work can be generalized to a variety of multilayer structures and laid the ground for an adapted curvature theory for these meshes. There are also efforts on segmenting surfaces into planar hexagonal panels. Though these are less constrained than planar quadrilateral panels, this problem is still waiting for an elegant solution. Inspired by freeform designs in architecture which involve circles and spheres, we present a new kind of triangle mesh whose faces\\' in-circles form a packing, i.e., the in-circles of two triangles with a common edge have the same contact point on that edge. These "circle packing (CP) meshes" exhibit an aesthetic balance of shape and size of their faces. They are closely tied to sphere packings on surfaces and to various remarkable structures and patterns which are of interest in art, architecture, and design. CP meshes constitute a new link between architectural freeform design and computational conformal geometry. Recently, certain timber structures motivated us to study discrete patterns of geodesics on surfaces. This
Antenna with Dielectric Having Geometric Patterns
Dudley, Kenneth L. (Inventor); Elliott, Holly A. (Inventor); Cravey, Robin L. (Inventor); Connell, John W. (Inventor); Ghose, Sayata (Inventor); Watson, Kent A. (Inventor); Smith, Jr., Joseph G. (Inventor)
2013-01-01
An antenna includes a ground plane, a dielectric disposed on the ground plane, and an electrically-conductive radiator disposed on the dielectric. The dielectric includes at least one layer of a first dielectric material and a second dielectric material that collectively define a dielectric geometric pattern, which may comprise a fractal geometry. The radiator defines a radiator geometric pattern, and the dielectric geometric pattern is geometrically identical, or substantially geometrically identical, to the radiator geometric pattern.
Geometrical product specifications. Datums and coordinate systems
Glukhov, V. I.; Ivleva, I. A.; Zlatkina, O. Y.
2017-06-01
The work is devoted to the relevant topic such as the technical products quality improvement due to the geometrical specifications accuracy. The research purpose is to ensure the quality indicators on the basis of the systematic approach to the values normalization and geometrical specifications accuracy in the workpiece coordinate systems in the process of design. To achieve the goal two tasks are completed such as the datum features classification according to the number of linear and angular freedom degrees constraints, called the datums informativeness, and the rectangular coordinate systems identification, materialized by workpiece datums sets. The datum features informativeness characterizes the datums functional purpose to limit product workpiece linear and angular degrees of freedom. The datum features informativeness numerically coincides with the kinematic pairs classes and couplings in mechanics. The datum features informativeness identifies the coordinate system without the location redundancy. Each coordinate plane of a rectangular coordinate system has different informativeness 3 + 2 + 1. Each coordinate axis also has different informativeness 4+2+Θ (zero). It is possible to establish the associated workpiece position with three linear and three angular coordinates relative to two axes with the informativeness 4 and 2. is higher, the more informativeness of the coordinate axis or a coordinate plane is, the higher is the linear and angular coordinates accuracy, the coordinate being plotted along the coordinate axis or plane. The systematic approach to the geometrical products specifications positioning in coordinate systems is the scientific basis for a natural transition to the functional dimensions of features position - coordinating dimensions and the size of the features form - feature dimensions of two measures: linear and angular ones. The products technical quality improving is possible due to the coordinate systems introduction materialized by
Kayigamba, Felix R.; van Santen, Daniëla; Bakker, Mirjam I.; Lammers, Judith; Mugisha, Veronicah; Bagiruwigize, Emmanuel; de Naeyer, Ludwig; Asiimwe, Anita; Schim van der Loeff, Maarten F.
2016-01-01
Provider-initiated HIV testing and counselling (PITC) is promoted as a means to increase HIV case finding. We assessed the effectiveness of PITC to increase HIV testing rate and HIV case finding among outpatients in Rwandan health facilities (HF). PITC was introduced in six HFs in 2009-2010. HIV
Lopes, Paula A; Bandarra, Narcisa M; Martins, Susana V; Martinho, Joana; Alfaia, Cristina M; Madeira, Marta S; Cardoso, Carlos; Afonso, Cláudia; Paulo, Maria C; Pinto, Rui M A; Guil-Guerrero, José L; Prates, José A M
2017-01-01
To overcome the current overexploitation of fish rich in n-3 long chain polyunsaturated fatty acids (LCPUFA), microalgae have become a promising marine lipid source. The purpose of this study was to assess eicosapentaenoic acid (EPA, 20:5n-3) and docosahexaenoic acid (DHA, 22:6n-3), isolated or combined from distinct marine origins, on the promotion of neuroprotective effects. The experiment lasted for 10 weeks and involved 32 Wistar rats, divided into 4 diets (n = 8): a diet rich in milk fat was taken as control (Milk Fat) and compared to n-3 LCPUFA enriched diets, either in EPA + DHA form through fish oil (Fish Oil), or EPA through Nannochloropsis oil (Nanno), or DHA through Schizochytrium oil (Schyzo), while maintaining Milk Fat incorporation. Plasma lipid profile and dopamine levels were more beneficial in Fish Oil diet. In addition, n-3 LCPUFA incorporation was found increased in liver and erythrocytes from Fish Oil fed rats, suggesting that fish oil is a better dietary source for fatty acids deposition in the organism than microalgae. The Forced Swimming Test revealed a positive behavioural action of EPA + DHA, in opposition to Milk Fat and Nanno diets, which had higher immobile times. mRNA levels of serotonin receptors, HT1A and HT2A along with CREB, the transmission factor for learning and memory, were higher in the hippocampus of rats fed n-3 LCPUFA diets comparative to Milk Fat. Taken together, the combination of EPA and DHA from fish oil can counteract the undesirable health effects of saturated fat based diets and benefit, in the long run, neurological function.
Geometric Mixing, Peristalsis, and the Geometric Phase of the Stomach.
Arrieta, Jorge; Cartwright, Julyan H E; Gouillart, Emmanuelle; Piro, Nicolas; Piro, Oreste; Tuval, Idan
2015-01-01
Mixing fluid in a container at low Reynolds number--in an inertialess environment--is not a trivial task. Reciprocating motions merely lead to cycles of mixing and unmixing, so continuous rotation, as used in many technological applications, would appear to be necessary. However, there is another solution: movement of the walls in a cyclical fashion to introduce a geometric phase. We show using journal-bearing flow as a model that such geometric mixing is a general tool for using deformable boundaries that return to the same position to mix fluid at low Reynolds number. We then simulate a biological example: we show that mixing in the stomach functions because of the "belly phase," peristaltic movement of the walls in a cyclical fashion introduces a geometric phase that avoids unmixing.
Reasoning with Geometric Shapes
Seah, Rebecca
2015-01-01
Geometry belongs to branches of mathematics that develop students' visualisation, intuition, critical thinking, problem solving, deductive reasoning, logical argument and proof (Jones, 2002). It provides the basis for the development of spatial sense and plays an important role in acquiring advanced knowledge in science, technology, engineering,…
Directory of Open Access Journals (Sweden)
Mohammed Mohammed A
2007-06-01
Full Text Available Abstract Background Despite increasing interest and publication of risk-adjusted hospital mortality rates, the relationship with underlying quality of care remains unclear. We undertook a systematic review to ascertain the extent to which variations in risk-adjusted mortality rates were associated with differences in quality of care. Methods We identified studies in which risk-adjusted mortality and quality of care had been reported in more than one hospital. We adopted an iterative search strategy using three databases – Medline, HealthSTAR and CINAHL from 1966, 1975 and 1982 respectively. We identified potentially relevant studies on the basis of the title or abstract. We obtained these papers and included those which met our inclusion criteria. Results From an initial yield of 6,456 papers, 36 studies met the inclusion criteria. Several of these studies considered more than one process-versus-risk-adjusted mortality relationship. In total we found 51 such relationships in a widen range of clinical conditions using a variety of methods. A positive correlation between better quality of care and risk-adjusted mortality was found in under half the relationships (26/51 51% but the remainder showed no correlation (16/51 31% or a paradoxical correlation (9/51 18%. Conclusion The general notion that hospitals with higher risk-adjusted mortality have poorer quality of care is neither consistent nor reliable.
Sabin, Lora L; Larson Williams, Anna; Le, Bao Ngoc; Herman, Augusta R; Viet Nguyen, Ha; Albanese, Rebecca R; Xiong, Wenjun; Shobiye, Hezekiah Oa; Halim, Nafisa; Tran, Lien Thi Ngoc; McNabb, Marion; Hoang, Hai; Falconer, Ariel; Nguyen, Tam Thi Thanh; Gill, Christopher J
2017-06-27
A randomized controlled trial was conducted in 2015 to evaluate a mobile continuing medical education (mCME) intervention that provided daily text messages to community-based physicians' assistants (CBPAs) in Thai Nguyen Province, Vietnam. Although the intervention failed to improve medical knowledge over a 6-month period, a companion qualitative study provided insights on the views and experiences of intervention participants. We conducted focus group discussions (FGDs) and in-depth interviews (IDIs) among participants randomized to receive text messages containing either simple medical facts or quiz questions. Trained interviewers collected data immediately following the conclusion of the trial in December 2015. Using semi-structured question guides, respondents were queried on their views of the intervention, positive and negative, and perceived impacts of the intervention. During analysis, after learning that the intervention had failed to increase knowledge among participants, we also examined reasons for lack of improvement in medical knowledge. All analyses were performed in NVivo using a thematic approach. A total of 70 CBPAs engaged in one of 8 FGDs or an IDI. One-half were men; average age among all respondents was 40 years. Most (81%) practiced in rural settings and most (51%) focused on general medicine. The mean length of work experience was 3 years. All respondents made positive comments about the intervention; convenience, relevance, and quick feedback (quiz format) were praised. Downsides encompassed lack of depth of information, weak interaction, technology challenges, and challenging/irrelevant messages. Respondents described perceived impacts encompassing increased motivation, knowledge, collegial discussions, Internet use to search for more information, and clinical skills. Overall, they expressed a desire for the intervention to continue and recommended expansion to other medical professionals. Overreliance on the text messages, lack of
Facades structure detection by geometric moment
Jiang, Diqiong; Chen, Hui; Song, Rui; Meng, Lei
2017-06-01
This paper proposes a novel method for extracting facades structure from real-world pictures by using local geometric moment. Compared with existing methods, the proposed method has advantages of easy-to-implement, low computational cost, and robustness to noises, such as uneven illumination, shadow, and shade from other objects. Besides, our method is faster and has a lower space complexity, making it feasible for mobile devices and the situation where real-time data processing is required. Specifically, a facades structure modal is first proposed to support the use of our special noise reduction method, which is based on a self-adapt local threshold with Gaussian weighted average for image binarization processing and the feature of the facades structure. Next, we divide the picture of the building into many individual areas, each of which represents a door or a window in the picture. Subsequently we calculate the geometric moment and centroid for each individual area, for identifying those collinear ones based on the feature vectors, each of which is thereafter replaced with a line. Finally, we comprehensively analyze all the geometric moment and centroid to find out the facades structure of the building. We compare our result with other methods and especially report the result from the pictures taken in bad environmental conditions. Our system is designed for two application, i.e, the reconstruction of facades based on higher resolution ground-based on imagery, and the positional system based on recognize the urban building.
Manfredini, Maria; Morbidelli, Daniele; Polidoro, Sergio; Uguzzoni, Francesco
2015-01-01
The analysis of PDEs is a prominent discipline in mathematics research, both in terms of its theoretical aspects and its relevance in applications. In recent years, the geometric properties of linear and nonlinear second order PDEs of elliptic and parabolic type have been extensively studied by many outstanding researchers. This book collects contributions from a selected group of leading experts who took part in the INdAM meeting "Geometric methods in PDEs", on the occasion of the 70th birthday of Ermanno Lanconelli. They describe a number of new achievements and/or the state of the art in their discipline of research, providing readers an overview of recent progress and future research trends in PDEs. In particular, the volume collects significant results for sub-elliptic equations, potential theory and diffusion equations, with an emphasis on comparing different methodologies and on their implications for theory and applications. .
Geometric phase shifts in biological oscillators.
Tourigny, David S
2014-08-21
Many intracellular processes continue to oscillate during the cell cycle. Although it is not well-understood how they are affected by discontinuities in the cellular environment, the general assumption is that oscillations remain robust provided the period of cell divisions is much larger than the period of the oscillator. Here, I will show that under these conditions a cell will in fact have to correct for an additional quantity added to the phase of oscillation upon every repetition of the cell cycle. The resulting phase shift is an analogue of the geometric phase, a curious entity first discovered in quantum mechanics. In this letter, I will discuss the theory of the geometric phase shift and demonstrate its relevance to biological oscillations. Copyright © 2014 Elsevier Ltd. All rights reserved.
Universal geometrical scaling of the elliptic flow
Directory of Open Access Journals (Sweden)
Andrés C.
2015-01-01
Full Text Available The presence of scaling variables in experimental observables provide very valuable indications of the dynamics underlying a given physical process. In the last years, the search for geometric scaling, that is the presence of a scaling variable which encodes all geometrical information of the collision as well as other external quantities as the total energy, has been very active. This is motivated, in part, for being one of the genuine predictions of the Color Glass Condensate formalism for saturation of partonic densities. Here we extend these previous findings to the case of experimental data on elliptic flow. We find an excellent scaling for all centralities and energies, from RHIC to LHC, with a simple generalization of the scaling previously found for other observables and systems. Interestingly, the case of the photons, difficult to reconcile in most formalisms, nicely fit the scaling curve. We discuss on the possible interpretations of this finding in terms of initial or final state effects.
Geometric modeling in probability and statistics
Calin, Ovidiu
2014-01-01
This book covers topics of Informational Geometry, a field which deals with the differential geometric study of the manifold probability density functions. This is a field that is increasingly attracting the interest of researchers from many different areas of science, including mathematics, statistics, geometry, computer science, signal processing, physics and neuroscience. It is the authors’ hope that the present book will be a valuable reference for researchers and graduate students in one of the aforementioned fields. This textbook is a unified presentation of differential geometry and probability theory, and constitutes a text for a course directed at graduate or advanced undergraduate students interested in applications of differential geometry in probability and statistics. The book contains over 100 proposed exercises meant to help students deepen their understanding, and it is accompanied by software that is able to provide numerical computations of several information geometric objects. The reader...
Preidis, Geoffrey A; McCollum, Eric D; Kamiyango, William; Garbino, Alejandro; Hosseinipour, Mina C; Kazembe, Peter N; Schutze, Gordon E; Kline, Mark W
2013-05-01
To determine how routine inpatient provider-initiated HIV testing differs from traditional community-based client-initiated testing with respect to clinical characteristics of children identified and outcomes of outpatient HIV care. Prospective observational cohort. Routine clinical data were collected from children identified as HIV-infected by either testing modality in Lilongwe, Malawi, in 2008. After 1 year of outpatient HIV care at the Baylor College of Medicine Clinical Center of Excellence, outcomes were assessed. Of 742 newly identified HIV-infected children enrolling into outpatient HIV care, 20.9% were identified by routine inpatient HIV testing. Compared with community-identified children, hospital-identified patients were younger (median 25.0 vs 53.5 months), with more severe disease (22.2% vs 7.8% WHO stage IV). Of 466 children with known outcomes, 15.0% died within the first year of HIV care; median time to death was 15.0 weeks for community-identified children vs 6.0 weeks for hospital-identified children. The strongest predictors of early mortality were severe malnutrition (hazard ratio, 4.3; 95% confidence interval, 2.2-8.3), moderate malnutrition (hazard ratio, 3.2; confidence interval, 1.6-6.6), age mortality. Routine inpatient HIV testing identifies a subset of younger HIV-infected children with more severe, rapidly progressing disease that traditional community-based testing modalities are currently missing.
A practical guide to geometric regulation for distributed parameter systems
Aulisa, Eugenio
2015-01-01
A Practical Guide to Geometric Regulation for Distributed Parameter Systems provides an introduction to geometric control design methodologies for asymptotic tracking and disturbance rejection of infinite-dimensional systems. The book also introduces several new control algorithms inspired by geometric invariance and asymptotic attraction for a wide range of dynamical control systems. The first part of the book is devoted to regulation of linear systems, beginning with the mathematical setup, general theory, and solution strategy for regulation problems with bounded input and output operators.
Geometric Langlands From Six Dimensions
Witten, Edward
2010-01-01
Geometric Langlands duality is usually formulated as a statement about Riemann surfaces, but it can be naturally understood as a consequence of electric-magnetic duality of four-dimensional gauge theory. This duality in turn is naturally understood as a consequence of the existence of a certain exotic supersymmetric conformal field theory in six dimensions. The same six-dimensional theory also gives a useful framework for understanding some recent mathematical results involving a counterpart of geometric Langlands duality for complex surfaces. (This article is based on a lecture at the Raoul Bott celebration, Montreal, June 2008.)
Asymptotic geometric analysis, part I
Artstein-Avidan, Shiri
2015-01-01
The authors present the theory of asymptotic geometric analysis, a field which lies on the border between geometry and functional analysis. In this field, isometric problems that are typical for geometry in low dimensions are substituted by an "isomorphic" point of view, and an asymptotic approach (as dimension tends to infinity) is introduced. Geometry and analysis meet here in a non-trivial way. Basic examples of geometric inequalities in isomorphic form which are encountered in the book are the "isomorphic isoperimetric inequalities" which led to the discovery of the "concentration phenomen
Catching homologies by geometric entropy
Felice, Domenico; Franzosi, Roberto; Mancini, Stefano; Pettini, Marco
2018-02-01
A geometric entropy is defined in terms of the Riemannian volume of the parameter space of a statistical manifold associated with a given network. As such it can be a good candidate for measuring networks complexity. Here we investigate its ability to single out topological features of networks proceeding in a bottom-up manner: first we consider small size networks by analytical methods and then large size networks by numerical techniques. Two different classes of networks, the random graphs and the scale-free networks, are investigated computing their Betti numbers and then showing the capability of geometric entropy of detecting homologies.
A geometric approach to complexity.
Ay, Nihat; Olbrich, Eckehard; Bertschinger, Nils; Jost, Jürgen
2011-09-01
We develop a geometric approach to complexity based on the principle that complexity requires interactions at different scales of description. Complex systems are more than the sum of their parts of any size and not just more than the sum of their elements. Using information geometry, we therefore analyze the decomposition of a system in terms of an interaction hierarchy. In mathematical terms, we present a theory of complexity measures for finite random fields using the geometric framework of hierarchies of exponential families. Within our framework, previously proposed complexity measures find their natural place and gain a new interpretation.
Geometric Algebra Model of Distributed Representations
Patyk, Agnieszka
Formalism based on GA is an alternative to distributed representation models developed so far: Smolensky's tensor product, Holographic Reduced Representations (HRR), and Binary Spatter Code (BSC). Convolutions are replaced by geometric products interpretable in terms of geometry, which seems to be the most natural language for visualization of higher concepts. This paper recalls the main ideas behind the GA model and investigates recognition test results using both inner product and a clipped version of matrix representation. The influence of accidental blade equality on recognition is also studied. Finally, the efficiency of the GA model is compared to that of previously developed models.
Unified Spatial Intersection Algorithms Based on Conformal Geometric Algebra
Directory of Open Access Journals (Sweden)
Feng Zhang
2016-01-01
Full Text Available Conformal Geometric Algebra has been introduced into geographic information science as a mathematical theory because of its advantages in terms of uniform multidimensional representation and computation. The traditional intersection computation between two geometric objects of different types is not unified. In this study, we propose algorithms based on Conformal Geometric Algebra to determine the spatial relationships between geographic objects in a unified manner. The unified representation and intersection computation can be realized for geometric objects of different dimensions. Different basic judgment rules are provided for different simple geometries. The algorithms are designed and implemented using MapReduce to improve the efficiency of the algorithms. From the results of several experiments we provide, the correctness and effectiveness of the algorithms can be verified.
Modeling interactome: scale-free or geometric?
Przulj, N; Corneil, D G; Jurisica, I
2004-12-12
Networks have been used to model many real-world phenomena to better understand the phenomena and to guide experiments in order to predict their behavior. Since incorrect models lead to incorrect predictions, it is vital to have as accurate a model as possible. As a result, new techniques and models for analyzing and modeling real-world networks have recently been introduced. One example of large and complex networks involves protein-protein interaction (PPI) networks. We analyze PPI networks of yeast Saccharomyces cerevisiae and fruitfly Drosophila melanogaster using a newly introduced measure of local network structure as well as the standardly used measures of global network structure. We examine the fit of four different network models, including Erdos-Renyi, scale-free and geometric random network models, to these PPI networks with respect to the measures of local and global network structure. We demonstrate that the currently accepted scale-free model of PPI networks fails to fit the data in several respects and show that a random geometric model provides a much more accurate model of the PPI data. We hypothesize that only the noise in these networks is scale-free. We systematically evaluate how well-different network models fit the PPI networks. We show that the structure of PPI networks is better modeled by a geometric random graph than by a scale-free model. Supplementary information is available at http://www.cs.utoronto.ca/~juris/data/data/ppiGRG04/
Components of Geometric Analogy Solution.
Mulholland, Timothy M.; And Others
1980-01-01
Adults' geometric analogy solution was investigated as a function of systematic variations in the information structure of items. Latency data from verification of true and false items were recorded. A model incorporating assumptions about the form of item representation, working memory factors, and processing components and strategies was…
Celestial mechanics with geometric algebra
Hestenes, D.
1983-01-01
Geometric algebra is introduced as a general tool for Celestial Mechanics. A general method for handling finite rotations and rotational kinematics is presented. The constants of Kepler motion are derived and manipulated in a new way. A new spinor formulation of perturbation theory is developed.
Experimentally accessible geometrical separability criteria
Energy Technology Data Exchange (ETDEWEB)
Badziag, Piotr [Alba Nova Fysikum, University of Stockholm, S-106 91 Stockholm (Sweden); Brukner, Caslav; Paterek, Tomasz [Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna (Austria); Laskowski, Wieslaw; Zukowski, Marek [Institute of Theoretical Physics and Astrophysics, University of Gdansk, ul.Wita Stwosza 57, PL-80-952 Gdansk (Poland)], E-mail: wieslaw.laskowski@univ.gda.pl
2009-07-15
We present an intuitive geometrical approach to entanglement detection. It allows one to formulate simple and experimentally feasible sufficient conditions for entanglement. Within the approach we derive the necessary and sufficient condition for separability and discuss its relation with entanglement witnesses and positive maps.
Metastable vacua and geometric deformations
Amariti, A; Girardello, L; Mariotti, A
2008-01-01
We study the geometric interpretation of metastable vacua for systems of D3 branes at non isolated toric deformable singularities. Using the L^{aba} examples, we investigate the relations between the field theoretic susy breaking and restoration and the complex deformations of the CY singularities.
On chromatic and geometrical calibration
DEFF Research Database (Denmark)
Folm-Hansen, Jørgen
1999-01-01
The main subject of the present thesis is different methods for the geometrical and chromatic calibration of cameras in various environments. For the monochromatic issues of the calibration we present the acquisition of monochrome images, the classic monochrome aberrations and the various sources...... to design calibration targets for both geometrical and chromatic calibration are described. We present some possible systematical errors on the detection of the objects in the calibration targets, if viewed in a non orthogonal angle, if the intensities are uneven or if the image blurring is uneven. Finally...... of non-uniformity of the illumination of the image plane. Only the image deforming aberrations and the non-uniformity of illumination are included in the calibration models. The topics of the pinhole camera model and the extension to the Direct Linear Transform (DLT) are described. It is shown how...
Geometrical interpretation of optical absorption
Energy Technology Data Exchange (ETDEWEB)
Monzon, J. J.; Barriuso, A. G.; Sanchez-Soto, L. L. [Departamento de Optica, Facultad de Fisica, Universidad Complutense, E-28040 Madrid (Spain); Montesinos-Amilibia, J. M. [Departamento de Geometria y Topologia, Facultad de Matematicas, Universidad Complutense, E-28040 Madrid (Spain)
2011-08-15
We reinterpret the transfer matrix for an absorbing system in very simple geometrical terms. In appropriate variables, the system appears as performing a Lorentz transformation in a (1 + 3)-dimensional space. Using homogeneous coordinates, we map that action on the unit sphere, which is at the realm of the Klein model of hyperbolic geometry. The effects of absorption appear then as a loxodromic transformation, that is, a rhumb line crossing all the meridians at the same angle.
Science, Art and Geometrical Imagination
Luminet, J. -P.
2009-01-01
From the geocentric, closed world model of Antiquity to the wraparound universe models of relativistic cosmology, the parallel history of space representations in science and art illustrates the fundamental role of geometric imagination in innovative findings. Through the analysis of works of various artists and scientists like Plato, Durer, Kepler, Escher, Grisey or the present author, it is shown how the process of creation in science and in the arts rests on aesthetical principles such as ...
On chromatic and geometrical calibration
Folm-Hansen, Jørgen
1999-01-01
The main subject of the present thesis is different methods for the geometrical and chromatic calibration of cameras in various environments. For the monochromatic issues of the calibration we present the acquisition of monochrome images, the classic monochrome aberrations and the various sources of non-uniformity of the illumination of the image plane. Only the image deforming aberrations and the non-uniformity of illumination are included in the calibration models. The topics of the pinhole...
Geometrical Aspects of Venus Transit
Bertuola, Alberto C; Magalhães, N S; Filho, Victo S
2016-01-01
We obtained two astronomical values, the Earth-Venus distance and Venus diameter, by means of a geometrical treatment of photos taken of Venus transit in June of 2012. Here we presented the static and translational modelsthat were elaborated taking into account the Earth and Venus orbital movements. An additional correction was also added by considering the Earth rotation movement. The results obtained were compared with the values of reference from literature, showing very good concordance.
Geometrical quantization in Fock space
Maslov, V P
1995-01-01
We investigate an infinite dimensional analog of the theory of Lagrangian manifolds with complex germs. To such a manifold we assign a canonical operator that depends on creation and annihilation operators. This operator is by definition the geometrical quantization for these isotropic manifolds with complex germs. We prove that for secondary quantized equations this quantization is the asymptotics for the Cauchy problem. Results of Berezin are used thouroughly in the construction of the canonical operator and in proofs of the theorems.
Geometric Tachyon and Warm Inflation
Bhattacharjee, Anindita; Deshamukhya, Atri
2013-03-01
The inflationary models developed in presence of a background radiation can be a solution to the reheating problem faced by common cold (isentropic) inflationary scenario. A D-brane system comprising of k Neuvo-Schwarz (NS) 5-branes with a transverse circle and BPS D3-branes with world volume parallel to the NS 5-branes, placed at a point on the transverse circle diametrically to NS 5-brane has a point of unstable equilibrium and the D3-brane has a geometric tachyonic mode associated with displacement of the brane along the circle. Cold inflationary scenario has been studied in connection with this geometric tachyon [S. Panda, M. Sami and S. Tsujikawa, Phys. Rev. D73, 023515 (2006)] where it was found that one needs a background of minimum 104 branes to realize a viable inflationary model. In this piece of work, we have tried to study a model of inflation driven by this geometric tachyon in presence of radiation. We have found that compared to the isentropic scenario, to satisfy the observational bounds, the number of background branes required in this case reduces drastically and a viable model can be obtained with even six to seven NS 5-branes in the background. In this context, we have also analyzed the non-gaussianity associated with the model and observed that the concerned parameter lies well within the observation limit.
Calculation of Weighted Geometric Dilution of Precision
Directory of Open Access Journals (Sweden)
Chien-Sheng Chen
2013-01-01
Full Text Available To achieve high accuracy in wireless positioning systems, both accurate measurements and good geometric relationship between the mobile device and the measurement units are required. Geometric dilution of precision (GDOP is widely used as a criterion for selecting measurement units, since it represents the geometric effect on the relationship between measurement error and positioning determination error. In the calculation of GDOP value, the maximum volume method does not necessarily guarantee the selection of the optimal four measurement units with minimum GDOP. The conventional matrix inversion method for GDOP calculation demands a large amount of operation and causes high power consumption. To select the subset of the most appropriate location measurement units which give the minimum positioning error, we need to consider not only the GDOP effect but also the error statistics property. In this paper, we employ the weighted GDOP (WGDOP, instead of GDOP, to select measurement units so as to improve the accuracy of location. The handheld global positioning system (GPS devices and mobile phones with GPS chips can merely provide limited calculation ability and power capacity. Therefore, it is very imperative to obtain WGDOP accurately and efficiently. This paper proposed two formations of WGDOP with less computation when four measurements are available for location purposes. The proposed formulae can reduce the computational complexity required for computing the matrix inversion. The simpler WGDOP formulae for both the 2D and the 3D location estimation, without inverting a matrix, can be applied not only to GPS but also to wireless sensor networks (WSN and cellular communication systems. Furthermore, the proposed formulae are able to provide precise solution of WGDOP calculation without incurring any approximation error.
Geometric Phase and Classical-Quantum Correspondence
Satija, Indubala I.; Balakrishnan, Radha
2004-01-01
We study the geometric phase factors underlying the classical and the corresponding quantum dynamics of a driven nonlinear oscillator exhibiting chaotic dynamics. For the classical problem, we compute the geometric phase factors associated with the phase space trajectories using Frenet-Serret formulation. For the corresponding quantum problem, the geometric phase associated with the time evolution of the wave function is computed. Our studies suggest that the classical geometric phase may be ...
Geometrical Visualisation--Epistemic and Emotional
Rodd, Melissa
2010-01-01
A well-documented experience of students of elementary Euclidean geometry is "seeing" a geometric result and being sure about its truth; this sort of experience gives rise to the notion of geometrical visualisation that is developed here. In this essay a philosophical argument for the epistemic potential of geometrical visualisation is reviewed,…
Invariant geodynamical information in geometric geodetic measurements
Xu, Peiliang; Shimada, Seiichi; Fujii, Yoichiro; Tanaka, Torao
2000-08-01
Repeated geodetic measurements have been used to extract geodynamical quantities such as displacements, velocities of movement and crustal strains. Historical geodetic networks, especially those established before the space geodetic era, were, and still are, very important in providing a unique insight into the (local or regional) historical deformation state of the Earth. For the geodetic network without a tie to an external reference frame, free network adjustment methods have been widely applied to derive geodynamical quantities. Currently, it is commonly accepted that absolute displacements cannot be uniquely determined from triangulation/trilateration measurements, but relative displacements can be found uniquely if the geodetic network is geometrically overdetermined (see e.g. Segall & Matthews 1988). Strain tensors were derived using the coordinate method and were reported to be uniquely determined. We have carried out a theoretical analysis of invariant geodynamical information in geometric geodetic observations and concluded: (1) that relative displacements are not invariant quantities and thus cannot be uniquely determined from the geodetic network without a tie to an external reference frame; and (2) the components of the strain tensors are not all invariant and thus cannot individually be determined uniquely from the network. However, certain combinations of strain components are indeed invariant and can be uniquely determined from geometric geodetic measurements. The theory of invariant information is then applied to the analysis of the Tokai first-order triangulation/trilateration network spanning an interval of more than 100yr. The results show that the normal and principal strains are significantly affected by the unknown scaling biases and orientation differences; thus any attempt at geophysical interpretation of these quantities must be exercised with great care. If the scaling bias and the orientation difference are small, the shear strain is
Giant Geometrically Amplified Piezoresistance in Metal-Semiconductor Hybrid Resistors
DEFF Research Database (Denmark)
Hansen, Ole; Reck, Kasper; Thomsen, Erik Vilain
2008-01-01
We show that very high geometrically amplified piezoresistance can indeed be obtained in microstructured metal-semiconductor hybrid devices, even significantly higher amplification factors than the factor of approximately 8 demonstrated recently by Rowe and co-workers may be achieved. However, we...... than the sensitivity of conventional piezoresistors fabricated in the same piezoresistive material. ©2008 American Institute of Physics...
Constrained ballistics and geometrical optics
Epstein, Marcelo
2014-01-01
The problem of constant-speed ballistics is studied under the umbrella of non-linear non-holonomic constrained systems. The Newtonian approach is shown to be equivalent to the use of Chetaev's rule to incorporate the constraint within the initially unconstrained formulation. Although the resulting equations are not, in principle, obtained from a variational statement, it is shown that the trajectories coincide with those of geometrical optics in a medium with a suitably chosen refractive index, as prescribed by Fermat's principle of least time. This fact gives rise to an intriguing mechano-optical analogy. The trajectories are further studied and discussed.
Science, art and geometrical imagination
Luminet, Jean-Pierre
2011-06-01
From the geocentric, closed world model of Antiquity to the wraparound universe models of relativistic cosmology, the parallel history of space representations in science and art illustrates the fundamental rôle of geometric imagination in innovative findings. Through the analysis of works of various artists and scientists like Plato, Dürer, Kepler, Escher, Grisey or the author, it is shown how the process of creation in science and in the arts rests on aesthetical principles such as symmetry, regular polyhedra, laws of harmonic proportion, tessellations, group theory, etc., as well as on beauty, conciseness and an emotional approach of the world.
A history of geometrical methods
Coolidge, Julian Lowell
2013-01-01
Full and authoritative, this history of the techniques for dealing with geometric questions begins with synthetic geometry and its origins in Babylonian and Egyptian mathematics; reviews the contributions of China, Japan, India, and Greece; and discusses the non-Euclidean geometries. Subsequent sections cover algebraic geometry, starting with the precursors and advancing to the great awakening with Descartes; and differential geometry, from the early work of Huygens and Newton to projective and absolute differential geometry. The author's emphasis on proofs and notations, his comparisons betwe
Duprey, Sonia; Bruyere, Karine; Verriest, Jean-Pierre
2010-01-01
Human body numerical models can help to develop protection devices against effects of road crashes. In the context of a side impact, a shoulder model able to predict shoulder injuries and more especially clavicle fracture would be helpful. A shoulder model derived from an existing finite element model of the human body representing an average male (50th percentile), HUMOS1, has been upgraded. An isolated clavicle model was assessed thanks to experimental corridors derived from dynamic tests up to failure. Then, the whole upgraded shoulder model was evaluated by comparison with results from experimental side impact tests on the shoulder. Eventually, the upgraded model was geometrically personalized toward the anthropometry of the subjects and its ability to simulate fractures was assessed. The isolated clavicle model was assessed as validated. The upgraded 50th percentile shoulder model provided accurate results in the subinjurious domain. At higher velocities, the personalized models produced realistic shoulder injuries: clavicle fracture was accurately predicted in four cases of six, the model was conservative for the two other cases. The upgraded shoulder model presented here was successfully submitted to a rigorous assessment process. Once geometrically personalized, it provided positive results for clavicle fracture prediction. As clavicle fracture is the major shoulder injury, this model could help the design of safety devices for shoulder protection. Furthermore, this study enhances the need for geometrical personalization methods when using finite element model for injury risk prediction.
Image understanding using geometric context
Zhang, Xiaochun; Liu, Chuancai
2017-07-01
A Gibbs Sampler based topic model for image annotation, which takes into account the interaction between visual geometric context and related topic, is presented. Most of the existing topic models for scene annotation use segmentation-based algorithm. However, topic models using segmentation algorithm alone sometimes can produce erroneous results when used to annotate real-life scene pictures. Therefore, our algorithm makes use of peaks of image surface instead of segmentation regions. Existing approaches use SIFT algorithm and treat the peaks as round blob features. In this paper, the peaks are treated as anisotropic blob features, which models low level visual elements more precisely. In order to better utilize visual features, our model not only takes into consideration visual codeword, but also considers influence of visual properties to topic formation, such as orientation, width, length and color. The basic idea is based on the assumption that different topics will produce distinct visual appearance, and different visual appearance is helpful to distinguish topics. During the learning stage, each topic will be associated with a set of distributions of visual properties, which depicts appearance of the topic. This paper considers more geometric properties, which will reduce topic uncertainty and learn the images better. Tested with Corel5K, SAIAPR-TC12 and Espgame100k Datasets, our method performs moderately better than some state of the arts methods.
Geometric correction of APEX hyperspectral data
Directory of Open Access Journals (Sweden)
Vreys Kristin
2016-03-01
Full Text Available Hyperspectral imagery originating from airborne sensors is nowadays widely used for the detailed characterization of land surface. The correct mapping of the pixel positions to ground locations largely contributes to the success of the applications. Accurate geometric correction, also referred to as “orthorectification”, is thus an important prerequisite which must be performed prior to using airborne imagery for evaluations like change detection, or mapping or overlaying the imagery with existing data sets or maps. A so-called “ortho-image” provides an accurate representation of the earth’s surface, having been adjusted for lens distortions, camera tilt and topographic relief. In this paper, we describe the different steps in the geometric correction process of APEX hyperspectral data, as applied in the Central Data Processing Center (CDPC at the Flemish Institute for Technological Research (VITO, Mol, Belgium. APEX ortho-images are generated through direct georeferencing of the raw images, thereby making use of sensor interior and exterior orientation data, boresight calibration data and elevation data. They can be referenced to any userspecified output projection system and can be resampled to any output pixel size.
Buckling strength of square composite plates with geometrical imperfections
DEFF Research Database (Denmark)
Berggreen, Christian; Jensen, Christian; Hayman, Brian
2007-01-01
Tests have been performed on square composite plates under in-plane compression. Theplateshad a width-to-thickness ratio close to the value for which the elastic critical load and the load for compres-sive fibre failure over a complete section would be equal, giving the maximum sensitivity...... to initial geometric imperfections. Some of the plates were manufactured with no intentional imperfections or defects, others with an intentional initial out-of-plane geometric imperfection. An advanced digital photogrammetry measurement system was used to monitor deformations of the tested plates....... The responses were also calculated by means of geometrically non-linear finite element analysis. With the assumption of rotationally fixed edges, the calcu-lated elastic critical loads were significantly higher than those deduced from the measurements. Closer ex-amination revealed that the loaded edges...
Waldinger, Marcel D; Zwinderman, Aeilko H; Olivier, Berend; Schweitzer, Dave H
2008-02-01
The intravaginal ejaculation latency time (IELT) behaves in a skewed manner and needs the appropriate statistics for correct interpretation of treatment results. To explain the rightful use of geometrical mean IELT values and the fold increase of the geometric mean IELT because of the positively skewed IELT distribution. Linking theoretical arguments to the outcome of several selective serotonin reuptake inhibitor and modern antidepressant study results. Geometric mean IELT and fold increase of geometrical mean IELT. Log-transforming each separate IELT measurement of each individual man is the basis for the calculation of the geometric mean IELT. A drug-induced positively skewed IELT distribution necessitates the calculation of the geometric mean IELTs at baseline and during drug treatment. In a positively skewed IELT distribution, the use of the "arithmetic" mean IELT risks an overestimation of the drug-induced ejaculation delay as the mean IELT is always higher than the geometric mean IELT. Strong ejaculation-delaying drugs give rise to a strong positively skewed IELT distribution, whereas weak ejaculation-delaying drugs give rise to (much) less skewed IELT distributions. Ejaculation delay is expressed in fold increase of the geometric mean IELT. Drug-induced ejaculatory performance discloses a positively skewed IELT distribution, requiring the use of the geometric mean IELT and the fold increase of the geometric mean IELT.
Influence of geometric nanoparticle rotation on cellular internalization process
Yang, Kai; Yuan, Bing; Ma, Yu-Qiang
2013-08-01
It is increasingly recognized that the investigation of the rotational motion of geometric nanoparticles in the cellular internalization process is significant to understand certain fundamental cellular activities, such as endocytosis. However, the mechanism of rotation of geometric nanoparticles in the internalization process is still largely unknown. Here, we investigate the rotational dynamics of geometric nanoparticles when they adhere onto or are wrapped by lipid membranes, by using dissipative particle dynamics. A variety of rotational modes of the nanoparticles are observed, which are closely related to the complicated competition in the internalization process. We find that the breaking of geometric symmetry of a nanoparticle is important for the occurrence of particle rotation, while its effect can be changed by the orientation of the nanoparticles and the affinity between the ligands and the receptors. Importantly, it is found by our simulations that the rotational mode even determines the possible perturbation of the geometric nanoparticle to the membrane and the configuration between the nanoparticle and lipid membrane in the internalization process. These results provide a new strategy and also provide pivotal insight for the design of nanoparticles as advanced drug-delivery vectors to cells.
