Search results for: topological data

Authors: Sahil Imtiyaz

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One of the biggest challenges has emerged from the ever-expanding, dynamic, and instantaneously changing space-Big Data; and to find a data point and inherit wisdom to this space is a hard task. In this paper, we reduce the space of big data in Hamiltonian formalism that is in concordance with Ising Model. For this formulation, we simulate the system using dye laser in FORTRAN and analyse the dynamics of the data point in energy well of rhodium atom. After mapping the photon intensity and pulse width with energy and potential we concluded that as we increase the energy there is also increase in probability of tunnelling up to some point and then it starts decreasing and then shows a randomizing behaviour. It is due to decoherence with the environment and hence there is a loss of ‘quantumness’. This interprets the efficiency parameter and the extent of quantum evolution. The results are strongly encouraging in favour of the use of ‘Topological Property’ as a source of information instead of the qubit.

Keywords: big data, optimization, quantum evolution, hamiltonian, dye laser, fermionic computations

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Authors: Elham Kiyani

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In this paper, we first introduce the concept of Q-efficient solutions in a real linear space not necessarily endowed with a topology, where Q is some nonempty (not necessarily convex) set. We also used the scalarization technique including the Gerstewitz function generated by a nonconvex set to characterize these Q-efficient solutions. The algebraic concepts of interior and closure are useful to study optimization problems without topology. Studying nonconvex vector optimization is valuable since topological interior is equal to algebraic interior for a convex cone. So, we use the algebraic concepts of interior and closure to define Q-weak efficient solutions and Q-Henig proper efficient solutions of set-valued optimization problems, where Q is not a convex cone. Optimization problems with set-valued maps have a wide range of applications, so it is expected that there will be a useful analytical tool in optimization theory for set-valued maps. These kind of optimization problems are closely related to stochastic programming, control theory, and economic theory. The paper focus on nonconvex problems, the results are obtained by assuming generalized non-convexity assumptions on the data of the problem. In convex problems, main mathematical tools are convex separation theorems, alternative theorems, and algebraic counterparts of some usual topological concepts, while in nonconvex problems, we need a nonconvex separation function. Thus, we consider the Gerstewitz function generated by a general set in a real linear space and re-examine its properties in the more general setting. A useful approach for solving a vector problem is to reduce it to a scalar problem. In general, scalarization means the replacement of a vector optimization problem by a suitable scalar problem which tends to be an optimization problem with a real valued objective function. The Gerstewitz function is well known and widely used in optimization as the basis of the scalarization. The essential properties of the Gerstewitz function, which are well known in the topological framework, are studied by using algebraic counterparts rather than the topological concepts of interior and closure. Therefore, properties of the Gerstewitz function, when it takes values just in a real linear space are studied, and we use it to characterize Q-efficient solutions of vector problems whose image space is not endowed with any particular topology. Therefore, we deal with a constrained vector optimization problem in a real linear space without assuming any topology, and also Q-weak efficient and Q-proper efficient solutions in the senses of Henig are defined. Moreover, by means of the Gerstewitz function, we provide some necessary and sufficient optimality conditions for set-valued vector optimization problems.

Keywords: algebraic interior, Gerstewitz function, vector closure, vector optimization

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Authors: Francisco Bulnes

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Through the Fukaya conjecture and the wrapped Floer cohomology, the correspondences between paths in a loop space and states of a wrapping space of states in a Hamiltonian space (the ramification of field in this case is the connection to the operator that goes from TM to T*M) are demonstrated where these last states are corresponding to bosonic extensions of a spectrum of the space-time or direct image of the functor Spec, on space-time. This establishes a distinguished diffeomorphism defined by the mapping from the corresponding loops space to wrapping category of the Floer cohomology complex which furthermore relates in certain proportion D-branes (certain D-modules) with strings. This also gives to place to certain conjecture that establishes equivalences between moduli spaces that can be consigned in a moduli identity taking as space-time the Hitchin moduli space on G, whose dual can be expressed by a factor of a bosonic moduli spaces.

