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Geometry and Topology - Science topic

Algebraic topology, algebraic geometry, differential geometry.
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Publications related to Geometry and Topology (698)
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The aim of this Special Issue is to attract leading researchers in different areas of discrete mathematics and theoretical computer science. To this end, it is intended to involve in this Special Issue new high-quality results on discrete mathematics including (but not limited to) graph theory, coding theory, cryptography, algorithms and complexity...
Preprint
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In quantum mechanics, supersymmetry (SUSY) posits an equivalence between two elementary degrees of freedom, bosons and fermions. Here we show how this fundamental concept can be applied to connect bosonic and fermionic lattice models in the realm of condensed matter physics, e.g., to identify a variety of (bosonic) phonon and magnon lattice models...
Book
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The aim of this conference is to exchange ideas, discuss developments in mathematics, develop collaborations and interact with professionals and researchers from all over the world about some of the following interesting topics: Functional Analysis, Approximation Theory, Real Analysis, Complex Analysis, Harmonic and non-Harmonic Analysis, Applied A...
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When this article was first planned, writing was going to be exclusively about two things - the origin of life and human evolution. But it turned out to be out of the question for the author to restrict himself to these biological and anthropological topics. A proper understanding of them required answering questions like “What is the nature of the...
Article
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Substantial leaps in the understanding of quantum systems have been driven by exploring geometry, topology, dimensionality and interactions in ultracold atomic ensembles1–6. A system where atoms evolve while confined on an ellipsoidal surface represents a heretofore unexplored geometry and topology. Realizing an ultracold bubble—potentially Bose–Ei...
Article
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The destructive interference of wavefunctions in a kagome lattice can give rise to topological flat bands (TFBs) with a highly degenerate state of electrons. Recently, TFBs have been observed in several kagome metals, including Fe3Sn2, FeSn, CoSn, and YMn6Sn6. Nonetheless, kagome materials that are both exfoliable and semiconducting are lacking, wh...
Article
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Contagion maps exploit activation times in threshold contagions to assign vectors in high-dimensional Euclidean space to the nodes of a network. A point cloud that is the image of a contagion map reflects both the structure underlying the network and the spreading behavior of the contagion on it. Intuitively, such a point cloud exhibits features of...
Chapter
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Simplicial synchronization reveals the role that topology and geometry have in determining the dynamical properties of simplicial complexes. Simplicial network geometry and topology are naturally encoded in the spectral properties of the graph Laplacian and of the higher-order Laplacians of simplicial complexes. Here we show how the geometry of sim...
Preprint
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Gromov hyperbolic spaces have become an essential concept in geometry, topology and group theory. Here we extend Ancona's potential theory on Gromov hyperbolic manifolds and graphs of bounded geometry to a large class of Schr\"odinger operators on Gromov hyperbolic metric measure spaces, unifying these settings in a common framework ready for appli...
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Kagome materials have become solid grounds to study the interplay among geometry, topology, correlation, and magnetism. Recently, semiconductors Nb3X8(X = Cl, Br, I) have been predicted to be two-dimensional (2D) magnets and importantly these materials possess breathing kagome geometry. Electronic structure study of these promising materials is sti...
Poster
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5th International Conference on Mathematical Advances and Applications (ICOMAA-2022) aims to present research, exchange ideas, discuss developments in mathematics, develop collaborations and interact with professionals and researchers from all over the world. Participants are invited to submit one-page summaries of their work, with some of the fol...
Presentation
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In this talk I will discuss the relation between higher geometric quantisation and the global geometry underlying string dualities. Higher geometric quantisation is a promising framework that makes quantisation of classical field theories achievable. This can be obtained by quantising either an ordinary prequantum bundle on the ∞-stack of solutions...
Preprint
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The massive amount of available neurodata suggests the existence of a mathematical backbone underlying the intricate oscillatory activity of the brain. Hidden, unexpected multidisciplinary relationships can be found when mathematics copes with neural phenomena, leading to novel answers for everlasting neuroscientific questions. We elucidate how and...