DOA estimation for conformal vector-sensor array using geometric algebra
Meng, Tianzhen; Wu, Minjie; Yuan, Naichang
2017-12-01
In this paper, the problem of direction of arrival (DOA) estimation is considered in the case of multiple polarized signals impinging on the conformal electromagnetic vector-sensor array (CVA). We focus on modeling the manifold holistically by a new mathematical tool called geometric algebra. Compared with existing methods, the presented one has two main advantages. Firstly, it acquires higher resolution by preserving the orthogonality of the signal components. Secondly, it avoids the cumbersome matrix operations while performing the coordinate transformations, and therefore, has a much lower computational complexity. Simulation results are provided to demonstrate the effectiveness of the proposed algorithm.
Geometrical charged-particle optics
Rose, Harald
2012-01-01
This second edition is an extended version of the first edition of Geometrical Charged-Particle Optics. The updated reference monograph is intended as a guide for researchers and graduate students who are seeking a comprehensive treatment of the design of instruments and beam-guiding systems of charged particles and their propagation in electromagnetic fields. Wave aspects are included in this edition for explaining electron holography, the Aharanov-Bohm effect and the resolution of electron microscopes limited by diffraction. Several methods for calculating the electromagnetic field are presented and procedures are outlined for calculating the properties of systems with arbitrarily curved axis. Detailed methods are presented for designing and optimizing special components such as aberration correctors, spectrometers, energy filters monochromators, ion traps, electron mirrors and cathode lenses. In particular, the optics of rotationally symmetric lenses, quadrupoles, and systems composed of these elements are...
Geometric Methods in Physics XXXV
Odzijewicz, Anatol; Previato, Emma
2018-01-01
This book features a selection of articles based on the XXXV Białowieża Workshop on Geometric Methods in Physics, 2016. The series of Białowieża workshops, attended by a community of experts at the crossroads of mathematics and physics, is a major annual event in the field. The works in this book, based on presentations given at the workshop, are previously unpublished, at the cutting edge of current research, typically grounded in geometry and analysis, and with applications to classical and quantum physics. In 2016 the special session "Integrability and Geometry" in particular attracted pioneers and leading specialists in the field. Traditionally, the Białowieża Workshop is followed by a School on Geometry and Physics, for advanced graduate students and early-career researchers, and the book also includes extended abstracts of the lecture series.
Probing Mixing of Photons and Axion-Like Particles by Geometric Phase
Directory of Open Access Journals (Sweden)
A. Capolupo
2015-01-01
Full Text Available We find that a geometric phase characterizes the phenomenon of mixing of photons with axion-like particles (ALPs. The laboratory observation of such a phase may provide a novel tool able to detect such a mixing phenomenon. We show that the geometric phase is dependent on the axion-like particle mass and coupling constant. We discuss an interferometric experiment able to detect the geometric phase associated with the ALPs-photon mixing.
Geometrical factors in the perception of sacredness
DEFF Research Database (Denmark)
Costa, Marco; Bonetti, Leonardo
2016-01-01
Geometrical and environmental factors in the perception of sacredness, dominance, and attractiveness were assessed by 137 participants in five tests. In the first test, a two-alternative forced-choice paradigm was used to test the perception of sacredness, dominance, and attractiveness in geometr......Geometrical and environmental factors in the perception of sacredness, dominance, and attractiveness were assessed by 137 participants in five tests. In the first test, a two-alternative forced-choice paradigm was used to test the perception of sacredness, dominance, and attractiveness...... in geometrical figures differing in shape, verticality, size, and symmetry. Verticality, symmetry, and convexity were found to be important factors in the perception of sacredness. In the second test, participants had to mark the point inside geometrical surfaces that was perceived as most sacred, dominant....... Geometrical factors in the perception of sacredness, dominance, and attractiveness were largely overlapping....
GEOMETRIC QUALITY ASSESSMENT OF LIDAR DATA BASED ON SWATH OVERLAP
Directory of Open Access Journals (Sweden)
A. Sampath
2016-06-01
Full Text Available This paper provides guidelines on quantifying the relative horizontal and vertical errors observed between conjugate features in the overlapping regions of lidar data. The quantification of these errors is important because their presence quantifies the geometric quality of the data. A data set can be said to have good geometric quality if measurements of identical features, regardless of their position or orientation, yield identical results. Good geometric quality indicates that the data are produced using sensor models that are working as they are mathematically designed, and data acquisition processes are not introducing any unforeseen distortion in the data. High geometric quality also leads to high geolocation accuracy of the data when the data acquisition process includes coupling the sensor with geopositioning systems. Current specifications (e.g. Heidemann 2014 do not provide adequate means to quantitatively measure these errors, even though they are required to be reported. Current accuracy measurement and reporting practices followed in the industry and as recommended by data specification documents also potentially underestimate the inter-swath errors, including the presence of systematic errors in lidar data. Hence they pose a risk to the user in terms of data acceptance (i.e. a higher potential for Type II error indicating risk of accepting potentially unsuitable data. For example, if the overlap area is too small or if the sampled locations are close to the center of overlap, or if the errors are sampled in flat regions when there are residual pitch errors in the data, the resultant Root Mean Square Differences (RMSD can still be small. To avoid this, the following are suggested to be used as criteria for defining the inter-swath quality of data: a Median Discrepancy Angle b Mean and RMSD of Horizontal Errors using DQM measured on sloping surfaces c RMSD for sampled locations from flat areas (defined as areas with less than 5
Landsat 8 Thermal Infrared Sensor Geometric Characterization and Calibration
Directory of Open Access Journals (Sweden)
James Storey
2014-11-01
Full Text Available The Landsat 8 spacecraft was launched on 11 February 2013 carrying two imaging payloads: the Operational Land Imager (OLI and the Thermal Infrared Sensor (TIRS. The TIRS instrument employs a refractive telescope design that is opaque to visible wavelengths making prelaunch geometric characterization challenging. TIRS geometric calibration thus relied heavily on on-orbit measurements. Since the two Landsat 8 payloads are complementary and generate combined Level 1 data products, the TIRS geometric performance requirements emphasize the co-alignment of the OLI and TIRS instrument fields of view and the registration of the OLI reflective bands to the TIRS long-wave infrared emissive bands. The TIRS on-orbit calibration procedures include measuring the TIRS-to-OLI alignment, refining the alignment of the three TIRS sensor chips, and ensuring the alignment of the two TIRS spectral bands. The two key TIRS performance metrics are the OLI reflective to TIRS emissive band registration accuracy, and the registration accuracy between the TIRS thermal bands. The on-orbit calibration campaign conducted during the commissioning period provided an accurate TIRS geometric model that enabled TIRS Level 1 data to meet all geometric accuracy requirements. Seasonal variations in TIRS-to-OLI alignment have led to several small calibration parameter adjustments since commissioning.
Landsat 8 thermal infrared sensor geometric characterization and calibration
Storey, James C.; Choate, Michael J.; Moe, Donald
2014-01-01
The Landsat 8 spacecraft was launched on 11 February 2013 carrying two imaging payloads: the Operational Land Imager (OLI) and the Thermal Infrared Sensor (TIRS). The TIRS instrument employs a refractive telescope design that is opaque to visible wavelengths making prelaunch geometric characterization challenging. TIRS geometric calibration thus relied heavily on on-orbit measurements. Since the two Landsat 8 payloads are complementary and generate combined Level 1 data products, the TIRS geometric performance requirements emphasize the co-alignment of the OLI and TIRS instrument fields of view and the registration of the OLI reflective bands to the TIRS long-wave infrared emissive bands. The TIRS on-orbit calibration procedures include measuring the TIRS-to-OLI alignment, refining the alignment of the three TIRS sensor chips, and ensuring the alignment of the two TIRS spectral bands. The two key TIRS performance metrics are the OLI reflective to TIRS emissive band registration accuracy, and the registration accuracy between the TIRS thermal bands. The on-orbit calibration campaign conducted during the commissioning period provided an accurate TIRS geometric model that enabled TIRS Level 1 data to meet all geometric accuracy requirements. Seasonal variations in TIRS-to-OLI alignment have led to several small calibration parameter adjustments since commissioning.
Analytic and geometric study of stratified spaces
Pflaum, Markus J
2001-01-01
The book provides an introduction to stratification theory leading the reader up to modern research topics in the field. The first part presents the basics of stratification theory, in particular the Whitney conditions and Mather's control theory, and introduces the notion of a smooth structure. Moreover, it explains how one can use smooth structures to transfer differential geometric and analytic methods from the arena of manifolds to stratified spaces. In the second part the methods established in the first part are applied to particular classes of stratified spaces like for example orbit spaces. Then a new de Rham theory for stratified spaces is established and finally the Hochschild (co)homology theory of smooth functions on certain classes of stratified spaces is studied. The book should be accessible to readers acquainted with the basics of topology, analysis and differential geometry.
Geometric methods for discrete dynamical systems
Easton, Robert W
1998-01-01
This book looks at dynamics as an iteration process where the output of a function is fed back as an input to determine the evolution of an initial state over time. The theory examines errors which arise from round-off in numerical simulations, from the inexactness of mathematical models used to describe physical processes, and from the effects of external controls. The author provides an introduction accessible to beginning graduate students and emphasizing geometric aspects of the theory. Conley''s ideas about rough orbits and chain-recurrence play a central role in the treatment. The book will be a useful reference for mathematicians, scientists, and engineers studying this field, and an ideal text for graduate courses in dynamical systems.
Geometric Analogue of Holographic Reduced Representation
Aerts, Diederik; Czachor, Marek; De Moor, Bart
2007-01-01
Holographic reduced representations (HRR) are based on superpositions of convolution-bound $n$-tuples, but the $n$-tuples cannot be regarded as vectors since the formalism is basis dependent. This is why HRR cannot be associated with geometric structures. Replacing convolutions by geometric products one arrives at reduced representations analogous to HRR but interpretable in terms of geometry. Variable bindings occurring in both HRR and its geometric analogue mathematically correspond to two ...
Optical Mode Control by Geometric Phase in Quasicrystal Metasurface.
Yulevich, Igor; Maguid, Elhanan; Shitrit, Nir; Veksler, Dekel; Kleiner, Vladimir; Hasman, Erez
2015-11-13
We report on the observation of optical spin-controlled modes from a quasicrystalline metasurface as a result of an aperiodic geometric phase induced by anisotropic subwavelength structure. When geometric phase defects are introduced in the aperiodic structured surface, the modes exhibit polarization helicity dependence resulting in the optical spin-Hall effect. The radiative thermal dispersion bands from a quasicrystal structure are studied where the observed bands arise from the optical spin-orbit interaction induced by the aperiodic space-variant orientations of anisotropic antennas. The optical spin-flip behavior of the revealed modes that arise from the geometric phase pickup is experimentally observed within the visible spectrum by measuring the spin-projected diffraction patterns. The introduced ability to manipulate the light-matter interaction of quasicrystals in a spin-dependent manner provides the route for molding light via spin-optical aperiodic artificial planar surfaces.
Optical Mode Control by Geometric Phase in Quasicrystal Metasurface
Yulevich, Igor; Shitrit, Nir; Veksler, Dekel; Kleiner, Vladimir; Hasman, Erez
2015-01-01
We report on the observation of optical spin-controlled modes from a quasicrystalline metasurface as a result of an aperiodic geometric phase induced by anisotropic subwavelength structure. When geometric phase defects are introduced in the aperiodic structured surface, the modes exhibit polarization helicity dependence resulting in the optical spin-Hall effect. The radiative thermal dispersion bands from a quasicrystal structure were studied where the observed bands arise from the optical spin-orbit interaction induced by the aperiodic space-variant orientations of anisotropic antennas. The optical spin-flip behavior of the revealed modes that arise from the geometric phase pickup was experimentally observed within the visible spectrum by measuring the spin-projected diffraction patterns. The introduced ability to manipulate the light-matter interaction of quasicrystals in a spin-dependent manner provides the route for molding light via spin-optical aperiodic artificial planar surfaces.
SIAM Conference on Geometric Design and Computing. Final Technical Report
Energy Technology Data Exchange (ETDEWEB)
None
2002-03-11
The SIAM Conference on Geometric Design and Computing attracted 164 domestic and international researchers, from academia, industry, and government. It provided a stimulating forum in which to learn about the latest developments, to discuss exciting new research directions, and to forge stronger ties between theory and applications. Final Report
Geometric and Network Model for Knowledge Structure and Mindspace
Chris Arney
2012-01-01
This paper describes an adaptive, complex network architecture for knowledge representation in virtual mindspace. Structures and processes for knowing, remembering, thinking, learning, deciding, and communicating describe a virtual geometric space (mathematical model) of a notional mind. This mindspace model can be visualized as a workspace and this paper provides a glimpse of a virtual model of the mind.
Geometric and Network Model for Knowledge Structure and Mindspace
Directory of Open Access Journals (Sweden)
Chris Arney
2012-02-01
Full Text Available This paper describes an adaptive, complex network architecture for knowledge representation in virtual mindspace. Structures and processes for knowing, remembering, thinking, learning, deciding, and communicating describe a virtual geometric space (mathematical model of a notional mind. This mindspace model can be visualized as a workspace and this paper provides a glimpse of a virtual model of the mind.
A new geometric description for Igusa's modular form $(azy)_5$
Fiorentino, Alessio
2011-01-01
The modular form $(azy)_5$ notably appears in one of Igusa's classic structure theorems as a generator of the ring of full modular forms in genus 2, being exhibited by means of a complicated algebraic expression. In this work a different description for this modular form is provided by resorting to a peculiar geometrical approach.
Geometrical and Graphical Solutions of Quadratic Equations.
Hornsby, E. John, Jr.
1990-01-01
Presented are several geometrical and graphical methods of solving quadratic equations. Discussed are Greek origins, Carlyle's method, von Staudt's method, fixed graph methods and imaginary solutions. (CW)
Geometric Aspects of Iterated Matrix Multiplication
DEFF Research Database (Denmark)
Gesmundo, Fulvio
2016-01-01
This paper studies geometric properties of the Iterated Matrix Multiplication polynomial and the hypersurface that it defines. We focus on geometric aspects that may be relevant for complexity theory such as the symmetry group of the polynomial, the dual variety and the Jacobian loci of the hyper......This paper studies geometric properties of the Iterated Matrix Multiplication polynomial and the hypersurface that it defines. We focus on geometric aspects that may be relevant for complexity theory such as the symmetry group of the polynomial, the dual variety and the Jacobian loci...
Quasirandom geometric networks from low-discrepancy sequences
Estrada, Ernesto
2017-08-01
We define quasirandom geometric networks using low-discrepancy sequences, such as Halton, Sobol, and Niederreiter. The networks are built in d dimensions by considering the d -tuples of digits generated by these sequences as the coordinates of the vertices of the networks in a d -dimensional Id unit hypercube. Then, two vertices are connected by an edge if they are at a distance smaller than a connection radius. We investigate computationally 11 network-theoretic properties of two-dimensional quasirandom networks and compare them with analogous random geometric networks. We also study their degree distribution and their spectral density distributions. We conclude from this intensive computational study that in terms of the uniformity of the distribution of the vertices in the unit square, the quasirandom networks look more random than the random geometric networks. We include an analysis of potential strategies for generating higher-dimensional quasirandom networks, where it is know that some of the low-discrepancy sequences are highly correlated. In this respect, we conclude that up to dimension 20, the use of scrambling, skipping and leaping strategies generate quasirandom networks with the desired properties of uniformity. Finally, we consider a diffusive process taking place on the nodes and edges of the quasirandom and random geometric graphs. We show that the diffusion time is shorter in the quasirandom graphs as a consequence of their larger structural homogeneity. In the random geometric graphs the diffusion produces clusters of concentration that make the process more slow. Such clusters are a direct consequence of the heterogeneous and irregular distribution of the nodes in the unit square in which the generation of random geometric graphs is based on.
Quasirandom geometric networks from low-discrepancy sequences.
Estrada, Ernesto
2017-08-01
We define quasirandom geometric networks using low-discrepancy sequences, such as Halton, Sobol, and Niederreiter. The networks are built in d dimensions by considering the d-tuples of digits generated by these sequences as the coordinates of the vertices of the networks in a d-dimensional I^{d} unit hypercube. Then, two vertices are connected by an edge if they are at a distance smaller than a connection radius. We investigate computationally 11 network-theoretic properties of two-dimensional quasirandom networks and compare them with analogous random geometric networks. We also study their degree distribution and their spectral density distributions. We conclude from this intensive computational study that in terms of the uniformity of the distribution of the vertices in the unit square, the quasirandom networks look more random than the random geometric networks. We include an analysis of potential strategies for generating higher-dimensional quasirandom networks, where it is know that some of the low-discrepancy sequences are highly correlated. In this respect, we conclude that up to dimension 20, the use of scrambling, skipping and leaping strategies generate quasirandom networks with the desired properties of uniformity. Finally, we consider a diffusive process taking place on the nodes and edges of the quasirandom and random geometric graphs. We show that the diffusion time is shorter in the quasirandom graphs as a consequence of their larger structural homogeneity. In the random geometric graphs the diffusion produces clusters of concentration that make the process more slow. Such clusters are a direct consequence of the heterogeneous and irregular distribution of the nodes in the unit square in which the generation of random geometric graphs is based on.
Investigation of possible neural architectures underlying information-geometric measures.
Tatsuno, Masami; Okada, Masato
2004-04-01
A novel analytical method based on information geometry was recently proposed, and this method may provide useful insights into the statistical interactions within neural groups. The link between informationgeometric measures and the structure of neural interactions has not yet been elucidated, however, because of the ill-posed nature of the problem. Here, possible neural architectures underlying information-geometric measures are investigated using an isolated pair and an isolated triplet of model neurons. By assuming the existence of equilibrium states, we derive analytically the relationship between the information-geometric parameters and these simple neural architectures. For symmetric networks, the first- and second-order information-geometric parameters represent, respectively, the external input and the underlying connections between the neurons provided that the number of neurons used in the parameter estimation in the log-linear model and the number of neurons in the network are the same. For asymmetric networks, however, these parameters are dependent on both the intrinsic connections and the external inputs to each neuron. In addition, we derive the relation between the information-geometric parameter corresponding to the two-neuron interaction and a conventional cross-correlation measure. We also show that the information-geometric parameters vary depending on the number of neurons assumed for parameter estimation in the log-linear model. This finding suggests a need to examine the information-geometric method carefully. A possible criterion for choosing an appropriate orthogonal coordinate is also discussed. This article points out the importance of a model-based approach and sheds light on the possible neural structure underlying the application of information geometry to neural network analysis.
Geometrical aspects on the dark matter problem
Energy Technology Data Exchange (ETDEWEB)
Capistrano, A.J.S., E-mail: abraao.capistrano@unila.edu.br [Federal University of Latin-American Integration, 85867-970, Foz do Iguaçu-PR (Brazil); Cabral, L.A. [Federal University of Tocantins, 77804-970, Araguaína-TO (Brazil)
2014-09-15
In the present paper we apply Nash’s theory of perturbative geometry to the study of dark matter gravity in a higher-dimensional space–time. It is shown that the dark matter gravitational perturbations at local scale can be explained by the extrinsic curvature of the standard cosmology. In order to test our model, we use a spherically symmetric metric embedded in a five-dimensional bulk. As a result, considering a sample of 10 low surface brightness and 6 high surface brightness galaxies, we find a very good agreement with the observed rotation curves of smooth hybrid alpha-HI measurements. - Highlights: • The metric perturbation and the embedding lead naturally to a “brane-world”-like higher dimensional structure. • Nash’s theorem as a cornerstone of the formation of geometrical structures. • The dark matter gravitational perturbations at local scale can be explained by the extrinsic curvature. • A good agreement was found with the observed rotation curves of smooth hybrid alpha-HI measurements.
Simulating geometrically complex blast scenarios
Directory of Open Access Journals (Sweden)
Ian G. Cullis
2016-04-01
Full Text Available The effects of blast waves generated by energetic and non-energetic sources are of continuing interest to the ballistics research community. Modern conflicts are increasingly characterised by asymmetric urban warfare, with improvised explosive devices (IEDs often playing a dominant role on the one hand and an armed forces requirement for minimal collateral effects from their weapons on the other. These problems are characterised by disparate length- and time-scales and may also be governed by complex physics. There is thus an increasing need to be able to rapidly assess and accurately predict the effects of energetic blast in topologically complex scenarios. To this end, this paper presents a new QinetiQ-developed advanced computational package called EAGLE-Blast, which is capable of accurately resolving the generation, propagation and interaction of blast waves around geometrically complex shapes such as vehicles and buildings. After a brief description of the numerical methodology, various blast scenario simulations are described and the results compared with experimental data to demonstrate the validation of the scheme and its ability to describe these complex scenarios accurately and efficiently. The paper concludes with a brief discussion on the use of the code in supporting the development of algorithms for fast running engineering models.
Geometric Computations On Indecisive Points
DEFF Research Database (Denmark)
Jørgensen, Allan Grønlund; Phillips, Jeff; Loffler, Maarten
2011-01-01
We study computing with indecisive point sets. Such points have spatial uncertainty where the true location is one of a finite number of possible locations. This data arises from probing distributions a few times or when the location is one of a few locations from a known database. In particular,......-hard. We generalize our polynomial-time algorithm to all LP-type problems. We also utilize our indecisive framework to deterministically and approximately compute on a more general class of uncertain data where the location of each point is given by a probability distribution.......We study computing with indecisive point sets. Such points have spatial uncertainty where the true location is one of a finite number of possible locations. This data arises from probing distributions a few times or when the location is one of a few locations from a known database. In particular......, we study computing distributions of geometric functions such as the radius of the smallest enclosing ball and the diameter. Surprisingly, we can compute the distribution of the radius of the smallest enclosing ball exactly in polynomial time, but computing the same distribution for the diameter is #P...
Geometric reasoning about assembly tools
Energy Technology Data Exchange (ETDEWEB)
Wilson, R.H.
1997-01-01
Planning for assembly requires reasoning about various tools used by humans, robots, or other automation to manipulate, attach, and test parts and subassemblies. This paper presents a general framework to represent and reason about geometric accessibility issues for a wide variety of such assembly tools. Central to the framework is a use volume encoding a minimum space that must be free in an assembly state to apply a given tool, and placement constraints on where that volume must be placed relative to the parts on which the tool acts. Determining whether a tool can be applied in a given assembly state is then reduced to an instance of the FINDPLACE problem. In addition, the author presents more efficient methods to integrate the framework into assembly planning. For tools that are applied either before or after their target parts are mated, one method pre-processes a single tool application for all possible states of assembly of a product in polynomial time, reducing all later state-tool queries to evaluations of a simple expression. For tools applied after their target parts are mated, a complementary method guarantees polynomial-time assembly planning. The author presents a wide variety of tools that can be described adequately using the approach, and surveys tool catalogs to determine coverage of standard tools. Finally, the author describes an implementation of the approach in an assembly planning system and experiments with a library of over one hundred manual and robotic tools and several complex assemblies.
Engineering Design by Geometric Programming
Directory of Open Access Journals (Sweden)
Chia-Hui Huang
2013-01-01
Full Text Available A geometric program (GP is a type of mathematical optimization problem characterized by objective and constraint functions, where all functions are of signomial form. The importance of GP comes from two relatively recent developments: (i new methods can solve even large-scale GP extremely efficiently and reliably; (ii a number of practical problems have recently been found to be equivalent to or approximated by GP. This study proposes an optimization approach for solving GP. Our approach is first to convert all signomial terms in GP into convex and concave terms. Then the concave terms are further treated with the proposed piecewise linearization method where only binary variables are used. It has the following features: (i it offers more convenient and efficient means of expressing a piecewise linear function; (ii fewer 0-1 variables are used; (iii the computational results show that the proposed method is much more efficient and faster than the conventional one, especially when the number of break points becomes large. In addition, the engineering design problems are illustrated to evaluate the usefulness of the proposed methods.
A plea for geometrical order in tectonics
Schmid, Stefan
2017-04-01
Ever since publishing his landmark book "Folding and Fracturing of Rocks" 50 years ago John G. Ramsay (Ramsay 1967) has fascinated many of us with his stringent mathematical-geometrical approach towards analyzing finite strain in rocks, in particular what the geometry and kinematics of folding are concerned. The figures in this early book, as well as John's drawings and photographs published in later books and articles, undoubtedly also impressed many of us by their sheer aesthetic value. This book and his later work conveyed the message that rock deformation behaves in an "orderly" way, a message that is shared by many, but not all, of John's colleagues in structural geology and tectonics. This contribution is a plea for careful structural analysis and extensive fieldwork, providing the indispensable base in any attempt to go further and also understand the physics of rock deformation and geological processes at all scales. Two large-scale examples will be discussed in this respect: (1) The problem of mélanges in an ophiolite-bearing unit of the Swiss Alps (Arosa Zone) showing that careful structural analysis leads to the view that such chaotic mélanges were postulated by some authors in the absence of a carful structural analysis, and that the geometry in fact is a result of polyphase deformation, and (2) the problem of orogen scale transects of across the Alps that reflect an amazing degree of order in the stacking of diverse paleogeographical units enabling geometrical-kinematic attempts of retrodeformation and contrasting with alternative and rather "chaotic" views. Reference: Ramsay, J.G. 1967: Folding and Fracturing of Rocks. McGraw-Hill New York, 568pp.
COMPARISON OF METHODS FOR GEOMETRIC CAMERA CALIBRATION
Directory of Open Access Journals (Sweden)
J. Hieronymus
2012-09-01
Full Text Available Methods for geometric calibration of cameras in close-range photogrammetry are established and well investigated. The most common one is based on test-fields with well-known pattern, which are observed from different directions. The parameters of a distortion model are calculated using bundle-block-adjustment-algorithms. This methods works well for short focal lengths, but is essentially more problematic to use with large focal lengths. Those would require very large test-fields and surrounding space. To overcome this problem, there is another common method for calibration used in remote sensing. It employs measurements using collimator and a goniometer. A third calibration method uses diffractive optical elements (DOE to project holograms of well known pattern. In this paper these three calibration methods are compared empirically, especially in terms of accuracy. A camera has been calibrated with those methods mentioned above. All methods provide a set of distortion correction parameters as used by the photogrammetric software Australis. The resulting parameter values are very similar for all investigated methods. The three sets of distortion parameters are crosscompared against all three calibration methods. This is achieved by inserting the gained distortion parameters as fixed input into the calibration algorithms and only adjusting the exterior orientation. The RMS (root mean square of the remaining image coordinate residuals are taken as a measure of distortion correction quality. There are differences resulting from the different calibration methods. Nevertheless the measure is small for every comparison, which means that all three calibration methods can be used for accurate geometric calibration.
Geometric integrators for stochastic rigid body dynamics
Tretyakov, Mikhail
2016-01-05
Geometric integrators play an important role in simulating dynamical systems on long time intervals with high accuracy. We will illustrate geometric integration ideas within the stochastic context, mostly on examples of stochastic thermostats for rigid body dynamics. The talk will be mainly based on joint recent work with Rusland Davidchak and Tom Ouldridge.
Parabolas: Connection between Algebraic and Geometrical Representations
Shriki, Atara
2011-01-01
A parabola is an interesting curve. What makes it interesting at the secondary school level is the fact that this curve is presented in both its contexts: algebraic and geometric. Being one of Apollonius' conic sections, the parabola is basically a geometric entity. It is, however, typically known for its algebraic characteristics, in particular…
GEOMETRIC IDENTITIES IN STEREOLOGICAL PARTICLE ANALYSIS
Directory of Open Access Journals (Sweden)
Stephan Kötzer
2011-05-01
Full Text Available The paper reviews recent findings about geometric identities in integral geometry and geometric tomography, and their statistical application to stereological particle analysis. Open questions are discussed. This survey can also serve as an introduction to modern stereological particle analysis for readers who are interested in the mathematical background of the new methods.
Geometric phases in discrete dynamical systems
Energy Technology Data Exchange (ETDEWEB)
Cartwright, Julyan H.E., E-mail: julyan.cartwright@csic.es [Instituto Andaluz de Ciencias de la Tierra, CSIC–Universidad de Granada, E-18100 Armilla, Granada (Spain); Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, E-18071 Granada (Spain); Piro, Nicolas, E-mail: nicolas.piro@epfl.ch [École Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne (Switzerland); Piro, Oreste, E-mail: piro@imedea.uib-csic.es [Departamento de Física, Universitat de les Illes Balears, E-07122 Palma de Mallorca (Spain); Tuval, Idan, E-mail: ituval@imedea.uib-csic.es [Mediterranean Institute for Advanced Studies, CSIC–Universitat de les Illes Balears, E-07190 Mallorca (Spain)
2016-10-14
In order to study the behaviour of discrete dynamical systems under adiabatic cyclic variations of their parameters, we consider discrete versions of adiabatically-rotated rotators. Parallelling the studies in continuous systems, we generalize the concept of geometric phase to discrete dynamics and investigate its presence in these rotators. For the rotated sine circle map, we demonstrate an analytical relationship between the geometric phase and the rotation number of the system. For the discrete version of the rotated rotator considered by Berry, the rotated standard map, we further explore this connection as well as the role of the geometric phase at the onset of chaos. Further into the chaotic regime, we show that the geometric phase is also related to the diffusive behaviour of the dynamical variables and the Lyapunov exponent. - Highlights: • We extend the concept of geometric phase to maps. • For the rotated sine circle map, we demonstrate an analytical relationship between the geometric phase and the rotation number. • For the rotated standard map, we explore the role of the geometric phase at the onset of chaos. • We show that the geometric phase is related to the diffusive behaviour of the dynamical variables and the Lyapunov exponent.
Morse theory for C*-algebras: a geometric interpretation of some noncommutative manifolds
Directory of Open Access Journals (Sweden)
Vida Milani
2011-10-01
Full Text Available The approach we present is a modification of the Morse theory for unital C*-algebras. We provide tools for the geometric interpretation of noncommutative CW complexes. Some examples are given to illustrate these geometric information. The main object of this work is a classification of unital C*-algebras by noncommutative CW complexes and the modified Morse functions on them.
Geometric entanglement in the Laughlin wave function
Zhang, Jiang-Min; Liu, Yu
2017-08-01
We study numerically the geometric entanglement in the Laughlin wave function, which is of great importance in condensed matter physics. The Slater determinant having the largest overlap with the Laughlin wave function is constructed by an iterative algorithm. The logarithm of the overlap, which is a geometric quantity, is then taken as a geometric measure of entanglement. It is found that the geometric entanglement is a linear function of the number of electrons to a good extent. This is especially the case for the lowest Laughlin wave function, namely the one with filling factor of 1/3. Surprisingly, the linear behavior extends well down to the smallest possible value of the electron number, namely, N = 2. The constant term does not agree with the expected topological entropy. In view of previous works, our result indicates that the relation between geometric entanglement and topological entropy is very subtle.
Geometric covers, graph orientations, counter games
DEFF Research Database (Denmark)
Berglin, Edvin
2017-01-01
Geometric Cover is a large family of NP-complete special cases of the broader Set Cover problem. Unlike the general problem, Geometric Cover involves objects that exist in a geometric setting, consequently implying that they are all restricted to obeying some inherent structure. The archetypal...... example is Line Cover, also known as Point-Line Cover, where a set of points in a geometric space are to be covered by placing a restricted number of lines. We present new FPT algorithms for the sub-family Curve Cover (which includes Line Cover), as well as for Hyperplane Cover restricted to R 3 (i.......e. Plane Cover), with improved time complexity compared to the previous best results. Our improvements are derived from a more careful treatment of the geometric properties of the covering objects than before, and invoking incidence bounds from pure geometry. An orientation of an un-directed graph...
Importance of Geometric Phase Effects in Ultracold Chemistry.
Hazra, Jisha; Kendrick, Brian K; Balakrishnan, Naduvalath
2015-12-17
It is demonstrated that the inclusion of the geometric phase has an important effect on ultracold chemical reaction rates. The effect appears in rotationally and vibrationally resolved integral cross sections as well as cross sections summed over all product quantum states. The effect arises from interference between scattering amplitudes of two reaction pathways: a direct path and a looping path that encircle the conical intersection between the two lowest adiabatic electronic potential energy surfaces. It is magnified when the two scattering amplitudes have comparable magnitude and they scatter into the same angular region which occurs in the isotropic scattering characteristic of the ultracold regime (s-wave scattering). Results are presented for the O + OH → H + O2 reaction for total angular momentum quantum number J = 0-5. Large geometric phase effects occur for collision energies below 0.1 K, but the effect vanishes at higher energies when contributions from different partial waves are included. It is also qualitatively demonstrated that the geometric phase effect can be modulated by applying an external electric field allowing the possibility of quantum control of chemical reactions in the ultracold regime. In this case, the geometric phase plays the role of a "quantum switch" which can turn the reaction "on" or "off".
Sung, KiHoon; Choi, Young Eun; Lee, Kyu Chan
2017-06-01
This is a dosimetric study to identify a simple geometric indicator to discriminate patients who meet the selection criterion for heart-sparing radiotherapy (RT). The authors proposed a cardiac risk index (CRI), directly measurable from the CT images at the time of scanning. Treatment plans were regenerated using the CT data of 312 consecutive patients with left-sided breast cancer. Dosimetric analysis was performed to estimate the risk of cardiac mortality using cardiac dosimetric parameters, such as the relative heart volumes receiving ≥25 Gy (heart V25 ). For each CT data set, in-field heart depth (HD) and in-field heart width (HW) were measured to generate the geometric parameters, including maximum HW (HWmax ) and maximum HD (HDmax ). Seven geometric parameters were evaluated as candidates for CRI. Receiver operating characteristic (ROC) curve analyses were used to examine the overall discriminatory power of the geometric parameters to select high-risk patients (heart V25 ≥ 10%). Seventy-one high-risk (22.8%) and 241 low-risk patients (77.2%) were identified by dosimetric analysis. The geometric and dosimetric parameters were significantly higher in the high-risk group. Heart V25 showed the strong positive correlations with all geometric parameters examined (r > 0.8, p Cardiac risk index proposed as a simple geometric indicator to select high-risk patients provides useful guidance for clinicians considering optimal implementation of heart-sparing RT. © 2016 The Royal Australian and New Zealand College of Radiologists.
Inverse Kinematics for Industrial Robots using Conformal Geometric Algebra
Directory of Open Access Journals (Sweden)
Adam L. Kleppe
2016-01-01
Full Text Available This paper shows how the recently developed formulation of conformal geometric algebra can be used for analytic inverse kinematics of two six-link industrial manipulators with revolute joints. The paper demonstrates that the solution of the inverse kinematics in this framework relies on the intersection of geometric objects like lines, circles, planes and spheres, which provides the developer with valuable geometric intuition about the problem. It is believed that this will be very useful for new robot geometries and other mechanisms like cranes and topside drilling equipment. The paper extends previous results on inverse kinematics using conformal geometric algebra by providing consistent solutions for the joint angles for the different configurations depending on shoulder left or right, elbow up or down, and wrist flipped or not. Moreover, it is shown how to relate the solution to the Denavit-Hartenberg parameters of the robot. The solutions have been successfully implemented and tested extensively over the whole workspace of the manipulators.
Geometric characterization and simulation of planar layered elastomeric fibrous biomaterials.
Carleton, James B; D'Amore, Antonio; Feaver, Kristen R; Rodin, Gregory J; Sacks, Michael S
2015-01-01
Many important biomaterials are composed of multiple layers of networked fibers. While there is a growing interest in modeling and simulation of the mechanical response of these biomaterials, a theoretical foundation for such simulations has yet to be firmly established. Moreover, correctly identifying and matching key geometric features is a critically important first step for performing reliable mechanical simulations. The present work addresses these issues in two ways. First, using methods of geometric probability, we develop theoretical estimates for the mean linear and areal fiber intersection densities for 2-D fibrous networks. These densities are expressed in terms of the fiber density and the orientation distribution function, both of which are relatively easy-to-measure properties. Secondly, we develop a random walk algorithm for geometric simulation of 2-D fibrous networks which can accurately reproduce the prescribed fiber density and orientation distribution function. Furthermore, the linear and areal fiber intersection densities obtained with the algorithm are in agreement with the theoretical estimates. Both theoretical and computational results are compared with those obtained by post-processing of scanning electron microscope images of actual scaffolds. These comparisons reveal difficulties inherent to resolving fine details of multilayered fibrous networks. The methods provided herein can provide a rational means to define and generate key geometric features from experimentally measured or prescribed scaffold structural data. Copyright © 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Computational toolbox for optical tweezers in geometrical optics
Callegari, Agnese; Mijalkov, Mite; Gököz, A. Burak; Volpe, Giovanni
2014-01-01
Optical tweezers have found widespread application in many fields, from physics to biology. Here, we explain in detail how optical forces and torques can be described within the geometrical optics approximation and we show that this approximation provides reliable results in agreement with experiments for particles whose characteristic dimensions are larger than the wavelength of the trapping light. Furthermore, we provide an object-oriented software package implemented in MatLab for the calc...
CGAlgebra: a Mathematica package for conformal geometric algebra
Aragon, Jose L.
2017-01-01
A tutorial of the Mathematica package CGAlgebra, for conformal geometric algebra calculations is presented. Using rule-based programming, the 5-dimensional conformal geometric algebra is implemented and defined functions simplify the calculations of geometric, outer and inner products, as well as many other calculations related with geometric transformations. CGAlgebra is available from https://github.com/jlaragonvera/Geometric-Algebra
Study of the Geometric Stiffening Effect: Comparison of Different Formulations
Energy Technology Data Exchange (ETDEWEB)
Mayo, Juana M., E-mail: juana@us.es; Garcia-Vallejo, Daniel; Dominguez, Jaime [Universidad de Sevilla, Departamento de Ingenieria Mecanica y de los Materiales (Spain)
2004-05-15
This paper reviews different formulations to account for the stress stiffening or geometric stiffening effect arising from deflections large enough to cause significant changes in the configuration of the system The importance of such effect on many engineering applications, such as the dynamic behavior of helicopter blades, flexible rotor arms, turbine blades, etc., is well known. The analysis is carried out only for one-dimensional elements in 2D.Formulations based on the floating frame of reference approach are computationally very efficient, as the use of the component synthesis method allows for a reduced number of coordinates. However, something must be done for them to account for the geometric stiffening effect. The easiest method is the application of the substructuring technique, because the formulation is not modified. This, however, is not the most efficient approach. In problems where deformation is moderated, the simple inclusion of the geometric stiffness matrix is enough. On the other hand, if the deformation is large, higher-order terms must be included in the strain energy. In order to achieve an efficient and stable formulation, an explicit geometrically nonlinear beam element was developed. The formulations that use absolute coordinates are, generally, computationally more costly than the previous ones, as they must use a large number of degrees of freedom. However, the geometric stiffening effect can be automatically accounted for with these formulations. The aim of this work is to investigate the applicability of the different existing formulations in order to help the user select the right one for his particular application.
A Geometrical View of Higgs Effective Theory
CERN. Geneva
2016-01-01
A geometric formulation of Higgs Effective Field Theory (HEFT) is presented. Experimental observables are given in terms of geometric invariants of the scalar sigma model sector such as the curvature of the scalar field manifold M. We show how the curvature can be measured experimentally via Higgs cross-sections, W_L scattering, and the S parameter. The one-loop action of HEFT is given in terms of geometric invariants of M. The distinction between the Standard Model (SM) and HEFT is whether M is flat or curved, with the curvature a signal of the scale of new physics.
Geometric comparison of popular mixture-model distances.
Energy Technology Data Exchange (ETDEWEB)
Mitchell, Scott A.
2010-09-01
Statistical Latent Dirichlet Analysis produces mixture model data that are geometrically equivalent to points lying on a regular simplex in moderate to high dimensions. Numerous other statistical models and techniques also produce data in this geometric category, even though the meaning of the axes and coordinate values differs significantly. A distance function is used to further analyze these points, for example to cluster them. Several different distance functions are popular amongst statisticians; which distance function is chosen is usually driven by the historical preference of the application domain, information-theoretic considerations, or by the desirability of the clustering results. Relatively little consideration is usually given to how distance functions geometrically transform data, or the distances algebraic properties. Here we take a look at these issues, in the hope of providing complementary insight and inspiring further geometric thought. Several popular distances, {chi}{sup 2}, Jensen - Shannon divergence, and the square of the Hellinger distance, are shown to be nearly equivalent; in terms of functional forms after transformations, factorizations, and series expansions; and in terms of the shape and proximity of constant-value contours. This is somewhat surprising given that their original functional forms look quite different. Cosine similarity is the square of the Euclidean distance, and a similar geometric relationship is shown with Hellinger and another cosine. We suggest a geodesic variation of Hellinger. The square-root projection that arises in Hellinger distance is briefly compared to standard normalization for Euclidean distance. We include detailed derivations of some ratio and difference bounds for illustrative purposes. We provide some constructions that nearly achieve the worst-case ratios, relevant for contours.