Keywords: Floer cohomology, Fukaya conjecture, Lagrangian submanifolds, quantum topological diffeomorphism

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Authors: Mohammad Saeed Bahramy

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Transition metal dichalcogenides have experienced a resurgence of interest in the past few years owing to their rich properties, ranging from metals and superconductors to strongly spin-orbit-coupled semiconductors and charge-density-wave systems. In all these cases, the transition metal d-electrons mainly determine the ground state properties. This presentation focuses on the chalcogen-derived states. Combining density-functional theory calculations with spin- and angle-resolved photoemission, it is shown that these states generically host a coexistence of type I and type II three-dimensional bulk Dirac fermions as well as ladders of topological surface states and surface resonances. It will be discussed how these naturally arise within a single p-orbital manifold as a general consequence of a trigonal crystal field, and as such can be expected across many compounds. Our finding opens a new route to design topological materials with advanced functionalities.

Keywords: topology, electronic structure, Dirac semimetals, transition metal dichalcogenides

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Authors: Eashwar V. Somasundaram, Raoul R. Wadhwa, Jacob G. Scott

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The use of radiomics in measuring geometric properties of tumor images such as size, surface area, and volume has been invaluable in assessing cancer diagnosis, treatment, and prognosis. In addition to analyzing geometric properties, radiomics would benefit from measuring topological properties using persistent homology. Intuitively, features uncovered by persistent homology may correlate to tumor structural features. One example is necrotic cavities (corresponding to 2D topological features), which are markers of very aggressive tumors. We develop a data pipeline in R that clusters tumors images based on persistent homology is used to identify meaningful clinical distinctions between tumors and possibly new relationships not captured by established clinical categorizations. A preliminary analysis was performed on 16 Magnetic Resonance Imaging (MRI) breast tissue segments downloaded from the 'Investigation of Serial Studies to Predict Your Therapeutic Response with Imaging and Molecular Analysis' (I-SPY TRIAL or ISPY1) collection in The Cancer Imaging Archive. Each segment represents a patient’s breast tumor prior to treatment. The ISPY1 dataset also provided the estrogen receptor (ER), progesterone receptor (PR), and human epidermal growth factor receptor 2 (HER2) status data. A persistent homology matrix up to 2-dimensional features was calculated for each of the MRI segmentation. Wasserstein distances were then calculated between all pairwise tumor image persistent homology matrices to create a distance matrix for each feature dimension. Since Wasserstein distances were calculated for 0, 1, and 2-dimensional features, three hierarchal clusters were constructed. The adjusted Rand Index was used to see how well the clusters corresponded to the ER/PR/HER2 status of the tumors. Triple-negative cancers (negative status for all three receptors) significantly clustered together in the 2-dimensional features dendrogram (Adjusted Rand Index of .35, p = .031). It is known that having a triple-negative breast tumor is associated with aggressive tumor growth and poor prognosis when compared to non-triple negative breast tumors. The aggressive tumor growth associated with triple-negative tumors may have a unique structure in an MRI segmentation, which persistent homology is able to identify. This preliminary analysis shows promising results in the use of persistent homology on tumor imaging to assess the severity of breast tumors. The next step is to apply this pipeline to other tumor segment images from The Cancer Imaging Archive at different sites such as the lung, kidney, and brain. In addition, whether other clinical parameters, such as overall survival, tumor stage, and tumor genotype data are captured well in persistent homology clusters will be assessed. If analyzing tumor MRI segments using persistent homology consistently identifies clinical relationships, this could enable clinicians to use persistent homology data as a noninvasive way to inform clinical decision making in oncology.

Keywords: cancer biology, oncology, persistent homology, radiomics, topological data analysis, tumor imaging

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Authors: Moustafa Osman Mohammed