Method
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We briefly consider the advantages of using the dynamical driven harmonic oscillator to prove the Riemann Hypothesis instead of the algebraic geometry topological approach using the mathematics of statics, not dynamics.
Preprint
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The destructive interference of wavefunctions in a kagome lattice can give rise to topological flat bands (TFBs) with a highly degenerate state of electrons. Recently, TFBs have been observed in several kagome metals, including Fe$_3$Sn$_2$, FeSn, CoSn, and YMn$_6$Sn$_6$. Nonetheless, kagome materials that are both exfoliable and semiconducting are...
Conference Paper
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Modern Intelligent Transport Systems are comprehensive applications that have to cope with a multitude of challenges while meeting strict service and security standards. A novel data-centric middleware that provides the foundation of such systems is presented in this paper. This middleware is designed for high scalability, fast data processing and...
Article
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Level of detail (LoD) is a key concept for 3D city modeling to optimise visualisation. The LoDs of CityGML shows this trend. This paper explores the relevance of having LoD for visualising 3D model of Underground Utility Networks (UUN). A new approach is proposed for designing multiple LoDs modeling in creating an explicit link between the content...
Article
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Cauchy-compact flat spacetimes with extreme BTZ are Lorentzian analogue of complete hyperbolic surfaces of finite volume. Indeed, the latter are 2-manifolds locally modeled on the hyperbolic plane, with group of isometries \(\mathrm {PSL}_2(\mathbb {R})\), admitting finitely many cuspidal ends while the regular part of the former are 3-manifolds lo...
Article
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Photoacoustic (PA) spectroscopy techniques enable the detection of trace substances. However, lower threshold detection requirements are increasingly common in practical applications. Thus, we propose a systematic geometry topology optimization approach on a PA cell to enhance the intensity of its detection signal. The model of topology optimizatio...
Article
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MATHEMATICS AND COMPUTER SCIENCE EDUCATION IN DEVELOPING COUNTRIES by Prof. Dr. R.B. Misra, Ex Vice-Chancellor, Avadh University, Faizabad / Ayodhya, (India); Ex Head, Dept. of Maths. & Computer Science, PNG University of Technology, Lae (PNG); Email: misrarb1@rediffmail.com, rambilas.misra@gmail.com 1. Importance of Computer Science developme...
Article
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Interindividual variability in drug response constitutes a major concern in pharmacotherapy. While polymorphisms in genes involved in drug disposition have been extensively studied, drug target variability remains underappreciated. By mapping the genomic variability of all human drug target genes onto high-resolution crystal structures of drug targ...
Article
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The technique of numerical analysis of three-dimensional tomographic images of the pore space of soil objects has been used in this paper. It applies methods of integral geometry, topology and morphological analysis. To characterize quantitatively the transformation of the pore space structure, tomographic images of four undisturbed soils were anal...
Article
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This paper presents the computational challenge on differential geometry and topology that happened within the ICLR 2021 workshop "Geometric and Topolog-ical Representation Learning". The competition asked participants to provide creative contributions to the fields of computational geometry and topology through the open-source repositories Geomsta...
Preprint
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This paper presents the computational challenge on differential geometry and topology that happened within the ICLR 2021 workshop "Geometric and Topological Representation Learning". The competition asked participants to provide creative contributions to the fields of computational geometry and topology through the open-source repositories Geomstat...
Preprint
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Significant leaps in the understanding of quantum systems have been driven by the exploration of geometry, topology, dimensionality, and interactions with ultracold atomic ensembles. A system where atoms evolve while confined on an ellipsoidal surface represents a heretofore unexplored geometry and topology. Realizing such an ultracold bubble syste...
Article
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The transition-metal-based kagome metals provide a versatile platform for correlated topological phases hosting various electronic instabilities. While superconductivity is rare in layered kagome compounds, its interplay with nontrivial topology could offer an engaging space to realize exotic excitations of quasiparticles. Here, we use scanning tun...
Preprint
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The study and mastery of linear and nonlinear, ordinary and partial differential equations, including systems of coupled differential equations over the real numbers, the complex numbers, and the quaternions does not offer any hint whatsoever on the physics that may underlie any plausible universe. Ditto the study of algebra, geometry, topology and...