Importance of geometric characteristics for salinity distribution in convergent estuaries
Nguyen, Duc H.; Umeyama, Motohiko; Shintani, Tetsuya
2012-07-01
SummaryWe investigate changes in geometric characteristics and related processes of the longitudinal salinity distribution in an alluvial estuarine system. We focus on tide-dominated estuaries, which are usually characterized by a convergent shape, and analyze effects of intra-tidal and sub-tidal variations of the geometric characteristics on the salinity distribution. A theoretical salt intrusion model is applied to the Red River estuarine system (RRES), where the channel shape and size greatly vary as a function of tidal amplitudes. The model was originally derived for single-channel estuaries by considering the cross-sectional profile only at tidally averaged condition. This assumption makes the application of the model to the RRES a challenging task. In this paper, we split the estuary branch into multi-connected segments to describe the longitudinal variation of geometric characteristics. In addition, by prescribing geometric parameters to exponentially vary under different tidal conditions, we were able to estimate spatial and temporal changes in the salinity distribution. A series of field surveys for salinity in the dry season of 2006, 2008, and 2009 were used to examine and validate the method. We found that the modified model described salt intrusion with a good fit between the computed and measured salinity. This finding provides a key for the further investigation of salt intrusion for estuaries having complex geometry.
Geometric and functional architecture of visceral sensory microcircuitry.
Negishi, Yoshikatsu; Kawai, Yoshinori
2011-03-01
Is microcircuit wiring designed deterministically or probabilistically? Does geometric architecture predict functional dynamics of a given neuronal microcircuit? These questions were addressed in the visceral sensory microcircuit of the caudal nucleus of the tractus solitarius (NTS), which is generally thought to be homogeneous rather than laminar in cytoarchitecture. Using in situ hybridization histochemistry and whole-cell patch clamp recordings followed by neuronal reconstruction with biocytin filling, anatomical and functional organization of NTS microcircuitry was quantified to determine associative relationships. Morphologic and chemical features of NTS neurons displayed different patterns of process arborization and sub-nuclear localization according to neuronal types: smaller cells featured presynaptic local axons and GABAergic cells were aggregated specifically within the ventral NTS. The results suggested both a laminar organization and a spatial heterogeneity of NTS microcircuit connectivity. Geometric analysis of pre- and postsynaptic axodendritic arbor overlap of reconstructed neurons (according to parent somal distance) confirmed a heterogeneity of microcircuit connectivity that could underlie differential functional dynamics along the dorsoventral axis. Functional dynamics in terms of spontaneous and evoked postsynaptic current patterns behaved in a strongly location-specific manner according to the geometric dimension, suggesting a spatial laminar segregation of neuronal populations: a dorsal group of high excitation and a ventral group of balanced excitation and inhibition. Recurrent polysynaptic activity was also noted in a subpopulation of the ventral group. Such geometric and functional laminar organization seems to provide the NTS microcircuit with both reverberation capability and a differentiated projection system for appropriate computation of visceral sensory information.
Geometric continuum mechanics and induced beam theories
R Eugster, Simon
2015-01-01
This research monograph discusses novel approaches to geometric continuum mechanics and introduces beams as constraint continuous bodies. In the coordinate free and metric independent geometric formulation of continuum mechanics as well as for beam theories, the principle of virtual work serves as the fundamental principle of mechanics. Based on the perception of analytical mechanics that forces of a mechanical system are defined as dual quantities to the kinematical description, the virtual work approach is a systematic way to treat arbitrary mechanical systems. Whereas this methodology is very convenient to formulate induced beam theories, it is essential in geometric continuum mechanics when the assumptions on the physical space are relaxed and the space is modeled as a smooth manifold. The book addresses researcher and graduate students in engineering and mathematics interested in recent developments of a geometric formulation of continuum mechanics and a hierarchical development of induced beam theories.
5th Dagstuhl Seminar on Geometric Modelling
Brunnett, Guido; Farin, Gerald; Goldman, Ron
2004-01-01
In 19 articles presented by leading experts in the field of geometric modelling the state-of-the-art on representing, modeling, and analyzing curves, surfaces as well as other 3-dimensional geometry is given. The range of applications include CAD/CAM-systems, computer graphics, scientific visualization, virtual reality, simulation and medical imaging. The content of this book is based on selected lectures given at a workshop held at IBFI Schloss Dagstuhl, Germany. Topics treated are: – curve and surface modelling – non-manifold modelling in CAD – multiresolution analysis of complex geometric models – surface reconstruction – variational design – computational geometry of curves and surfaces – 3D meshing – geometric modelling for scientific visualization – geometric models for biomedical applications
Geometric U-folds in four dimensions
Lazaroiu, C. I.; Shahbazi, C. S.
2018-01-01
We describe a general construction of geometric U-folds compatible with a non-trivial extension of the global formulation of four-dimensional extended supergravity on a differentiable spin manifold. The topology of geometric U-folds depends on certain flat fiber bundles which encode how supergravity fields are globally glued together. We show that smooth non-trivial U-folds of this type can exist only in theories where both the scalar and space-time manifolds have non-trivial fundamental group and in addition the scalar map of the solution is homotopically non-trivial. Consistency with string theory requires smooth geometric U-folds to be glued using subgroups of the effective discrete U-duality group, implying that the fundamental group of the scalar manifold of such solutions must be a subgroup of the latter. We construct simple examples of geometric U-folds in a generalization of the axion–dilaton model of \
Hidden geometric correlations in real multiplex networks
Kleineberg, Kaj-Kolja; Boguñá, Marián; Ángeles Serrano, M.; Papadopoulos, Fragkiskos
2016-11-01
Real networks often form interacting parts of larger and more complex systems. Examples can be found in different domains, ranging from the Internet to structural and functional brain networks. Here, we show that these multiplex systems are not random combinations of single network layers. Instead, they are organized in specific ways dictated by hidden geometric correlations between the layers. We find that these correlations are significant in different real multiplexes, and form a key framework for answering many important questions. Specifically, we show that these geometric correlations facilitate the definition and detection of multidimensional communities, which are sets of nodes that are simultaneously similar in multiple layers. They also enable accurate trans-layer link prediction, meaning that connections in one layer can be predicted by observing the hidden geometric space of another layer. And they allow efficient targeted navigation in the multilayer system using only local knowledge, outperforming navigation in the single layers only if the geometric correlations are sufficiently strong.
Energy Technology Data Exchange (ETDEWEB)
Shin, Dong Seok; Kim, Dong Su; Kim, Tae Ho; Kim, Kyeong Hyeon; Yoon, Do Kun; Suh, Tae Suk [The Catholic University of Korea, Seoul (Korea, Republic of); Kang, Seong Hee [Seoul National University Hospital, Seoul (Korea, Republic of); Cho, Min Seok [Asan Medical Center, Seoul (Korea, Republic of); Noh, Yu Yoon [Eulji University Hospital, Daejeon (Korea, Republic of)
2017-04-15
Three-dimensional dose (3D dose) can consider coverage of moving target, however it is difficult to provide dosimetric effect which occurs by respiratory motions. Four-dimensional dose (4D dose) which uses deformable image registration (DIR) algorithm from four-dimensional computed tomography (4DCT) images can consider dosimetric effect by respiratory motions. The dose difference between 3D dose and 4D dose can be varied according to the geometrical relationship between a planning target volume (PTV) and an organ at risk (OAR). The purpose of this study is to evaluate the correlation between the overlap volume histogram (OVH), which quantitatively shows the geometrical relationship between the PTV and OAR, and the dose differences. In conclusion, no significant statistical correlation was found between the OVH and dose differences. However, it was confirmed that a higher difference between the 3D and 4D doses could occur in cases that have smaller OVH value. No significant statistical correlation was found between the OVH and dose differences. However, it was confirmed that a higher difference between the 3D and 4D doses could occur in cases that have smaller OVH value.
Geometric Beam Coupling Impedance of LHC Secondary Collimators
Frasciello, O; Zobov, M; Grudiev, A; Mounet, N; Salvant, B
2016-01-01
The High Luminosity LHC project is aimed at increasing the LHC luminosity by an order of magnitude. One of the key ingredients to achieve the luminosity goal is the beam intensity increase. In order to keep under control beam instabilities and to avoid excessive power losses a careful design of new vacuum chamber components and an improvement of the present LHC impedance model are required. Collimators are the main impedance contributors. Measurements with beam have revealed that the betatron coherent tune shifts were by about a factor of 2 higher with respect to the theoretical predictions based on the current model. Up to now the resistive wall impedance has been considered as the major impedance contribution for collimators. By carefully simulating their geometric impedance we show that for the graphite collimators with half-gaps higher than 10 mm the geometric impedance exceeds the resistive wall one. In turn, for the tungsten collimators the geometric impedance dominates for all used gap values. Hence, i...
Mechanisms of geometrical seismic attenuation
Directory of Open Access Journals (Sweden)
Igor B. Morozov
2011-07-01
Full Text Available In several recent reports, we have explained the frequency dependence of the apparent seismic quality-factor (Q observed in many studies according to the effects of geometrical attenuation, which was defined as the zero-frequency limit of the temporal attenuation coefficient. In particular, geometrical attenuation was found to be positive for most waves traveling within the lithosphere. Here, we present three theoretical models that illustrate the origin of this geometrical attenuation, and we investigate the causes of its preferential positive values. In addition, we discuss the physical basis and limitations of both the conventional and new attenuation models. For waves in media with slowly varying properties, geometrical attenuation is caused by variations in the wavefront curvature, which can be both positive (for defocusing and negative (for focusing. In media with velocity/density contrasts, incoherent reflectivity leads to geometrical-attenuation coefficients which are proportional to the mean squared reflectivity and are always positive. For «coherent» reflectivity, the geometrical attenuation is approximately zero, and the attenuation process can be described according to the concept of «scattering Q». However, the true meaning of this parameter is in describing the mean reflectivity within the medium, and not that of the traditional resonator quality factor known in mechanics. The general conclusion from these models is that non-zero and often positive levels of geometrical attenuation are common in realistic, heterogeneous media, both observationally and theoretically. When transformed into the conventional Q-factor form, this positive geometrical attenuation leads to Q values that quickly increase with frequency. These predictions show that the positive frequency-dependent Q observed in many datasets might represent artifacts of the transformations of the attenuation coefficients into Q.
Medicare Provider Data - Hospice Providers
U.S. Department of Health & Human Services — The Hospice Utilization and Payment Public Use File provides information on services provided to Medicare beneficiaries by hospice providers. The Hospice PUF...
DEFF Research Database (Denmark)
Andrade-Molina, Melissa
2015-01-01
Geometry within school mathematics is a form of geometry that leads to a restricted understanding of space. Despite the fact that it seeks to develop spatial abilities of students, and also provide them with a set of tools which can help them to solve any situation about real life, about real obj...
Geometric features of microtubule dynamics
Ponce-Dawson, Silvina; Pearson, John E.; Reynolds, William N.
Microtubules are long and stiff polymers that form the cytoskeleton of eucaryotic cells. They perform a series of tasks, such as determining the cell shape and providing a network of “rails” along which molecular motors transport organelles to different parts of the cell. They are particularly important during the process of cell division, since they provide the forces by which replicated chromosomes are segregated into what will be the two daughter cells. Microtubules are formed from a protein called tubulin and undergo a process called dynamic instability. In this paper we study, via numerical simulations of some simplified models, how the interaction between microtubules and the diffusion of free tubulin affects their spatial organization.
Geometric Phase Generated Optical Illusion
Yue, Fuyong; Zang, XiaoFei; Wen, Dandan; Li, Zile; Zhang, Chunmei; Liu, Huigang; Gerardot, Brian D.; Wang, Wei; Zheng, Guoxing; Chen, Xianzhong
2017-01-01
An optical illusion, such as ?Rubin?s vase?, is caused by the information gathered by the eye, which is processed in the brain to give a perception that does not tally with a physical measurement of the stimulus source. Metasurfaces are metamaterials of reduced dimensionality which have opened up new avenues for flat optics. The recent advancement in spin-controlled metasurface holograms has attracted considerate attention, providing a new method to realize optical illusions. We propose and e...
Geometrical and frequential watermarking scheme using similarities
Bas, Patrick; Chassery, Jean-Marc; Davoine, Franck
1999-04-01
Watermarking schemes are more and more robust to classical degradations. The NEC system developed by Cox, using both original and marked images, can detect the mark with a JPEG compression ratio of 30. Nevertheless a very simple geometric attack done by the program Stirmark can remove the watermark. Most of the present watermarking schemes only map a mark on the image without geometric reference and therefore are not robust to geometric transformation. We present a scheme based on the modification of a collage map (issued from a fractal code used in fractal compression). We add a mark introducing similarities in the image. The embedding of the mark is done by selection of points of interest supporting blocks on which similarities are hided. This selection is done by the Stephens-Harris detector. The similarity is embedded locally to be robust to cropping. Contrary to many schemes, the reference mark used for the detection comes from the marked image and thus undergoes geometrical distortions. The detection of the mark is done by searching interest blocks and their similarities. It does not use the original image and the robustness is guaranteed by a key. Our first results show that the similarities-based watermarking is quite robust to geometric transformation such as translations, rotations and cropping.
Similarity of Ferrosilicon Submerged Arc Furnaces With Different Geometrical Parameters
Directory of Open Access Journals (Sweden)
Machulec B.
2017-12-01
Full Text Available In order to determine reasons of unsatisfactory production output regarding one of the 12 MVA furnaces, a comparative analysis with a furnace of higher power that showed a markedly better production output was performed. For comparison of ferrosilicon furnaces with different geometrical parameters and transformer powers, the theory of physical similarity was applied. Geometrical, electrical and thermal parameters of the reaction zones are included in the comparative analysis. For furnaces with different geometrical parameters, it is important to ensure the same temperature conditions of the reaction zones. Due to diverse mechanisms of heat generation, different criteria for determination of thermal and electrical similarity for the upper and lower reaction zones were assumed contrary to other publications. The parameter c3 (Westly was assumed the similarity criterion for the upper furnace zones where heat is generated as a result of resistive heating while the parameter J1 (Jaccard was assumed the similarity criterion for the lower furnace zones where heat is generated due to arc radiation.
Edge anisotropy and the geometric perspective on flow networks
Molkenthin, Nora; Kutza, Hannes; Tupikina, Liubov; Marwan, Norbert; Donges, Jonathan F.; Feudel, Ulrike; Kurths, Jürgen; Donner, Reik V.
2017-03-01
Spatial networks have recently attracted great interest in various fields of research. While the traditional network-theoretic viewpoint is commonly restricted to their topological characteristics (often disregarding the existing spatial constraints), this work takes a geometric perspective, which considers vertices and edges as objects in a metric space and quantifies the corresponding spatial distribution and alignment. For this purpose, we introduce the concept of edge anisotropy and define a class of measures characterizing the spatial directedness of connections. Specifically, we demonstrate that the local anisotropy of edges incident to a given vertex provides useful information about the local geometry of geophysical flows based on networks constructed from spatio-temporal data, which is complementary to topological characteristics of the same flow networks. Taken both structural and geometric viewpoints together can thus assist the identification of underlying flow structures from observations of scalar variables.
Nanoscale geometric electric field enhancement in organic photovoltaics.
Pegg, Lara-Jane; Hatton, Ross A
2012-06-26
Generic design rules for electrode-organic semiconductor contacts that transcend specific materials are urgently required to guide the development of new electrodes and provide a framework for engineering this important class of interface. Herein a novel nanostructured window electrode is utilized in conjunction with three-dimensional electrostatic modeling to elucidate the importance of geometric electric field enhancement effects at the electrode interfaces in organic photovoltaics. The results of this study show that nanoscale protrusions at the electrode surfaces in organic photovoltaics dramatically improve the efficiency of photogenerated charge carrier extraction to the external circuit and that the origin of this improvement is the local amplification of the electrostatic field in the vicinity of said protrusions. This wholly geometric approach to engineering electrodes at the nanoscale is materials generic and can be employed to enhance the efficiency of charge carrier injection or extraction in a wide range of organic electronic devices.
The geometric nature of weights in real complex networks
Allard, Antoine; Serrano, M. Ángeles; García-Pérez, Guillermo; Boguñá, Marián
2017-01-01
The topology of many real complex networks has been conjectured to be embedded in hidden metric spaces, where distances between nodes encode their likelihood of being connected. Besides of providing a natural geometrical interpretation of their complex topologies, this hypothesis yields the recipe for sustainable Internet's routing protocols, sheds light on the hierarchical organization of biochemical pathways in cells, and allows for a rich characterization of the evolution of international trade. Here we present empirical evidence that this geometric interpretation also applies to the weighted organization of real complex networks. We introduce a very general and versatile model and use it to quantify the level of coupling between their topology, their weights and an underlying metric space. Our model accurately reproduces both their topology and their weights, and our results suggest that the formation of connections and the assignment of their magnitude are ruled by different processes.
On the relationship between topological and geometric defects
Griffin, Sinéad M.; Spaldin, Nicola A.
2017-08-01
The study of topology in solids is undergoing a renaissance following renewed interest in the properties of ferroic domain walls as well as recent discoveries regarding skyrmionic lattices. Each of these systems possess a property that is ‘protected’ in a symmetry sense, and is defined rigorously using a branch of mathematics known as topology. In this article we review the formal definition of topological defects as they are classified in terms of homotopy theory, and discuss the precise symmetry-breaking conditions that lead to their formation. We distinguish topological defects from defects that arise from the details of the stacking or structure of the material but are not protected by symmetry, and we propose the term ‘geometric defects’ to describe the latter. We provide simple material examples of both topological and geometric defect types, and discuss the implications of the classification on the resulting material properties.
Developments and retrospectives in Lie theory geometric and analytic methods
Penkov, Ivan; Wolf, Joseph
2014-01-01
This volume reviews and updates a prominent series of workshops in representation/Lie theory, and reflects the widespread influence of those workshops in such areas as harmonic analysis, representation theory, differential geometry, algebraic geometry, and mathematical physics. Many of the contributors have had leading roles in both the classical and modern developments of Lie theory and its applications. This Work, entitled Developments and Retrospectives in Lie Theory, and comprising 26 articles, is organized in two volumes: Algebraic Methods and Geometric and Analytic Methods. This is the Geometric and Analytic Methods volume. The Lie Theory Workshop series, founded by Joe Wolf and Ivan Penkov and joined shortly thereafter by Geoff Mason, has been running for over two decades. Travel to the workshops has usually been supported by the NSF, and local universities have provided hospitality. The workshop talks have been seminal in describing new perspectives in the field covering broad areas of current re...
Beyond teaching language: Towards terminological primacy in learners’ geometric conceptualisation
Directory of Open Access Journals (Sweden)
Humphrey U. Atebe
2010-07-01
Full Text Available This paper reports on a specific aspect of a broader geometry conceptualisation study that sought to explore and explicate learners’ knowledge of basic geometric terminology in selected Nigerian and South African high schools. It is framed by the notion that students’ acquisition of the correct terminology in school geometry is important for their success in the subject. The original study further aimed to determine the relationship that might exist between a learner’s ability in verbal geometry terminology tasks and his/her ability in visual geometry terminology tasks. A total of 144 learners (72 each from South Africa and Nigeria were selected for the study, using both the stratified and the fish‐bowl sampling techniques. A questionnaire consisting of a sixty‐item multiple‐choice objective test provided the data for the study. An overall percentage mean score of 44,17% obtained in the test indicated that learners in this study had only a limited knowledge of basic geometric terminology. The Nigerian subsample in the study had a weaker understanding of basic geometric terminology than their South African counterparts. Importantly, there were high positive correlations between participants’ ability in verbal geometry terminology tasks and their ability in visual geometry terminology tasks. These results are consistent with those of several earlier studies, and provide a reasonably firm basis for certain recommendations to be made.
Development of a Geoid Model by Geometric Method
Mishra, Upendra Nath; Ghosh, Jayanta Kumar
2017-12-01
Engineering projects require orthometric heights of points where as Global Navigation Satellite System (GNSS) provide height above ellipsoid. Thus, to make use of GNSS in engineering surveying, the relationship between ellipsoidal height and orthometric height as a function of position needs to be established through geoid modeling. In this study, an attempt has been made to develop a geoid model using the geometric method. Observations were taken in a network of sixteen stations spread over 600 km2 around Dehra Dun, India. GPS observations were taken using dual frequency geodetic GPS receivers and leveling done using digital levels with 0.1 mm accuracy. Orthometric height of stations from developed model have been found to be near to those from field levelling which is considered most accurate. Further, the values have been compared with those obtained from the recent GOCE-GRACE-LAGEOS geoid model EIGEN6C3stat. It has been found that the geometric model provides far better accuracy than that obtained from the global geoid model. Therefore, it can be concluded that the geometric method of geoid modeling can better be used for reduction of GPS observed ellipsoidal height to orthometric height in a local area. This model may gainfully be employed in a project area as a substitute for densification of leveling lines, thereby reducing the project cost substantially.
Wolter, Andrä
2009-01-01
During the last five years higher education research in Germany seems to be in a significant upturn. This is a side effect partly of the obvious boom of empirical educational research in general and partly of the reform movement that has affected the German higher education system since middle of the 1990s. The demand for data in the field of higher education will increase considerably in future. The available data infrastructure for higher education research in Germany consists of two comple...
Hermite-Hadamard type fractional integral inequalities for geometric-geometric convex functions
Directory of Open Access Journals (Sweden)
Shenda Liu
2015-05-01
Full Text Available By utilizing two fractional integral identities and elementaryinequalities via geometric-geometric (GG for short convex functions, we derive new type Hermite-Hadamard inequalities involving Hadamard fractional integrals. Some applications to special means of real numbers are given.
Estimating motors from a variety of geometric data in 3D conformal geometric algebra
Valkenburg, R.; Dorst, L.; Dorst, L.; Lasenby, J.
2011-01-01
The motion rotors, or motors, are used to model Euclidean motion in 3D conformal geometric algebra. In this chapter we present a technique for estimating the motor which best transforms one set of noisy geometric objects onto another. The technique reduces to an eigenrotator problem and has some
The Geometric Phase of Stock Trading.
Directory of Open Access Journals (Sweden)
Claudio Altafini
Full Text Available Geometric phases describe how in a continuous-time dynamical system the displacement of a variable (called phase variable can be related to other variables (shape variables undergoing a cyclic motion, according to an area rule. The aim of this paper is to show that geometric phases can exist also for discrete-time systems, and even when the cycles in shape space have zero area. A context in which this principle can be applied is stock trading. A zero-area cycle in shape space represents the type of trading operations normally carried out by high-frequency traders (entering and exiting a position on a fast time-scale, while the phase variable represents the cash balance of a trader. Under the assumption that trading impacts stock prices, even zero-area cyclic trading operations can induce geometric phases, i.e., profits or losses, without affecting the stock quote.
MM Algorithms for Geometric and Signomial Programming.
Lange, Kenneth; Zhou, Hua
2014-02-01
This paper derives new algorithms for signomial programming, a generalization of geometric programming. The algorithms are based on a generic principle for optimization called the MM algorithm. In this setting, one can apply the geometric-arithmetic mean inequality and a supporting hyperplane inequality to create a surrogate function with parameters separated. Thus, unconstrained signomial programming reduces to a sequence of one-dimensional minimization problems. Simple examples demonstrate that the MM algorithm derived can converge to a boundary point or to one point of a continuum of minimum points. Conditions under which the minimum point is unique or occurs in the interior of parameter space are proved for geometric programming. Convergence to an interior point occurs at a linear rate. Finally, the MM framework easily accommodates equality and inequality constraints of signomial type. For the most important special case, constrained quadratic programming, the MM algorithm involves very simple updates.
An Underlying Geometrical Manifold for Hamiltonian Mechanics
Horwitz, L P; Levitan, J; Lewkowicz, M
2015-01-01
We show that there exists an underlying manifold with a conformal metric and compatible connection form, and a metric type Hamiltonian (which we call the geometrical picture) that can be put into correspondence with the usual Hamilton-Lagrange mechanics. The requirement of dynamical equivalence of the two types of Hamiltonians, that the momenta generated by the two pictures be equal for all times, is sufficient to determine an expansion of the conformal factor, defined on the geometrical coordinate representation, in its domain of analyticity with coefficients to all orders determined by functions of the potential of the Hamilton-Lagrange picture, defined on the Hamilton-Lagrange coordinate representation, and its derivatives. Conversely, if the conformal function is known, the potential of a Hamilton-Lagrange picture can be determined in a similar way. We show that arbitrary local variations of the orbits in the Hamilton-Lagrange picture can be generated by variations along geodesics in the geometrical pictu...
Normed algebras and the geometric series test
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Robert Kantrowitz
2017-11-01
Full Text Available The purpose of this article is to survey a class of normed algebras that share many central features of Banach algebras, save for completeness. The likeness of these algebras to Banach algebras derives from the fact that the geometric series test is valid, whereas the lack of completeness points to the failure of the absolute convergence test for series in the algebra. Our main result is a compendium of conditions that are all equivalent to the validity of the geometric series test for commutative unital normed algebras. Several examples in the final section showcase some incomplete normed algebras for which the geometric series test is valid, and still others for which it is not.
Geometric optimization and sums of algebraic functions
Vigneron, Antoine E.
2014-01-01
We present a new optimization technique that yields the first FPTAS for several geometric problems. These problems reduce to optimizing a sum of nonnegative, constant description complexity algebraic functions. We first give an FPTAS for optimizing such a sum of algebraic functions, and then we apply it to several geometric optimization problems. We obtain the first FPTAS for two fundamental geometric shape-matching problems in fixed dimension: maximizing the volume of overlap of two polyhedra under rigid motions and minimizing their symmetric difference. We obtain the first FPTAS for other problems in fixed dimension, such as computing an optimal ray in a weighted subdivision, finding the largest axially symmetric subset of a polyhedron, and computing minimum-area hulls.
The Geometric Phase of Stock Trading.
Altafini, Claudio
2016-01-01
Geometric phases describe how in a continuous-time dynamical system the displacement of a variable (called phase variable) can be related to other variables (shape variables) undergoing a cyclic motion, according to an area rule. The aim of this paper is to show that geometric phases can exist also for discrete-time systems, and even when the cycles in shape space have zero area. A context in which this principle can be applied is stock trading. A zero-area cycle in shape space represents the type of trading operations normally carried out by high-frequency traders (entering and exiting a position on a fast time-scale), while the phase variable represents the cash balance of a trader. Under the assumption that trading impacts stock prices, even zero-area cyclic trading operations can induce geometric phases, i.e., profits or losses, without affecting the stock quote.
The geometric phase controls ultracold chemistry.
Kendrick, B K; Hazra, Jisha; Balakrishnan, N
2015-07-30
The geometric phase is shown to control the outcome of an ultracold chemical reaction. The control is a direct consequence of the sign change on the interference term between two scattering pathways (direct and looping), which contribute to the reactive collision process in the presence of a conical intersection (point of degeneracy between two Born-Oppenheimer electronic potential energy surfaces). The unique properties of the ultracold energy regime lead to an effective quantization of the scattering phase shift enabling maximum constructive or destructive interference between the two pathways. By taking the O+OH→H+O2 reaction as an illustrative example, it is shown that inclusion of the geometric phase modifies ultracold reaction rates by nearly two orders of magnitude. Interesting experimental control possibilities include the application of external electric and magnetic fields that might be used to exploit the geometric phase effect reported here and experimentally switch on or off the reactivity.
Connecting Information Geometry and Geometric Mechanics
Directory of Open Access Journals (Sweden)
Melvin Leok
2017-09-01
Full Text Available The divergence function in information geometry, and the discrete Lagrangian in discrete geometric mechanics each induce a differential geometric structure on the product manifold Q × Q . We aim to investigate the relationship between these two objects, and the fundamental role that duality, in the form of Legendre transforms, plays in both fields. By establishing an analogy between these two approaches, we will show how a fruitful cross-fertilization of techniques may arise from switching formulations based on the cotangent bundle T * Q (as in geometric mechanics and the tangent bundle T Q (as in information geometry. In particular, we establish, through variational error analysis, that the divergence function agrees with the exact discrete Lagrangian up to third order if and only if Q is a Hessian manifold.
Quantum Critical Scaling of the Geometric Tensors
Campos Venuti, Lorenzo; Zanardi, Paolo
2007-08-01
Berry phases and the quantum-information theoretic notion of fidelity have been recently used to analyze quantum phase transitions from a geometrical perspective. In this Letter we unify these two approaches showing that the underlying mechanism is the critical singular behavior of a complex tensor over the Hamiltonian parameter space. This is achieved by performing a scaling analysis of this quantum geometric tensor in the vicinity of the critical points. In this way most of the previous results are understood on general grounds and new ones are found. We show that criticality is not a sufficient condition to ensure superextensive divergence of the geometric tensor, and state the conditions under which this is possible. The validity of this analysis is further checked by exact diagonalization of the spin-1/2 XXZ Heisenberg chain.
Usunáriz Balanzategui, Ubaldo; Usunáriz Sala, Ignacio
2012-01-01
Este libro, Problemas de Geometría, junto con otros dos, Problemas de Matemáticas y Problemas de Geometría Analítica y Diferencial, están dedicados a la presentación y resolución de problemas que se planteaban hace unas décadas, en la preparación para ingreso en las carreras de ingeniería técnica superior. Incluye 744 problemas que se presentan en dos grandes grupos: • Geometría del plano, con 523 problemas referentes a lugares geométricos, rectas, ángulos, triángulos y su construcción, cuadr...
Primary School Teacher Candidates' Geometric Habits of Mind
Köse, Nilu¨fer Y.; Tanisli, Dilek
2014-01-01
Geometric habits of mind are productive ways of thinking that support learning and using geometric concepts. Identifying primary school teacher candidates' geometric habits of mind is important as they affect the development of their future students' geometric thinking. Therefore, this study attempts to determine primary school teachers' geometric…
Graba, M.
2017-12-01
This paper provides a comparative analysis of selected parameters of the geometric constraints for cracked plates subjected to tension. The results of three-dimensional numerical calculations were used to assess the distribution of these parameters around the crack front and their changes along the crack front. The study also involved considering the influence of the external load on the averaged values of the parameters of the geometric constraints as well as the relationship between the material constants and the level of the geometric constraints contributing to the actual fracture toughness for certain geometries.
Ratschek, H
2003-01-01
This undergraduate and postgraduate text will familiarise readers with interval arithmetic and related tools to gain reliable and validated results and logically correct decisions for a variety of geometric computations plus the means for alleviating the effects of the errors. It also considers computations on geometric point-sets, which are neither robust nor reliable in processing with standard methods. The authors provide two effective tools for obtaining correct results: (a) interval arithmetic, and (b) ESSA the new powerful algorithm which improves many geometric computations and makes th
Linearization: Geometric, Complex, and Conditional
Directory of Open Access Journals (Sweden)
Asghar Qadir
2012-01-01
Full Text Available Lie symmetry analysis provides a systematic method of obtaining exact solutions of nonlinear (systems of differential equations, whether partial or ordinary. Of special interest is the procedure that Lie developed to transform scalar nonlinear second-order ordinary differential equations to linear form. Not much work was done in this direction to start with, but recently there have been various developments. Here, first the original work of Lie (and the early developments on it, and then more recent developments based on geometry and complex analysis, apart from Lie’s own method of algebra (namely, Lie group theory, are reviewed. It is relevant to mention that much of the work is not linearization but uses the base of linearization.
Geometric nonlinear functional analysis volume 1
Benyamini, Yoav
1999-01-01
The book presents a systematic and unified study of geometric nonlinear functional analysis. This area has its classical roots in the beginning of the twentieth century and is now a very active research area, having close connections to geometric measure theory, probability, classical analysis, combinatorics, and Banach space theory. The main theme of the book is the study of uniformly continuous and Lipschitz functions between Banach spaces (e.g., differentiability, stability, approximation, existence of extensions, fixed points, etc.). This study leads naturally also to the classification of
Geometric phase morphology of Jones matrices.
Lopez-Mago, Dorilian; Canales-Benavides, Arturo; Hernandez-Aranda, Raul I; Gutiérrez-Vega, Julio C
2017-07-15
We demonstrate an innovative technique based on the Pancharatnam-Berry phase that can be used to determine whether an optical system characterized by a Jones matrix is homogeneous or inhomogeneous, containing orthogonal or nonorthogonal eigenpolarizations, respectively. Homogeneous systems have a symmetric geometric phase morphology showing line dislocations and sets of polarization states with an equal geometric phase. In contrast, the morphology of inhomogeneous systems exhibits phase singularities, where the Pancharatnam-Berry phase is undetermined. The results show an alternative to extract polarization properties such as diattenuation and retardance, and can be used to study the transformation of space-variant polarized beams.
Workshop on Topology and Geometric Group Theory
Fowler, James; Lafont, Jean-Francois; Leary, Ian
2016-01-01
This book presents articles at the interface of two active areas of research: classical topology and the relatively new field of geometric group theory. It includes two long survey articles, one on proofs of the Farrell–Jones conjectures, and the other on ends of spaces and groups. In 2010–2011, Ohio State University (OSU) hosted a special year in topology and geometric group theory. Over the course of the year, there were seminars, workshops, short weekend conferences, and a major conference out of which this book resulted. Four other research articles complement these surveys, making this book ideal for graduate students and established mathematicians interested in entering this area of research.
Classical light beams and geometric phases.
Mukunda, N; Chaturvedi, S; Simon, R
2014-06-01
We present a study of geometric phases in classical wave and polarization optics using the basic mathematical framework of quantum mechanics. Important physical situations taken from scalar wave optics, pure polarization optics, and the behavior of polarization in the eikonal or ray limit of Maxwell's equations in a transparent medium are considered. The case of a beam of light whose propagation direction and polarization state are both subject to change is dealt with, attention being paid to the validity of Maxwell's equations at all stages. Global topological aspects of the space of all propagation directions are discussed using elementary group theoretical ideas, and the effects on geometric phases are elucidated.
The geometric structure of the Landau bands
Brüning, J; Geyler, V
2002-01-01
We have proposed a semiclassical explanation of the geometric structure of the spectrum for the two-dimensional Landau Hamiltonian with a two-periodic electric field without any additional assumptions on the potential. Applying an iterative averaging procedure we approximately, with any degree of accuracy, separate variables and describe a given Landau band as the spectrum of a Harper-like operator. The quantized Reeb graph for such an operator is used to obtain the following structure of the Landau band: localized states on the band wings and extended states near the middle of the band. Our approach also shows that different Landau bands have different geometric structure.
Cormann, Mirko; Caudano, Yves
2017-07-01
We express modular and weak values of observables of three- and higher-level quantum systems in their polar form. The Majorana representation of N-level systems in terms of symmetric states of N - 1 qubits provides us with a description on the Bloch sphere. With this geometric approach, we find that modular and weak values of observables of N-level quantum systems can be factored in N - 1 contributions. Their modulus is determined by the product of N - 1 ratios involving projection probabilities between qubits, while their argument is deduced from a sum of N - 1 solid angles on the Bloch sphere. These theoretical results allow us to study the geometric origin of the quantum phase discontinuity around singularities of weak values in three-level systems. We also analyze the three-box paradox (Aharonov and Vaidman 1991 J. Phys. A: Math. Gen. 24 2315-28) from the point of view of a bipartite quantum system. In the Majorana representation of this paradox, an observer comes to opposite conclusions about the entanglement state of the particles that were successfully pre- and postselected.
Geometric approach to string analysis for biosequence classification.
Brimkov, Boris
2014-10-23
Tools that effectively analyze and compare sequences are of great importance in various areas of applied computational research, especially in the framework of molecular biology. In the present paper, we introduce simple geometric criteria based on the notion of string linearity and use them to compare DNA sequences of various organisms, as well as to distinguish them from random sequences. Several other theoretical and statistical results are outlined as well. Our experiments reveal a substantial difference between biosequences and random sequences – the former having much higher deviation from linearity than the latter – as well as a general trend of increasing deviation from linearity between primitive and biologically complex organisms.
Geometrical themes inspired by the n-body problem
Herrera, Haydeé; Herrera, Rafael
2018-01-01
Presenting a selection of recent developments in geometrical problems inspired by the N-body problem, these lecture notes offer a variety of approaches to study them, ranging from variational to dynamical, while developing new insights, making geometrical and topological detours, and providing historical references. A. Guillot’s notes aim to describe differential equations in the complex domain, motivated by the evolution of N particles moving on the plane subject to the influence of a magnetic field. Guillot studies such differential equations using different geometric structures on complex curves (in the sense of W. Thurston) in order to find isochronicity conditions. R. Montgomery’s notes deal with a version of the planar Newtonian three-body equation. Namely, he investigates the problem of whether every free homotopy class is realized by a periodic geodesic. The solution involves geometry, dynamical systems, and the McGehee blow-up. A novelty of the approach is the use of energy-balance in order t...
Fractal supersymmetric QM, Geometric Probability and the Riemann Hypothesis
Castro, C
2004-01-01
The Riemann's hypothesis (RH) states that the nontrivial zeros of the Riemann zeta-function are of the form $ s_n =1/2+i\\lambda_n $. Earlier work on the RH based on supersymmetric QM, whose potential was related to the Gauss-Jacobi theta series, allows to provide the proper framework to construct the well defined algorithm to compute the probability to find a zero (an infinity of zeros) in the critical line. Geometric probability theory furnishes the answer to the very difficult question whether the probability that the RH is true is indeed equal to unity or not. To test the validity of this geometric probabilistic framework to compute the probability if the RH is true, we apply it directly to the the hyperbolic sine function $ \\sinh (s) $ case which obeys a trivial analog of the RH (the HSRH). Its zeros are equally spaced in the imaginary axis $ s_n = 0 + i n \\pi $. The geometric probability to find a zero (and an infinity of zeros) in the imaginary axis is exactly unity. We proceed with a fractal supersymme...
Geometric Stability and Lens Decentering in Compact Digital Cameras
Sanz-Ablanedo, Enoc; Rodríguez-Pérez, José Ramón; Armesto, Julia; Taboada, María Flor Álvarez
2010-01-01
A study on the geometric stability and decentering present in sensor-lens systems of six identical compact digital cameras has been conducted. With regard to geometrical stability, the variation of internal geometry parameters (principal distance, principal point position and distortion parameters) was considered. With regard to lens decentering, the amount of radial and tangential displacement resulting from decentering distortion was related with the precision of the camera and with the offset of the principal point from the geometric center of the sensor. The study was conducted with data obtained after 372 calibration processes (62 per camera). The tests were performed for each camera in three situations: during continuous use of the cameras, after camera power off/on and after the full extension and retraction of the zoom-lens. Additionally, 360 new calibrations were performed in order to study the variation of the internal geometry when the camera is rotated. The aim of this study was to relate the level of stability and decentering in a camera with the precision and quality that can be obtained. An additional goal was to provide practical recommendations about photogrammetric use of such cameras. PMID:22294886
A geometric rationale for invariance, covariance and constitutive relations
Romano, Giovanni; Barretta, Raffaele; Diaco, Marina
2017-09-01
There are, in each branch of science, statements which, expressed in ambiguous or even incorrect but seemingly friendly manner, were repeated for a long time and eventually became diffusely accepted. Objectivity of physical fields and of their time rates and frame indifference of constitutive relations are among such notions. A geometric reflection on the description of frame changes as spacetime automorphisms, on induced push-pull transformations and on proper physico-mathematical definitions of material, spatial and spacetime tensor fields and of their time-derivatives along the motion, is here carried out with the aim of pointing out essential notions and of unveiling false claims. Theoretical and computational aspects of nonlinear continuum mechanics, and especially those pertaining to constitutive relations, involving material fields and their time rates, gain decisive conceptual and operative improvement from a proper geometric treatment. Outcomes of the geometric analysis are frame covariance of spacetime velocity, material stretching and material spin. A univocal and frame-covariant tool for evaluation of time rates of material fields is provided by the uc(Lie) derivative along the motion. The postulate of frame covariance of material fields is assessed to be a natural physical requirement which cannot interfere with the formulation of constitutive laws, with claims of the contrary stemming from an improper imposition of equality in place of equivalence.
Research on Geometric Calibration of Spaceborne Linear Array Whiskbroom Camera.