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This paper introduces topological order in descried social systems starting with the original concept of autopoiesis by biologists and scientists, including the modification of general systems based on socialized medicine. Topological order is important in describing the physical systems for exploiting optical systems and improving photonic devices. The stats of topological order have some interesting properties of topological degeneracy and fractional statistics that reveal the entanglement origin of topological order, etc. Topological ideas in photonics form exciting developments in solid-state materials, that being; insulating in the bulk, conducting electricity on their surface without dissipation or back-scattering, even in the presence of large impurities. A specific type of autopoiesis system is interrelated to the main categories amongst existing groups of the ecological phenomena interaction social and medical sciences. The hypothesis, nevertheless, has a nonlinear interaction with its natural environment 'interactional cycle' for exchange photon energy with molecules without changes in topology. The engineering topology of a biosensor is based on the excitation boundary of surface electromagnetic waves in photonic band gap multilayer films. The device operation is similar to surface Plasmonic biosensors in which a photonic band gap film replaces metal film as the medium when surface electromagnetic waves are excited. The use of photonic band gap film offers sharper surface wave resonance leading to the potential of greatly enhanced sensitivity. So, the properties of the photonic band gap material are engineered to operate a sensor at any wavelength and conduct a surface wave resonance that ranges up to 470 nm. The wavelength is not generally accessible with surface Plasmon sensing. Lastly, the photonic band gap films have robust mechanical functions that offer new substrates for surface chemistry to understand the molecular design structure and create sensing chips surface with different concentrations of DNA sequences in the solution to observe and track the surface mode resonance under the influences of processes that take place in the spectroscopic environment. These processes led to the development of several advanced analytical technologies: which are; automated, real-time, reliable, reproducible, and cost-effective. This results in faster and more accurate monitoring and detection of biomolecules on refractive index sensing, antibody-antigen reactions with a DNA or protein binding. Ultimately, the controversial aspect of molecular frictional properties is adjusted to each other in order to form unique spatial structure and dynamics of biological molecules for providing the environment mutual contribution in investigation of changes due to the pathogenic archival architecture of cell clusters.

Keywords: autopoiesis, photonics systems, quantum topology, molecular structure, biosensing

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Authors: Omar Concepcion, Osvaldo De Melo, Arturo Escobosa

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Topological insulator (TI) materials are insulating in the bulk and conducting in the surface. The unique electronic properties associated with these surface states make them strong candidates for exploring innovative quantum phenomena and as practical applications for quantum computing, spintronic and nanodevices. Many materials, including Bi₂Te₃, have been proposed as TIs and, in some cases, it has been demonstrated experimentally by angle-resolved photoemission spectroscopy (ARPES), scanning tunneling spectroscopy (STM) and/or magnetotransport measurements. A clean surface is necessary in order to make any of this measurements. Several techniques have been used to produce films and different kinds of nanostructures. Growth and characterization in situ is usually the best option although cleaving the films can be an alternative to have a suitable surface. In the present work, we report a comparison of Bi₂Te₃ grown by physical vapor transport (PVT) and molecular beam epitaxy (MBE). The samples were characterized by X-ray diffraction (XRD), Scanning electron microscopy (SEM), Atomic force microscopy (AFM), X-ray photoelectron spectroscopy (XPS) and ARPES. The Bi₂Te₃ samples grown by PVT, were cleaved in the ultra-high vacuum in order to obtain a surface free of contaminants. In both cases, the XRD shows a c-axis orientation and the pole diagrams proved the epitaxial relationship between film and substrate. The ARPES image shows the linear dispersion characteristic of the surface states of the TI materials. The samples grown by PVT, a relatively simple and cost-effective technique shows the same high quality and TI properties than the grown by MBE.

Keywords: Bismuth telluride, molecular beam epitaxy, physical vapor transport, topological insulator

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Authors: Jake Gonzalez, Tommy Dang

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This paper proposes a temporal graph approach to visualize and analyze the evolution of gene relationships and nomenclature over time. An interactive web-based tool implements this temporal graph, enabling researchers to traverse a timeline and observe coupled dynamics in network topology and naming conventions. Analysis of a real human genomic dataset reveals the emergence of densely interconnected functional modules over time, representing groups of genes involved in key biological processes. For example, the antimicrobial peptide DEFA1A3 shows increased connections to related alpha-defensins involved in infection response. Tracking degree and betweenness centrality shifts over timeline iterations also quantitatively highlight the reprioritization of certain genes’ topological importance as knowledge advances. Examination of the CNR1 gene encoding the cannabinoid receptor CB1 demonstrates changing synonymous relationships and consolidating naming patterns over time, reflecting its unique functional role discovery. The integrated framework interconnecting these topological and nomenclature dynamics provides richer contextual insights compared to isolated analysis methods. Overall, this temporal graph approach enables a more holistic study of knowledge evolution to elucidate complex biology.