Preprint
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Room temperature single-photon sources (SPSs) are critical for the emerging practical quantum applications such as on-chip photonic circuity for quantum communications systems and integrated quantum sensors. However, direct integration of an SPS into on-chip photonic systems remains challenging due to low coupling efficiencies between the SPS and t...
Article
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Accurate and efficient simulation of fluid and heat flow in fractures has long been a topic of interest for fractured reservoirs, e.g., enhanced geothermal systems (EGS) and unconventional oil/gas formations. In this paper, we propose a flexible and effective modeling approach, the extended embedded discrete fracture model (XEDFM), to simulate flui...
Article
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The quantum Hall effect is the seminal example of topological protection, as charge carriers are transmitted through one-dimensional edge channels where backscattering is prohibited. Graphene has made its marks as an exceptional platform to reveal new facets of this remarkable property. However, in conventional Hall bar geometries, topological prot...
Preprint
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We prove the existence of various adelic-style models for rigidly small-generated tensor-triangulated categories whose Balmer spectrum is a one-dimensional Noetherian topological space. This special case of our general programme of giving adelic models is particularly concrete and accessible, and we illustrate it with examples from algebra, geometr...
Conference Paper
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The design and analysis of the secondary air system (SAS) of gas turbine engine is a complex and time-consuming process because of its complicated geometry topology. The conventional SAS design-analysis model generation process is quite tedious, time consuming. It is still heavily dependent on human expertise and thus incurs high time-cost. This pa...
Preprint
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Mechanical metamaterials owe their extraordinary properties and functionalities to their micro-/nanoscale design of which shape, including both geometry and topology, is perhaps the most important aspect. 4D printing enables programmed, predictable, and precise change in the shape of mechanical metamaterials to achieve multi-functionality, adaptive...
Poster
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4th INTERNATIONAL E-CONFERENCE ON MATHEMATICAL ADVANCES AND APPLICATIONS (ICOMAA-2021) 26-29 MAY 2021, Yildiz Technical University Istanbul, TURKEY online video conferencing 2021.icomaas.com Dear Collegue, We are pleased to invite you to participate in the upcoming "4th International E-Conference on Mathematical Advances and Applications (ICOM...
Preprint
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Simplicial synchronization reveals the role that topology and geometry have in determining the dynamical properties of simplicial complexes. Simplicial network geometry and topology are naturally encoded in the spectral properties of the graph Laplacian and of the higher-order Laplacians of simplicial complexes. Here we show how the geometry of sim...
Preprint
Full-text available
Kirigami, the art of introducing cuts in thin sheets to enable articulation and deployment, has till recently been the domain of artists. With the realization that these structures form a novel class of mechanical metamaterials, there is increasing interest in using periodic tiling patterns as the basis for the space of designs. Here, we show that...
Article
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In this paper, we extend the notion of semi-hypergroups (resp. hypergroups) to neutro-semihypergroups (resp. neutro-hypergroups). We investigate the property of anti-semihypergroups (resp. anti-hypergroups). We also give a new alternative of neutro-hyperoperations (resp. anti-hyperoperations), neutro-hyperoperation-sophications (resp. anti-hypersop...
Preprint
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We propose a deep neural network (DNN) as a fast surrogate model for local stress (and in principle strain) calculation in inhomogeneous non-linear material systems. We show that the DNN predicts the local stresses with about 3.8% mean absolute percentage error (MAPE) for the case of heterogeneous elastic media and a mechanical phase contrast of up...
Article
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Abstract Establishing the relationship between elements of alternative network-based representations of a system is an important component of conflation, error/uncertainty assessment, change detection, and other geospatial analyses. An array of techniques have been proposed in support of such tasks to relate arcs and nodes in one network with those...
Article
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Consistency of Weyl natural gauge, Lorentz gauge and nonlinear gauge is studied in Weyl geometry. Field equations in generalized Weyl-Dirac theory show that spinless electron and photon are topological defects. Statistical metric and fluctuating metric in 3D space with time as a measure of spatial relations are discussed to propose a statistical in...