Sheng, Qinghong; Wang, Qi; Xiao, Hui; Wang, Qing
2018-01-16
The geometric calibration of a spaceborne thermal-infrared camera with a high spatial resolution and wide coverage can set benchmarks for providing an accurate geographical coordinate for the retrieval of land surface temperature. The practice of using linear array whiskbroom Charge-Coupled Device (CCD) arrays to image the Earth can help get thermal-infrared images of a large breadth with high spatial resolutions. Focusing on the whiskbroom characteristics of equal time intervals and unequal angles, the present study proposes a spaceborne linear-array-scanning imaging geometric model, whilst calibrating temporal system parameters and whiskbroom angle parameters. With the help of the YG-14-China's first satellite equipped with thermal-infrared cameras of high spatial resolution-China's Anyang Imaging and Taiyuan Imaging are used to conduct an experiment of geometric calibration and a verification test, respectively. Results have shown that the plane positioning accuracy without ground control points (GCPs) is better than 30 pixels and the plane positioning accuracy with GCPs is better than 1 pixel.
Size, shape, and form: concepts of allometry in geometric morphometrics.
Klingenberg, Christian Peter
2016-06-01
Allometry refers to the size-related changes of morphological traits and remains an essential concept for the study of evolution and development. This review is the first systematic comparison of allometric methods in the context of geometric morphometrics that considers the structure of morphological spaces and their implications for characterizing allometry and performing size correction. The distinction of two main schools of thought is useful for understanding the differences and relationships between alternative methods for studying allometry. The Gould-Mosimann school defines allometry as the covariation of shape with size. This concept of allometry is implemented in geometric morphometrics through the multivariate regression of shape variables on a measure of size. In the Huxley-Jolicoeur school, allometry is the covariation among morphological features that all contain size information. In this framework, allometric trajectories are characterized by the first principal component, which is a line of best fit to the data points. In geometric morphometrics, this concept is implemented in analyses using either Procrustes form space or conformation space (the latter also known as size-and-shape space). Whereas these spaces differ substantially in their global structure, there are also close connections in their localized geometry. For the model of small isotropic variation of landmark positions, they are equivalent up to scaling. The methods differ in their emphasis and thus provide investigators with flexible tools to address specific questions concerning evolution and development, but all frameworks are logically compatible with each other and therefore unlikely to yield contradictory results.
A geometric rationale for invariance, covariance and constitutive relations
Romano, Giovanni; Barretta, Raffaele; Diaco, Marina
2018-01-01
There are, in each branch of science, statements which, expressed in ambiguous or even incorrect but seemingly friendly manner, were repeated for a long time and eventually became diffusely accepted. Objectivity of physical fields and of their time rates and frame indifference of constitutive relations are among such notions. A geometric reflection on the description of frame changes as spacetime automorphisms, on induced push-pull transformations and on proper physico-mathematical definitions of material, spatial and spacetime tensor fields and of their time-derivatives along the motion, is here carried out with the aim of pointing out essential notions and of unveiling false claims. Theoretical and computational aspects of nonlinear continuum mechanics, and especially those pertaining to constitutive relations, involving material fields and their time rates, gain decisive conceptual and operative improvement from a proper geometric treatment. Outcomes of the geometric analysis are frame covariance of spacetime velocity, material stretching and material spin. A univocal and frame-covariant tool for evaluation of time rates of material fields is provided by the Lie derivative along the motion. The postulate of frame covariance of material fields is assessed to be a natural physical requirement which cannot interfere with the formulation of constitutive laws, with claims of the contrary stemming from an improper imposition of equality in place of equivalence.
Geometric Model of Black Hole Quantum N-portrait, Extradimensions and Thermodynamics
Directory of Open Access Journals (Sweden)
Antonia M. Frassino
2016-05-01
Full Text Available Recently a short scale modified black hole metric, known as holographic metric, has been proposed in order to capture the self-complete character of gravity. In this paper we show that such a metric can reproduce some geometric features expected from the quantum N-portrait beyond the semi-classical limit. We show that for a generic N this corresponds to having an effective energy momentum tensor in Einstein equations or, equivalently, non-local terms in the gravity action. We also consider the higher dimensional extension of the metric and the case of an AdS cosmological term. We provide a detailed thermodynamic analysis of both cases, with particular reference to the repercussions on the Hawking-Page phase transition.
Chen, Chenglong; Ni, Jiangqun; Shen, Zhaoyi; Shi, Yun Qing
2017-06-01
Geometric transformations, such as resizing and rotation, are almost always needed when two or more images are spliced together to create convincing image forgeries. In recent years, researchers have developed many digital forensic techniques to identify these operations. Most previous works in this area focus on the analysis of images that have undergone single geometric transformations, e.g., resizing or rotation. In several recent works, researchers have addressed yet another practical and realistic situation: successive geometric transformations, e.g., repeated resizing, resizing-rotation, rotation-resizing, and repeated rotation. We will also concentrate on this topic in this paper. Specifically, we present an in-depth analysis in the frequency domain of the second-order statistics of the geometrically transformed images. We give an exact formulation of how the parameters of the first and second geometric transformations influence the appearance of periodic artifacts. The expected positions of characteristic resampling peaks are analytically derived. The theory developed here helps to address the gap left by previous works on this topic and is useful for image security and authentication, in particular, the forensics of geometric transformations in digital images. As an application of the developed theory, we present an effective method that allows one to distinguish between the aforementioned four different processing chains. The proposed method can further estimate all the geometric transformation parameters. This may provide useful clues for image forgery detection.
Geometric and Road Environmental Effects against Total Number of Traffic Accidents in Kendari
Kurdin, M. Akbar; Welendo, La; Annisa, Nur
2017-05-01
From the large number of traffic accidents that occurred, the carrying of Kendari as the biggest contributor to accidents in the Southeast. The number of accidents in Kendari row since 2011 was recorded at 18 accidents due to the influence of geometric road, in 2012 registered at 13 accident and in 2013 amounted to 6 accidents, with accident data because of the influence Geometric recorded for 3 consecutive years the biggest contributor to accidents because of the influence of geometric is Abeli districts. This study aimed to determine the road which common point of accident-prone (Black spot) in Kecamatan Abeli as accident-prone areas in Kendari, analyze the influence of geometric and road environment against accidents on roads in Kecamatan Abeli, provide alternative treatment based on the causes of accidents on the location of the accident-prone points (blackspot) to reduce the rate of traffic accidents. From the results of a study of 6 curve the accident-prone locations, that the curve I, II, and VI is the “Black Spot” influenced by the amount and condition of traffic accidents, while at the curve II, a traffic accident that occurred also be caused by unsafe geometric where the type of geometric should be changed from Spiral-Spiral type to Spiral-Circle-Spiral type. This indicates geometric effect on the number of accidents.
Geometric Abstract Art and Public Health Data
Centers for Disease Control (CDC) Podcasts
2016-10-18
Dr. Salaam Semaan, a CDC behavioral scientist, discusses the similarities between geometric abstract art and public health data analysis. Created: 10/18/2016 by National Center for Emerging and Zoonotic Infectious Diseases (NCEZID). Date Released: 10/18/2016.
Geometric phase topology in weak measurement
Samlan, C. T.; Viswanathan, Nirmal K.
2017-12-01
The geometric phase visualization proposed by Bhandari (R Bhandari 1997 Phys. Rep. 281 1–64) in the ellipticity-ellipse orientation basis of the polarization ellipse of light is implemented to understand the geometric aspects of weak measurement. The weak interaction of a pre-selected state, acheived via spin-Hall effect of light (SHEL), results in a spread in the polarization ellipticity (η) or ellipse orientation (χ) depending on the resulting spatial or angular shift, respectively. The post-selection leads to the projection of the η spread in the complementary χ basis results in the appearance of a geometric phase with helical phase topology in the η ‑ χ parameter space. By representing the weak measurement on the Poincaré sphere and using Jones calculus, the complex weak value and the geometric phase topology are obtained. This deeper understanding of the weak measurement process enabled us to explore the techniques’ capabilities maximally, as demonstrated via SHEL in two examples—external reflection at glass-air interface and transmission through a tilted half-wave plate.
Robust Geometric Control of a Distillation Column
DEFF Research Database (Denmark)
Kymmel, Mogens; Andersen, Henrik Weisberg
1987-01-01
A frequency domain method, which makes it possible to adjust multivariable controllers with respect to both nominal performance and robustness, is presented. The basic idea in the approach is that the designer assigns objectives such as steady-state tracking, maximum resonance peaks, bandwidth, m...... is used to examine and improve geometric control of a binary distillation column....
Pancharatnam geometric phase originating from successive partial ...
Indian Academy of Sciences (India)
Abstract. The spin of a polarized neutron beam subjected to a partial projection in another direction, traces a geodesic arc in the 2-sphere ray space. We delineate the geometric phase resulting from two successive partial projections on a general quantal state and derive the direction and strength of the third partial ...
On Arithmetic-Geometric-Mean Polynomials
Griffiths, Martin; MacHale, Des
2017-01-01
We study here an aspect of an infinite set "P" of multivariate polynomials, the elements of which are associated with the arithmetic-geometric-mean inequality. In particular, we show in this article that there exist infinite subsets of probability "P" for which every element may be expressed as a finite sum of squares of real…
Impossible Geometric Constructions: A Calculus Writing Project
Awtrey, Chad
2013-01-01
This article discusses a writing project that offers students the opportunity to solve one of the most famous geometric problems of Greek antiquity; namely, the impossibility of trisecting the angle [pi]/3. Along the way, students study the history of Greek geometry problems as well as the life and achievements of Carl Friedrich Gauss. Included is…
Geometric singular perturbation theory in biological practice
Hek, G.
2010-01-01
Geometric singular perturbation theory is a useful tool in the analysis of problems with a clear separation in time scales. It uses invariant manifolds in phase space in order to understand the global structure of the phase space or to construct orbits with desired properties. This paper explains
Geometrical origin of supersymmetric gauge theories
Energy Technology Data Exchange (ETDEWEB)
Caicedo, S.; Gambini, R.
1989-01-15
We show that the kinematical properties of any supersymmetric gauge theory may be obtained by mapping a geometric group structure of loops in superspace into some particular Lie group. The underlying group structure of the usual constrained supergauge theories turns out to be the group of even (bosonic) loops.
The geometrical significance of the Laplacian
Styer, Daniel F.
2015-12-01
The Laplacian operator can be defined, not only as a differential operator, but also through its averaging properties. Such a definition lends geometric significance to the operator: a large Laplacian at a point reflects a "nonconformist" (i.e., different from average) character for the function there. This point of view is used to motivate the wave equation for a drumhead.
Geometric Algorithms for Part Orienting and Probing
Panahi, F.
2015-01-01
In this thesis, detailed solutions are presented to several problems dealing with geometric shape and orientation of an object in the field of robotics and automation. We first have considered a general model for shape variations that allows variation along the entire boundary of an object, both in
Geometric Interpretations of Some Psychophysical Results.
Levine, Michael V.
A theory of psychophysics is discussed that enlarges the classical theory in three general ways: (1) the multidimensional nature of perception is made explicit; (2) the transformations of the theory are interpreted geometrically; and (3) attributes are distinguished from sensations and only partially ordered. It is shown that, with the enlarged…
Spherical projections and liftings in geometric tomography
DEFF Research Database (Denmark)
Goodey, Paul; Kiderlen, Markus; Weil, Wolfgang
2011-01-01
We consider a variety of integral transforms arising in Geometric Tomography. It will be shown that these can be put into a common framework using spherical projection and lifting operators. These operators will be applied to support functions and surface area measures of convex bodies and to rad...
A graph spectrum based geometric biclustering algorithm.
Wang, Doris Z; Yan, Hong
2013-01-21
Biclustering is capable of performing simultaneous clustering on two dimensions of a data matrix and has many applications in pattern classification. For example, in microarray experiments, a subset of genes is co-expressed in a subset of conditions, and biclustering algorithms can be used to detect the coherent patterns in the data for further analysis of function. In this paper, we present a graph spectrum based geometric biclustering (GSGBC) algorithm. In the geometrical view, biclusters can be seen as different linear geometrical patterns in high dimensional spaces. Based on this, the modified Hough transform is used to find the Hough vector (HV) corresponding to sub-bicluster patterns in 2D spaces. A graph can be built regarding each HV as a node. The graph spectrum is utilized to identify the eigengroups in which the sub-biclusters are grouped naturally to produce larger biclusters. Through a comparative study, we find that the GSGBC achieves as good a result as GBC and outperforms other kinds of biclustering algorithms. Also, compared with the original geometrical biclustering algorithm, it reduces the computing time complexity significantly. We also show that biologically meaningful biclusters can be identified by our method from real microarray gene expression data. Copyright © 2012 Elsevier Ltd. All rights reserved.
Robust topology optimization accounting for geometric imperfections
DEFF Research Database (Denmark)
Schevenels, M.; Jansen, M.; Lombaert, Geert
2013-01-01
performance. As a consequence, the actual structure may be far from optimal. In this paper, a robust approach to topology optimization is presented, taking into account two types of geometric imperfections: variations of (1) the crosssections and (2) the locations of structural elements. The first type...
Symbolic Constraints in Constructive Geometric Constraint Solving
Hoffmann, Christoph M.; Joan-Arinyo, Robert
1997-01-01
In design and manufacturing applications, users of computer aided design systems want to define relationships between dimension variables, since such relationships express design intent very flexibly. This work reports on a technique developed to enhance a class of constructive geometric constraint solvers with the capability of managing functional relationships between dimension variables. The method is shown to be correct.
Evaluation of Design Methods for Geometric Control
DEFF Research Database (Denmark)
Kymmel, Mogens; Beran, M.; Foldager, L.
1985-01-01
Geometric control can produce desirable control by decoupling the input disturbances from the selected output variables. The basic principle for this method was originally introduced by Wonham. The mathematical complexity involved, however, makes the method very hard to get accepted by the chemic...... of the designer, transparency, computer demand, and potential for pole shift....
Left ventricular hypertrophy, geometric patterns and clinical ...
African Journals Online (AJOL)
Background: Left ventricular hypertrophy can be due to various reasons including hypertension. It constitutes an increased cardiovascular risk. Various left ventricular geometric patterns occur in hypertension and may affect the cardiovascular risk profile of hypertensive subjects. Methods: One hundred and eighty eight ...
Geometric properties of optimal photonic crystals
DEFF Research Database (Denmark)
Sigmund, Ole; Hougaard, Kristian G.
2008-01-01
on numerical optimization studies, we have discovered some surprisingly simple geometric properties of optimal planar band gap structures. We conjecture that optimal structures for gaps between bands n and n+1 correspond to n elliptic rods with centers defined by the generators of an optimal centroidal Voronoi...
Probability density cloud as a geometrical tool to describe statistics of scattered light.
Yaitskova, Natalia
2017-04-01
First-order statistics of scattered light is described using the representation of the probability density cloud, which visualizes a two-dimensional distribution for complex amplitude. The geometric parameters of the cloud are studied in detail and are connected to the statistical properties of phase. The moment-generating function for intensity is obtained in a closed form through these parameters. An example of exponentially modified normal distribution is provided to illustrate the functioning of this geometrical approach.
Probability density cloud as a geometrical tool to describe statistics of scattered light
Yaitskova, Natalia
2017-04-01
First-order statistics of scattered light is described using the representation of probability density cloud which visualizes a two-dimensional distribution for complex amplitude. The geometric parameters of the cloud are studied in detail and are connected to the statistical properties of phase. The moment-generating function for intensity is obtained in a closed form through these parameters. An example of exponentially modified normal distribution is provided to illustrate the functioning of this geometrical approach.
Jaskolski, Z.
1986-10-01
In the context of Polyakov's theory the geometrical approach, in which the functional measure is defined as a formal volume ∞-form, is developed. The special version of the Fubini theorem on manifolds is derived, which provides the geometrical interpretation of the Faddeev-Popov method. The conformal gauge is studied within this framework. As a result, the explicit form of functional measure in effective Liouville quantum field theory is obtained.
Checking the Geometric Accuracy of a Machine Tool for Selected Geometric Parameters
Directory of Open Access Journals (Sweden)
Adam Janásek
2012-01-01
Full Text Available This paper deals with the control parameters for selected geometric accuracy measurements for a machine tool. The parameters were needed after a refurbished milling machine was purchased. After setting up the machine, it was necessary to check the geometric accuracy that can be used for precise milling. The whole check was performed in accordance with ISO 10791. Only selected parameters of geometric accuracy were inspected, and they were later compared with the prescribed values. On the basis of a comparison of these values we were able to determine whether the machine tool can be used for accurate machining.
Optimization approach for the evaluation of geometric errors in computer-aided inspection
Jiang, Guohua
Geometric dimensioning and tolerancing (GD&T) is a set of standards that defines a clear and concise mathematical language for communicating product definition. A design based on GD&T clearly reflects the functional requirements of a product, provides unique definition of a drawing among design, manufacturing and inspection engineers and conveys the design intention clearly without any ambiguity. The latest version of this standard is ASME Y14.5M-1994. Traditional methods for the inspection of geometric tolerances have been mostly with the use of functional gages and Coordinate Measuring Machines (CMM). Function gages are very expensive and only provide a yes/no result. CMMs have embedded algorithms to verify geometric tolerances according to the design specification. However, it has been shown that these embedded algorithms neither provide accurate evaluation of geometric errors nor do they conform to the ASME standards. High accuracy requirements in the manufacture of precision parts with complex geometries have made accurate evaluation and verification of geometric tolerances very critical. Over the years, researchers have developed many algorithms to evaluate some of the geometric errors. However, there is still a significant lack of evaluation procedures for complex geometric errors. In this dissertation, mathematical models have been built for the evaluation of a certain set of complex geometric characteristics. The concentration has been on the evaluation of 3D feature relating positional error, cylindricity error and straightness error of spatial line. Research has been carried out to understand the mathematical natures of these problems. Based on the research results, efficient solution methodologies have been developed according to the ASME standards. A robust and efficient procedure has also been developed for the identification of candidate datum sets. The proposed procedures have been implemented using the C++ or C programming language. Experimental
Constrained variational calculus for higher order classical field theories
Energy Technology Data Exchange (ETDEWEB)
Campos, Cedric M; De Leon, Manuel; De Diego, David MartIn, E-mail: cedricmc@icmat.e, E-mail: mdeleon@icmat.e, E-mail: david.martin@icmat.e [Instituto de Ciencias Matematicas, CSIC-UAM-UC3M-UCM, Serrano 123, 28006 Madrid (Spain)
2010-11-12
We develop an intrinsic geometrical setting for higher order constrained field theories. As a main tool we use an appropriate generalization of the classical Skinner-Rusk formalism. Some examples of applications are studied, in particular to the geometrical description of optimal control theory for partial differential equations.
Spinning particle approach to higher spin field theory
Energy Technology Data Exchange (ETDEWEB)
Corradini, Olindo, E-mail: Olindo.Corradini@bo.infn.it [Centro de Estudios en Fisica y Matematicas Basicas y Aplicadas Universidad Autonoma de Chiapas, Tuxtla Gutierrez, Chiapas (Mexico); Dipartimento di Fisica, Universita di Bologna via Irnerio 46, I-40126 Bologna (Italy); INFN, Sezione di Bologna via Irnerio 46, I-40126 Bologna (Italy)
2011-04-01
We shortly review on the connection between higher-spin gauge field theories and supersymmetric spinning particle models. In such approach the higher spin equations of motion are linked to the first-class constraint algebra associated with the quantization of particle models. Here we consider a class of spinning particle models characterized by local O(N)-extended supersymmetry since these models are known to provide an alternative approach to the geometric formulation of higher spin field theory. We describe the canonical quantization of the models in curved target space and discuss the obstructions that appear in presence of an arbitrarily curved background. We then point out the special role that conformally flat spaces appear to have in such models and present a derivation of the higher-spin curvatures for maximally symmetric spaces.
Higher-order Brunnian structures and possible physical realizations
DEFF Research Database (Denmark)
A. Baas, Nils; V. Fedorov, D.; S. Jensen, A.
2014-01-01
We consider few-body bound state systems and provide precise definitions of Borromean and Brunnian systems. The initial concepts are more than a hundred years old and originated in mathematical knot-theory as purely geometric considerations. About thirty years ago they were generalized and applied...... to the binding of systems in nature. It now appears that recent generalization to higher order Brunnian structures may potentially be realized as laboratory made or naturally occurring systems. With the binding energy as measure, we discuss possibilities of physical realization in nuclei, cold atoms...
Directory of Open Access Journals (Sweden)
Delma Maria Cunha
2001-01-01
Full Text Available OBJECTIVE: To identiy left ventricular geometric patterns in hypertensive patients on echocardiography, and to correlate those patterns with casual blood pressure measurements and with the parameters obtained on a 24-hour ambulatory blood pressure monitoring. METHODS: We studied sixty hypertensive patients, grouped according to the Joint National Committee stages of hypertension.. Using the single- and two-dimensional Doppler Echocardiography, we analyzed the left ventricular mass and the geometric patterns through the correlation of left ventricular mass index and relative wall thickness. On ambulatory blood pressure monitoring we assessed the means and pressure loads in the different geometric patterns detected on echocardiography RESULTS: We identified three left ventricular geometric patterns: 1 concentric hypertrophy, in 25% of the patients; 2 concentric remodeling, in 25%; and 3 normal geometry, in 50%. Casual systolic blood pressure was higher in the group with concentric hypertrophy than in the other groups (p=0.001. Mean systolic pressure in the 24h, daytime and nighttime periods was also higher in patients with concentric hypertrophy, as compared to the other groups (p=0.003, p=0.004 and p=0.007. Daytime systolic load and nighttime diastolic load were higher in patients with concentric hypertrophy ( p=0.004 and p=0.01, respectively. CONCLUSIONS: Left ventricular geometric patterns show significant correlation with casual systolic blood pressure, and with means and pressure loads on ambulatory blood pressure monitoring.
Aubrun, Guillaume
2017-01-01
The quest to build a quantum computer is arguably one of the major scientific and technological challenges of the twenty-first century, and quantum information theory (QIT) provides the mathematical framework for that quest. Over the last dozen or so years, it has become clear that quantum information theory is closely linked to geometric functional analysis (Banach space theory, operator spaces, high-dimensional probability), a field also known as asymptotic geometric analysis (AGA). In a nutshell, asymptotic geometric analysis investigates quantitative properties of convex sets, or other geometric structures, and their approximate symmetries as the dimension becomes large. This makes it especially relevant to quantum theory, where systems consisting of just a few particles naturally lead to models whose dimension is in the thousands, or even in the billions. Alice and Bob Meet Banach is aimed at multiple audiences connected through their interest in the interface of QIT and AGA: at quantum information resea...
Geometric constructions for repulsive gravity and quantization
Energy Technology Data Exchange (ETDEWEB)
Hohmann, Manuel
2010-11-15
In this thesis we present two geometric theories designed to extend general relativity. It can be seen as one of the aims of such theories to model the observed accelerating expansion of the universe as a gravitational phenomenon, or to provide a mathematical structure for the formulation of quantum field theories on curved spacetimes and quantum gravity. This thesis splits into two parts: In the first part we consider multimetric gravity theories containing N>1 standard model copies which interact only gravitationally and repel each other in the Newtonian limit. The dynamics of each of the standard model copies is governed by its own metric tensor. We show that the antisymmetric case, in which the mutual repulsion between the different matter sectors is of equal strength compared to the attractive gravitational force within each sector, is prohibited by a no-go theorem for N=2. We further show that this theorem does not hold for N>2 by explicitly constructing an antisymmetric multimetric repulsive gravity theory. We then examine several properties of this theory. Most notably, we derive a simple cosmological model and show that the accelerating expansion of the late universe can indeed be explained by the mutual repulsion between the different matter sectors. We further present a simple model for structure formation and show that our model leads to the formation of filament-like structures and voids. Finally, we show that multimetric repulsive gravity is compatible with high-precision solar system data using the parametrized post-Newtonian formalism. In the second part of the thesis we propose a mathematical model of quantum spacetime as an infinite-dimensional manifold locally homeomorphic to an appropriate Schwartz space. This extends and unifies both the standard function space construction of quantum mechanics and the differentiable manifold structure of classical spacetime. In this picture we demonstrate that classical spacetime emerges as a finite
Energy Technology Data Exchange (ETDEWEB)
Bora, B., E-mail: bbora@cchen.cl; Soto, L. [Comisión Chilena de Energía Nuclear, Santiago, Chile and Center for Research and Applications in Plasma Physics and Pulsed Power, P4 (Chile)
2014-08-15
Capacitively coupled radio frequency (CCRF) plasmas are widely studied in last decades due to the versatile applicability of energetic ions, chemically active species, radicals, and also energetic neutral species in many material processing fields including microelectronics, aerospace, and biology. A dc self-bias is known to generate naturally in geometrically asymmetric CCRF plasma because of the difference in electrode sizes known as geometrical asymmetry of the electrodes in order to compensate electron and ion flux to each electrode within one rf period. The plasma series resonance effect is also come into play due to the geometrical asymmetry and excited several harmonics of the fundamental in low pressure CCRF plasma. In this work, a 13.56 MHz CCRF plasma is studied on the based on the nonlinear global model of asymmetric CCRF discharge to understand the influences of finite geometrical asymmetry of the electrodes in terms of generation of dc self-bias and plasma heating. The nonlinear global model on asymmetric discharge has been modified by considering the sheath at the grounded electrode to taking account the finite geometrical asymmetry of the electrodes. The ion density inside both the sheaths has been taken into account by incorporating the steady-state fluid equations for ions considering that the applied rf frequency is higher than the typical ion plasma frequency. Details results on the influences of geometrical asymmetry on the generation of dc self-bias and plasma heating are discussed.
Geometric critical exponents in classical and quantum phase transitions.
Kumar, Prashant; Sarkar, Tapobrata
2014-10-01
We define geometric critical exponents for systems that undergo continuous second-order classical and quantum phase transitions. These relate scalar quantities on the information theoretic parameter manifolds of such systems, near criticality. We calculate these exponents by approximating the metric and thereby solving geodesic equations analytically, near curvature singularities of two-dimensional parameter manifolds. The critical exponents are seen to be the same for both classical and quantum systems that we consider, and we provide evidence about the possible universality of our results.
Radio resource management using geometric water-filling
He, Peter; Zhou, Sheng; Niu, Zhisheng
2014-01-01
This brief introduces the fundamental theory and development of managing radio resources using a water-filling algorithm that can optimize system performance in wireless communication. Geometric Water-Filling (GWF) is a crucial underlying tool in emerging communication systems such as multiple input multiple output systems, cognitive radio systems, and green communication systems. Early chapters introduce emerging wireless technologies and provide a detailed analysis of water-filling. The brief investigates single user and multi-user issues of radio resource management, allocation of resources
Geometric and Texture Inpainting by Gibbs Sampling
DEFF Research Database (Denmark)
Gustafsson, David Karl John; Pedersen, Kim Steenstrup; Nielsen, Mads
2007-01-01
This paper discuss a method suitable for inpainting both large scale geometric structures and more stochastic texture components. Image inpainting concerns the problem of reconstructing the intensity contents inside regions of missing data. Common techniques for solving this problem are methods....... In this paper we use the well-known FRAME (Filters, Random Fields and Maximum Entropy) for inpainting. We introduce a temperature term in the learned FRAME Gibbs distribution. By sampling using different temperature in the FRAME Gibbs distribution, different contents of the image are reconstructed. We propose...... a two step method for inpainting using FRAME. First the geometric structure of the image is reconstructed by sampling from a cooled Gibbs distribution, then the stochastic component is reconstructed by sample froma heated Gibbs distribution. Both steps in the reconstruction process are necessary...
Geometric complexity theory and matrix powering
DEFF Research Database (Denmark)
Gesmundo, Fulvio; Ikenmeyer, Christian; Panova, Greta
2017-01-01
. Their approach works by multiplying the permanent polynomial with a high power of a linear form (a process called padding) and then comparing the orbit closures of the determinant and the padded permanent. This padding was recently used heavily to show no-go results for the method of shifted partial derivatives...... matrix power. This gives an equivalent but much cleaner homogeneous formulation of geometric complexity theory in which the padding is removed. This radically changes the representation theoretic questions involved to prove complexity lower bounds. We prove that in this homogeneous formulation...... there are no orbit occurrence obstructions that prove even superlinear lower bounds on the complexity of the permanent. This is the first no-go result in geometric complexity theory that rules out superlinear lower bounds in some model. Interestingly---in contrast to the determinant---the trace of a variable matrix...
New computation methods for geometrical optics
Lin, Psang Dain
2014-01-01
This book employs homogeneous coordinate notation to compute the first- and second-order derivative matrices of various optical quantities. It will be one of the important mathematical tools for automatic optical design. The traditional geometrical optics is based on raytracing only. It is very difficult, if possible, to compute the first- and second-order derivatives of a ray and optical path length with respect to system variables, since they are recursive functions. Consequently, current commercial software packages use a finite difference approximation methodology to estimate these derivatives for use in optical design and analysis. Furthermore, previous publications of geometrical optics use vector notation, which is comparatively awkward for computations for non-axially symmetrical systems.
Geometric formulation of Berezin deformation quantization
Directory of Open Access Journals (Sweden)
R. Roknizadeh
2002-06-01
Full Text Available In this paper we try to formulate the Berezin quantization on projective Hilbert space P(H and use its geometric structure to construct a correspondence between a given classical theory and a given quantum theory. It wil be shown that the star product in berezin quantization is equivalent to the Posson bracket on coherent states manifold M, embodded in P(H, and the Berezin method is used to define a classical limit for geometric quantum mechnics. With this construction to all of the quantum observables are associated their covariant symbols, which form a poisson algebra on P(H and since the corresponding classical phase space has a natural Poisson structure, the Berezin quantization is then a systematic procedure to relate these tow piosson algebras.
Geometrical dynamics of Born-Infeld objects
Energy Technology Data Exchange (ETDEWEB)
Cordero, Ruben [Departamento de Fisica, Escuela Superior de Fisica y Matematicas del I.P.N., Unidad Adolfo Lopez Mateos, Edificio 9, 07738 Mexico, D.F. (Mexico); Molgado, Alberto [Facultad de Ciencias, Universidad de Colima, Bernal DIaz del Castillo 340, Col. Villas San Sebastian, Colima (Mexico); Rojas, Efrain [Facultad de Fisica e Inteligencia Artificial, Universidad Veracruzana, 91000 Xalapa, Veracruz (Mexico)
2007-03-21
We present a geometrically inspired study of the dynamics of Dp-branes. We focus on the usual non-polynomial Dirac-Born-Infeld action for the worldvolume swept out by the brane in its evolution in general background spacetimes. We emphasize the form of the resulting equations of motion which are quite simple and resemble Newton's second law, complemented with a conservation law for a worldvolume bicurrent. We take a closer look at the classical Hamiltonian analysis which is supported by the ADM framework of general relativity. The constraints and their algebra are identified as well as the geometrical role they play in phase space. In order to illustrate our results, we review the dynamics of a D1-brane immersed in a AdS{sub 3} x S{sup 3} background spacetime. We exhibit the mechanical properties of Born-Infeld objects paving the way to a consistent quantum formulation.
Geometric description of images as topographic maps
Caselles, Vicent
2010-01-01
This volume discusses the basic geometric contents of an image and presents a tree data structure to handle those contents efficiently. The nodes of the tree are derived from connected components of level sets of the intensity, while the edges represent inclusion information. Grain filters, morphological operators simplifying these geometric contents, are analyzed and several applications to image comparison and registration, and to edge and corner detection, are presented. The mathematically inclined reader may be most interested in Chapters 2 to 6, which generalize the topological Morse description to continuous or semicontinuous functions, while mathematical morphologists may more closely consider grain filters in Chapter 3. Computer scientists will find algorithmic considerations in Chapters 6 and 7, the full justification of which may be found in Chapters 2 and 4 respectively. Lastly, all readers can learn more about the motivation for this work in the image processing applications presented in Chapter 8...
A practical guide to experimental geometrical optics
Garbovskiy, Yuriy A
2017-01-01
A concise, yet deep introduction to experimental, geometrical optics, this book begins with fundamental concepts and then develops the practical skills and research techniques routinely used in modern laboratories. Suitable for students, researchers and optical engineers, this accessible text teaches readers how to build their own optical laboratory and to design and perform optical experiments. It uses a hands-on approach which fills a gap between theory-based textbooks and laboratory manuals, allowing the reader to develop their practical skills in this interdisciplinary field, and also explores the ways in which this knowledge can be applied to the design and production of commercial optical devices. Including supplementary online resources to help readers track and evaluate their experimental results, this text is the ideal companion for anyone with a practical interest in experimental geometrical optics.
Color fringe projection profilometry using geometric constraints
Cheng, Teng; Du, Qingyu; Jiang, Yaxi
2017-09-01
A recently proposed phase unwrapping method using geometric constraints performs well without requiring additional camera, more patterns or global search. The major limitation of this technique is the confined measurement depth range (MDR) within 2π in phase domain. To enlarge the MDR, this paper proposes using color fringes for three-dimensional (3D) shape measurement. Each six fringe periods encoded with six different colors are treated as one group. The local order within one group can be identified with reference to the color distribution. Then the phase wrapped period-by-period is converted into the phase wrapped group-by-group. The geometric constraints of the fringe projection system are used to determine the group order. Such that the MDR is extended from 2π to 12π by six times. Experiment results demonstrate the success of the proposed method to measure two isolated objects with large MDR.
Geometric calibration of ERS satellite SAR images
DEFF Research Database (Denmark)
Mohr, Johan Jacob; Madsen, Søren Nørvang
2001-01-01
Geometric calibration of the European Remote Sensing (ERS) Satellite synthetic aperture radar (SAR) slant range images is important in relation to mapping areas without ground reference points and also in relation to automated processing. The relevant SAR system parameters are discussed and calib......Geometric calibration of the European Remote Sensing (ERS) Satellite synthetic aperture radar (SAR) slant range images is important in relation to mapping areas without ground reference points and also in relation to automated processing. The relevant SAR system parameters are discussed...... on a seven-year ERS-1 and a four-year ERS-2 time series, the long term stability is found to be sufficient to allow a single calibration covering the entire mission period. A descending and an ascending orbit tandem pair of the ESA calibration site on Flevoland, suitable for calibration of ERS SAR processors...
Geometric evolutionary dynamics of protein interaction networks.
Przulj, Natasa; Kuchaiev, Oleksii; Stevanović, Aleksandar; Hayes, Wayne
2010-01-01
Understanding the evolution and structure of protein-protein interaction (PPI) networks is a central problem of systems biology. Since most processes in the cell are carried out by groups of proteins acting together, a theoretical model of how PPI networks develop based on duplications and mutations is an essential ingredient for understanding the complex wiring of the cell. Many different network models have been proposed, from those that follow power-law degree distributions and those that model complementarity of protein binding domains, to those that have geometric properties. Here, we introduce a new model for PPI network (and thus gene) evolution that produces well-fitting network models for currently available PPI networks. The model integrates geometric network properties with evolutionary dynamics of PPI network evolution.
Geometric simulation of flexible motion in proteins.
Wells, Stephen A
2014-01-01
This chapter describes the use of physically simplified analysis and simulation methods-pebble-game rigidity analysis, coarse-grained elastic network modeling, and template-based geometric simulation-to explore flexible motion in protein structures. Substantial amplitudes of flexible motion can be explored rapidly in an all-atom model, retaining realistic covalent bonding, steric exclusion, and a user-defined network of noncovalent polar and hydrophobic interactions, using desktop computing resources. Detailed instructions are given for simulations using FIRST/FRODA software installed on a UNIX/Linux workstation. Other implementations of similar methods exist, particularly NMSim and FRODAN, and are available online. Topics covered include rigidity analysis and constraints, geometric simulation of flexible motion, targeting between known structures, and exploration of motion along normal mode eigenvectors.
The Geometric Nonlinear Generalized Brazier Effect
DEFF Research Database (Denmark)
Nikolajsen, Jan Ánike; Lauridsen, Peter Riddersholm; Damkilde, Lars
2016-01-01
denoted the generalized Brazier effect. The original work of Brazier dealt with very large deformations that changed the cross section significantly and hereby also the bending moment of inertia and the bending moment capacity. In this paper the aim is to describe the Brazier effect for smaller...... to solve the complex non-linear geometric problem with a high accuracy. This is of importance in simulations of wind turbine blades, where the wind load simulations are based on small Finite Element models based on beam type elements in order to be realistic. The linearized solution exploits...... that the generalized Brazier effect is a local effect not influencing the overall mechanical behavior of the structure significantly. The offset is a nonlinear geometric beam-type Finite Element calculation, which takes into account the large displacements and rotations. The beam-type model defines the stresses which...
Multiphase flow in geometrically simple fracture intersections
Basagaoglu, H.; Meakin, P.; Green, C.T.; Mathew, M.; ,
2006-01-01
A two-dimensional lattice Boltzmann (LB) model with fluid-fluid and solid-fluid interaction potentials was used to study gravity-driven flow in geometrically simple fracture intersections. Simulated scenarios included fluid dripping from a fracture aperture, two-phase flow through intersecting fractures and thin-film flow on smooth and undulating solid surfaces. Qualitative comparisons with recently published experimental findings indicate that for these scenarios the LB model captured the underlying physics reasonably well.
Evolution equation for geometric quantum correlation measures
Hu, Ming-Liang; Fan, Heng
2014-01-01
A simple relation is established for the evolution equation of quantum information processing protocols such as quantum teleportation, remote state preparation, Bell-inequality violation and particularly dynamics of the geometric quantum correlation measures. This relation shows that when the system traverses the local quantum channel, various figures of merit of the quantum correlations for different protocols demonstrate a factorization decay behavior for dynamics. We identified the family ...
Geometric measure theory a beginner's guide
Morgan, Frank
1995-01-01
Geometric measure theory is the mathematical framework for the study of crystal growth, clusters of soap bubbles, and similar structures involving minimization of energy. Morgan emphasizes geometry over proofs and technicalities, and includes a bibliography and abundant illustrations and examples. This Second Edition features a new chapter on soap bubbles as well as updated sections addressing volume constraints, surfaces in manifolds, free boundaries, and Besicovitch constant results. The text will introduce newcomers to the field and appeal to mathematicians working in the field.
Geometric Measure Theory and Minimal Surfaces
Bombieri, Enrico
2011-01-01
W.K. ALLARD: On the first variation of area and generalized mean curvature.- F.J. ALMGREN Jr.: Geometric measure theory and elliptic variational problems.- E. GIUSTI: Minimal surfaces with obstacles.- J. GUCKENHEIMER: Singularities in soap-bubble-like and soap-film-like surfaces.- D. KINDERLEHRER: The analyticity of the coincidence set in variational inequalities.- M. MIRANDA: Boundaries of Caciopoli sets in the calculus of variations.- L. PICCININI: De Giorgi's measure and thin obstacles.
Constellation design with geometric and probabilistic shaping
Zhang, Shaoliang; Yaman, Fatih
2018-02-01
A systematic study, including theory, simulation and experiments, is carried out to review the generalized pairwise optimization algorithm for designing optimized constellation. In order to verify its effectiveness, the algorithm is applied in three testing cases: 2-dimensional 8 quadrature amplitude modulation (QAM), 4-dimensional set-partitioning QAM, and probabilistic-shaped (PS) 32QAM. The results suggest that geometric shaping can work together with PS to further bridge the gap toward the Shannon limit.
Robot arm geometric link parameter estimation
Hayati, S. A.
1983-01-01
A general method for estimating serial link manipulator geometric parameter errors is proposed in this paper. The positioning accuracy of the end-effector may be increased significantly by updating the nominal link parameters in the control software to represent the physical system more accurately. The proposed method is applicable for serial link manipulators with any combination of revolute or prismatic joints, and is not limited to a specific measurement technique.
Multiphase Flow in Geometrically Simple Fracture Intersections
Energy Technology Data Exchange (ETDEWEB)
Hakan Basagaoglu; Paul Meakin; Sauro Succi; Timothy R. Ginn
2006-03-01
A two-dimensional lattice Boltzmann (LB) model with fluid-fluid and solid-fluid interaction potentials was used to Study gravity-driven flow in geometrically simple fracture intersections. simulated scenarios included fluid dripping from a fracture aperture, two-phase flow through intersecting fractures and thin-filin flow oil smooth and undulating solid surfaces. Qualitative comparisons with recently published experimental findings indicate that for these scenarios the LB model captured the underlying physics reasonably well.