Keywords: temporal graph, gene relationships, nomenclature evolution, interactive visualization, biological insights

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Authors: Alexa Rakoski, Yun Suk Eo, Cagliyan Kurdak, Priscila F. S. Rosa, Zachary Fisk, Monica Ciomaga Hatnean, Geetha Balakrishnan, Boyoun Kang, Myungsuk Song, Byungki Cho

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Samarium hexaboride (SmB6) is a strongly correlated mixed valence material and Kondo insulator. In the resistance-temperature curve, SmB6 exhibits activated behavior from 4-40 K after the Kondo gap forms. However, below 4 K, the resistivity is temperature independent or weakly temperature dependent due to the appearance of a topologically protected surface state. Current research suggests that the surface of SmB6 is conductive while the bulk is truly insulating, different from conventional 3D TIs (Topological Insulators) like Bi₂Se₃ which are plagued by bulk conduction due to impurities. To better understand why the bulk of SmB6 is so different from conventional TIs, this study employed a new method, called inverted resistance, to explore the lowest temperatures, as well as standard Hall measurements for the rest of the temperature range. In the inverted resistance method, current flows from an inner contact to an outer ring, and voltage is measured outside of this outer ring. This geometry confines the surface current and allows for measurement of the bulk resistivity even when the conductive surface dominates transport (below 4 K). The results confirm that the bulk of SmB6 is truly insulating down to 2 K. Hall measurements on a number of samples show consistent bulk behavior from 4-40 K, but widely varying behavior among samples above 40 K. This is attributed to a combination of the growth process and purity of the starting material, and the relationship between the high and low temperature behaviors is still being explored.

Keywords: bulk transport, Hall effect, inverted resistance, Kondo insulator, samarium hexaboride, topological insulator

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Authors: Dairo Jose Hernandez Paez

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The quantum theory of atoms in molecules (QTAIM) allows us to obtain topological information on electronic density in quantum mechanical systems. The QTAIM starts by considering the electron density as a continuous mathematical object. On the other hand, the discretization of electron density is also a mathematical object, which, from discrete mathematics, would allow a new approach to its topological study. From this point of view, it is necessary to develop a series of steps that provide the theoretical support that guarantees its application. Some of the steps that we consider most important are mentioned below: (1) obtain good representations of the electron density through computational calculations, (2) design a methodology for the discretization of electron density, and construct the simplicial complex. (3) Make an analysis of the discrete vector field associating the simplicial complex. (4) Finally, in this research, we propose to use the discrete Morse theory as a mathematical tool to carry out studies of electron density topology.

Keywords: discrete mathematics, Discrete Morse theory, electronic density, computational calculations

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Authors: Michela Quadrini

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Chord diagrams occur in mathematics, from the study of RNA to knot theory. They are widely used in theory of knots and links for studying the finite type invariants, whereas in molecular biology one important motivation to study chord diagrams is to deal with the problem of RNA structure prediction. An RNA molecule is a linear polymer, referred to as the backbone, that consists of four types of nucleotides. Each nucleotide is represented by a point, whereas each chord of the diagram stands for one interaction for Watson-Crick base pairs between two nonconsecutive nucleotides. A chord diagram is an oriented circle with a set of n pairs of distinct points, considered up to orientation preserving diffeomorphisms of the circle. A linear chord diagram (LCD) is a special kind of graph obtained cutting the oriented circle of a chord diagram. It consists of a line segment, called its backbone, to which are attached a number of chords with distinct endpoints. There is a natural fattening on any linear chord diagram; the backbone lies on the real axis, while all the chords are in the upper half-plane. Each linear chord diagram has a natural genus of its associated surface. To each chord diagram and linear chord diagram, it is possible to associate the intersection graph. It consists of a graph whose vertices correspond to the chords of the diagram, whereas the chord intersections are represented by a connection between the vertices. Such intersection graph carries a lot of information about the diagram. Our goal is to define an LCD equivalence class in terms of identity of intersection graphs, from which many chord diagram invariants depend. For studying these invariants, we introduce a new representation of Linear Chord Diagrams based on a set of appropriate topological operators that permits to model LCD in terms of the relations among chords. Such set is composed of: crossing, nesting, and concatenations. The crossing operator is able to generate the whole space of linear chord diagrams, and a multiple context free grammar able to uniquely generate each LDC starting from a linear chord diagram adding a chord for each production of the grammar is defined. In other words, it allows to associate a unique algebraic term to each linear chord diagram, while the remaining operators allow to rewrite the term throughout a set of appropriate rewriting rules. Such rules define an LCD equivalence class in terms of the identity of intersection graphs. Starting from a modelled RNA molecule and the linear chord, some authors proposed a topological classification and folding. Our LCD equivalence class could contribute to the RNA folding problem leading to the definition of an algorithm that calculates the free energy of the molecule more accurately respect to the existing ones. Such LCD equivalence class could be useful to obtain a more accurate estimate of link between the crossing number and the topological genus and to study the relation among other invariants.