Preprint
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The quantum Hall effect is the seminal example of topological protection, as charge carriers are transmitted through one-dimensional edge channels where backscattering is prohibited. Graphene has made its marks as an exceptional platform to reveal new facets of this remarkable property. However, in conventional Hall bar geometries, topological prot...
Article
Full-text available
2- and 3-dimensional lead-halide perovskite (LHP) materials are novel semiconductors that have generated broad interest owing to their outstanding optical and electronic properties. Characterization and understanding of their atomic structure and structure-property relationships are often non-trivial, as a result of the vast structural and composit...
Article
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The synthesis of shape-persistent organic cage compounds by the formation of imine bonds opens the possibility to realize cages of different sizes, geometries, topologies and functions. It is generally assumed that the imine bond is rather chemically labile allowing a self-correction mechanism until thermodynamic equilibrium is reached, which is of...
Article
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We present a methodology for a numerical analysis of three-dimensional tomographic images in this paper. The methodology is based on integral geometry, topology, and morphological analysis methods. It involves calculating cumulative and non-cumulative pore size distributions of Minkowski functionals and Betti numbers. We investigated 13 samples in...
Chapter
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Due to the potential to generate forms with high efficiency and elegant geometry, topology optimization is widely used in architectural and structural designs. This paper presents a working flow of form-finding and robotic fabrication based BESO (Bi-directional Evolutionary Structure Optimization) optimization method. In case there are some other f...
Preprint
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The Autopoiesis and Cognition Theory (ACT), by Maturana and Varela, based on the notions of Biological Closure and Structural Coupling, is a well-known theory on how to understand biological organization [1, 2, 3]. Although, for example, the Free Energy Principle framework evokes some entailments of autopoiesis in a more formal setting [4, 5]; and...
Article
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Tensegrity structures provide both structural integrity and flexibility through the combination of stiff struts and a network of flexible tendons. These structures exhibit useful properties: high stiffness-to-mass ratio, controllability, reliability, structural flexibility, and large deployment. The integration of smart materials into tensegrity st...
Book
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The mathematical combinatorics is a subject that applying combinatorial notion to all mathematics and all sciences for understanding the reality of things in the universe, motivated by CC Conjecture of Dr.Linfan MAO on mathematical sciences. The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, s...
Book
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The mathematical combinatorics is a subject that applying combinatorial notion to all mathematics and all sciences for understanding the reality of things in the universe, motivated by CC Conjecture of Dr.Linfan MAO on mathematical sciences. The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, s...
Book
Full-text available
The mathematical combinatorics is a subject that applying combinatorial notion to all mathematics and all sciences for understanding the reality of things in the universe, motivated by CC Conjecture of Dr.Linfan MAO on mathematical sciences. The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, s...
Article
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We discuss the possibility of torsional Nieh-Yan anomaly of the type ∂μ(ej5μ)=γT2(Ta∧Ta) in Weyl superfluids, where T is the infrared (IR) temperature scale and Ta is the effective or emergent torsion from the superfluid order parameter. As distinct from the dimensionful ultraviolet (UV) parameter Λ2 in the conventional torsional Nieh-Yan anomaly,...
Article
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Biological macromolecules have intricate structures that underpin their biological functions. Understanding their structure–function relationships remains a challenge due to their structural complexity and functional variability. Although de Rham–Hodge theory, a landmark of twentieth-century mathematics, has had a tremendous impact on mathematics a...
Article
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The quantum-level interplay between geometry, topology and correlation is at the forefront of fundamental physics1–15. Kagome magnets are predicted to support intrinsic Chern quantum phases owing to their unusual lattice geometry and breaking of time-reversal symmetry14,15. However, quantum materials hosting ideal spin–orbit-coupled kagome lattices...
Article
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OuLiPo – Ouvroir de Littérature Potentielle – was created in 1960 at the initiative of Raymond Queneau – a man of letters interested in mathematics – and François Le Lionnais – a man of science interested in literature –, and supported by a group of writers , mathematicians and painters. OuLiPo rejects inspiration as the only source of creativity;...