Geometric errors measurement for coordinate measuring machines
Pan, Fangyu; Nie, Li; Bai, Yuewei; Wang, Xiaogang; Wu, Xiaoyan
2017-08-01
Error compensation is a good choice to improve Coordinate Measuring Machines’ (CMM) accuracy. In order to achieve the above goal, the basic research is done. Firstly, analyzing the error source which finds out 21 geometric errors affecting CMM’s precision seriously; secondly, presenting the measurement method and elaborating the principle. By the experiment, the feasibility is validated. Therefore, it lays a foundation for further compensation which is better for CMM’s accuracy.
a Geometrical Particle Model for Anyons
Nersessian, Armen; Ramos, Eduardo
We consider the simplest geometrical particle model associated with light-like curves in (2+1) dimensions. The action is proportional to the pseudo-arc length of the particle's path. We show that under quantization, it yields the (2+1)-dimensional anyonic field equation supplemented with a Majorana-like relation on mass and spin, i.e. mass × spin =α2, with α the coupling constant in front of the action.
Quantum Particle-Trajectories and Geometric Phase
Dima, M.
1999-01-01
"Particle"-trajectories are defined as integrable $dx_\\mu dp^\\mu = 0$ paths in projective space. Quantum states evolving on such trajectories, open or closed, do not delocalise in $(x, p)$ projection, the phase associated with the trajectories being related to the geometric (Berry) phase and the Classical Mechanics action. High Energy Physics properties of states evolving on "particle"-trajectories are discussed.
Noncommutative Geometric Gauge Theory from Superconnections
Lee, Chang-Yeong
1996-01-01
Noncommutative geometric gauge theory is reconstructed based on the superconnection concept. The bosonic action of the Connes-Lott model including the symmetry breaking Higgs sector is obtained by using a new generalized derivative, which consists of the usual 1-form exterior derivative plus an extra element called the matrix derivative, for the curvatures. We first derive the matrix derivative based on superconnections and then show how the matrix derivative can give rise to spontaneous symm...
Stabilization of LCD devices via geometric alteration.
Jeon, Il; Yoon, MinSung; Lee, Je-Hoon
2013-02-20
Glass bending in LCD displays is an inherent problem that has challenged many engineers. As a solution to this problem, we propose a methodology that can tackle the root of the phenomenon in terms of linear elastic beam theory. Using this hypothesis, we devised a background theory and a solution. In this paper, we present a glass panel to which geometrical changes, such as furrow, groove, and curb have been applied. These geometrical changes are applied to the nonactive area of the glass panel. To confirm the validity of our approach, we conducted simulation tests as well as hands-on experiments to observe the thermo-mechanical behavior of the device under various conditions. The simulation results using the Ansys simulator show that the proposed technique can reduce the deformation level of panel bending by 40%. In the experiment using a bare cell with polarizer films attached and with performing the high temperature reliability test, the deformation level of panel bending is reduced by half compared to the reference glass panel without any geometric alteration.
Geometric Deep Learning: Going beyond Euclidean data
Bronstein, Michael M.; Bruna, Joan; LeCun, Yann; Szlam, Arthur; Vandergheynst, Pierre
2017-07-01
Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging, regulatory networks in genetics, and meshed surfaces in computer graphics. In many applications, such geometric data are large and complex (in the case of social networks, on the scale of billions), and are natural targets for machine learning techniques. In particular, we would like to use deep neural networks, which have recently proven to be powerful tools for a broad range of problems from computer vision, natural language processing, and audio analysis. However, these tools have been most successful on data with an underlying Euclidean or grid-like structure, and in cases where the invariances of these structures are built into networks used to model them. Geometric deep learning is an umbrella term for emerging techniques attempting to generalize (structured) deep neural models to non-Euclidean domains such as graphs and manifolds. The purpose of this paper is to overview different examples of geometric deep learning problems and present available solutions, key difficulties, applications, and future research directions in this nascent field.
Edit propagation using geometric relationship functions
Guerrero, Paul
2014-03-01
We propose a method for propagating edit operations in 2D vector graphics, based on geometric relationship functions. These functions quantify the geometric relationship of a point to a polygon, such as the distance to the boundary or the direction to the closest corner vertex. The level sets of the relationship functions describe points with the same relationship to a polygon. For a given query point, we first determine a set of relationships to local features, construct all level sets for these relationships, and accumulate them. The maxima of the resulting distribution are points with similar geometric relationships. We show extensions to handle mirror symmetries, and discuss the use of relationship functions as local coordinate systems. Our method can be applied, for example, to interactive floorplan editing, and it is especially useful for large layouts, where individual edits would be cumbersome. We demonstrate populating 2D layouts with tens to hundreds of objects by propagating relatively few edit operations. © 2014 ACM 0730-0301/2014/03- ART15 $15.00.
Hendrickson, Robert M.
This chapter reviews litigation in higher education for 1986. The first section discusses the relationship between postsecondary institutions and various governmental agencies, in which litigation covers questions on the authority of boards, access to information through sunshine laws, questions of tax exempt status, and issues of accreditation.…
Geometric Approaches to Quadratic Equations from Other Times and Places.
Allaire, Patricia R.; Bradley, Robert E.
2001-01-01
Focuses on geometric solutions of quadratic problems. Presents a collection of geometric techniques from ancient Babylonia, classical Greece, medieval Arabia, and early modern Europe to enhance the quadratic equation portion of an algebra course. (KHR)
Some Hermite–Hadamard type inequalities for geometrically quasi ...
Indian Academy of Sciences (India)
Abstract. In the paper, we introduce a new concept 'geometrically quasi-convex function' and establish some Hermite–Hadamard type inequalities for functions whose derivatives are of geometric quasi-convexity.
Representation of Crystallographic Subperiodic Groups by Geometric Algebra
Hitzer, Eckhard; Ichikawa, Daisuke
2013-01-01
We explain how following the representation of 3D crystallographic space groups in geometric algebra it is further possible to similarly represent the 162 socalled subperiodic groups of crystallography in geometric algebra. We construct a new compact geometric algebra group representation symbol, which allows to read off the complete set of geometric algebra generators. For clarity we moreover state explicitly what generators are chosen. The group symbols are based on the representation of po...
Geometric Error Analysis in Applied Calculus Problem Solving
Usman, Ahmed Ibrahim
2017-01-01
The paper investigates geometric errors students made as they tried to use their basic geometric knowledge in the solution of the Applied Calculus Optimization Problem (ACOP). Inaccuracies related to the drawing of geometric diagrams (visualization skills) and those associated with the application of basic differentiation concepts into ACOP…
LEICA DMC III CALIBRATION AND GEOMETRIC SENSOR ACCURACY
Directory of Open Access Journals (Sweden)
C. Mueller
2016-03-01
Full Text Available As an evolution of the successful DMC II digital camera series, Leica Geosystems has introduced the Leica DMC III digital aerial camera using, for the first time in the industry, a large-format CMOS sensor as a panchromatic high-resolution camera head. This paper describes the Leica DMC III calibration and its quality assurance and quality control (QA/QC procedures. It will explain how calibration was implemented within the production process for the Leica DMC III camera. Based on many years of experience with the DMC and DMC II camera series, it is know that the sensor flatness has a huge influence on the final achievable results. The Leica DMC III panchromatic CMOS sensor with its 100.3mm x 56.9mm size shows remaining errors in a range of 0.1 to 0.2μm for the root mean square and shows maximum values not higher that 1.0μm. The Leica DMC III is calibrated based on a 5cm Ground Sample Distance (GSD grid pattern flight and evaluated with three different flying heights at 5cm, 8cm and 11cm GSD. The geometric QA/QC has been performed using the calibration field area, as well as using an independent test field. The geometric performance and accuracy is unique and gives ground accuracies far better than the flown GSD.
Why do animals differ in their susceptibility to geometrical illusions?
Feng, Lynna C; Chouinard, Philippe A; Howell, Tiffani J; Bennett, Pauleen C
2017-04-01
In humans, geometrical illusions are thought to reflect mechanisms that are usually helpful for seeing the world in a predictable manner. These mechanisms deceive us given the right set of circumstances, correcting visual input where a correction is not necessary. Investigations of non-human animals' susceptibility to geometrical illusions have yielded contradictory results, suggesting that the underlying mechanisms with which animals see the world may differ across species. In this review, we first collate studies showing that different species are susceptible to specific illusions in the same or reverse direction as humans. Based on a careful assessment of these findings, we then propose several ecological and anatomical factors that may affect how a species perceives illusory stimuli. We also consider the usefulness of this information for determining whether sight in different species might be more similar to human sight, being influenced by contextual information, or to how machines process and transmit information as programmed. Future testing in animals could provide new theoretical insights by focusing on establishing dissociations between stimuli that may or may not alter perception in a particular species. This information could improve our understanding of the mechanisms behind illusions, but also provide insight into how sight is subjectively experienced by different animals, and the degree to which vision is innate versus acquired, which is difficult to examine in humans.
Quantum algorithm for topological and geometric analysis of data
Lloyd, Seth; Zanardi, Paolo; Garnerone, Silvano
2015-03-01
Topological methods for analyzing data sets provide a powerful technique for extracting useful information from data. Data that represents geometric features of the world typically gives a distorted picture of those features, if only because the devices and systems that sense the world and that generate the data by their very nature induce distortions. By definition, topological features are those that persist under continuous distortions of the data. Topological methods can therefore identify features of the real system from which the data was collected, but that have been distorted by the data collection process. Persistent homology is a sophisticated tool for identifying such topological features -connected components, holes, or voids - and for determining how such features persist as the data is viewed at different scales. This talk presents quantum machine learning algorithms for calculating Betti numbers in persistent homology, and for finding eigenvectors and eigenvalues of the combinatorial Laplacian (the quantities that famously allow one to ``hear the shape of a drum''). The algorithms provide an exponential speedup over classical algorithms for topological and geometrical data analysis.
Directory of Open Access Journals (Sweden)
Changho Yun
2016-01-01
Full Text Available The nonnegligible propagation delay of acoustic signals causes spatiotemporal uncertainty that occasionally enables simultaneous, collision-free packet transmission among underwater nodes (UNs. These transmissions can be handled by efficiently managing the channel access of the UNs in the data-link layer. To this end, Geometric Spatial Reuse-TDMA (GSR-TDMA, a new TDMA-based MAC protocol, is designed for use in centralized, multihop underwater acoustic sensor networks (UASNs, and in this case all UNs are periodically scheduled after determining a geometric map according to the information on their location. The scheduling strategy increases the number of UNs that send packets coincidentally via two subscheduling configurations (i.e., interhop and intrahop scheduling. Extensive simulations are used to investigate the reception success rate (RSR and the multihop delay (MHD of GSR-TDMA, and the results are compared to those of previous approaches, including C-MAC and HSR-TDMA. GSR-TDMA outperforms C-MAC; the RSR of GSR-TDMA is 15% higher than that of C-MAC, and the MHD of GSR-TDMA is 30% lower than that of C-MAC at the most. In addition, GSR-TDMA provides even better performance improvements over HSR-TDMA; the RSR of GSR-TDMA is 50% higher than that of HSR-TDMA, and the MHD of GSR-TDMA is an order of 102 lower than that of HSR-TDMA at the most.
Mapping the Geometric Evolution of Protein Folding Motor.
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Gaurav Jerath
Full Text Available Polypeptide chain has an invariant main-chain and a variant side-chain sequence. How the side-chain sequence determines fold in terms of its chemical constitution has been scrutinized extensively and verified periodically. However, a focussed investigation on the directive effect of side-chain geometry may provide important insights supplementing existing algorithms in mapping the geometrical evolution of protein chains and its structural preferences. Geometrically, folding of protein structure may be envisaged as the evolution of its geometric variables: ϕ, and ψ dihedral angles of polypeptide main-chain directed by χ1, and χ2 of side chain. In this work, protein molecule is metaphorically modelled as a machine with 4 rotors ϕ, ψ, χ1 and χ2, with its evolution to the functional fold is directed by combinations of its rotor directions. We observe that differential rotor motions lead to different secondary structure formations and the combinatorial pattern is unique and consistent for particular secondary structure type. Further, we found that combination of rotor geometries of each amino acid is unique which partly explains how different amino acid sequence combinations have unique structural evolution and functional adaptation. Quantification of these amino acid rotor preferences, resulted in the generation of 3 substitution matrices, which later on plugged in the BLAST tool, for evaluating their efficiency in aligning sequences. We have employed BLOSUM62 and PAM30 as standard for primary evaluation. Generation of substitution matrices is a logical extension of the conceptual framework we attempted to build during the development of this work. Optimization of matrices following the conventional routines and possible application with biologically relevant data sets are beyond the scope of this manuscript, though it is a part of the larger project design.
The Impact of Using Synchronous Collaborative Virtual Tangram in Children's Geometric
Lin, Chiu-Pin; Shao, Yin-juan; Wong, Lung-Hsiang; Li, Yin-Jen; Niramitranon, Jitti
2011-01-01
This study aimed to develop a collaborative and manipulative virtual Tangram puzzle to facilitate children to learn geometry in the computer-supported collaborative learning environment with Tablet PCs. In promoting peer interactions and stimulating students' higher-order thinking and creativity toward geometric problem-solving, we designed a…
Electronic structure theory: Applications and geometrical aspects
Coh, Sinisa
This thesis contains several applications of the first-principles electronic-structure theory with special emphasis in parts of the thesis on the geometrical aspects of the theory. We start by reviewing the basics of the first-principles electronic-structure methods which are then used throughout the thesis. The first application of these methods is on the analysis of the stability and lattice dynamics of alpha- and beta-cristobalite phases of SiO2. We also map the complete low-energy landscape connecting these two structures and give implications on the phase transition in this compound. Next we study a family of Pbnm perovskites that are promising candidates for silicon-compatible high-K dielectrics. We calculate their structure and dielectric response, and compare with experimental results where available. The third application of these methods is to the large isosymmetric reorientation of oxygen octahedra rotation axes in epitaxially strained perovskites. We explain the origin of the peculiar energy landscape topology as a function of epitaxial strain. In the part of the thesis devoted to the geometrical aspects of electronic structure theory, we begin by extending the concept of electronic polarization to a Chern insulators. These insulators are characterized by a non-zero off-diagonal sigma_xy conductivity tensor component, quantized in units of e 2/h. Finally we discuss another geometrical quantity, the Chern-Simons orbital magnetoelectric coupling. We present a first-principles based calculation of this quantity in several compounds, and motivated by recent developments in the theory of topological insulators, we speculate about the existence of "large-theta materials," in which this kind of coupling could be unusually large.
Optimization of biotechnological systems through geometric programming
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Torres Nestor V
2007-09-01
Full Text Available Abstract Background In the past, tasks of model based yield optimization in metabolic engineering were either approached with stoichiometric models or with structured nonlinear models such as S-systems or linear-logarithmic representations. These models stand out among most others, because they allow the optimization task to be converted into a linear program, for which efficient solution methods are widely available. For pathway models not in one of these formats, an Indirect Optimization Method (IOM was developed where the original model is sequentially represented as an S-system model, optimized in this format with linear programming methods, reinterpreted in the initial model form, and further optimized as necessary. Results A new method is proposed for this task. We show here that the model format of a Generalized Mass Action (GMA system may be optimized very efficiently with techniques of geometric programming. We briefly review the basics of GMA systems and of geometric programming, demonstrate how the latter may be applied to the former, and illustrate the combined method with a didactic problem and two examples based on models of real systems. The first is a relatively small yet representative model of the anaerobic fermentation pathway in S. cerevisiae, while the second describes the dynamics of the tryptophan operon in E. coli. Both models have previously been used for benchmarking purposes, thus facilitating comparisons with the proposed new method. In these comparisons, the geometric programming method was found to be equal or better than the earlier methods in terms of successful identification of optima and efficiency. Conclusion GMA systems are of importance, because they contain stoichiometric, mass action and S-systems as special cases, along with many other models. Furthermore, it was previously shown that algebraic equivalence transformations of variables are sufficient to convert virtually any types of dynamical models into
Anyons in geometric models of matter
Atiyah, Michael; Marcolli, Matilde
2017-07-01
We show that the "geometric models of matter" approach proposed by the first author can be used to construct models of anyon quasiparticles with fractional quantum numbers, using 4-dimensional edge-cone orbifold geometries with orbifold singularities along embedded 2-dimensional surfaces. The anyon states arise through the braid representation of surface braids wrapped around the orbifold singularities, coming from multisections of the orbifold normal bundle of the embedded surface. We show that the resulting braid representations can give rise to a universal quantum computer.
Samper, Carmen; Leguizamón, Cecilia; Camago, Leonor
2001-01-01
Este artículo presenta algunas reflexiones adelantadas en el trabajo de investigación "Desarrollo del razonamiento a través de la geometría euclidiana" que llevamos a cabo en la actualidad. Se centra en dar una visión sobre el razonamiento en la actividad geométrica, los tipos de razonamiento que hemos identificado y una caracterización particular del razonamiento visual. Las ideas se ilustran por medio de relatos de situaciones vivenciadas con nuestros estudiantes de primer semestre, en curs...
Static spherical metrics: a geometrical approach
Tiwari, A. K.; Maharaj, S. D.; Narain, R.
2017-08-01
There exist several solution generating algorithms for static spherically symmetric metrics. Here we use the geometrical approach of Lie point symmetries to solve the condition of pressure isotropy by finding the associated five-dimensional Lie algebra of symmetry generators. For the non-Abelian subalgebras the underlying equation is solved to obtain a general solution. Contained within this class are vacuum models, constant density models, metrics with linear equations of state and the Buchdahl representation of the polytrope with index five. For a different particular symmetry generator the condition of pressure isotropy is transformed to a Riccati equation which admits particular solutions.
Geometric Algebra Techniques in Flux Compactifications
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Calin Iuliu Lazaroiu
2016-01-01
Full Text Available We study “constrained generalized Killing (spinors,” which characterize supersymmetric flux compactifications of supergravity theories. Using geometric algebra techniques, we give conceptually clear and computationally effective methods for translating supersymmetry conditions into differential and algebraic constraints on collections of differential forms. In particular, we give a synthetic description of Fierz identities, which are an important ingredient of such problems. As an application, we show how our approach can be used to efficiently treat N=1 compactification of M-theory on eight manifolds and prove that we recover results previously obtained in the literature.
Geometric Total Variation for Texture Deformation
DEFF Research Database (Denmark)
Bespalov, Dmitriy; Dahl, Anders Lindbjerg; Shokoufandeh, Ali
2010-01-01
In this work we propose a novel variational method that we intend to use for estimating non-rigid texture deformation. The method is able to capture variation in grayscale images with respect to the geometry of its features. Our experimental evaluations demonstrate that accounting for geometry...... of features in texture images leads to significant improvements in localization of these features, when textures undergo geometrical transformations. Accurate localization of features in the presense of unkown deformations is a crucial property for texture characterization methods, and we intend to expoit...
Femtosecond pulse shaping using the geometric phase.
Gökce, Bilal; Li, Yanming; Escuti, Michael J; Gundogdu, Kenan
2014-03-15
We demonstrate a femtosecond pulse shaper that utilizes polarization gratings to manipulate the geometric phase of an optical pulse. This unique approach enables circular polarization-dependent shaping of femtosecond pulses. As a result, it is possible to create coherent pulse pairs with orthogonal polarizations in a 4f pulse shaper setup, something until now that, to our knowledge, was only achieved via much more complex configurations. This approach could be used to greatly simplify and enhance the functionality of multidimensional spectroscopy and coherent control experiments, in which multiple coherent pulses are used to manipulate quantum states in materials of interest.
Geometric phase shaping of terahertz vortex beams.
Minasyan, Amalya; Trovato, Clément; Degert, Jérôme; Freysz, Eric; Brasselet, Etienne; Abraham, Emmanuel
2017-01-01
We propose a topological beam-shaping strategy of terahertz (THz) beams using geometric phase elements made of space-variant birefringent slabs. Quasi-monochromatic THz vortex beams are produced and characterized both in amplitude and phase from the reconstructed real-time two-dimensional imaging of the electric field. Nonseparable superpositions of such vortex beams are also obtained and characterized by two-dimensional polarimetric analysis. These results emphasize the versatility of the spin-orbit electromagnetic toolbox to prepare on-demand structured light endowed with polarization-controlled orbital angular momentum content in the THz domain, which should find many uses in future THz technologies.
Toroidal Precession as a Geometric Phase
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J.W. Burby and H. Qin
2012-09-26
Toroidal precession is commonly understood as the orbit-averaged toroidal drift of guiding centers in axisymmetric and quasisymmetric configurations. We give a new, more natural description of precession as a geometric phase effect. In particular, we show that the precession angle arises as the holonomy of a guiding center's poloidal trajectory relative to a principal connection. The fact that this description is physically appropriate is borne out with new, manifestly coordinate-independent expressions for the precession angle that apply to all types of orbits in tokamaks and quasisymmetric stellarators alike. We then describe how these expressions may be fruitfully employed in numerical calculations of precession.
ERC Workshop on Geometric Partial Differential Equations
Novaga, Matteo; Valdinoci, Enrico
2013-01-01
This book is the outcome of a conference held at the Centro De Giorgi of the Scuola Normale of Pisa in September 2012. The aim of the conference was to discuss recent results on nonlinear partial differential equations, and more specifically geometric evolutions and reaction-diffusion equations. Particular attention was paid to self-similar solutions, such as solitons and travelling waves, asymptotic behaviour, formation of singularities and qualitative properties of solutions. These problems arise in many models from Physics, Biology, Image Processing and Applied Mathematics in general, and have attracted a lot of attention in recent years.
A Geometric Framework for Rectangular Shape Detection.
Li, Qi
2014-07-25
Rectangular shape detection has a wide range of applications, such as license plate detection, vehicle detection and building detection. In this paper, we propose a geometric framework for rectangular shape detection based on the channelscale space of RGB images. The framework consists of algorithms developed to address three issues of a candidate shape (i.e., a connected component of edge points), including: i) outliers, ii) open shape, and iii) fragmentation. Furthermore, we propose an interestness measure for rectangular shapes by integrating imbalanced points (one type of interest points). Our experimental study shows the promise of the proposed framework.
Geometric frustration of icosahedron in metallic glasses.
Hirata, A; Kang, L J; Fujita, T; Klumov, B; Matsue, K; Kotani, M; Yavari, A R; Chen, M W
2013-07-26
Icosahedral order has been suggested as the prevalent atomic motif of supercooled liquids and metallic glasses for more than half a century, because the icosahedron is highly close-packed but is difficult to grow, owing to structure frustration and the lack of translational periodicity. By means of angstrom-beam electron diffraction of single icosahedra, we report experimental observation of local icosahedral order in metallic glasses. All the detected icosahedra were found to be distorted with partially face-centered cubic symmetry, presenting compelling evidence on geometric frustration of local icosahedral order in metallic glasses.
Conformal invariants topics in geometric function theory
Ahlfors, Lars V
2010-01-01
Most conformal invariants can be described in terms of extremal properties. Conformal invariants and extremal problems are therefore intimately linked and form together the central theme of this classic book which is primarily intended for students with approximately a year's background in complex variable theory. The book emphasizes the geometric approach as well as classical and semi-classical results which Lars Ahlfors felt every student of complex analysis should know before embarking on independent research. At the time of the book's original appearance, much of this material had never ap
Geometric and numerical foundations of movements
Mansard, Nicolas; Lasserre, Jean-Bernard
2017-01-01
This book aims at gathering roboticists, control theorists, neuroscientists, and mathematicians, in order to promote a multidisciplinary research on movement analysis. It follows the workshop “ Geometric and Numerical Foundations of Movements ” held at LAAS-CNRS in Toulouse in November 2015[1]. Its objective is to lay the foundations for a mutual understanding that is essential for synergetic development in motion research. In particular, the book promotes applications to robotics --and control in general-- of new optimization techniques based on recent results from real algebraic geometry.
The minimal geometric deformation approach extended
Casadio, R.; Ovalle, J.; da Rocha, Roldão
2015-11-01
The minimal geometric deformation approach was introduced in order to study the exterior spacetime around spherically symmetric self-gravitating systems, such as stars or similar astrophysical objects, in the Randall-Sundrum brane-world framework. A consistent extension of this approach is developed here, which contains modifications of both the time component and the radial component of a spherically symmetric metric. A modified Schwarzschild geometry is obtained as an example of its simplest application, and a new solution that is potentially useful to describe stars in the brane-world is also presented.
Auxiliary fields in the geometrical relativistic particle dynamics
Energy Technology Data Exchange (ETDEWEB)
Amador, A; Bagatella, N; Rojas, E [Departamento de Fisica, Facultad de Fisica e Inteligencia Artificial, Universidad Veracruzana, 91000 Xalapa, Veracruz (Mexico); Cordero, R [Departamento de Fisica, Escuela Superior de Fisica y Matematicas del I.P.N, Edificio 9, 07738 Mexico D.F (Mexico)], E-mail: aramador@gmail.com, E-mail: nbagatella@uv.mx, E-mail: cordero@esfm.ipn.mx, E-mail: efrojas@uv.mx
2008-03-21
We describe how to construct the dynamics of relativistic particles, following either timelike or null curves, by means of an auxiliary variables method instead of the standard theory of deformations for curves. There are interesting physical particle models governed by actions that involve higher order derivatives of the embedding functions of the worldline. We point out that the mechanical content of such models can be extracted wisely from a lower order action, which can be performed by implementing in the action a finite number of constraints that involve the geometrical relationship structures inherent to a curve and by using a covariant formalism. We emphasize our approach for null curves. For such systems, the natural time parameter is a pseudo-arclength whose properties resemble those of the standard proper time. We illustrate the formalism by applying it to some models for relativistic particles.
Implicit face prototype learning from geometric information.
Or, Charles C-F; Wilson, Hugh R
2013-04-19
There is evidence that humans implicitly learn an average or prototype of previously studied faces, as the unseen face prototype is falsely recognized as having been learned (Solso & McCarthy, 1981). Here we investigated the extent and nature of face prototype formation where observers' memory was tested after they studied synthetic faces defined purely in geometric terms in a multidimensional face space. We found a strong prototype effect: The basic results showed that the unseen prototype averaged from the studied faces was falsely identified as learned at a rate of 86.3%, whereas individual studied faces were identified correctly 66.3% of the time and the distractors were incorrectly identified as having been learned only 32.4% of the time. This prototype learning lasted at least 1 week. Face prototype learning occurred even when the studied faces were further from the unseen prototype than the median variation in the population. Prototype memory formation was evident in addition to memory formation of studied face exemplars as demonstrated in our models. Additional studies showed that the prototype effect can be generalized across viewpoints, and head shape and internal features separately contribute to prototype formation. Thus, implicit face prototype extraction in a multidimensional space is a very general aspect of geometric face learning. Copyright © 2013 Elsevier Ltd. All rights reserved.
Geometric reconstruction methods for electron tomography
Energy Technology Data Exchange (ETDEWEB)
Alpers, Andreas, E-mail: alpers@ma.tum.de [Zentrum Mathematik, Technische Universität München, D-85747 Garching bei München (Germany); Gardner, Richard J., E-mail: Richard.Gardner@wwu.edu [Department of Mathematics, Western Washington University, Bellingham, WA 98225-9063 (United States); König, Stefan, E-mail: koenig@ma.tum.de [Zentrum Mathematik, Technische Universität München, D-85747 Garching bei München (Germany); Pennington, Robert S., E-mail: robert.pennington@uni-ulm.de [Center for Electron Nanoscopy, Technical University of Denmark, DK-2800 Kongens Lyngby (Denmark); Boothroyd, Chris B., E-mail: ChrisBoothroyd@cantab.net [Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons and Peter Grünberg Institute, Forschungszentrum Jülich, D-52425 Jülich (Germany); Houben, Lothar, E-mail: l.houben@fz-juelich.de [Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons and Peter Grünberg Institute, Forschungszentrum Jülich, D-52425 Jülich (Germany); Dunin-Borkowski, Rafal E., E-mail: rdb@fz-juelich.de [Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons and Peter Grünberg Institute, Forschungszentrum Jülich, D-52425 Jülich (Germany); Joost Batenburg, Kees, E-mail: Joost.Batenburg@cwi.nl [Centrum Wiskunde and Informatica, NL-1098XG, Amsterdam, The Netherlands and Vision Lab, Department of Physics, University of Antwerp, B-2610 Wilrijk (Belgium)
2013-05-15
Electron tomography is becoming an increasingly important tool in materials science for studying the three-dimensional morphologies and chemical compositions of nanostructures. The image quality obtained by many current algorithms is seriously affected by the problems of missing wedge artefacts and non-linear projection intensities due to diffraction effects. The former refers to the fact that data cannot be acquired over the full 180° tilt range; the latter implies that for some orientations, crystalline structures can show strong contrast changes. To overcome these problems we introduce and discuss several algorithms from the mathematical fields of geometric and discrete tomography. The algorithms incorporate geometric prior knowledge (mainly convexity and homogeneity), which also in principle considerably reduces the number of tilt angles required. Results are discussed for the reconstruction of an InAs nanowire. - Highlights: ► Four algorithms for electron tomography are introduced that utilize prior knowledge. ► Objects are assumed to be homogeneous; convexity and regularity is also discussed. ► We are able to reconstruct slices of a nanowire from as few as four projections. ► Algorithms should be selected based on the specific reconstruction task at hand.
Geometric Modelling of Octagonal Lamp Poles
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T. O. Chan
2014-06-01
Full Text Available Lamp poles are one of the most abundant highway and community components in modern cities. Their supporting parts are primarily tapered octagonal cones specifically designed for wind resistance. The geometry and the positions of the lamp poles are important information for various applications. For example, they are important to monitoring deformation of aged lamp poles, maintaining an efficient highway GIS system, and also facilitating possible feature-based calibration of mobile LiDAR systems. In this paper, we present a novel geometric model for octagonal lamp poles. The model consists of seven parameters in which a rotation about the z-axis is included, and points are constrained by the trigonometric property of 2D octagons after applying the rotations. For the geometric fitting of the lamp pole point cloud captured by a terrestrial LiDAR, accurate initial parameter values are essential. They can be estimated by first fitting the points to a circular cone model and this is followed by some basic point cloud processing techniques. The model was verified by fitting both simulated and real data. The real data includes several lamp pole point clouds captured by: (1 Faro Focus 3D and (2 Velodyne HDL-32E. The fitting results using the proposed model are promising, and up to 2.9 mm improvement in fitting accuracy was realized for the real lamp pole point clouds compared to using the conventional circular cone model. The overall result suggests that the proposed model is appropriate and rigorous.
GEOMETRIC AND RADIOMETRIC EVALUATION OF RASAT IMAGES
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A. Cam
2016-06-01
Full Text Available RASAT, the second remote sensing satellite of Turkey, was designed and assembled, and also is being operated by TÜBİTAK Uzay (Space Technologies Research Institute (Ankara. RASAT images in various levels are available free-of-charge via Gezgin portal for Turkish citizens. In this paper, the images in panchromatic (7.5 m GSD and RGB (15 m GSD bands in various levels were investigated with respect to its geometric and radiometric characteristics. The first geometric analysis is the estimation of the effective GSD as less than 1 pixel for radiometrically processed level (L1R of both panchromatic and RGB images. Secondly, 2D georeferencing accuracy is estimated by various non-physical transformation models (similarity, 2D affine, polynomial, affine projection, projective, DLT and GCP based RFM reaching sub-pixel accuracy using minimum 39 and maximum 52 GCPs. The radiometric characteristics are also investigated for 8 bits, estimating SNR between 21.8-42.2, and noise 0.0-3.5 for panchromatic and MS images for L1R when the sea is masked to obtain the results for land areas. The analysis show that RASAT images satisfies requirements for various applications. The research is carried out in Zonguldak test site which is mountainous and partly covered by dense forest and urban areas.
The elastic theory of shells using geometric algebra.
Gregory, A L; Lasenby, J; Agarwal, A
2017-03-01
We present a novel derivation of the elastic theory of shells. We use the language of geometric algebra, which allows us to express the fundamental laws in component-free form, thus aiding physical interpretation. It also provides the tools to express equations in an arbitrary coordinate system, which enhances their usefulness. The role of moments and angular velocity, and the apparent use by previous authors of an unphysical angular velocity, has been clarified through the use of a bivector representation. In the linearized theory, clarification of previous coordinate conventions which have been the cause of confusion is provided, and the introduction of prior strain into the linearized theory of shells is made possible.
A geometric measure of dark energy with pairs of galaxies.
Marinoni, Christian; Buzzi, Adeline
2010-11-25
Observations indicate that the expansion of the Universe is accelerating, which is attributed to a ‘dark energy’ component that opposes gravity. There is a purely geometric test of the expansion of the Universe (the Alcock–Paczynski test), which would provide an independent way of investigating the abundance (Ω(X)) and equation of state (W(X)) of dark energy. It is based on an analysis of the geometrical distortions expected from comparing the real-space and redshift-space shape of distant cosmic structures, but it has proved difficult to implement. Here we report an analysis of the symmetry properties of distant pairs of galaxies from archival data. This allows us to determine that the Universe is flat. By alternately fixing its spatial geometry at Ω(k)≡0 and the dark energy equation-of-state parameter at W(X)≡-1, and using the results of baryon acoustic oscillations, we can establish at the 68.3% confidence level that and -0.85>W(X)>-1.12 and 0.60<Ω(X)<0.80.
Triangular Geometrized Sampling Heuristics for Fast Optimal Motion Planning
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Ahmed Hussain Qureshi
2015-02-01
Full Text Available Rapidly-exploring Random Tree (RRT-based algorithms have become increasingly popular due to their lower computational complexity as compared with other path planning algorithms. The recently presented RRT* motion planning algorithm improves upon the original RRT algorithm by providing optimal path solutions. While RRT determines an initial collision-free path fairly quickly, RRT* guarantees almost certain convergence to an optimal, obstacle-free path from the start to the goal points for any given geometrical environment. However, the main limitations of RRT* include its slow processing rate and high memory consumption, due to the large number of iterations required for calculating the optimal path. In order to overcome these limitations, we present another improvement, i.e, the Triangular Geometerized-RRT* (TG-RRT* algorithm, which utilizes triangular geometrical methods to improve the performance of the RRT* algorithm in terms of the processing time and a decreased number of iterations required for an optimal path solution. Simulations comparing the performance results of the improved TG-RRT* with RRT* are presented to demonstrate the overall improvement in performance and optimal path detection.
A Geometric Algebra Co-Processor for Color Edge Detection
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Biswajit Mishra
2015-01-01
Full Text Available This paper describes advancement in color edge detection, using a dedicated Geometric Algebra (GA co-processor implemented on an Application Specific Integrated Circuit (ASIC. GA provides a rich set of geometric operations, giving the advantage that many signal and image processing operations become straightforward and the algorithms intuitive to design. The use of GA allows images to be represented with the three R, G, B color channels defined as a single entity, rather than separate quantities. A novel custom ASIC is proposed and fabricated that directly targets GA operations and results in significant performance improvement for color edge detection. Use of the hardware described in this paper also shows that the convolution operation with the rotor masks within GA belongs to a class of linear vector filters and can be applied to image or speech signals. The contribution of the proposed approach has been demonstrated by implementing three different types of edge detection schemes on the proposed hardware. The overall performance gains using the proposed GA Co-Processor over existing software approaches are more than 3.2× faster than GAIGEN and more than 2800× faster than GABLE. The performance of the fabricated GA co-processor is approximately an order of magnitude faster than previously published results for hardware implementations.
Percolation and cooperation with mobile agents: geometric and strategy clusters.
Vainstein, Mendeli H; Brito, Carolina; Arenzon, Jeferson J
2014-08-01
We study the conditions for persistent cooperation in an off-lattice model of mobile agents playing the Prisoner's Dilemma game with pure, unconditional strategies. Each agent has an exclusion radius r(P), which accounts for the population viscosity, and an interaction radius r(int), which defines the instantaneous contact network for the game dynamics. We show that, differently from the r(P)=0 case, the model with finite-sized agents presents a coexistence phase with both cooperators and defectors, besides the two absorbing phases, in which either cooperators or defectors dominate. We provide, in addition, a geometric interpretation of the transitions between phases. In analogy with lattice models, the geometric percolation of the contact network (i.e., irrespective of the strategy) enhances cooperation. More importantly, we show that the percolation of defectors is an essential condition for their survival. Differently from compact clusters of cooperators, isolated groups of defectors will eventually become extinct if not percolating, independently of their size.
Mask roughness induced LER: geometric model at long correlation lengths
Energy Technology Data Exchange (ETDEWEB)
McClinton, Brittany M.; Naulleau, Patrick P.
2011-02-11
Collective understanding of how both the resist and line-edge roughness (LER) on the mask affect the final printed LER has made significant advances. What is poorly understood, however, is the extent to which mask surface roughness couples to image plane LER as a function of illumination conditions, NA, and defocus. Recently, progress has been made in formulating a simplified solution for mask roughness induced LER. Here, we investigate the LER behavior at long correlation lengths of surface roughness on the mask. We find that for correlation lengths greater than 3/NA in wafer dimensions and CDs greater than approximately 0.75/NA, the previously described simplified model, which remains based on physical optics, converges to a 'geometric regime' which is based on ray optics and is independent of partial coherence. In this 'geometric regime', the LER is proportional to the mask slope error as it propagates through focus, and provides a faster alternative to calculating LER in contrast to either full 2D aerial image simulation modeling or the newly proposed physical optics model. Data is presented for both an NA = 0.32 and an NA = 0.5 imaging system for CDs of 22-nm and 50-nm horizontal-line-dense structures.
Unconstrained Finite Element for Geometrical Nonlinear Dynamics of Shells
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Humberto Breves Coda
2009-01-01
Full Text Available This paper presents a positional FEM formulation to deal with geometrical nonlinear dynamics of shells. The main objective is to develop a new FEM methodology based on the minimum potential energy theorem written regarding nodal positions and generalized unconstrained vectors not displacements and rotations. These characteristics are the novelty of the present work and avoid the use of large rotation approximations. A nondimensional auxiliary coordinate system is created, and the change of configuration function is written following two independent mappings from which the strain energy function is derived. This methodology is called positional and, as far as the authors' knowledge goes, is a new procedure to approximated geometrical nonlinear structures. In this paper a proof for the linear and angular momentum conservation property of the Newmark algorithm is provided for total Lagrangian description. The proposed shell element is locking free for elastic stress-strain relations due to the presence of linear strain variation along the shell thickness. The curved, high-order element together with an implicit procedure to solve nonlinear equations guarantees precision in calculations. The momentum conserving, the locking free behavior, and the frame invariance of the adopted mapping are numerically confirmed by examples.
Metatarsal Shape and Foot Type: A Geometric Morphometric Analysis.
Telfer, Scott; Kindig, Matthew W; Sangeorzan, Bruce J; Ledoux, William R
2017-03-01
Planus and cavus foot types have been associated with an increased risk of pain and disability. Improving our understanding of the geometric differences between bones in different foot types may provide insights into injury risk profiles and have implications for the design of musculoskeletal and finite-element models. In this study, we performed a geometric morphometric analysis on the geometry of metatarsal bones from 65 feet, segmented from computed tomography (CT) scans. These were categorized into four foot types: pes cavus, neutrally aligned, asymptomatic pes planus, and symptomatic pes planus. Generalized procrustes analysis (GPA) followed by permutation tests was used to determine significant shape differences associated with foot type and sex, and principal component analysis was used to find the modes of variation for each metatarsal. Significant shape differences were found between foot types for all the metatarsals (p foot types. Analysis of the principal components of variation showed pes cavus bones to have reduced cross-sectional areas in the sagittal and frontal planes. The first (p = 0.02) and fourth metatarsals (p = 0.003) were found to have significant sex-based differences, with first metatarsals from females shown to have reduced width, and fourth metatarsals from females shown to have reduced frontal and sagittal plane cross-sectional areas. Overall, these findings suggest that metatarsal bones have distinct morphological characteristics that are associated with foot type and sex, with implications for our understanding of anatomy and numerical modeling of the foot.
Probabilistic atlas and geometric variability estimation to drive tissue segmentation.
Xu, Hao; Thirion, Bertrand; Allassonnière, Stéphanie
2014-09-10
Computerized anatomical atlases play an important role in medical image analysis. While an atlas usually refers to a standard or mean image also called template, which presumably represents well a given population, it is not enough to characterize the observed population in detail. A template image should be learned jointly with the geometric variability of the shapes represented in the observations. These two quantities will in the sequel form the atlas of the corresponding population. The geometric variability is modeled as deformations of the template image so that it fits the observations. In this paper, we provide a detailed analysis of a new generative statistical model based on dense deformable templates that represents several tissue types observed in medical images. Our atlas contains both an estimation of probability maps of each tissue (called class) and the deformation metric. We use a stochastic algorithm for the estimation of the probabilistic atlas given a dataset. This atlas is then used for atlas-based segmentation method to segment the new images. Experiments are shown on brain T1 MRI datasets. Copyright © 2014 John Wiley & Sons, Ltd.