Keywords: chord diagrams, linear chord diagram, equivalence class, topological language

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Authors: Alka Jakhar, Harmanpreet Kaur Sandhu, Samaresh Das

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The Terahertz (THz) technology-based devices are heightening at an alarming rate on account of the wide range of applications in imaging, security, communication, and spectroscopic field. The various available room operational THz detectors, including Golay cell, pyroelectric detector, field-effect transistors, and photoconductive antennas, have some limitations such as narrow-band response, slow response speed, transit time limits, and complex fabrication process. There is an urgent demand to explore new materials and device structures to accomplish efficient THz detection systems. Recently, TMDs including topological semimetals and topological insulators such as PtSe₂, MoTe₂, WSe₂, and PtTe₂ provide novel feasibility for photonic and optical devices. The peculiar properties of these materials, such as Dirac cone, fermions presence, nonlinear optical response, high conductivity, and ambient stability, make them worthy for the development of the THz devices. Here, the platinum telluride (PtTe₂) based devices have been demonstrated for THz detection in the frequency range of 0.1-1 THz. The PtTe₂ is synthesized by direct selenization of the sputtered platinum film on the high-resistivity silicon substrate by using the chemical vapor deposition (CVD) method. The Raman spectra, XRD, and XPS spectra confirm the formation of the thin PtTe₂ film. The PtTe₂ channel length is 5µm and it is connected with a bow-tie antenna for strong THz electric field confinement in the channel. The characterization of the devices has been carried out in a wide frequency range from 0.1-1 THz. The induced THz photocurrent is measured by using lock-in-amplifier after preamplifier. The maximum responsivity is achieved up to 1 A/W under self-biased mode. Further, this responsivity has been increased by applying biasing voltage. This photo response corresponds to low energy THz photons is mainly due to the photo galvanic effect in PtTe₂. The DC current is induced along the PtTe₂ channel, which is directly proportional to the amplitude of the incident THz electric field. Thus, these new topological semimetal materials provide new pathways for sensitive detection and sensing applications in the THz domain.

Keywords: terahertz, detector, responsivity, topological-semimetals

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Authors: Ferid Hammami

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The molecular geometries of the possible conformations of pyruvic acid-water complexes (PA-(H₂O)ₙ = 1- 4) have been fully optimized at DFT/B3LYP/6-311G ++ (d, p) levels of calculation. Among several optimized molecular clusters, the most stable molecular arrangements obtained when one, two, three, and four water molecules are hydrogen-bonded to a central pyruvic acid molecule are presented in this paper. Apposite topological and geometrical parameters are considered as primary indicators of H-bond strength. Atoms in molecules (AIM) analysis shows that pyruvic acid can form a ring structure with water, and the molecular structures are stabilized by both strong O-H...O and C-H...O hydrogen bonds. In large clusters, classical O-H...O hydrogen bonds still exist between water molecules, and a cage-like structure is built around some parts of the central molecule of pyruvic acid. The electrostatic potential energy map (MEP) and the HOMO-LUMO molecular orbital (highest occupied molecular orbital-lowest unoccupied molecular orbital) analysis has been performed for all considered complexes.

Keywords: pyruvic acid, PA-water complex, hydrogen bonding, DFT, AIM, MEP, HOMO-LUMO

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Authors: M. Y. Bakeir

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Rough set theory is a recent approach for reasoning about data. It has achieved a large amount of applications in various real-life fields. The main idea of rough sets corresponds to the lower and upper set approximations. These two approximations are exactly the interior and the closure of the set with respect to a certain topology on a collection U of imprecise data acquired from any real-life field. The base of the topology is formed by equivalence classes of an equivalence relation E defined on U using the available information about data. The theory of generalized topology was studied by Cs´asz´ar. It is well known that generalized topology in the sense of Cs´asz´ar is a generalization of the topology on a set. On the other hand, many important collections of sets related with the topology on a set form a generalized topology. The notion of Nano topology was introduced by Lellis Thivagar, which was defined in terms of approximations and boundary region of a subset of an universe using an equivalence relation on it. The purpose of this paper is to introduce a new generalized topology in terms of rough set called nano generalized topology