Article
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Metal-organic frameworks (MOFs) comprise a class of highly porous nanomaterials formed by the assembly of organic molecular templates connected by metal ions. These materials exhibit a large diversity of pore size and geometry, topology, surface area, and chemical functionality. MOFs are particularly promising materials for developing new technolog...
Conference Paper
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Findings from cognitive science link the architectural complexity of multilevel buildings with occupants' difficulty in orienting and finding their way. Nevertheless, current approaches to modelling occupants' wayfinding reduce the representation of 3D multilevel buildings to isolated 2D graphs of each floor. These graphs do not take account of the...
Article
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With the growing popularity and application of microfabricated devices in oral drug delivery (ODD), masking technologies for drug loading and surface modification become highly relevant. Considering the speed of design and fabrication processes and the necessity for continuous alterations of e.g. the shape and sizes of the devices during the optimi...
Article
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This paper addresses a combined method of reinforcement learning and graph embedding for binary topology optimization of trusses to minimize total structural volume under stress and displacement constraints. Although conventional deep learning methods owe their success to a convolutional neural network that is capable of capturing higher level late...
Article
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Traditional adaption of CAD geometry, which plays an important role in generating effective and fit-for-purpose finite element models, is usually carried out manually and optionally with excessive dependence on engineer’s experience. Automatic and efficient geometry modification before simulation evidently improves design efficiency and quality, an...
Presentation
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En el siglo XVIII, Carl Friedrich Gauss da una primera clasificación delas superficies a partir de su curvatura y en este mismo estudio da su apa-rición las geometrias no euclideas en los trabajos de Bolyai y Lobachevsky.Dicho trabajo dio una inspiración a Bernhard Riemann en la introducción deespacios mas generales conocidas como Variedades Rieman...
Article
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Semantic compositionality—the way that meanings of complex entities obtain from meanings of constituent entities and their structural relations—is supposed to explain certain concomitant cognitive capacities, such as systematicity. Yet, cognitive scientists are divided on mechanisms for compositionality: e.g. a language of thought on one side versu...
Article
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In this minireview, we outline the recent experimental and theoretical progress in the creation, characterization and manipulation of Majorana bound states (MBSs) in semiconductor-superconductor (SC) hybrid structures. After an introductory overview of the broader field we specifically focus on four of our recent projects in this direction. We show...
Article
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Trajectory optimization precisely scanning an irregular terrain is a challenging problem since the trajectory optimizer needs to handle complex geometry topology, vehicle performance, and a sensor specification. To address these problems, this paper introduces a novel framework of a multi-UAV trajectory optimization method for an aerial imaging mis...
Preprint
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We give a presentation of Feynman categories from a representation--theoretical viewpoint. Feynman categories are a special type of monoidal categories and their representations are monoidal functors. They can be viewed as a far reaching generalization of groups, algebras and modules. Taking a new algebraic approach, we provide more examples and mo...
Preprint
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We discuss the possibility of a gravitional Nieh-Yan anomaly of the type $\partial_\mu j^\mu_5 =\gamma T^2{\cal T}^a\wedge {\cal T}_a$ in topological Weyl materials, where $T$ is temperature and ${\cal T}^a$ is the effective or emergent torsion. As distinct from the non-universal parameter $\Lambda$ in the conventional (zero temperature) Nieh-Yan a...
Preprint
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To the person who has taken a derivative and computed an integral at least once in their life, the step by step pedagogical treatment of the examples provides an outline of the workings of our universe from the grandest observational astronomical scales down to the quark-gluon plasmas produced by our most energetic particle accelerators for some ti...
Book
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This book discusses the computational geometry, topology and physics of digital images and video frame sequences. This trio of computational approaches encompasses the study of shape complexes, optical vortex nerves and proximities embedded in triangulated video frames and single images, while computational geometry focuses on the geometric structu...
Thesis
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It is known that the chirality of depolarisation and repolarisation processes may be basis for heart electrical instability. Purpose: The purpose of this investigation was to use graph theory, topology, convex analysis, mathematical modelling for diagnosis of the racemic Moebius strip like disturbances of heart rhythm and conduction. Object: The ob...
Conference Paper
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