Geometric Hamilton-Jacobi theory on Nambu-Poisson manifolds
de León, M.; Sardón, C.
2017-03-01
The Hamilton-Jacobi theory is a formulation of classical mechanics equivalent to other formulations as Newtonian, Lagrangian, or Hamiltonian mechanics. The primordial observation of a geometric Hamilton-Jacobi theory is that if a Hamiltonian vector field XH can be projected into the configuration manifold by means of a 1-form dW, then the integral curves of the projected vector field XHd Wcan be transformed into integral curves of XH provided that W is a solution of the Hamilton-Jacobi equation. Our aim is to derive a geometric Hamilton-Jacobi theory for physical systems that are compatible with a Nambu-Poisson structure. For it, we study Lagrangian submanifolds of a Nambu-Poisson manifold and obtain explicitly an expression for a Hamilton-Jacobi equation on such a manifold. We apply our results to two interesting examples in the physics literature: the third-order Kummer-Schwarz equations and a system of n copies of a first-order differential Riccati equation. From the first example, we retrieve the original Nambu bracket in three dimensions and from the second example, we retrieve Takhtajan's generalization of the Nambu bracket to n dimensions.
Geometrical modelling and calibration of video cameras for underwater navigation
Energy Technology Data Exchange (ETDEWEB)
Melen, T.
1994-11-01
Video cameras and other visual sensors can provide valuable navigation information for underwater remotely operated vehicles. The thesis relates to the geometric modelling and calibration of video cameras. To exploit the accuracy potential of a video camera, all systematic errors must be modelled and compensated for. This dissertation proposes a new geometric camera model, where linear image plane distortion (difference in scale and lack of orthogonality between the image axes) is compensated for after, and separately from, lens distortion. The new model can be viewed as an extension of the linear or DLT (Direct Linear Transformation) model and as a modification of the model traditionally used in photogrammetry. The new model can be calibrated from both planar and nonplanar calibration objects. The feasibility of the model is demonstrated in a typical camera calibration experiment, which indicates that the new model is more accurate than the traditional one. It also gives a simple solution to the problem of computing undistorted image coordinates from distorted ones. Further, the dissertation suggests how to get initial estimates for all the camera model parameters, how to select the number of parameters modelling lens distortion and how to reduce the dimension of the search space in the nonlinear optimization. There is also a discussion on the use of analytical partial derivates. The new model is particularly well suited for video images with non-square pixels, but it may also advantagely be used with professional photogrammetric equipment. 63 refs., 11 figs., 6 tabs.
An investigation the effects of geometric tolerances on the natural frequencies of rotating shafts
Directory of Open Access Journals (Sweden)
Ali Akbar Ansarifard
2015-04-01
Full Text Available This paper presents the effects of geometric tolerances on the rotating shafts natural frequencies. Due to modeling the tolerances, a code is written in MATLAB 2013 software that produces deviated points. Deviated points are controlled by different geometric tolerances, including cylindricity, total run-out and coaxiality tolerances. Final surfaces and models passing through the points are created using SolidWorks 2013 software and finally modal analysis is carried out with the FE software. It is observed whatever the natural frequency is higher or the geometric tolerances are greater, the real and ideal shafts natural frequencies are more distant. Also difference percentage between ideal and real frequencies is investigated. The results show that the percentage value is approximately constant for every mode shapes.
A UGV-based laser scanner system for measuring tree geometric characteristics
Wang, Yonghui; Lan, Yubin; Zheng, Yongjun; Lee, Kevin; Cui, Suxia; Lian, Jian-ao
2013-09-01
This paper introduces a laser scanner based measurement system for measuring crop/tree geometric characteristics. The measurement system, which is mounted on a Unmanned Ground Vehicle (UGV), contains a SICK LMS511 PRO laser scanner, a GPS, and a computer. The LMS511 PRO scans objects within distance up to 80 meters with a scanning frequency of 25 up to 100Hz and with an angular resolution of 0.1667° up to 1°. With an Ethernet connection, this scanner can output the measured values in real time. The UGV is a WIFI based remotely controlled agricultural robotics system. During field tests, the laser scanner was mounted on the UGV vertically to scan crops or trees. The UGV moved along the row direction with certain average travel speed. The experimental results show that the UGV's travel speed significantly affects the measurement accuracy. A slower speed produces more accurate measuring results. With the developed measurement system, crop/tree canopy height, width, and volume can be accurately measured in a real-time manner. With a higher spatial resolution, the original data set may even provide useful information in predicting crop/tree growth and productivity. In summary, the UGV based measurement system developed in this research can measure the crop/tree geometric characteristics with good accuracy and will work as a step stone for our future UGV based intelligent agriculture system, which will include variable rate spray and crop/tree growth and productivity prediction through analyzing the measured results of the laser scanner system.
Trigonometry of the quantum state space, geometric phases and relative phases
Ortega, R
2003-01-01
A complete set of invariants for three states in the quantum space of states P is obtained together with a complete set of relationships linking them. This is done in a way that preserves the self-duality of P and leads to a clear geometric description of invariants (distances, lateral phases; Hermitian angles, angular phases; and two purely triangular phases). Some of these invariants appear here for the first time. Symplectic area (and hence the triangle geometric phase) is proportional to a 'mixed phase excess', thus extending to P the relation 'area-angular excess' in the real sphere. The new triangle lateral phases provide a description, intrinsic to P, of relative phases in a superposition. This approach also provides closed expressions for the triangle holonomy associated with the usual Fubini-Study metric in P, as well as many other expressions for similar 'loop' operators along the triangle, including closed and exact expressions for the triangle Aharonov-Anandan geometric phase.
Influence of geometrical characteristics of sidewall-type multiple aneurysms on hemodynamic factors
Directory of Open Access Journals (Sweden)
Yufeng Hua
2015-06-01
Full Text Available Multiple aneurysms occur rarely and have not been well investigated. The purpose of this study is to verify whether high rupture risk of multiple aneurysms is due to the interaction between multiple aneurysms’ geometrical characteristics. The following geometrical characteristics were varied in an idealized sidewall-type model: aneurysm a1’s dome-neck length (S, size ratio, inflow angle (α, distance between two aneurysms (D, and the parent vessel’s angle (θ. We varied the parent blood vessel and aneurysm sac a1’s geometrical characteristics to analyze their hemodynamic influence on aneurysm a2. By comparing the influence on aneurysm a2, we found that parent blood vessel geometrical characteristics such as the distance between aneurysms (D and the parent vessel’s angle (θ were the most hemodynamically influential characteristics examined. The impact of varying the aneurysm’s geometrical characteristics such as dome-neck length (S, size ratio, and inflow angle (α was not obvious. The reason for the higher rupture rate of multiple aneurysms is not due to interactions between the aneurysm sacs but due to factors of each individual aneurysm.
Pluecker, T.; Wegewijs, M. R.; Splettstoesser, J.
2017-04-01
We set up a general density-operator approach to geometric steady-state pumping through slowly driven open quantum systems. This approach applies to strongly interacting systems that are weakly coupled to multiple reservoirs at high temperature, illustrated by an Anderson quantum dot. Pumping gives rise to a nonadiabatic geometric phase that can be described by a framework originally developed for classical dissipative systems by Landsberg. This geometric phase is accumulated by the transported observable (charge, spin, energy) and not by the quantum state. It thus differs radically from the adiabatic Berry-Simon phase, even when generalizing it to mixed states, following Sarandy and Lidar. As a key feature, our geometric formulation of pumping stays close to a direct physical intuition (i) by tying gauge transformations to calibration of the meter registering the transported observable and (ii) by deriving a geometric connection from a driving-frequency expansion of the current. Furthermore, our approach provides a systematic and efficient way to compute the geometric pumping of various observables, including charge, spin, energy, and heat. These insights seem to be generalizable beyond the present paper's working assumptions (e.g., Born-Markov limit) to more general open-system evolutions involving memory and strong-coupling effects due to low-temperature reservoirs as well. Our geometric curvature formula reveals a general experimental scheme for performing geometric transport spectroscopy that enhances standard nonlinear spectroscopies based on measurements for static parameters. We indicate measurement strategies for separating the useful geometric pumping contribution to transport from nongeometric effects. A large part of the paper is devoted to an explicit comparison with the Sinitsyn-Nemenmann full-counting-statistics (FCS) approach to geometric pumping, restricting attention to the first moments of the pumped observable. Covering all key aspects, gauge
Energy Technology Data Exchange (ETDEWEB)
Watts, Seth [Computational Engineering Division, Lawrence Livermore National Laboratory, 7000 East Ave Livermore 94550 CA USA; Tortorelli, Daniel A. [Center for Design and Optimization, Lawrence Livermore National Laboratory, 7000 East Ave Livermore 94550 CA USA; Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, 1206 W. Green St., Urbana IL 61821 USA
2017-07-27
Topology optimization is a methodology for assigning material or void to each point in a design domain in a way that extremizes some objective function, such as the compliance of a structure under given loads, subject to various imposed constraints, such as an upper bound on the mass of the structure. Geometry projection is a means to parameterize the topology optimization problem, by describing the design in a way that is independent of the mesh used for analysis of the design's performance; it results in many fewer design parameters, necessarily resolves the ill-posed nature of the topology optimization problem, and provides sharp descriptions of the material interfaces. We extend previous geometric projection work to 3 dimensions and design unit cells for lattice materials using inverse homogenization. We perform a sensitivity analysis of the geometric projection and show it has smooth derivatives, making it suitable for use with gradient-based optimization algorithms. The technique is demonstrated by designing unit cells comprised of a single constituent material plus void space to obtain light, stiff materials with cubic and isotropic material symmetry. We also design a single-constituent isotropic material with negative Poisson's ratio and a light, stiff material comprised of 2 constituent solids plus void space.
Modern Geometric Methods of Distance Determination
Thévenin, Frédéric; Falanga, Maurizio; Kuo, Cheng Yu; Pietrzyński, Grzegorz; Yamaguchi, Masaki
2017-11-01
Building a 3D picture of the Universe at any distance is one of the major challenges in astronomy, from the nearby Solar System to distant Quasars and galaxies. This goal has forced astronomers to develop techniques to estimate or to measure the distance of point sources on the sky. While most distance estimates used since the beginning of the 20th century are based on our understanding of the physics of objects of the Universe: stars, galaxies, QSOs, the direct measures of distances are based on the geometric methods as developed in ancient Greece: the parallax, which has been applied to stars for the first time in the mid-19th century. In this review, different techniques of geometrical astrometry applied to various stellar and cosmological (Megamaser) objects are presented. They consist in parallax measurements from ground based equipment or from space missions, but also in the study of binary stars or, as we shall see, of binary systems in distant extragalactic sources using radio telescopes. The Gaia mission will be presented in the context of stellar physics and galactic structure, because this key space mission in astronomy will bring a breakthrough in our understanding of stars, galaxies and the Universe in their nature and evolution with time. Measuring the distance to a star is the starting point for an unbiased description of its physics and the estimate of its fundamental parameters like its age. Applying these studies to candles such as the Cepheids will impact our large distance studies and calibration of other candles. The text is constructed as follows: introducing the parallax concept and measurement, we shall present briefly the Gaia satellite which will be the future base catalogue of stellar astronomy in the near future. Cepheids will be discussed just after to demonstrate the state of the art in distance measurements in the Universe with these variable stars, with the objective of 1% of error in distances that could be applied to our closest
On the geometrization of quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Tavernelli, Ivano, E-mail: ita@zurich.ibm.com
2016-08-15
Nonrelativistic quantum mechanics is commonly formulated in terms of wavefunctions (probability amplitudes) obeying the static and the time-dependent Schrödinger equations (SE). Despite the success of this representation of the quantum world a wave–particle duality concept is required to reconcile the theory with observations (experimental measurements). A first solution to this dichotomy was introduced in the de Broglie–Bohm theory according to which a pilot-wave (solution of the SE) is guiding the evolution of particle trajectories. Here, I propose a geometrization of quantum mechanics that describes the time evolution of particles as geodesic lines in a curved space, whose curvature is induced by the quantum potential. This formulation allows therefore the incorporation of all quantum effects into the geometry of space–time, as it is the case for gravitation in the general relativity.
Non-geometric branes are DFT monopoles
Energy Technology Data Exchange (ETDEWEB)
Bakhmatov, Ilya [Kazan Federal University, Institute of Physics, General Relativity Department,Kremlevskaya 16a, 420111, Kazan (Russian Federation); Kleinschmidt, Axel [Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut),Am Mühlenberg 1, DE-14476 Potsdam (Germany); International Solvay Institutes,Campus Plaine C.P. 231, Boulevard du Triomphe, 1050 Bruxelles (Belgium); Musaev, Edvard T. [Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut),Am Mühlenberg 1, DE-14476 Potsdam (Germany); Kazan Federal University, Institute of Physics, General Relativity Department,Kremlevskaya 16a, 420111, Kazan (Russian Federation)
2016-10-14
The double field theory monopole solution by Berman and Rudolph is shown to reproduce non-geometric backgrounds with non-vanishing Q- and R-flux upon an appropriate choice of physical and dual coordinates. The obtained backgrounds depend non-trivially on dual coordinates and have only trivial monodromies. Upon smearing the solutions along the dual coordinates one reproduces the known 5{sub 2}{sup 2} solution for the Q-brane and co-dimension 1 solution for the R-brane. The T-duality invariant magnetic charge is explicitly calculated for all these backgrounds and is found to be equal to the magnetic charge of (unsmeared) NS5-brane.
Monolithic geometric anti-spring blades
Energy Technology Data Exchange (ETDEWEB)
Cella, G. [Universita di Pisa, Pisa (Italy); Sannibale, V. [LIGO Project, California Institute of Technology, 1200 E. California Blvd, Pasadena, CA 91125 (United States)]. E-mail: sannibale_v@ligo.caltech.edu; DeSalvo, R. [LIGO Project, California Institute of Technology, 1200 E. California Blvd, Pasadena, CA 91125 (United States); Marka, S. [LIGO Project, California Institute of Technology, 1200 E. California Blvd, Pasadena, CA 91125 (United States); Takamori, A. [University of Tokyo, Tokyo (Japan)
2005-03-21
In this article we investigate the principle and properties of a vertical passive seismic noise attenuator conceived for ground based gravitational wave interferometers. This mechanical attenuator based on a particular geometry of cantilever blades called monolithic geometric anti springs (MGAS) permits the design of mechanical harmonic oscillators with very low resonant frequency (below 10 mHz). Here we address the theoretical description of the mechanical device, focusing on the most important quantities for the low-frequency regime, on the distribution of internal stresses, and on the thermal stability. In order to obtain physical insight of the attenuator peculiarities, we devise some simplified models, rather than use the brute force of finite element analysis. Those models have been used to optimize the design of a seismic attenuation system prototype for LIGO advanced configurations and for the next generation of the TAMA interferometer.
Geometrical shock dynamics of fast magnetohydrodynamic shocks
Mostert, Wouter; Pullin, Dale I.; Samtaney, Ravi; Wheatley, Vincent
2016-11-01
We extend the theory of geometrical shock dynamics (GSD, Whitham 1958), to two-dimensional fast magnetohydrodynamic (MHD) shocks moving in the presence of nonuniform magnetic fields of general orientation and strength. The resulting generalized area-Mach number rule is adapted to MHD shocks moving in two spatial dimensions. A partially-spectral numerical scheme developed from that of Schwendeman (1993) is described. This is applied to the stability of plane MHD fast shocks moving into a quiescent medium containing a uniform magnetic field whose field lines are inclined to the plane-shock normal. In particular, we consider the time taken for an initially planar shock subject to an initial perturbed magnetosonic Mach number distribution, to first form shock-shocks. Supported by KAUST OCRF Award No. URF/1/2162-01.
Geometric covers, graph orientations, counter games
DEFF Research Database (Denmark)
Berglin, Edvin
.e. Plane Cover), with improved time complexity compared to the previous best results. Our improvements are derived from a more careful treatment of the geometric properties of the covering objects than before, and invoking incidence bounds from pure geometry. An orientation of an un-directed graph...... is a directed version of it, i.e. where every un-directed edge in the original graph has been replaced by a directed edge, incident on the same two vertices, in either direction. Graph orientations with low out-degree are desirable as the foundation of data structures with many applications. If the un......-directed graph is dynamic (can be altered by some outside actor), some orientations may need to be reversed in order to maintain the low out-degree. We present a new algorithm that is simpler than earlier work, yet matches or outperforms the efficiency of these results with very few exceptions. Counter games...
Random broadcast on random geometric graphs
Energy Technology Data Exchange (ETDEWEB)
Bradonjic, Milan [Los Alamos National Laboratory; Elsasser, Robert [UNIV OF PADERBORN; Friedrich, Tobias [ICSI/BERKELEY; Sauerwald, Tomas [ICSI/BERKELEY
2009-01-01
In this work, we consider the random broadcast time on random geometric graphs (RGGs). The classic random broadcast model, also known as push algorithm, is defined as: starting with one informed node, in each succeeding round every informed node chooses one of its neighbors uniformly at random and informs it. We consider the random broadcast time on RGGs, when with high probability: (i) RGG is connected, (ii) when there exists the giant component in RGG. We show that the random broadcast time is bounded by {Omicron}({radical} n + diam(component)), where diam(component) is a diameter of the entire graph, or the giant component, for the regimes (i), or (ii), respectively. In other words, for both regimes, we derive the broadcast time to be {Theta}(diam(G)), which is asymptotically optimal.
Efficient broadcast on random geometric graphs
Energy Technology Data Exchange (ETDEWEB)
Bradonjic, Milan [Los Alamos National Laboratory; Elsasser, Robert [UNIV OF PADERBORN; Friedrich, Tobias [INTERNATIONAL COMPUTER SCI.; Sauerwald, Thomas [INTERNATIONAL COMPUTER SCI.
2009-01-01
A Randon Geometric Graph (RGG) is constructed by distributing n nodes uniformly at random in the unit square and connecting two nodes if their Euclidean distance is at most r, for some prescribed r. They analyze the following randomized broadcast algorithm on RGGs. At the beginning, there is only one informed node. Then in each round, each informed node chooses a neighbor uniformly at random and informs it. They prove that this algorithm informs every node in the largest component of a RGG in {Omicron}({radical}n/r) rounds with high probability. This holds for any value of r larger than the critical value for the emergence of a giant component. In particular, the result implies that the diameter of the giant component is {Theta}({radical}n/r).
Point- and curve-based geometric conflation
López-Vázquez, C.
2013-01-01
Geometric conflation is the process undertaken to modify the coordinates of features in dataset A in order to match corresponding ones in dataset B. The overwhelming majority of the literature considers the use of points as features to define the transformation. In this article we present a procedure to consider one-dimensional curves also, which are commonly available as Global Navigation Satellite System (GNSS) tracks, routes, coastlines, and so on, in order to define the estimate of the displacements to be applied to each object in A. The procedure involves three steps, including the partial matching of corresponding curves, the computation of some analytical expression, and the addition of a correction term in order to satisfy basic cartographic rules. A numerical example is presented. © 2013 Copyright Taylor and Francis Group, LLC.
Geometric Phase of a Transported Oscillator
Energy Technology Data Exchange (ETDEWEB)
Dittirich, W.
2004-02-25
An oscillator constrained to a plane that is transported along some surface will rotate by an angle dependent only on the path and the surface, not on the speed at which it is transported. This is thus an example of a geometric phase. We analyze this phase using the methods of parallel transport. This concept plays a key role in General Relativity, but it can also be applied in classical mechanics. The Foucault pendulum can be seen as an application of this analysis, where the surface is a sphere and the curve is a line of constant latitude. In view of some considerable confusion and erroneous treatments in the recent literature, we here present a rather simple way for visualizing the motion of the Foucault pendulum using concepts that are based on Frenet's formulae and the methods of parallel displacement.
GEOMETRICAL CHARACTERIZATION OF MICRO END MILLING TOOLS
DEFF Research Database (Denmark)
Borsetto, Francesca; Bariani, Paolo
/lubricants, milling strategies and controls. Moreover the accuracy of tool geometry directly affects the performance of the milling process influencing the dimensional tolerances of the machined part, the surface topography, the chip formation, the cutting forces and the tool-life. The dimensions of certain......The milling process is one of the most common metal removal operation used in industry. This machining process is well known since the beginning of last century and has experienced, along the years, many improvements of the basic technology, as concerns tools, machine tools, coolants...... geometrical details, as for instance the cutting edge radius, are determined by characteristics of the manufacturing process, tool material, coating etc. While for conventional size end mills the basic tool manufacturing process is well established, the reduction of the size of the tools required...
Frictional Sliding without Geometrical Reflection Symmetry
Directory of Open Access Journals (Sweden)
Michael Aldam
2016-10-01
Full Text Available The dynamics of frictional interfaces plays an important role in many physical systems spanning a broad range of scales. It is well known that frictional interfaces separating two dissimilar materials couple interfacial slip and normal stress variations, a coupling that has major implications on their stability, failure mechanism, and rupture directionality. In contrast, it is traditionally assumed that interfaces separating identical materials do not feature such a coupling because of symmetry considerations. We show, combining theory and experiments, that interfaces that separate bodies made of macroscopically identical materials but lack geometrical reflection symmetry generically feature such a coupling. We discuss two applications of this novel feature. First, we show that it accounts for a distinct, and previously unexplained, experimentally observed weakening effect in frictional cracks. Second, we demonstrate that it can destabilize frictional sliding, which is otherwise stable. The emerging framework is expected to find applications in a broad range of systems.
Geometric flows in Horava-Lifshitz gravity
Bakas, Ioannis; Lust, Dieter; Petropoulos, Marios
2010-01-01
We consider instanton solutions of Euclidean Horava-Lifshitz gravity in four dimensions satisfying the detailed balance condition. They are described by geometric flows in three dimensions driven by certain combinations of the Cotton and Ricci tensors as well as the cosmological-constant term. The deformation curvature terms can have competing behavior leading to a variety of fixed points. The instantons interpolate between any two fixed points, which are vacua of topologically massive gravity with Lambda > 0, and their action is finite. Special emphasis is placed on configurations with SU(2) isometry associated with homogeneous but generally non-isotropic Bianchi IX model geometries. In this case, the combined Ricci-Cotton flow reduces to an autonomous system of ordinary differential equations whose properties are studied in detail for different couplings. The occurrence and stability of isotropic and anisotropic fixed points are investigated analytically and some exact solutions are obtained. The correspond...
Implicit quasilinear differential systems: a geometrical approach
Directory of Open Access Journals (Sweden)
Miguel C. Munoz-Lecanda
1999-04-01
Full Text Available This work is devoted to the study of systems of implicit quasilinear differential equations. In general, no set of initial conditions is admissible for the system. It is shown how to obtain a vector field whose integral curves are the solution of the system, thus reducing the system to one that is ordinary. Using geometrical techniques, we give an algorithmic procedure in order to solve these problems for systems of the form $A(xdot x =alpha (x$ with $A(x$ being a singular matrix. As particular cases, we recover some results of Hamiltonian and Lagrangian Mechanics. In addition, a detailed study of the symmetries of these systems is carried out. This algorithm is applied to several examples arising from technical applications related to control theory.
Geometric Properties of Grassmannian Frames for and
Directory of Open Access Journals (Sweden)
Benedetto John J
2006-01-01
Full Text Available Grassmannian frames are frames satisfying a min-max correlation criterion. We translate a geometrically intuitive approach for two- and three-dimensional Euclidean space ( and into a new analytic method which is used to classify many Grassmannian frames in this setting. The method and associated algorithm decrease the maximum frame correlation, and hence give rise to the construction of specific examples of Grassmannian frames. Many of the results are known by other techniques, and even more generally, so that this paper can be viewed as tutorial. However, our analytic method is presented with the goal of developing it to address unresovled problems in -dimensional Hilbert spaces which serve as a setting for spherical codes, erasure channel modeling, and other aspects of communications theory.
Random geometric graphs with general connection functions.
Dettmann, Carl P; Georgiou, Orestis
2016-03-01
In the original (1961) Gilbert model of random geometric graphs, nodes are placed according to a Poisson point process, and links formed between those within a fixed range. Motivated by wireless ad hoc networks "soft" or "probabilistic" connection models have recently been introduced, involving a "connection function" H(r) that gives the probability that two nodes at distance r are linked (directly connect). In many applications (not only wireless networks), it is desirable that the graph is connected; that is, every node is linked to every other node in a multihop fashion. Here the connection probability of a dense network in a convex domain in two or three dimensions is expressed in terms of contributions from boundary components for a very general class of connection functions. It turns out that only a few quantities such as moments of the connection function appear. Good agreement is found with special cases from previous studies and with numerical simulations.
Geometric documentation of underwater archaeological sites
Directory of Open Access Journals (Sweden)
Eleni Diamanti
2013-12-01
Full Text Available Photogrammetry has often been the most preferable method for the geometric documentation of monuments, especially in cases of highly complex objects, of high accuracy and quality requirements and, of course, budget, time or accessibility limitations. Such limitations, requirements and complexities are undoubtedly features of the highly challenging task of surveying an underwater archaeological site. This paper is focused on the case of a Hellenistic shipwreck found in Greece at the Southern Euboean gulf, 40-47 meters below the sea surface. Underwater photogrammetry was chosen as the ideal solution for the detailed and accurate mapping of a shipwreck located in an environment with limited accessibility. There are time limitations when diving at these depths so it is essential that the data collection time is kept as short as possible. This makes custom surveying techniques rather impossible to apply. However, with the growing use of consumer cameras and photogrammetric software, this application is becoming easier, thus benefiting a wide variety of underwater sites. Utilizing cameras for underwater photogrammetry though, poses some crucial modeling problems, due to the refraction effect and further additional parameters which have to be co-estimated [1]. The applied method involved an underwater calibration of the camera as well as conventional field survey measurements in order to establish a reference frame. The application of a three-dimensional trilateration using common tape measures was chosen for this reason. Among the software that was used for surveying and photogrammetry processing, were Site Recorder SE, Eos Systems Photomodeler, ZI’s SSK and Rhinoceros. The underwater archaeological research at the Southern Euboean gulf is a continuing project carried out by the Hellenic Institute for Marine Archaeology (H.I.M.A. in collaboration with the Greek Ephorate of Underwater Antiquities, under the direction of the archaeologist G
A Geometric Representation of Collective Attention Flows.
Directory of Open Access Journals (Sweden)
Peiteng Shi
Full Text Available With the fast development of Internet and WWW, "information overload" has become an overwhelming problem, and collective attention of users will play a more important role nowadays. As a result, knowing how collective attention distributes and flows among different websites is the first step to understand the underlying dynamics of attention on WWW. In this paper, we propose a method to embed a large number of web sites into a high dimensional Euclidean space according to the novel concept of flow distance, which both considers connection topology between sites and collective click behaviors of users. With this geometric representation, we visualize the attention flow in the data set of Indiana university clickstream over one day. It turns out that all the websites can be embedded into a 20 dimensional ball, in which, close sites are always visited by users sequentially. The distributions of websites, attention flows, and dissipations can be divided into three spherical crowns (core, interim, and periphery. 20% popular sites (Google.com, Myspace.com, Facebook.com, etc. attracting 75% attention flows with only 55% dissipations (log off users locate in the central layer with the radius 4.1. While 60% sites attracting only about 22% traffics with almost 38% dissipations locate in the middle area with radius between 4.1 and 6.3. Other 20% sites are far from the central area. All the cumulative distributions of variables can be well fitted by "S"-shaped curves. And the patterns are stable across different periods. Thus, the overall distribution and the dynamics of collective attention on websites can be well exhibited by this geometric representation.
A Geometric Representation of Collective Attention Flows.
Shi, Peiteng; Huang, Xiaohan; Wang, Jun; Zhang, Jiang; Deng, Su; Wu, Yahui
2015-01-01
With the fast development of Internet and WWW, "information overload" has become an overwhelming problem, and collective attention of users will play a more important role nowadays. As a result, knowing how collective attention distributes and flows among different websites is the first step to understand the underlying dynamics of attention on WWW. In this paper, we propose a method to embed a large number of web sites into a high dimensional Euclidean space according to the novel concept of flow distance, which both considers connection topology between sites and collective click behaviors of users. With this geometric representation, we visualize the attention flow in the data set of Indiana university clickstream over one day. It turns out that all the websites can be embedded into a 20 dimensional ball, in which, close sites are always visited by users sequentially. The distributions of websites, attention flows, and dissipations can be divided into three spherical crowns (core, interim, and periphery). 20% popular sites (Google.com, Myspace.com, Facebook.com, etc.) attracting 75% attention flows with only 55% dissipations (log off users) locate in the central layer with the radius 4.1. While 60% sites attracting only about 22% traffics with almost 38% dissipations locate in the middle area with radius between 4.1 and 6.3. Other 20% sites are far from the central area. All the cumulative distributions of variables can be well fitted by "S"-shaped curves. And the patterns are stable across different periods. Thus, the overall distribution and the dynamics of collective attention on websites can be well exhibited by this geometric representation.
Forward error correction based on algebraic-geometric theory
A Alzubi, Jafar; M Chen, Thomas
2014-01-01
This book covers the design, construction, and implementation of algebraic-geometric codes from Hermitian curves. Matlab simulations of algebraic-geometric codes and Reed-Solomon codes compare their bit error rate using different modulation schemes over additive white Gaussian noise channel model. Simulation results of Algebraic-geometric codes bit error rate performance using quadrature amplitude modulation (16QAM and 64QAM) are presented for the first time and shown to outperform Reed-Solomon codes at various code rates and channel models. The book proposes algebraic-geometric block turbo codes. It also presents simulation results that show an improved bit error rate performance at the cost of high system complexity due to using algebraic-geometric codes and Chase-Pyndiah’s algorithm simultaneously. The book proposes algebraic-geometric irregular block turbo codes (AG-IBTC) to reduce system complexity. Simulation results for AG-IBTCs are presented for the first time.
Generalizations of fuzzy linguistic control points in geometric design
Sallehuddin, M. H.; Wahab, A. F.; Gobithaasan, R. U.
2014-07-01
Control points are geometric primitives that play an important role in designing the geometry curve and surface. When these control points are blended with some basis functions, there are several geometric models such as Bezier, B-spline and NURBS(Non-Uniform Rational B-Spline) will be produced. If the control points are defined by the theory of fuzzy sets, then fuzzy geometric models are produced. But the fuzzy geometric models can only solve the problem of uncertainty complex. This paper proposes a new definition of fuzzy control points with linguistic terms. When the fuzzy control points with linguistic terms are blended with basis functions, then a fuzzy linguistic geometric model is produced. This paper ends with some numerical examples illustrating linguistic control attributes of fuzzy geometric models.
Zhou, Junxiao; Liu, Yachao; Ke, Yougang; Luo, Hailu; Wen, Shuangchun
2015-07-01
We propose a novel method for the generation of Airy vortex and Airy vector beams based on the modulation of dynamic and geometric phases. In our scheme, the Airy beam is generated by the dynamic phase with a spatial light modulator, and the vortex phase or the vector polarization is modulated by the geometric phase with a dielectric metasurface. The modulation of the geometric phase provides an extra degree of freedom to manipulate the phase and the polarization of Airy beams. This scheme can be extended to generate any other types of optical beams with desirable phase and polarization.
Zhang, B.; MacFadden, D.; Damyanovich, A. Z.; Rieker, M.; Stainsby, J.; Bernstein, M.; Jaffray, D. A.; Mikulis, D.; Ménard, C.
2010-11-01
The purpose of this study is to develop a geometrically accurate imaging protocol at 3 T magnetic resonance imaging (MRI) for stereotactic radiosurgery (SRS) treatment planning. In order to achieve this purpose, a methodology is developed to investigate the geometric accuracy and stability of 3 T MRI for SRS in phantom and patient evaluations. Forty patients were enrolled on a prospective clinical trial. After frame placement prior to SRS, each patient underwent 3 T MRI after 1.5 T MRI and CT. MR imaging protocols included a T1-weighted gradient echo sequence and a T2-weighted spin echo sequence. Phantom imaging was performed on 3 T prior to patient imaging using the same set-up and imaging protocols. Geometric accuracy in patients and phantoms yielded comparable results for external fiducial reference deviations and internal landmarks between 3 T and 1.5 T MRI (mean stereotactic reference deviations between phantoms and patients correlated well (T1: R = 0.79; T2: R = 0.84). Statistical process control analysis on phantom QA data demonstrated the stability of our SRS imaging protocols, where the geometric accuracy of the 3 T SRS imaging protocol is operating within the appropriate tolerance. Our data provide evidence supporting the spatial validity of 3 T MRI for targeting SRS under imaging conditions investigated. We have developed a systematic approach to achieve confidence on the geometric integrity of a given imaging system/technique for clinical integration in SRS application.
Coherent cancellation of geometric phase for the OH molecule in external fields
Bhattacharya, M.; Marin, S.; Kleinert, M.
2014-05-01
The OH molecule in its ground state presents a versatile platform for precision measurement and quantum information processing. These applications vitally depend on the accurate measurement of transition energies between the OH levels. Significant sources of systematic errors in these measurements are shifts based on the geometric phase arising from the magnetic and electric fields used for manipulating OH. In this article, we present these geometric phases for fields that vary harmonically in time, as in the Ramsey technique. Our calculation of the phases is exact within the description provided by our recent analytic solution of an effective Stark-Zeeman Hamiltonian for the OH ground state. This Hamiltonian has been shown to model experimental data accurately. We find that the OH geometric phases exhibit rich structure as a function of the field rotation rate. Remarkably, we find rotation rates where the geometric phase accumulated by a specific state is zero, or where the relative geometric phase between two states vanishes. We expect these findings to be of importance to precision experiments on OH involving time-varying fields. More specifically, our analysis quantitatively characterizes an important item in the error budget for precision spectroscopy of ground-state OH.
The Madelung Picture as a Foundation of Geometric Quantum Theory
Reddiger, Maik
2017-10-01
Despite its age, quantum theory still suffers from serious conceptual difficulties. To create clarity, mathematical physicists have been attempting to formulate quantum theory geometrically and to find a rigorous method of quantization, but this has not resolved the problem. In this article we argue that a quantum theory recursing to quantization algorithms is necessarily incomplete. To provide an alternative approach, we show that the Schrödinger equation is a consequence of three partial differential equations governing the time evolution of a given probability density. These equations, discovered by Madelung, naturally ground the Schrödinger theory in Newtonian mechanics and Kolmogorovian probability theory. A variety of far-reaching consequences for the projection postulate, the correspondence principle, the measurement problem, the uncertainty principle, and the modeling of particle creation and annihilation are immediate. We also give a speculative interpretation of the equations following Bohm, Vigier and Tsekov, by claiming that quantum mechanical behavior is possibly caused by gravitational background noise.
Probing the geometric nature of particles mass in graphene systems
Dolce, Donatello
2014-01-01
According to undulatory mechanics, the Compton periodicity, which is the intrinsic proper-time recurrence of a wave function, determines the mass of the corresponding elementary particles. This provides a geometric description of the rest mass which can be consistently applied to derive the effective mass spectrum and electronic properties of the elementary charge carriers in carbon nanotubes and other condensed matter systems. The Compton periodicity is determined by the boundary conditions associated to the curled-up dimension of carbon nanotubes or analogous constraints of the charge carrier wave function. This approach shows an interesting interplay between particle physics and relativistic space-time, as well as analogies with the Kaluza-Klein theory and Holography.
Geometric properties of Banach spaces and nonlinear iterations
Chidume, Charles
2009-01-01
Nonlinear functional analysis and applications is an area of study that has provided fascination for many mathematicians across the world. This monograph delves specifically into the topic of the geometric properties of Banach spaces and nonlinear iterations, a subject of extensive research over the past thirty years. Chapters 1 to 5 develop materials on convexity and smoothness of Banach spaces, associated moduli and connections with duality maps. Key results obtained are summarized at the end of each chapter for easy reference. Chapters 6 to 23 deal with an in-depth, comprehensive and up-to-date coverage of the main ideas, concepts and results on iterative algorithms for the approximation of fixed points of nonlinear nonexpansive and pseudo-contractive-type mappings. This includes detailed workings on solutions of variational inequality problems, solutions of Hammerstein integral equations, and common fixed points (and common zeros) of families of nonlinear mappings. Carefully referenced and full of recent,...
Emergent Space-Time via a Geometric Renormalization Method
Rastgoo, Saeed
2016-01-01
We present a purely geometric renormalization scheme for metric spaces (including uncolored graphs), which consists of a coarse graining and a rescaling operation on such spaces. The coarse graining is based on the concept of quasi-isometry, which yields a sequence of discrete coarse grained spaces each having a continuum limit under the rescaling operation. We provide criteria under which such sequences do converge within a superspace of metric spaces, or may constitute the basin of attraction of a common continuum limit, which hopefully, may represent our space-time continuum. We discuss some of the properties of these coarse grained spaces as well as their continuum limits, such as scale invariance and metric similarity, and show that different layers of spacetime can carry different distance functions while being homeomorphic. Important tools in this analysis are the Gromov-Hausdorff distance functional for general metric spaces and the growth degree of graphs or networks. The whole construction is in the...
A geometrical view of modulation instability in optical fibers
Hernandez, S M; Bonetti, J; Sánchez, A D; Grosz, D F
2016-01-01
We derive a simple geometrical description of the gain of modulation instability (MI) in optical fibers based on a model which takes into account all relevant linear and nonlinear effects. This novel approach allows us to relate the shape of the MI gain to any arbitrary dispersion profile of the waveguide in a simple manner. It also yields a straightforward explanation of the non-trivial dependence of the cutoff power on high-order dispersion. Further, we show that the power level maximizing the MI gain, a unique feature enabled by self-steepening, is greatly influenced by high-order dispersion and can be explicitly obtained. Finally, our model provides a powerful tool to synthesize a desired MI gain profile by appropriate waveguide design, with the potential application to a vast number of parametric-amplification and supercontinuum-generation devices whose functioning relies upon modulation instability.
Peyronie's Reconstruction for Maximum Length and Girth Gain: Geometrical Principles
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Paulo H. Egydio
2008-01-01
Full Text Available Peyronie's disease has been associated with penile shortening and some degree of erectile dysfunction. Surgical reconstruction should be based on giving a functional penis, that is, rectifying the penis with rigidity enough to make the sexual intercourse. The procedure should be discussed preoperatively in terms of length and girth reconstruction in order to improve patient satisfaction. The tunical reconstruction for maximum penile length and girth restoration should be based on the maximum length of the dissected neurovascular bundle possible and the application of geometrical principles to define the precise site and size of tunical incision and grafting procedure. As penile rectification and rigidity are required to achieve complete functional restoration of the penis and 20 to 54% of patients experience associated erectile dysfunction, penile straightening alone may not be enough to provide complete functional restoration. Therefore, phosphodiesterase inhibitors, self-injection, or penile prosthesis may need to be added in some cases.
Wang, Ling; Abdel-Aty, Mohamed; Lee, Jaeyoung; Shi, Qi
2017-07-07
There have been numerous studies on real-time crash prediction seeking to link real-time crash likelihood with traffic and environmental predictors. Nevertheless, none has explored the impact of socio-demographic and trip generation parameters on real-time crash risk. This study analyzed the real-time crash risk for expressway ramps using traffic, geometric, socio-demographic, and trip generation predictors. Two Bayesian logistic regression models were utilized to identify crash precursors and their impact on ramp crash risk. Meanwhile, four Support Vector Machines (SVM) were applied to predict crash occurrence. Bayesian logistic regression models and SVMs commonly showed that the models with the socio-demographic and trip generation variables outperform their counterparts without those parameters. It indicates that the socio-demographic and trip generation parameters have significant impact on the real-time crash risk. The Bayesian logistic regression model results showed that the logarithm of vehicle count, speed, and percentage of home-based-work production had positive impact on crash risk. Meanwhile, off-ramps or non-diamond-ramps experienced higher crash potential than on-ramps or diamond-ramps, respectively. Though the SVMs provided good model performance, the SVM model with all variables (i.e., all traffic, geometric, socio-demographic, and trip generation variables) had an overfitting problem. Therefore, it is recommended to build SVM models based on significant variables identified by other models, such as logistic regression. Copyright © 2017 Elsevier Ltd. All rights reserved.
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Kurt E. Clothier
2010-01-01
Full Text Available This paper presents a geometric approach to solve the unknown joint angles required for the autonomous positioning of a robotic arm. A plethora of complex mathematical processes is reduced using basic trigonometric in the modeling of the robotic arm. This modeling and analysis approach is tested using a five-degree-of-freedom arm with a gripper style end effector mounted to an iRobot Create mobile platform. The geometric method is easily modifiable for similar robotic system architectures and provides the capability of local autonomy to a system which is very difficult to manually control.
The Spacetime Memory of Geometric Phases and Quantum Computing
Binder, B
2002-01-01
Spacetime memory is defined with a holonomic approach to information processing, where multi-state stability is introduced by a non-linear phase-locked loop. Geometric phases serve as the carrier of physical information and geometric memory (of orientation) given by a path integral measure of curvature that is periodically refreshed. Regarding the resulting spin-orbit coupling and gauge field, the geometric nature of spacetime memory suggests to assign intrinsic computational properties to the electromagnetic field.
On Geometric Variational Models for Inpainting Surface Holes (PREPRINT)
2006-01-01
ON GEOMETRIC VARIATIONAL MODELS FOR INPAINTING SURFACE HOLES By Vicent Caselles Gloria Haro Guillermo Sapiro and Joan Verdera IMA Preprint Series...TITLE AND SUBTITLE On Geometric Variational Models for Inpainting Surface Holes (PREPRINT) 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM...Geometric Variational Models for Inpainting Surface Holes V.Caselles1, G.Haro,1,2 G.Sapiro,3 and J.Verdera1 Corresponding author: Gloria Haro Full
Optimal control for mathematical models of cancer therapies an application of geometric methods
Schättler, Heinz
2015-01-01
This book presents applications of geometric optimal control to real life biomedical problems with an emphasis on cancer treatments. A number of mathematical models for both classical and novel cancer treatments are presented as optimal control problems with the goal of constructing optimal protocols. The power of geometric methods is illustrated with fully worked out complete global solutions to these mathematically challenging problems. Elaborate constructions of optimal controls and corresponding system responses provide great examples of applications of the tools of geometric optimal control and the outcomes aid the design of simpler, practically realizable suboptimal protocols. The book blends mathematical rigor with practically important topics in an easily readable tutorial style. Graduate students and researchers in science and engineering, particularly biomathematics and more mathematical aspects of biomedical engineering, would find this book particularly useful.
APPROACHES TO GEOMETRIC DATA ANALYSIS ON BIG AREA ADDITIVELY MANUFACTURED (BAAM) PARTS
Energy Technology Data Exchange (ETDEWEB)
Dreifus, Gregory D [ORNL; Ally, Nadya R [ORNL; Post, Brian K [ORNL; Jin, Yuan [ORNL
2016-01-01
The promise of additive manufacturing is that a user can design and print complex geometries that are very difficult, if not impossible, to machine. The capabilities of 3D printing are restricted by a number of factors, including properties of the build material, time constraints, and geometric design restrictions. In this paper, a thorough accounting and study of the geometric restrictions that exist in the current iteration of additive manufacturing (AM) fused deposition modeling (FDM) technologies are discussed. Offline and online methodologies for collecting data sets for qualitative analysis of large scale AM, in particular Oak Ridge National Laboratory s (ORNL) big area additive manufacturing (BAAM) system, are summarized. In doing so, a survey of tools for designers and software developers is provided. In particular, strategies in which geometric data can be used as training sets for smarter AM technologies in the future are explained as well.
Loop Closing Detection in RGB-D SLAM Combining Appearance and Geometric Constraints
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Heng Zhang
2015-06-01
Full Text Available A kind of multi feature points matching algorithm fusing local geometric constraints is proposed for the purpose of quickly loop closing detection in RGB-D Simultaneous Localization and Mapping (SLAM. The visual feature is encoded with BRAND (binary robust appearance and normals descriptor, which efficiently combines appearance and geometric shape information from RGB-D images. Furthermore, the feature descriptors are stored using the Locality-Sensitive-Hashing (LSH technique and hierarchical clustering trees are used to search for these binary features. Finally, the algorithm for matching of multi feature points using local geometric constraints is provided, which can effectively reject the possible false closure hypotheses. We demonstrate the efficiency of our algorithms by real-time RGB-D SLAM with loop closing detection in indoor image sequences taken with a handheld Kinect camera and comparative experiments using other algorithms in RTAB-Map dealing with a benchmark dataset.
Loop Closing Detection in RGB-D SLAM Combining Appearance and Geometric Constraints.
Zhang, Heng; Liu, Yanli; Tan, Jindong
2015-06-19
A kind of multi feature points matching algorithm fusing local geometric constraints is proposed for the purpose of quickly loop closing detection in RGB-D Simultaneous Localization and Mapping (SLAM). The visual feature is encoded with BRAND (binary robust appearance and normals descriptor), which efficiently combines appearance and geometric shape information from RGB-D images. Furthermore, the feature descriptors are stored using the Locality-Sensitive-Hashing (LSH) technique and hierarchical clustering trees are used to search for these binary features. Finally, the algorithm for matching of multi feature points using local geometric constraints is provided, which can effectively reject the possible false closure hypotheses. We demonstrate the efficiency of our algorithms by real-time RGB-D SLAM with loop closing detection in indoor image sequences taken with a handheld Kinect camera and comparative experiments using other algorithms in RTAB-Map dealing with a benchmark dataset.
A Genetic Programming Approach to Geometrical Digital Content Modeling in Web Oriented Applications
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Dragos PALAGHITA
2011-01-01
Full Text Available The paper presents the advantages of using genetic techniques in web oriented problems. The specific area of genetic programming applications that paper approaches is content modeling. The analyzed digital content is formed through the accumulation of targeted geometrical structured entities that have specific characteristics and behavior. The accumulated digital content is analyzed and specific features are extracted in order to develop an analysis system through the use of genetic programming. An experiment is presented which evolves a model based on specific features of each geometrical structured entity in the digital content base. The results show promising expectations with a low error rate which provides fair approximations related to analyzed geometrical structured entities.
Knot soliton in DNA and geometric structure of its free-energy density.
Wang, Ying; Shi, Xuguang
2017-11-13
In general, the geometric structure of DNA is characterized using an elastic rod model. The Landau model provides us a new theory to study the geometric structure of DNA. By using the decomposition of the arc unit in the helical axis of DNA, we find that the free-energy density of DNA is similar to the free-energy density of a two-condensate superconductor. By using the φ-mapping topological current theory, the torus knot soliton hidden in DNA is demonstrated. We show the relation between the geometric structure and free-energy density of DNA and the Frenet equations in differential geometry theory are considered. Therefore, the free-energy density of DNA can be expressed by the curvature and torsion of the helical axis.
Geometrical symmetries of nuclear systems: {{ D }}_{3h} and {{ T }}_{d} symmetries in light nuclei
Bijker, Roelof
2016-07-01
The role of discrete (or point-group) symmetries in α-cluster nuclei is discussed in the framework of the algebraic cluster model which describes the relative motion of the α-particles. Particular attention is paid to the discrete symmetry of the geometric arrangement of the α-particles, and the consequences for the structure of the corresponding rotational bands. The method is applied to study cluster states in the nuclei 12C and 16O. The observed level sequences can be understood in a simple way as a consequence of the underlying discrete symmetry that characterizes the geometrical configuration of the α-particles, i.e. an equilateral triangle with {{ D }}3h symmetry for 12C, and a tetrahedron with {{ T }}d symmetry for 16O. The structure of rotational bands provides a fingerprint of the underlying geometrical configuration of α-particles.
Rule-based spatial modeling with diffusing, geometrically constrained molecules
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Lohel Maiko
2010-06-01
Full Text Available Abstract Background We suggest a new type of modeling approach for the coarse grained, particle-based spatial simulation of combinatorially complex chemical reaction systems. In our approach molecules possess a location in the reactor as well as an orientation and geometry, while the reactions are carried out according to a list of implicitly specified reaction rules. Because the reaction rules can contain patterns for molecules, a combinatorially complex or even infinitely sized reaction network can be defined. For our implementation (based on LAMMPS, we have chosen an already existing formalism (BioNetGen for the implicit specification of the reaction network. This compatibility allows to import existing models easily, i.e., only additional geometry data files have to be provided. Results Our simulations show that the obtained dynamics can be fundamentally different from those simulations that use classical reaction-diffusion approaches like Partial Differential Equations or Gillespie-type spatial stochastic simulation. We show, for example, that the combination of combinatorial complexity and geometric effects leads to the emergence of complex self-assemblies and transportation phenomena happening faster than diffusion (using a model of molecular walkers on microtubules. When the mentioned classical simulation approaches are applied, these aspects of modeled systems cannot be observed without very special treatment. Further more, we show that the geometric information can even change the organizational structure of the reaction system. That is, a set of chemical species that can in principle form a stationary state in a Differential Equation formalism, is potentially unstable when geometry is considered, and vice versa. Conclusions We conclude that our approach provides a new general framework filling a gap in between approaches with no or rigid spatial representation like Partial Differential Equations and specialized coarse-grained spatial
Rizkianto, Ilham; Zulkardi; Darmawijaya
2013-01-01
Previous studies have provided that when learning shapes for the first time, young children tend to use the prototype as the reference point for comparisons, but often fail when doing so since they do not yet think about the defining attributes or the geometric properties of the shapes. Most of the time, elementary students learn geometric…
Anisotropy without tensors: a novel approach using geometric algebra.
Matos, Sérgio A; Ribeiro, Marco A; Paiva, Carlos R
2007-11-12
The most widespread approach to anisotropic media is dyadic analysis. However, to get a geometrical picture of a dielectric tensor, one has to resort to a coordinate system for a matrix form in order to obtain, for example, the index-ellipsoid, thereby obnubilating the deeper coordinate-free meaning of anisotropy itself. To overcome these shortcomings we present a novel approach to anisotropy: using geometric algebra we introduce a direct geometrical interpretation without the intervention of any coordinate system. By applying this new approach to biaxial crystals we show the effectiveness and insight that geometric algebra can bring to the optics of anisotropic media.
Geometric cutaneous melanoma: a helpful clinical sign of malignancy?
Morris, Andrew D; Gee, Bruce C; Millard, Leslie G
2003-08-01
Malignant melanomas change shape in a random pattern, with ovoid, crescentic, or nodular shapes seen most frequently. We have observed a number of malignant melanomas that have presented with a geometric, angular shape and have noted that pigmented lesions with this configuration are often found to be malignant. We present 20 patients with malignant melanoma whose lesion displayed a geometric, angular shape. Before excision for formal histopathology, all lesions were scored using the seven-point checklist and ABCDE systems and were divided into low-risk or significant risk of melanoma. Five different geometric shapes were observed. Depending on the scoring system employed, 20% to 40% of the geometric melanomas were considered to be of low risk of malignancy. The development of geometrical angular patterns in a malignant melanoma may represent a morphologic growth pattern that can be used as a clinical risk sign. Even apparently benign low-risk lesions with a geometric shape may pose a significant risk of malignant melanoma. By definition, the majority of lesions that are morphologically geometric are symmetrical in shape, which is more in favor of a benign diagnosis. This may increase the likelihood that early cutaneous melanomas with a geometric shape may be missed. Any pigmented lesion with a geometric configuration should raise the clinician's suspicion of malignancy even if considered otherwise to be of low risk by the standard melanoma checklists.
Geometric phase for collinear conical intersections. I. Geometric phase angle and vector potentials.
Li, Xuan; Brue, Daniel A; Kendrick, Brian K; Blandon, Juan D; Parker, Gregory A
2011-02-14
We present a method for properly treating collinear conical intersections in triatomic systems. The general vector potential (gauge theory) approach for including the geometric phase effects associated with collinear conical intersections in hyperspherical coordinates is presented. The current study develops an introductory method in the treatment of collinear conical intersections by using the phase angle method. The geometric phase angle, η, in terms of purely internal coordinates is derived using the example of a spin-aligned quartet lithium triatomic system. A numerical fit and thus an analytical form for the associated vector potentials are explicitly derived for this triatomic A(3) system. The application of this methodology to AB(2) and ABC systems is also discussed.
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Mauricio Valenzuela
2017-10-01
Full Text Available We propose a hybrid class of theories for higher spin gravity and matrix models, i.e., which handle simultaneously higher spin gravity fields and matrix models. The construction is similar to Vasiliev’s higher spin gravity, but part of the equations of motion are provided by the action principle of a matrix model. In particular, we construct a higher spin (gravity matrix model related to type IIB matrix models/string theory that have a well defined classical limit, and which is compatible with higher spin gravity in A d S space. As it has been suggested that higher spin gravity should be related to string theory in a high energy (tensionless regime, and, therefore to M-Theory, we expect that our construction will be useful to explore concrete connections.
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Youssef S. Al Jabbari
2012-12-01
Full Text Available OBJECTIVE: The aim of this study was to quantify the surface area, volume and specific surface area of endodontic files employing quantitative X-ray micro computed tomography (mXCT. MATERIAL AND METHODS: Three sets (six files each of the Flex-Master Ni-Ti system (Nº 20, 25 and 30, taper .04 were utilized in this study. The files were scanned by mXCT. The surface area and volume of all files were determined from the cutting tip up to 16 mm. The data from the surface area, volume and specific area were statistically evaluated using the one-way ANOVA and SNK multiple comparison tests at α=0.05, employing the file size as a discriminating variable. The correlation between the surface area and volume with nominal ISO sizes were tested employing linear regression analysis. RESULTS: The surface area and volume of Nº 30 files showed the highest value followed by Nº 25 and Nº 20 and the differences were statistically significant. The Nº 20 files showed a significantly higher specific surface area compared to Nº 25 and Nº 30. The increase in surface and volume towards higher file sizes follows a linear relationship with the nominal ISO sizes (r²=0.930 for surface area and r²=0.974 for volume respectively. Results indicated that the surface area and volume demonstrated an almost linear increase while the specific surface area exhibited an abrupt decrease towards higher sizes. CONCLUSIONS: This study demonstrates that mXCT can be effectively applied to discriminate very small differences in the geometrical features of endodontic micro-instruments, while providing quantitative information for their geometrical properties.
Higher-order techniques for some problems of nonlinear control
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Sarychev Andrey V.
2002-01-01
Full Text Available A natural first step when dealing with a nonlinear problem is an application of some version of linearization principle. This includes the well known linearization principles for controllability, observability and stability and also first-order optimality conditions such as Lagrange multipliers rule or Pontryagin's maximum principle. In many interesting and important problems of nonlinear control the linearization principle fails to provide a solution. In the present paper we provide some examples of how higher-order methods of differential geometric control theory can be used for the study nonlinear control systems in such cases. The presentation includes: nonlinear systems with impulsive and distribution-like inputs; second-order optimality conditions for bang–bang extremals of optimal control problems; methods of high-order averaging for studying stability and stabilization of time-variant control systems.
Klapa, Przemyslaw; Mitka, Bartosz; Zygmunt, Mariusz
2017-12-01
Capability of obtaining a multimillion point cloud in a very short time has made the Terrestrial Laser Scanning (TLS) a widely used tool in many fields of science and technology. The TLS accuracy matches traditional devices used in land surveying (tacheometry, GNSS – RTK), but like any measurement it is burdened with error which affects the precise identification of objects based on their image in the form of a point cloud. The point’s coordinates are determined indirectly by means of measuring the angles and calculating the time of travel of the electromagnetic wave. Each such component has a measurement error which is translated into the final result. The XYZ coordinates of a measuring point are determined with some uncertainty and the very accuracy of determining these coordinates is reduced as the distance to the instrument increases. The paper presents the results of examination of geometrical stability of a point cloud obtained by means terrestrial laser scanner and accuracy evaluation of solids determined using the cloud. Leica P40 scanner and two different settings of measuring points were used in the tests. The first concept involved placing a few balls in the field and then scanning them from various sides at similar distances. The second part of measurement involved placing balls and scanning them a few times from one side but at varying distances from the instrument to the object. Each measurement encompassed a scan of the object with automatic determination of its position and geometry. The desk studies involved a semiautomatic fitting of solids and measurement of their geometrical elements, and comparison of parameters that determine their geometry and location in space. The differences of measures of geometrical elements of balls and translations vectors of the solids centres indicate the geometrical changes of the point cloud depending on the scanning distance and parameters. The results indicate the changes in the geometry of scanned objects
Conical refraction and higher microlocalization
Liess, Otto
1993-01-01
The main topic of the book is higher analytic microlocalization and its application to problems of propagation of singularities. The part on higher microlocalization could serve as an introduction to the subject. The results on propagation refer to solutions of linear partial differentialoperators with characteristics of variable multiplicity and are of conical refraction type. The relation and interplay between these results and results or constructions from geometrical optics in crystal theory is discussed with many details. The notes are written foremost for researchers working in microlocal analysis, but it is hoped that they can also be of interest for mathematicians and physicists who work in propagation phenomena from a more classical point of view.
Geometric Methods in Physics : XXXIII Workshop
Bieliavsky, Pierre; Odzijewicz, Anatol; Schlichenmaier, Martin; Voronov, Theodore
2015-01-01
This book presents a selection of papers based on the XXXIII Białowieża Workshop on Geometric Methods in Physics, 2014. The Białowieża Workshops are among the most important meetings in the field and attract researchers from both mathematics and physics. The articles gathered here are mathematically rigorous and have important physical implications, addressing the application of geometry in classical and quantum physics. Despite their long tradition, the workshops remain at the cutting edge of ongoing research. For the last several years, each Białowieża Workshop has been followed by a School on Geometry and Physics, where advanced lectures for graduate students and young researchers are presented; some of the lectures are reproduced here. The unique atmosphere of the workshop and school is enhanced by its venue, framed by the natural beauty of the Białowieża forest in eastern Poland. The volume will be of interest to researchers and graduate students in mathematical physics, theoretical physics and m...
Uav Cameras: Overview and Geometric Calibration Benchmark
Cramer, M.; Przybilla, H.-J.; Zurhorst, A.
2017-08-01
Different UAV platforms and sensors are used in mapping already, many of them equipped with (sometimes) modified cameras as known from the consumer market. Even though these systems normally fulfil their requested mapping accuracy, the question arises, which system performs best? This asks for a benchmark, to check selected UAV based camera systems in well-defined, reproducible environments. Such benchmark is tried within this work here. Nine different cameras used on UAV platforms, representing typical camera classes, are considered. The focus is laid on the geometry here, which is tightly linked to the process of geometrical calibration of the system. In most applications the calibration is performed in-situ, i.e. calibration parameters are obtained as part of the project data itself. This is often motivated because consumer cameras do not keep constant geometry, thus, cannot be seen as metric cameras. Still, some of the commercial systems are quite stable over time, as it was proven from repeated (terrestrial) calibrations runs. Already (pre-)calibrated systems may offer advantages, especially when the block geometry of the project does not allow for a stable and sufficient in-situ calibration. Especially for such scenario close to metric UAV cameras may have advantages. Empirical airborne test flights in a calibration field have shown how block geometry influences the estimated calibration parameters and how consistent the parameters from lab calibration can be reproduced.
Mathematical methods in geometrization of coal field
Shurygin, D. N.; Kalinchenko, V. M.; Tkachev, V. A.; Tretyak, A. Ya
2017-10-01
In the work, the approach to increase overall performance of collieries on the basis of an increase in accuracy of geometrization of coal thicknesses is considered. The sequence of stages of mathematical modelling of spatial placing of indicators of a deposit taking into account allocation of homogeneous sites of thickness and an establishment of quantitative interrelations between mountain-geological indicators of coal layers is offered. As a uniform mathematical method for modelling of various interrelations, it is offered to use a method of the group accounting of arguments (MGUA), one of versions of the regressive analysis. This approach can find application during delimitation between geological homogeneous sites of coal thicknesses in the form of a linear discriminant function. By an example of division into districts of a mine field in the conditions of mine “Sadkinsky” (East Donbass), the use of the complex approach for forecasting of zones of the small amplitude of disturbance of a coal layer on the basis of the discriminant analysis and MGUA is shown.
Geometrical shock dynamics for magnetohydrodynamic fast shocks
Mostert, W.
2016-12-12
We describe a formulation of two-dimensional geometrical shock dynamics (GSD) suitable for ideal magnetohydrodynamic (MHD) fast shocks under magnetic fields of general strength and orientation. The resulting area–Mach-number–shock-angle relation is then incorporated into a numerical method using pseudospectral differentiation. The MHD-GSD model is verified by comparison with results from nonlinear finite-volume solution of the complete ideal MHD equations applied to a shock implosion flow in the presence of an oblique and spatially varying magnetic field ahead of the shock. Results from application of the MHD-GSD equations to the stability of fast MHD shocks in two dimensions are presented. It is shown that the time to formation of triple points for both perturbed MHD and gas-dynamic shocks increases as (Formula presented.), where (Formula presented.) is a measure of the initial Mach-number perturbation. Symmetry breaking in the MHD case is demonstrated. In cylindrical converging geometry, in the presence of an azimuthal field produced by a line current, the MHD shock behaves in the mean as in Pullin et al. (Phys. Fluids, vol. 26, 2014, 097103), but suffers a greater relative pressure fluctuation along the shock than the gas-dynamic shock. © 2016 Cambridge University Press
Geometrical modeling of fibrous materials under compression
Maze, Benoit; Tafreshi, Hooman Vahedi; Pourdeyhimi, Behnam
2007-10-01
Many fibrous materials such as nonwovens are consolidated via compaction rolls in a so-called calendering process. Hot rolls compress the fiber assembly and cause fiber-to-fiber bonding resulting in a strong yet porous structure. In this paper, we describe an algorithm for generating three dimensional virtual fiberwebs and simulating the geometrical changes that happen to the structure during the calendering process. Fibers are assumed to be continuous filaments with square cross sections lying randomly in the x or y direction. The fibers are assumed to be flexible to allow bending over one another during the compression process. Lateral displacement is not allowed during the compaction process. The algorithm also does not allow the fibers to interpenetrate or elongate and so the mass of the fibers is conserved. Bending of the fibers is modeled either by considering a constant "slope of bending" or constant "span of bending." The influence of the bending parameters on the propagation of compression through the material's thickness is discussed. In agreement with our experimental observations, it was found that the average solid volume fraction profile across the thickness becomes U shaped after the calendering. The application of these virtual structures in studying transport phenomena in fibrous materials is also demonstrated.
Diabatic Definition of Geometric Phase Effects.
Izmaylov, Artur F; Li, Jiaru; Joubert-Doriol, Loïc
2016-11-08
Electronic wave functions in the adiabatic representation acquire nontrivial geometric phases (GPs) when corresponding potential energy surfaces undergo conical intersection (CI). These GPs have profound effects on the nuclear quantum dynamics and cannot be eliminated in the adiabatic representation without changing the physics of the system. To define dynamical effects arising from the GP presence, the nuclear quantum dynamics of the CI containing system is compared with that of the system with artificially removed GP. We explore a new construction of the system with removed GP via a modification of the diabatic representation for the original CI containing system. Using an absolute value function of diabatic couplings, we remove the GP while preserving adiabatic potential energy surfaces and CI. We assess GP effects in dynamics of a two-dimensional linear vibronic coupling model both for ground and excited state dynamics. Results are compared with those obtained with a conventional removal of the GP by ignoring double-valued boundary conditions of the real electronic wave functions. Interestingly, GP effects appear similar in two approaches only for the low energy dynamics. In contrast with the conventional approach, the new approach does not have substantial GP effects in the ultrafast excited state dynamics.
Minimizing stellarator turbulent transport by geometric optimization
Mynick, H. E.
2010-11-01
Up to now, a transport optimized stellarator has meant one optimized to minimize neoclassical transport,ootnotetextH.E. Mynick, Phys. Plasmas 13, 058102 (2006). while the task of also mitigating turbulent transport, usually the dominant transport channel in such designs, has not been addressed, due to the complexity of plasma turbulence in stellarators. However, with the advent of gyrokinetic codes valid for 3D geometries such as GENE,ootnotetextF. Jenko, W. Dorland, M. Kotschenreuther, B.N. Rogers, Phys. Plasmas 7, 1904 (2000). and stellarator optimization codes such as STELLOPT,ootnotetextA. Reiman, G. Fu, S. Hirshman, L. Ku, et al, Plasma Phys. Control. Fusion 41 B273 (1999). designing stellarators to also reduce turbulent transport has become a realistic possibility. We have been using GENE to characterize the dependence of turbulent transport on stellarator geometry,ootnotetextH.E Mynick, P.A. Xanthopoulos, A.H. Boozer, Phys.Plasmas 16 110702 (2009). and to identify key geometric quantities which control the transport level. From the information obtained from these GENE studies, we are developing proxy functions which approximate the level of turbulent transport one may expect in a machine of a given geometry, and have extended STELLOPT to use these in its cost function, obtaining stellarator configurations with turbulent transport levels substantially lower than those in the original designs.
Induced subgraph searching for geometric model fitting
Xiao, Fan; Xiao, Guobao; Yan, Yan; Wang, Xing; Wang, Hanzi
2017-11-01
In this paper, we propose a novel model fitting method based on graphs to fit and segment multiple-structure data. In the graph constructed on data, each model instance is represented as an induced subgraph. Following the idea of pursuing the maximum consensus, the multiple geometric model fitting problem is formulated as searching for a set of induced subgraphs including the maximum union set of vertices. After the generation and refinement of the induced subgraphs that represent the model hypotheses, the searching process is conducted on the "qualified" subgraphs. Multiple model instances can be simultaneously estimated by solving a converted problem. Then, we introduce the energy evaluation function to determine the number of model instances in data. The proposed method is able to effectively estimate the number and the parameters of model instances in data severely corrupted by outliers and noises. Experimental results on synthetic data and real images validate the favorable performance of the proposed method compared with several state-of-the-art fitting methods.
Geometric Structures on Spaces of Weighted Submanifolds
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Brian Lee
2009-11-01
Full Text Available In this paper we use a diffeo-geometric framework based on manifolds that are locally modeled on ''convenient'' vector spaces to study the geometry of some infinite dimensional spaces. Given a finite dimensional symplectic manifold (M,ω, we construct a weak symplectic structure on each leaf I_w of a foliation of the space of compact oriented isotropic submanifolds in M equipped with top degree forms of total measure 1. These forms are called weightings and such manifolds are said to be weighted. We show that this symplectic structure on the particular leaves consisting of weighted Lagrangian submanifolds is equivalent to a heuristic weak symplectic structure of Weinstein [Adv. Math. 82 (1990, 133-159]. When the weightings are positive, these symplectic spaces are symplectomorphic to reductions of a weak symplectic structure of Donaldson [Asian J. Math. 3 (1999, 1-15] on the space of embeddings of a fixed compact oriented manifold into M. When M is compact, by generalizing a moment map of Weinstein we construct a symplectomorphism of each leaf I_w consisting of positive weighted isotropic submanifolds onto a coadjoint orbit of the group of Hamiltonian symplectomorphisms of M equipped with the Kirillov-Kostant-Souriau symplectic structure. After defining notions of Poisson algebras and Poisson manifolds, we prove that each space I_w can also be identified with a symplectic leaf of a Poisson structure. Finally, we discuss a kinematic description of spaces of weighted submanifolds.
Geometric investigation of a gaming active device
Menna, Fabio; Remondino, Fabio; Battisti, Roberto; Nocerino, Erica
2011-07-01
3D imaging systems are widely available and used for surveying, modeling and entertainment applications, but clear statements regarding their characteristics, performances and limitations are still missing. The VDI/VDE and the ASTME57 committees are trying to set some standards but the commercial market is not reacting properly. Since many new users are approaching these 3D recording methodologies, clear statements and information clarifying if a package or system satisfies certain requirements before investing are fundamental for those users who are not really familiar with these technologies. Recently small and portable consumer-grade active sensors came on the market, like TOF rangeimaging cameras or low-cost triangulation-based range sensor. A quite interesting active system was produced by PrimeSense and launched on the market thanks to the Microsoft Xbox project with the name of Kinect. The article reports the geometric investigation of the Kinect active sensors, considering its measurement performances, the accuracy of the retrieved range data and the possibility to use it for 3D modeling application.
Algebraic and Geometric Approach in Function Problem Solving
Mousoulides, Nikos; Gagatsis, Athanasios
2004-01-01
This study explores students algebraic and geometric approach in solving tasks in functions and the relation of these approaches with complex geometric problem solving. Data were obtained from 95 sophomore pre-service teachers, enrolled in a basic algebra course. Implicative statistical analysis was performed to evaluate the relation between…
Geometric visualization of parallel bivariate Pareto distribution surfaces
Directory of Open Access Journals (Sweden)
N.H. Abdel-All
2016-04-01
Full Text Available In the present paper, the differential-geometrical framework for parallel bivariate Pareto distribution surfaces (P,P¯ is given. Curvatures of a curve lying on (P,P¯, are interpreted in terms of the parameters of P. Geometrical and statistical interpretations of some results are introduced and plotted.
Creativity and Motivation for Geometric Tasks Designing in Education
Rumanová, Lucia; Smiešková, Edita
2015-01-01
In this paper we focus on creativity needed for geometric tasks designing, visualization of geometric problems and use of ICT. We present some examples of various problems related to tessellations. Altogether 21 students--pre-service teachers participated in our activity within a geometry course at CPU in Nitra, Slovakia. Our attempt was to…
On an Assumption of Geometric Foundation of Numbers
Anatriello, Giuseppina; Tortoriello, Francesco Saverio; Vincenzi, Giovanni
2016-01-01
In line with the latest positions of Gottlob Frege, this article puts forward the hypothesis that the cognitive bases of mathematics are geometric in nature. Starting from the geometry axioms of the "Elements" of Euclid, we introduce a geometric theory of proportions along the lines of the one introduced by Grassmann in…
What is a Singularity in Geometrized Newtonian Gravitation?
Weatherall, James Owen
2013-01-01
I discuss singular spacetimes in the context of the geometrized formulation of Newtonian gravitation. I argue first that geodesic incompleteness is a natural criterion for when a model of geometrized Newtonian gravitation is singular, and then I show that singularities in this sense arise naturally in classical physics by stating and proving a classical version of the Raychaudhuri-Komar singularity theorem.
Reduction Arguments for Geometric Inequalities Associated With Asymptotically Hyperboloidal Slices
Cha, Ye Sle; Sakovich, Anna
2016-01-01
We consider several geometric inequalities in general relativity involving mass, area, charge, and angular momentum for asymptotically hyperboloidal initial data. We show how to reduce each one to the known maximal (or time symmetric) case in the asymptotically flat setting, whenever a geometrically motivated system of elliptic equations admits a solution.
3D facial geometric features for constrained local model
Cheng, Shiyang; Zafeiriou, Stefanos; Asthana, Ashish; Asthana, Akshay; Pantic, Maja
2014-01-01
We propose a 3D Constrained Local Model framework for deformable face alignment in depth image. Our framework exploits the intrinsic 3D geometric information in depth data by utilizing robust histogram-based 3D geometric features that are based on normal vectors. In addition, we demonstrate the
Growing and Growing: Promoting Functional Thinking with Geometric Growing Patterns
Markworth, Kimberly A.
2010-01-01
Design research methodology is used in this study to develop an empirically-substantiated instruction theory about students' development of functional thinking in the context of geometric growing patterns. The two research questions are: (1) How does students' functional thinking develop in the context of geometric growing patterns? (2) What are…
Active Learning Environment with Lenses in Geometric Optics
Tural, Güner
2015-01-01
Geometric optics is one of the difficult topics for students within physics discipline. Students learn better via student-centered active learning environments than the teacher-centered learning environments. So this study aimed to present a guide for middle school teachers to teach lenses in geometric optics via active learning environment…
Practical application of the geometric geoid for heighting over ...
African Journals Online (AJOL)
Geoid determination is one of the main current geodetic problems in Kenya. This is because a geoid model is required to convert ellipsoidal heights to orthometric heights that are used in practice. A local geometric geoid covering Nairobi County and its environs has been determined by a geometric approach. Nineteen ...
Model based object recognition using stereo vision and geometric hashing
van Dijck, H.A.L.; van der Heijden, Ferdinand; Korsten, Maarten J.
1996-01-01
this paper we will show that the inherent robustness of geometric hashing to spurious data can be used to overcome the problems in stereo vision. The organisation of this paper is as follows. Section 2 discusses the geometric hashing technique and some previous work in this area. In section 3 we
Developing a Network of and for Geometric Reasoning
Mamolo, Ami; Ruttenberg-Rozen, Robyn; Whiteley, Walter
2015-01-01
In this article, we develop a theoretical model for restructuring mathematical tasks, usually considered advanced, with a network of spatial visual representations designed to support geometric reasoning for learners of disparate ages, stages, strengths, and preparation. Through our geometric reworking of the well-known "open box…
Mathematical calculation model for geometrical parameters of timber mesh design with orthogonal grid
Directory of Open Access Journals (Sweden)
Loktev Dmitriy Aleksandrovich
Full Text Available Mesh cover design, a multi-element design, which ensures the correct geometrical arrangement of the elements, is a very important task. The purpose of the given article is the development of a mathematical model for selecting the geometric parameters of wooden arches with mesh orthogonal grid with different input data. In this article three variants of design were observed. The main differences between them are in the relative position of longitudinal and transverse components. When performing static calculations of such designs in order to achieve their subsequent correct assembly, the following location conditions were observed: all the items must strictly match with each other without a gap and without overlap. However, these conditions must be met for any ratio of height to the arch span, the number of longitudinal members and the thickness of longitudinal members. Inverse problems also take place. In this case, the geometric calculation is not possible to vary the cross-section elements, and the stress-strain state of the cover is provided by varying the pitch of the transverse arches of the elements, on which the geometric calculation has no influence. All this determines the need for universal mathematical models describing any geometrical parameter of the designs needed for their geometrical calculation. The basic approach for the development of such models is the use of the known trigonometric formulas, giving a complete description of the desired geometry of the arch. Finally three transcendental equations were obtained, the solution algorithm of which using Newton’s method is presented in the MathCAD. The complexity of solving such equations using the proposed algorithm in the MathCAD is reduced to a minimum.
Checlair, Jade; McKay, Christopher P.; Imanaka, Hiroshi
2016-01-01
Extensive studies characterizing Titan present an opportunity to study the atmospheric properties of Titan-like exoplanets. Using an existing model of Titan's atmospheric haze, we computed geometric albedo spectra and effective transit height spectra for six values of the haze production rate (zero haze to twice present) over a wide range of wavelengths (0.2-2 microns). In the geometric albedo spectra, the slope in the UV-visible changes from blue to red when varying the haze production rate values from zero to twice the current Titan value. This spectral feature is the most effective way to characterize the haze production rates. Methane absorption bands in the visible-NIR compete with the absorbing haze, being more prominent for smaller haze production rates. The effective transit heights probe a region of the atmosphere where the haze and gas are optically thin and that is thus not effectively probed by the geometric albedo. The effective transit height decreases smoothly with increasing wavelength, from 376 km to 123 km at 0.2 and 2 microns, respectively. When decreasing the haze production rate, the methane absorption bands become more prominent, and the effective transit height decreases with a steeper slope with increasing wavelength. The slope of the geometric albedo in the UV-visible increases smoothly with increasing haze production rate, while the slope of the effective transit height spectra is not sensitive to the haze production rate other than showing a sharp rise when the haze production rate increases from zero. We conclude that geometric albedo spectra provide the most sensitive indicator of the haze production rate and the background Rayleigh gas. Our results suggest that important and complementary information can be obtained from the geometric albedo and motivates improvements in the technology for direct imaging of nearby exoplanets.
Spatial Non-Cyclic Geometric Phase in Neutron Interferometry.
Filipp, Stefan; Hasegawa, Yuji; Loidl, Rudolf; Rauch, Helmut
2005-01-01
We present a split-beam neutron interferometric experiment to test the non-cyclic geometric phase tied to the spatial evolution of the system: the subjacent two-dimensional Hilbert space is spanned by the two possible paths in the interferometer and the evolution of the state is controlled by phase shifters and absorbers. A related experiment was reported previously by some of the authors to verify the cyclic spatial geometric phase. The interpretation of this experiment, namely to ascribe a geometric phase to this particular state evolution, has met severe criticism. The extension to non-cyclic evolution manifests the correctness of the interpretation of the previous experiment by means of an explicit calculation of the non-cyclic geometric phase in terms of paths on the Bloch-sphere. The theoretical treatment comprises the cyclic geometric phase as a special case, which is confirmed by experiment.
Geometric control theory and sub-Riemannian geometry
Boscain, Ugo; Gauthier, Jean-Paul; Sarychev, Andrey; Sigalotti, Mario
2014-01-01
This volume presents recent advances in the interaction between Geometric Control Theory and sub-Riemannian geometry. On the one hand, Geometric Control Theory used the differential geometric and Lie algebraic language for studying controllability, motion planning, stabilizability and optimality for control systems. The geometric approach turned out to be fruitful in applications to robotics, vision modeling, mathematical physics etc. On the other hand, Riemannian geometry and its generalizations, such as sub-Riemannian, Finslerian geometry etc., have been actively adopting methods developed in the scope of geometric control. Application of these methods has led to important results regarding geometry of sub-Riemannian spaces, regularity of sub-Riemannian distances, properties of the group of diffeomorphisms of sub-Riemannian manifolds, local geometry and equivalence of distributions and sub-Riemannian structures, regularity of the Hausdorff volume.
Effective action for non-geometric fluxes duality covariant actions
Lee, Kanghoon; Rey, Soo-Jong; Sakatani, Yuho
2017-07-01
The (heterotic) double field theories and the exceptional field theories are manifestly duality covariant formulations, describing low-energy limit of various super-string and M-theory compactifications. These field theories are known to be reduced to the standard descriptions by introducing appropriately parameterized generalized metric and by applying suitably chosen section conditions. In this paper, we apply these formulations to non-geometric backgrounds. We introduce different parameterizations for the generalized metric in terms of the dual fields which are pertinent to non-geometric fluxes. Under certain simplifying assumptions, we construct new effective action for non-geometric backgrounds. We then study the non-geometric backgrounds sourced by exotic branes and find their U -duality monodromy matrices. The charge of exotic branes obtained from these monodromy matrices agrees with the charge obtained from the non-geometric flux integral.
Sudden change of geometric quantum discord in finite temperature reservoirs
Energy Technology Data Exchange (ETDEWEB)
Hu, Ming-Liang, E-mail: mingliang0301@163.com; Sun, Jian
2015-03-15
We investigate sudden change (SC) behaviors of the distance-based measures of geometric quantum discords (GQDs) for two non-interacting qubits subject to the two-sided and the one-sided thermal reservoirs. We found that the GQDs defined by different distances exhibit different SCs, and thus the SCs are the combined result of the chosen discord measure and the property of a state. We also found that the thermal reservoir may generate states having different orderings related to different GQDs. These inherent differences of the GQDs reveal that they are incompatible in characterizing quantum correlations both quantitatively and qualitatively. - Highlights: • Comparable study of different distance-based geometric quantum discords. • Evolution of the geometric quantum discords in finite temperature reservoirs. • Different geometric quantum discords exhibit distinct sudden changes. • Nonunique states ordering imposed by different geometric quantum discords.
Geometric Calibration and Accuracy Verification of the GF-3 Satellite.
Zhao, Ruishan; Zhang, Guo; Deng, Mingjun; Xu, Kai; Guo, Fengcheng
2017-08-29
The GF-3 satellite is the first multi-polarization synthetic aperture radar (SAR) imaging satellite in China, which operates in the C band with a resolution of 1 m. Although the SAR satellite system was geometrically calibrated during the in-orbit commissioning phase, there are still some system errors that affect its geometric positioning accuracy. In this study, these errors are classified into three categories: fixed system error, time-varying system error, and random error. Using a multimode hybrid geometric calibration of spaceborne SAR, and considering the atmospheric propagation delay, all system errors can be effectively corrected through high-precision ground control points and global atmospheric reference data. The geometric calibration experiments and accuracy evaluation for the GF-3 satellite are performed using ground control data from several regions. The experimental results show that the residual system errors of the GF-3 SAR satellite have been effectively eliminated, and the geometric positioning accuracy can be better than 3 m.
Geometrical modulus of a casting and its influence on solidification process
Directory of Open Access Journals (Sweden)
F. Havlicek
2011-10-01
Full Text Available Object: The work analyses the importance of the known criterion for evaluating the controlled solidification of castings, so called geometrical modulus defined by N. Chvorinov as the first one. Geometrical modulus influences the solidification process. The modulus has such specificity that during the process of casting formation it is not a constant but its initial value decreases with the solidification progress because the remaining melt volume can decrease faster than its cooling surface.Methodology: The modulus is determined by a simple calculation from the ratio of the casting volume after pouring the metal in the mould to the cooled mould surface. The solidified metal volume and the cooled surface too are changed during solidification. That calculation is much more complicated. Results were checked up experimentally by measuring the temperatures in the cross-section of heavy steel castings during cooling them.Results: The given experimental results have completed the original theoretical calculations by Chvorinov and recent researches done with use of numerical calculations. The contribution explains how the geometrical modulus together with the thermal process in the casting causes the higher solidification rate in the axial part of the casting cross-section and shortening of solidification time. Practical implications: Change of the geometrical modulus negatively affects the casting internal quality. Melt feeding by capillary filtration in the dendritic network in the casting central part decreases and in such a way the shrinkage porosity volume increases. State of stress character in the casting is changed too and it increases.
Geometric method for stability of non-linear elastic thin shells
Ivanova, Jordanka
2002-01-01
PREFACE This book deals with the new developments and applications of the geometric method to the nonlinear stability problem for thin non-elastic shells. There are no other published books on this subject except the basic ones of A. V. Pogorelov (1966,1967,1986), where variational principles defined over isometric surfaces, are postulated, and applied mainly to static and dynamic problems of elastic isotropic thin shells. A. V. Pogorelov (Harkov, Ukraine) was the first to provide in his monographs the geometric construction of the deformed shell surface in a post-critical stage and deriving explicitely the asymptotic formulas for the upper and lower critical loads. In most cases, these formulas were presented in a closed analytical form, and confirmed by experimental data. The geometric method by Pogorelov is one of the most important analytical methods developed during the last century. Its power consists in its ability to provide a clear geometric picture of the postcritical form of a deformed shell surfac...
Geometric perturbation theory and plasma physics
Energy Technology Data Exchange (ETDEWEB)
Omohundro, S.M.
1985-04-04
Modern differential geometric techniques are used to unify the physical asymptotics underlying mechanics, wave theory and statistical mechanics. The approach gives new insights into the structure of physical theories and is suited to the needs of modern large-scale computer simulation and symbol manipulation systems. A coordinate-free formulation of non-singular perturbation theory is given, from which a new Hamiltonian perturbation structure is derived and related to the unperturbed structure. The theory of perturbations in the presence of symmetry is developed, and the method of averaging is related to reduction by a circle group action. The pseudo-forces and magnetic Poisson bracket terms due to reduction are given a natural asymptotic interpretation. Similar terms due to changing reference frames are related to the method of variation of parameters, which is also given a Hamiltonian formulation. These methods are used to answer a question about nearly periodic systems. The answer leads to a new secular perturbation theory that contains no ad hoc elements. Eikonal wave theory is given a Hamiltonian formulation that generalizes Whitham's Lagrangian approach. The evolution of wave action density on ray phase space is given a Hamiltonian structure using a Lie-Poisson bracket. The relationship between dissipative and Hamiltonian systems is discussed. A new type of attractor is defined which attracts both forward and backward in time and is shown to occur in infinite-dimensional Hamiltonian systems with dissipative behavior. The theory of Smale horseshoes is applied to gyromotion in the neighborhood of a magnetic field reversal and the phenomenon of reinsertion in area-preserving horseshoes is introduced. The central limit theorem is proved by renormalization group techniques. A natural symplectic structure for thermodynamics is shown to arise asymptotically from the maximum entropy formalism.
GEOMETRICAL PARAMETERS OF EGGS IN BIRD SYSTEMATICS
Directory of Open Access Journals (Sweden)
I. S. Mityay
2014-12-01
Full Text Available Our ideas are based on the following assumptions. Egg as a standalone system is formed within another system, which is the body of the female. Both systems are implemented on the basis of a common genetic code. In this regard, for example, the dendrogram constructed by morphological criteria eggs should be approximately equal to those constructed by other molecular or morphological criteria adult birds. It should be noted that the dendrogram show only the degree of genetic similarity of taxa, therefore, the identity of materials depends on the number of analyzed criteria and their quality, ie, they should be the backbone. The greater the number of system-features will be included in the analysis and in one other case, the like are dendrogram. In other cases, we will have a fragmentary similarity, which is also very important when dealing with controversial issues. The main message of our research was to figure out the eligibility of usage the morphological characteristics of eggs as additional information in taxonomy and phylogeny of birds. Our studies show that the shape parameters of bird eggs show a stable attachment to certain types of birds and complex traits are species-specific. Dendrogram and diagrams built by the quantitative value of these signs, exhibit significant similarity with the dendrogram constructed by morphological, comparative anatomy, paleontology and molecular criteria for adult birds. This suggests the possibility of using morphological parameters eggs as additional information in dealing with taxonomy and phylogeny of birds. Keywords: oology, geometrical parameters of eggs, bird systematics
Li, Yingbo; Zhao, Sisi; Hu, Bin; Zhao, Haibo; He, Jinping; Zhao, Xuemin
2017-10-01
Aimed at key problems the system of 1:5000 scale space stereo mapping and the shortage of the surveying capability of urban area, in regard of the performance index and the surveying systems of the existing domestic optical mapping satellites are unable to meet the demand of the large scale stereo mapping, it is urgent to develop the very high accuracy space photogrammetric satellite system which has a 1:5000 scale (or larger).The new surveying systems of double baseline stereo photogrammetric mode with combined of linear array sensor and area array sensor was proposed, which aims at solving the problems of barriers, distortions and radiation differences in complex ground object mapping for the existing space stereo mapping technology. Based on collinearity equation, double baseline stereo photogrammetric method and the model of combined adjustment were presented, systematic error compensation for this model was analyzed, position precision of double baseline stereo photogrammetry based on both simulated images and images acquired under lab conditions was studied. The laboratory tests showed that camera geometric calibration accuracy is better than 1μm, the height positioning accuracy is better than 1.5GSD with GCPs. The results showed that the mode of combined of one linear array sensor and one plane array sensor had higher positioning precision. Explore the new system of 1:5000 scale very high accuracy space stereo mapping can provide available new technologies and strategies for achieving demotic very high accuracy space stereo mapping.
Directory of Open Access Journals (Sweden)
B. Attaf
2015-08-01
Full Text Available The present investigation aims to examine the influence of geometric ratios and fibre orientation on the natural frequencies of fibre-reinforced laminated composite plates using finite element method based on Yang’s theory and his collaborators. The transverse shear and rotatory inertia effects were taken into consideration in the developed Fortran computer program. It has been shown that the use of first-order displacement field provides the same accuracy as higher-order displacement field when the number of elements representing the plate structure is increased (refined mesh. However, poor precision may appear for plates with high thickness-to-side ratio h/a (thickness/side length. This discrepancy limits the application of the developed theory to thick plates (h/a<0.5. The various curves show the evolution of the dimensionless frequency (w* versus fibre orientation angle (q and illustrate the apparition of a “triple-point” phenomenon engendered by the increase of the plate aspect ratio a/b (length/width for a specific value of h/a. This point defines the maximum natural frequency and the associated fibre orientation. Also, results show that for high and/or low aspect ratios, the triple-point phenomenon does not occur. This latter is rapidly reached for thick plates than thin plates when the plate aspect ratio a/b is progressively increased.
Geometrical specifications accuracy influence on the quality of electromechanical devices
Glukhov, V. I.; Lakeenko, M. N.; Dolzhikov, S. N.
2017-06-01
To improve the quality of electromechanical products is possible due to the geometrical specifications optimization of values and tolerances. Electromechanical products longevity designates the rolling-contact bearings of the armature shaft. Longevity of the rolling-contact bearings is less than designed one, since assembly and fitting alter gaps, sizes and geometric tolerances for the working parts of the basic rolling bearing details. Geometrical models of the rolling-contact bearing details for the armature shaft and the end shield are developed on the basis of an electric locomotive traction motor in the present work. The basic elements of the details conjugating with the adjacent details and materializing the generalized and auxiliary coordinate systems are determined. Function, informativeness and the number of geometrical specifications for the elements location are specified. The recommendations on amending the design documentation due to geometrical models to improve the accuracy and the quality of the products are developed: the replacement of the common axis of the shaft’s technological datums by the common axis of the basic design datums; coaxiality tolerances for these design datums with respect to their common axis; the modifiers for these auxiliary datums and these datums location tolerances according to the principles of datums uniformity, inversion and the shortest dimension chains. The investigation demonstrated that the problem of enhancing the durability, longevity, and efficiency coefficient for electromechanical products can be solved with the systematic normalizations of geometrical specifications accuracy on the basis of the coordinate systems introduced in the standards on geometrical product specifications (GPS).
DEFF Research Database (Denmark)
Ernst, Erik
2003-01-01
This paper introduces the notion of higher-order inheritance hierarchies. They are useful because they provide well-known benefits of object-orientation at the level of entire hierarchies-benefits which are not available with current approaches. Three facets must be adressed: First, it must...
Geometric Calibration of the H-4RG Detector
Pravdo, Steven Howard; Shaklan, S.; Dorland, B.; Dudik, R.
2012-05-01
A Hawaii-4RG detector was developed for the Joint Milli-Arcsecond Pathfinder Survey (JMAPS). JMAPS was to have been an all-sky astrometric survey designed to observe stars in the range mI = 0-14, with the capability to observe QSOs as faint as mI = 16. Stars with mI = 0-12 and quasars out to 16 mag were to be observed with single measurement precision guide windows (GWs)” that read out 15 x 15 pixel squares on the focal plane at far higher rates than the other pixels, thereby forestalling saturation. The increase in dynamic range is as large as 1000, equal to the ratio of the readout time in the full frame versus that of the GWs. The space mission has been cancelled. However, laboratory tests of the geometrical and projected astrometric accuracy of the camera were started and continue. The H-4RG is a 4K x 4K CMOS device with 10-micron pitch developed by Teledyne Imaging Systems, Inc. under contract to the Navy. We report preliminary data that show features in the apparent pixel locations in the full frame, and an investigation of the effects of the GWs on pixel locations. Copyright JPL.
Geometric VOF-PLIC simulations of Hollow Cone Sprays
Nelson, Thomas; Benson, Michael; Vanpoppel, Brett; Bravo, Luis; USMA Team Spray Collaboration; ARL Vehicle Combustion Lab Collaboration; Stanford University Collaboration
2014-11-01
This work examines a Computational Fluid Dynamics (CFD) approach to provide temporally resolved simulations of a novel pressure swirl atomizer presently studied at Stanford University. In a pressure swirl atomizer, the liquid spreads out to form an air-cored vortex within the nozzle and an emerging thin annular film. Due to instabilities the film breaks up to form a hollow cone spray. The numerical simulations focus on the near field nozzle flow physics and primary atomization of the spray. An incompressible flow formulation is adopted with a geometric unsplit Volume of Fluid (VOF) method to track the interface between two immiscible fluids in interfacial flow simulations. Here, the interface is modeled via an advection equation implicitly tracked using a discrete indicator function, f, with values representing the volume fraction of the tagged fluid within a cell. An Adaptive Mesh Refinement (AMR) scheme is also employed to efficiently capture the shear layers near the liquid-gas interface. The study is carried out for two atomizers with 2 mm and 3 mm diameters at intermediate Re = 2.6-3.9 × 103, We = 0.11-0.17 × 105. An in depth comparison is then provided between the CFD results and measurements obtained via shadowgraphy and CT scans.
Topological and geometric measurements of force-chain structure.
Giusti, Chad; Papadopoulos, Lia; Owens, Eli T; Daniels, Karen E; Bassett, Danielle S
2016-09-01
Developing quantitative methods for characterizing structural properties of force chains in densely packed granular media is an important step toward understanding or predicting large-scale physical properties of a packing. A promising framework in which to develop such methods is network science, which can be used to translate particle locations and force contacts into a graph in which particles are represented by nodes and forces between particles are represented by weighted edges. Recent work applying network-based community-detection techniques to extract force chains opens the door to developing statistics of force-chain structure, with the goal of identifying geometric and topological differences across packings, and providing a foundation on which to build predictions of bulk material properties from mesoscale network features. Here we discuss a trio of related but fundamentally distinct measurements of the mesoscale structure of force chains in two-dimensional (2D) packings, including a statistic derived using tools from algebraic topology, which together provide a tool set for the analysis of force chain architecture. We demonstrate the utility of this tool set by detecting variations in force-chain architecture with pressure. Collectively, these techniques can be generalized to 3D packings, and to the assessment of continuous deformations of packings under stress or strain.
Some Differential Geometric Relations in the Elastic Shell
Directory of Open Access Journals (Sweden)
Xiaoqin Shen
2016-01-01
Full Text Available The theory of the elastic shells is one of the most important parts of the theory of solid mechanics. The elastic shell can be described with its middle surface; that is, the three-dimensional elastic shell with equal thickness comprises a series of overlying surfaces like middle surface. In this paper, the differential geometric relations between elastic shell and its middle surface are provided under the curvilinear coordinate systems, which are very important for forming two-dimensional linear and nonlinear elastic shell models. Concretely, the metric tensors, the determinant of metric matrix field, the Christoffel symbols, and Riemann tensors on the three-dimensional elasticity are expressed by those on the two-dimensional middle surface, which are featured by the asymptotic expressions with respect to the variable in the direction of thickness of the shell. Thus, the novelty of this work is that we can further split three-dimensional mechanics equations into two-dimensional variation problems. Finally, two kinds of special shells, hemispherical shell and semicylindrical shell, are provided as the examples.
Reputation in Higher Education
DEFF Research Database (Denmark)
Martensen, Anne; Grønholdt, Lars
2005-01-01
The purpose of this paper is to develop a reputation model for higher education programmes, provide empirical evidence for the model and illustrate its application by using Copenhagen Business School (CBS) as the recurrent case. The developed model is a cause-and-effect model linking image...... for higher education reputation and which relations exist between the included determinants from a theoretical perspective. It is demonstrated how the model and measurement system may be a useful management tool for the improvement of the reputation of a higher education. In this way, the model can help...... leaders of higher education institutions to set strategic directions and support their decisions in an effort to create even better study programmes with a better reputation. Finally, managerial implications and directions for future research are discussed.Keywords: Reputation, image, corporate identity...
Electro-gravity via geometric chrononfield
Suchard, Eytan H.
2017-05-01
In De Sitter / Anti De Sitter space-time and in other geometries, reference sub-manifolds from which proper time is measured along integral curves, are described as events. We introduce here a foliation with the help of a scalar field. The scalar field need not be unique but from the gradient of the scalar field, an intrinsic Reeb vector of the foliations perpendicular to the gradient vector is calculated. The Reeb vector describes the acceleration of a physical particle that moves along the integral curves that are formed by the gradient of the scalar field. The Reeb vector appears as a component of an anti-symmetric matrix which is a part of a rank-2, 2-Form. The 2-form is extended into a non-degenerate 4-form and into rank-4 matrix of a 2-form, which when multiplied by a velocity of a particle, becomes the acceleration of the particle. The matrix has one U(1) degree of freedom and an additional SU(2) degrees of freedom in two vectors that span the plane perpendicular to the gradient of the scalar field and to the Reeb vector. In total, there are U(1) x SU(2) degrees of freedom. SU(3) degrees of freedom arise from three dimensional foliations but require an additional symmetry to exist in order to have a valid covariant meaning. Matter in the Einstein Grossmann equation is replaced by the action of the acceleration field, i.e. by a geometric action which is not anticipated by the metric alone. This idea leads to a new formalism that replaces the conventional stress-energy-momentum-tensor. The formalism will be mainly developed for classical physics but will also be discussed for quantized physics based on events instead of particles. The result is that a positive charge manifests small attracting gravity and a stronger but small repelling acceleration field that repels even uncharged particles that have a rest mass. Negative charge manifests a repelling anti-gravity but also a stronger acceleration field that attracts even uncharged particles that have rest mass
Geometrical optimization for strictly localized structures
Mo, Yirong
2003-07-01
Recently we proposed the block localized wavefunction (BLW) approach which takes the advantages of valence bond theory and molecular orbital theory and defines the wavefunctions for resonance structures based on the assumption that all electrons and orbitals are partitioned into a few subgroups. In this work, we implement the geometrical optimization of the BLW method based on the algorithm proposed by Gianinetti and coworkers. Thus, we can study the conjugation effect on not only the molecular stability, but also the molecular geometry. With this capability, the π conjugation effect in trans-polyenes C2nH2n+2 (n=2-5) as well as in formamide and its analogs are studied by optimizing their delocalized and strictly localized forms with the 6-31G(d) and 6-311+G(d,p) basis sets. Although it has been well presumed that the π resonance shortens the single bonds and lengthens the double bonds with the delocalization of π electrons across the whole line in polyenes, our optimization of the strictly localized structures quantitatively shows that when the conjugation effect is "turned off," the double bond lengths will be identical to the CC bond length in ethylene and the single Csp2-Csp2 bond length will be about 1.513-1.517 Å. In agreement with the classical Hückel theory, the resonance energies in polyenes are approximately in proportion to the number of double bonds. Similarly, resonance is responsible not only for the planarity of formamide, thioformamide, and selenoformamide, but also for the lengthening of the CX (X=O,S,Se) double bond and the shortening of the CN bonds. Although it is assumed that the CX bond polarization decreases in the order of O>S>Se, the π electronic delocalization increases in the opposite order, i.e., formamide
Krishnadas, K R; Baksi, Ananya; Ghosh, Atanu; Natarajan, Ganapati; Pradeep, Thalappil
2017-06-27
Monolayer protected clusters exhibit rich diversity in geometric and electronic structures. However, structure-reactivity relationships in these clusters are rarely explored. In this context, [Ag44(SR)30]4-, where -SR is an alkyl/aryl thiolate, is an interesting system due to its geometrically and electronically closed-shell structures and distinct charge states. We demonstrate that these structural features of [Ag44(SR)30]4- are distinctly manifested in its solution-state reaction with another cluster, [Au25(SR)18]-. Through this reaction, an alloy cluster anion, [Au12Ag32(SR)30]4-, evolves spontaneously as revealed by high-resolution electrospray ionization mass spectrometry. Ultraviolet-visible absorption spectroscopy and density functional theory calculations indicate that [Au12Ag32(SR)30]4- is formed by the substitution of all of the Ag atoms in the innermost icosahedral shell of [Ag44(SR)30]4- and the abundance is attributed to its higher stability due to closed geometric as well as electronic shell structure, similar to the reactant clusters. We further demonstrate that the substitution of metal atoms in the middle dodecahedral shell and the outermost mount sites are also possible, however such substitutions produce AuxAg44-x(SR)30 alloy clusters with geometrically and electronically open shells. Depending on specific sites of substitution, an unexpected superatom-nonsuperatom transition occurs in the distribution of AuxAg44-x(SR)30 alloy clusters formed in this reaction. Our results present a unique example of a structure-reactivity relationship in the metal atom substitution chemistry of monolayer protected clusters, wherein a systematic trend, reflecting the geometric and the electronic shell structures of the reactant as well as the product clusters, was observed.
Geometric phases for mixed states of the Kitaev chain.
Andersson, Ole; Bengtsson, Ingemar; Ericsson, Marie; Sjöqvist, Erik
2016-05-28
The Berry phase has found applications in building topological order parameters for certain condensed matter systems. The question whether some geometric phase for mixed states can serve the same purpose has been raised, and proposals are on the table. We analyse the intricate behaviour of Uhlmann's geometric phase in the Kitaev chain at finite temperature, and then argue that it captures quite different physics from that intended. We also analyse the behaviour of a geometric phase introduced in the context of interferometry. For the Kitaev chain, this phase closely mirrors that of the Berry phase, and we argue that it merits further investigation. © 2016 The Author(s).
Measurable quantum geometric phase from a rotating single spin.
Maclaurin, D; Doherty, M W; Hollenberg, L C L; Martin, A M
2012-06-15
We demonstrate that the internal magnetic states of a single nitrogen-vacancy defect, within a rotating diamond crystal, acquire geometric phases. The geometric phase shift is manifest as a relative phase between components of a superposition of magnetic substates. We demonstrate that under reasonable experimental conditions a phase shift of up to four radians could be measured. Such a measurement of the accumulation of a geometric phase, due to macroscopic rotation, would be the first for a single atom-scale quantum system.
A geometric Newton method for Oja's vector field.
Absil, P A; Ishteva, M; De Lathauwer, L; Van Huffel, S
2009-05-01
Newton's method for solving the matrix equation F(X) identical to AX-XX(T) AX = 0 runs up against the fact that its zeros are not isolated. This is due to a symmetry of F by the action of the orthogonal group. We show how differential-geometric techniques can be exploited to remove this symmetry and obtain a "geometric" Newton algorithm that finds the zeros of F. The geometric Newton method does not suffer from the degeneracy issue that stands in the way of the original Newton method.
Finite-Size Geometric Entanglement from Tensor Network Algorithms
Shi, Qian-Qian; Orus, Roman; Fjaerestad, John Ove; Zhou, Huan-Qiang
2009-01-01
The global geometric entanglement is studied in the context of newly-developed tensor network algorithms for finite systems. For one-dimensional quantum spin systems it is found that, at criticality, the leading finite-size correction to the global geometric entanglement per site behaves as $b/n$, where $n$ is the size of the system and $b$ a given coefficient. Our conclusion is based on the computation of the geometric entanglement per spin for the quantum Ising model in a transverse magneti...
Innovative education networking aimed at multimedia tools for geometrical optics learning
García-Martínez, P.; Zapata-Rodríguez, C. J.; Ferreira, C.; Fernández, I.; Pastor, D.; Nasenpour, M.; Moreno, I.; Sánchez-López, M. M.; Espinosa, J.; Mas, D.; Miret, J. J.
2015-10-01
We present a purposeful initiative to open new grounds for teaching Geometrical Optics. It is based on the creation of an innovative education networking involving academic staff from three Spanish universities linked together around Optics. Nowadays, students demand online resources such as innovative multimedia tools for complementing the understanding of their studies. Geometrical Optics relies on basics of light phenomena like reflection and refraction and the use of simple optical elements such as mirrors, prisms, lenses, and fibers. The mathematical treatment is simple and the equations are not too complicated. But from our long time experience in teaching to undergraduate students, we realize that important concepts are missed by these students because they do not work ray tracing as they should do. Moreover, Geometrical Optics laboratory is crucial by providing many short Optics experiments and thus stimulating students interest in the study of such a topic. Multimedia applications help teachers to cover those student demands. In that sense, our educational networking shares and develops online materials based on 1) video-tutorials of laboratory experiences and of ray tracing exercises, 2) different online platforms for student self-examinations and 3) computer assisted geometrical optics exercises. That will result in interesting educational synergies and promote student autonomy for learning Optics.
Estimation of geometric properties of three-component signals for system monitoring
Granjon, Pierre; Phua, Gailene Shih Lyn
2017-12-01
Most methods for condition monitoring are based on the analysis and characterization of physical quantities that are three-dimensional in nature. Plotted in a three-dimensional Euclidian space as a function of time, such quantities follow a trajectory whose geometric characteristics are representative of the state of the monitored system. Usual condition monitoring techniques often study the measured quantities component by component, without taking into account their three-dimensional nature and the geometric properties of their trajectory. A significant part of the information is thus ignored. This article details a method dedicated to the analysis and processing of three-component quantities, capable of highlighting the special geometric features of such data and providing complementary information for condition monitoring. The proposed method is applied to two experimental cases: bearing fault monitoring in rotating machines, and voltage dips monitoring in three-phase power networks. In this two cases, the obtained results are promising and show that the estimated geometric indicators lead to complementary information that can be useful for condition monitoring.
Automatic tree stem detection – a geometric feature based approach for MLS point clouds
Directory of Open Access Journals (Sweden)
N. Hetti Arachchige
2013-10-01
Full Text Available Recognition of tree stem is a fundamental task for obtaining various geometric attributes of trees such as diameter, height, stem position and so on for diverse of urban application. We propose a novel tree stem segmentation approach using geometric features corresponding to trees for high density MLS point data covering in urban environments. The principal direction and shape of point subsets are used as geometric features. Point orientation exhibits the most variance (shape of point set of a point neighbourhood, assists to measure similarity, while shape provides the dimensional information of a group of points. Points residing on a stem can be isolated by defining various rules based on these geometric features. The shape characterization step is accomplished by estimating the structure tensor with principal component analysis. These features are assigned to different steps of our segmentation algorithm. Wrong segmentations mainly occur in the area where our rules have failed, such as vertical type objects, road poles and light post. To overcome these problems, global shape is further checked. The experiment is performed to evaluate the method; it shows that more than 90% of tree stems are detected. The overall accuracy of the proposed method is 90.6%. The results show that principal direction and shape analysis are sufficient for the tree stem recognition from MLS point cloud in a relatively complex urban area.
Demonstration of Geometric Landau-Zener Interferometry in a Superconducting Phase Qubit
Yu, Yang; Tan, Xinsheng; Zhang, Zhentao; Zhu, Shiliang; Zhang, Danwei; Han, Siyuan
2014-03-01
Geometric quantum manipulation and Landau-Zener interferometry have been separately explored in many quantum systems. Here we fill this gap by combining these two approaches in the study of the dynamics of a superconducting phase qubit. We propose and then experimentally demonstrate Landau-Zener interferometry based on pure geometric phases in this solid-state qubit. We observe the interference due to geometric phases accumulated in the evolution between two consecutive Landau-Zener transitions, while the dynamical phase is eliminated by a spin-echo pulse. Our numerical simulation results using measured energy relaxation and dephasing times agree well with the experimental results. The full controllability of the qubit population as a function of intrinsically fault-tolerant geometric phases provides a promising approach to fault-tolerant quantum computation. This work is partially supported by the SKPBR of China (2011CB922104, 2011CBA00200), NSFC (91021003, 11274156,11125417), PAPD, and the PCSIRT. Han is supported in part by NSF of United States (PHY-1314861).
Verburgt, Lukas M
2016-01-01
This paper provides a detailed account of the period of the complex history of British algebra and geometry between the publication of George Peacock's Treatise on Algebra in 1830 and William Rowan Hamilton's paper on quaternions of 1843. During these years, Duncan Farquharson Gregory and William Walton published several contributions on 'algebraical geometry' and 'geometrical algebra' in the Cambridge Mathematical Journal. These contributions enabled them not only to generalize Peacock's symbolical algebra on the basis of geometrical considerations, but also to initiate the attempts to question the status of Euclidean space as the arbiter of valid geometrical interpretations. At the same time, Gregory and Walton were bound by the limits of symbolical algebra that they themselves made explicit; their work was not and could not be the 'abstract algebra' and 'abstract geometry' of figures such as Hamilton and Cayley. The central argument of the paper is that an understanding of the contributions to 'algebraical geometry' and 'geometrical algebra' of the second generation of 'scientific' symbolical algebraists is essential for a satisfactory explanation of the radical transition from symbolical to abstract algebra that took place in British mathematics in the 1830s-1840s.
Navigability of Random Geometric Graphs in the Universe and Other Spacetimes.
Cunningham, William; Zuev, Konstantin; Krioukov, Dmitri
2017-08-18
Random geometric graphs in hyperbolic spaces explain many common structural and dynamical properties of real networks, yet they fail to predict the correct values of the exponents of power-law degree distributions observed in real networks. In that respect, random geometric graphs in asymptotically de Sitter spacetimes, such as the Lorentzian spacetime of our accelerating universe, are more attractive as their predictions are more consistent with observations in real networks. Yet another important property of hyperbolic graphs is their navigability, and it remains unclear if de Sitter graphs are as navigable as hyperbolic ones. Here we study the navigability of random geometric graphs in three Lorentzian manifolds corresponding to universes filled only with dark energy (de Sitter spacetime), only with matter, and with a mixture of dark energy and matter. We find these graphs are navigable only in the manifolds with dark energy. This result implies that, in terms of navigability, random geometric graphs in asymptotically de Sitter spacetimes are as good as random hyperbolic graphs. It also establishes a connection between the presence of dark energy and navigability of the discretized causal structure of spacetime, which provides a basis for a different approach to the dark energy problem in cosmology.
Higher-order Brunnian structures and possible physical realizations
Baas, N. A.; Fedorov, D. V.; Jensen, A. S.; Riisager, K.; Volosniev, A. G.; Zinner, N. T.
2014-03-01
We consider few-body bound state systems and provide precise definitions of Borromean and Brunnian systems. The initial concepts are more than a hundred years old and originated in mathematical knot-theory as purely geometric considerations. About thirty years ago they were generalized and applied to the binding of systems in nature. It now appears that recent generalization to higher-order Brunnian structures may potentially be realized as laboratory-made or naturally occurring systems. With the binding energy as measure, we discuss possibilities of physical realization in nuclei, cold atoms, and condensedmatter systems. Appearance is not excluded. However, both the form and the strengths of the interactions must be rather special. The most promising subfields for present searches would be in cold atoms because of external control of effective interactions, or perhaps in condensed-matter systems with nonlocal interactions. In nuclei, it would only be by sheer luck due to a lack of tunability.
Geometric and dynamic distortions in anisotropic galaxy clustering
Blazek, Jonathan; Seljak, Uroš; Vlah, Zvonimir; Okumura, Teppei
2014-04-01
We examine the signature of dynamic (redshift-space) distortions and geometric distortions (including the Alcock-Paczynski effect) in the context of the galaxy power spectrum measured in upcoming galaxy redshift surveys. Information comes from both the baryon acoustic oscillation (BAO) feature and the broadband power spectrum shape. Accurate modeling is required to extract this information without systematically biasing the result. We consider an analytic model for the power spectrum of dark matter halos in redshift space, based on the distribution function expansion, and compare with halo clustering measured in N-body simulations. We forecast that the distribution function model is sufficiently accurate to allow the inclusion of broadband information on scales down to k ~ 0.2h Mpc-1, with somewhat better accuracy for higher bias halos. Compared with a BAO-only analysis with reconstruction, including broadband shape information can improve unbiased constraints on distance measures H(z) and DA(z) by ~ 30% and 20%, respectively, for a galaxy sample similar to the DESI luminous red galaxies. The gains in precision are larger in the absence of BAO reconstruction. Furthermore, including broadband shape information allows the measurement of structure growth, through redshift-space distortions. For the same galaxy sample, the distribution function model is able to constrain fσ8 to ~ 2%, when simultaneously fitting for H(z) and DA(z). We discuss techniques to optimize the analysis of the power spectrum, including removing modes near the line-of-sight that are particularly challenging to model, and whether these approaches can improve parameter constraints. We find that such techniques are unlikely to significantly improve constraints on geometry, although they may allow higher precision measurements of redshift-space distortions.
Evaluating conducting network based transparent electrodes from geometrical considerations
Energy Technology Data Exchange (ETDEWEB)
Kumar, Ankush [Chemistry and Physics of Materials Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, 560064 Bangalore (India); Kulkarni, G. U., E-mail: guk@cens.res.in [Centre for Nano and Soft Matter Sciences, 560013 Bangalore (India)
2016-01-07
Conducting nanowire networks have been developed as viable alternative to existing indium tin oxide based transparent electrode (TE). The nature of electrical conduction and process optimization for electrodes have gained much from the theoretical models based on percolation transport using Monte Carlo approach and applying Kirchhoff's law on individual junctions and loops. While most of the literature work pertaining to theoretical analysis is focussed on networks obtained from conducting rods (mostly considering only junction resistance), hardly any attention has been paid to those made using template based methods, wherein the structure of network is neither similar to network obtained from conducting rods nor similar to well periodic geometry. Here, we have attempted an analytical treatment based on geometrical arguments and applied image analysis on practical networks to gain deeper insight into conducting networked structure particularly in relation to sheet resistance and transmittance. Many literature examples reporting networks with straight or curvilinear wires with distributions in wire width and length have been analysed by treating the networks as two dimensional graphs and evaluating the sheet resistance based on wire density and wire width. The sheet resistance values from our analysis compare well with the experimental values. Our analysis on various examples has revealed that low sheet resistance is achieved with high wire density and compactness with straight rather than curvilinear wires and with narrower wire width distribution. Similarly, higher transmittance for given sheet resistance is possible with narrower wire width but of higher thickness, minimal curvilinearity, and maximum connectivity. For the purpose of evaluating active fraction of the network, the algorithm was made to distinguish and quantify current carrying backbone regions as against regions containing only dangling or isolated wires. The treatment can be helpful in
An introduction to the theory of higher-dimensional quasiconformal mappings
Gehring, Frederick W; Palka, Bruce P
2016-01-01
This book offers a modern, up-to-date introduction to quasiconformal mappings from an explicitly geometric perspective, emphasizing both the extensive developments in mapping theory during the past few decades and the remarkable applications of geometric function theory to other fields, including dynamical systems, Kleinian groups, geometric topology, differential geometry, and geometric group theory. It is a careful and detailed introduction to the higher-dimensional theory of quasiconformal mappings from the geometric viewpoint, based primarily on the technique of the conformal modulus of a curve family. Notably, the final chapter describes the application of quasiconformal mapping theory to Mostow's celebrated rigidity theorem in its original context with all the necessary background. This book will be suitable as a textbook for graduate students and researchers interested in beginning to work on mapping theory problems or learning the basics of the geometric approach to quasiconformal mappings. Only a bas...
常盤, 欣文
2015-01-01
Quantum criticality can be induced by quantum fluctuations due to geometrical frustration. I show the evidence of quantum criticality in frustrated magnets and the characteristic behavior of a system at frustration-induced quantum critical point.
geometric models for lateritic soil stabilized with cement
African Journals Online (AJOL)
user
stabilized soil. Constant cement contents ... Keywords: Bagasse-Ash, Cement, Lateritic Soil, Compaction and Strength Characteristics, Geometric Models. 1. INTRODUCTION ..... [1] Arora, K. R. “Soil Mechanics and Foundation. Engineering” Seventh ...
Geometric Procedures for Graphing the General Quadratic Equation.
DeTemple, Duane W.
1984-01-01
How tedious algebraic manipulations for simplifying general quadratic equations can be supplemented with simple geometric procedures is discussed. These procedures help students determine the type of conic and its axes and allow a graph to be sketched quickly. (MNS)
Geometric Algebra Software for Teaching Complex Numbers, Vectors and Spinors.
Lounesto, Pertti; And Others
1990-01-01
Presents a calculator-type computer program, CLICAL, in conjunction with complex number, vector, and other geometric algebra computations. Compares the CLICAL with other symbolic programs for algebra. (Author/YP)
A Differential-Geometrical Theory of Binocular Visual Space
Takiyama, Ryuzo; Kitajima, Noriyuki
2007-01-01
The binocular visual space (BVS), that is, the space perceived by our binocular vision, is treated in the Riemannian geometrical framework. By introducing appropriately parametrized fundamental metric into the BVS, various non-Euclidean phenomena are unifyingly interpreted.
Multipartite geometric entanglement in finite size XY model
Energy Technology Data Exchange (ETDEWEB)
Blasone, Massimo; Dell' Anno, Fabio; De Siena, Silvio; Giampaolo, Salvatore Marco; Illuminati, Fabrizio, E-mail: blasone@sa.infn.i [Dipartimento di Matematica e Informatica, Universita degli Studi di Salerno, Via Ponte don Melillo, I-84084 Fisciano (Italy)
2009-06-01
We investigate the behavior of the multipartite entanglement in the finite size XY model by means of the hierarchical geometric measure of entanglement. By selecting specific components of the hierarchy, we study both global entanglement and genuinely multipartite entanglement.
Geometric curvature and phase of the Rabi model
Energy Technology Data Exchange (ETDEWEB)
Mao, Lijun; Huai, Sainan; Guo, Liping; Zhang, Yunbo, E-mail: ybzhang@sxu.edu.cn
2015-11-15
We study the geometric curvature and phase of the Rabi model. Under the rotating-wave approximation (RWA), we apply the gauge independent Berry curvature over a surface integral to calculate the Berry phase of the eigenstates for both single and two-qubit systems, which is found to be identical with the system of spin-1/2 particle in a magnetic field. We extend the idea to define a vacuum-induced geometric curvature when the system starts from an initial state with pure vacuum bosonic field. The induced geometric phase is related to the average photon number in a period which is possible to measure in the qubit–cavity system. We also calculate the geometric phase beyond the RWA and find an anomalous sudden change, which implies the breakdown of the adiabatic theorem and the Berry phases in an adiabatic cyclic evolution are ill-defined near the anti-crossing point in the spectrum.
Measurement of a vacuum-induced geometric phase.
Gasparinetti, Simone; Berger, Simon; Abdumalikov, Abdufarrukh A; Pechal, Marek; Filipp, Stefan; Wallraff, Andreas J
2016-05-01
Berry's geometric phase naturally appears when a quantum system is driven by an external field whose parameters are slowly and cyclically changed. A variation in the coupling between the system and the external field can also give rise to a geometric phase, even when the field is in the vacuum state or any other Fock state. We demonstrate the appearance of a vacuum-induced Berry phase in an artificial atom, a superconducting transmon, interacting with a single mode of a microwave cavity. As we vary the phase of the interaction, the artificial atom acquires a geometric phase determined by the path traced out in the combined Hilbert space of the atom and the quantum field. Our ability to control this phase opens new possibilities for the geometric manipulation of atom-cavity systems also in the context of quantum information processing.
A geometric construction of traveling waves in a bioremediation model
Beck, M.A.; Doelman, A.; Kaper, T.J.
2006-01-01
Bioremediation is a promising technique for cleaning contaminated soil. We study an idealized bioremediation model involving a substrate (contaminant to be removed), electron acceptor (added nutrient), and microorganisms in a one-dimensional soil column. Using geometric singular perturbation theory,
Spatial non-adiabatic passage using geometric phases
National Research Council Canada - National Science Library
Benseny, Albert; Kiely, Anthony; Zhang, Yongping; Busch, Thomas; Ruschhaupt, Andreas
2017-01-01
.... In particular, we consider a charged particle in a system of three tunnel-coupled quantum wells, where the presence of a magnetic field can induce a geometric phase during the tunnelling processes...
Non-stoquastic Hamiltonians in quantum annealing via geometric phases
National Research Council Canada - National Science Library
Walter Vinci; Daniel A Lidar
2017-01-01
We argue that a complete description of quantum annealing implemented with continuous variables must take into account the non-adiabatic Aharonov-Anandan geometric phase that arises when the system...
Modelling of fabric draping: Finite elements versus a geometrical method
Lamers, E.A.D.; Wijskamp, Sebastiaan; Akkerman, Remko
2001-01-01
Thermoplastic composite materials can be processed by Rubber Press Forming at elevated temperatures. Process specific boundary conditions are difficult to incorporate in the classical geometric drape simulation methods. Therefore, a fabric reinforced fluid model was implemented in the Finite Element
The Geometric Construct of Multivariate Analysis of Variance
Wiersma, William; Hall, Charles
1973-01-01
In the geometrical construct of the MANOVA, the dimensions of interest are primarily those of the significant canonical variates, rather than either those of the original n variables or even the total possible canonical variates. (Authors)
The Minimal Geometric Deformation Approach: A Brief Introduction
Directory of Open Access Journals (Sweden)
J. Ovalle
2017-01-01
Full Text Available We review the basic elements of the Minimal Geometric Deformation approach in detail. This method has been successfully used to generate brane-world configurations from general relativistic perfect fluid solutions.
Proof in geometry with "mistakes in geometric proofs"
Fetisov, A I
2006-01-01
This single-volume compilation of 2 books explores the construction of geometric proofs. It offers useful criteria for determining correctness and presents examples of faulty proofs that illustrate common errors. 1963 editions.
Wake and higher order mode computations for the CMS experimental chamber at the LHC
Wanzenberg, R
2010-01-01
Wakefields and trapped Higher Order Modes (HOMs) in the CMS experimental chamber at the LHC are investigated using a geometrical model which closely reflects the presently installed vacuum chamber. The basic rf-parameters of the HOMs including the frequency, loss parameter, and the Q-value are provided. To cover also transient effects the short range wakefields and the total loss parameter has been calculated, too. Most numerical calculations are performed with the computer code MAFIA. The calculations of the Modes are complemented with an analysis of the multi-bunch instabilities due to the longitudinal and dipole modes in the CMS vacuum chamber.