Keywords: rough sets, topological space, generalized topology, nano topology

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Authors: Avichal Malhotra, Jerome Frisch, Christoph van Treeck

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The utilization of semantic, cadastral and topological data from geographic information systems (GIS) has exponentially increased for building and urban-scale energy performance simulations. Urban planners, simulation scientists, and researchers use virtual 3D city models for energy analysis, algorithms and simulation tools. For dynamic energy simulations at city and district level, this paper provides an overview of the available GIS data models and their levels of detail. Adhering to different norms and standards, these models also intend to describe building and construction industry data. For further investigations, CityGML data models are considered for simulations. Though geographical information modelling has considerably many different implementations, extensions of virtual city data can also be made for domain specific applications. Highlighting the use of the extended CityGML models for energy researches, a brief introduction to the Energy Application Domain Extension (ADE) along with its significance is made. Consequently, addressing specific input simulation data, a workflow using Modelica underlining the usage of GIS information and the quantification of its significance over annual heating energy demand is presented in this paper.

Keywords: CityGML, EnergyADE, energy performance simulation, GIS

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Authors: Ezgi Kaya, A. Dilek Maden

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A topological index is a number related to graph which is invariant under graph isomorphism. In theoretical chemistry, molecular structure descriptors (also called topological indices) are used for modeling physicochemical, pharmacologic, toxicologic, biological and other properties of chemical compounds. Let G be a graph with n vertices and m edges. For a given edge uv, the quantity nu(e) denotes the number of vertices closer to u than v, the quantity nv(e) is defined analogously. The vertex PI index defined as the sum of the nu(e) and nv(e). Here the sum is taken over all edges of G. The energy of a graph is defined as the sum of the eigenvalues of adjacency matrix of G and the Laplacian energy of a graph is defined as the sum of the absolute value of difference of laplacian eigenvalues and average degree of G. In theoretical chemistry, the π-electron energy of a conjugated carbon molecule, computed using the Hückel theory, coincides with the energy. Hence results on graph energy assume special significance. The Laplacian matrix of a graph G weighted by the vertex PI weighting is the Laplacian vertex PI matrix and the Laplacian vertex PI eigenvalues of a connected graph G are the eigenvalues of its Laplacian vertex PI matrix. In this study, Laplacian vertex PI energy of a graph is defined of G. We also give some bounds for the Laplacian vertex PI energy of graphs in terms of vertex PI index, the sum of the squares of entries in the Laplacian vertex PI matrix and the absolute value of the determinant of the Laplacian vertex PI matrix.

Keywords: energy, Laplacian energy, laplacian vertex PI eigenvalues, Laplacian vertex PI energy, vertex PI index

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Authors: Elham Kiyani, S. Mansour Vaezpour, Javad Tavakoli

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In this paper, we first introduce a new distance function in a linear space not necessarily endowed with a topology. The algebraic concepts of interior and closure are useful to study optimization problems without topology. So, we define Q-weak efficient solutions generated by the algebraic interior of a set Q, where Q is not necessarily convex. Studying nonconvex vector optimization is valuable since, for a convex cone K in topological spaces, we have int(K)=cor(K), which means that topological interior of a convex cone K is equal to the algebraic interior of K. Moreover, we used the scalarization technique including the distance function generated by the vectorial closure of a set to characterize these Q-weak efficient solutions. Scalarization is a useful approach for solving vector optimization problems. This technique reduces the optimization problem to a scalar problem which tends to be an optimization problem with a real-valued objective function. For instance, Q-weak efficient solutions of vector optimization problems can be characterized and computed as solutions of appropriate scalar optimization problems. In the convex case, linear functionals can be used as objective functionals of the scalar problems. But in the nonconvex case, we should present a suitable objective function. It is the aim of this paper to present a new distance function that be useful to obtain sufficient and necessary conditions for Q-weak efficient solutions of general optimization problems via scalarization.

Keywords: weak efficient, algebraic interior, vector closure, linear space

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Authors: Peter Sauer, Thomas Hinze, Petra Hofstedt

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To avoid obstacles in the surrounding environment and to navigate to a given target belong to the most important tasks for mobile robots. According to these tasks different data structures are suitable. To avoid near obstacles, occupancy grid maps are an ideal representation of the surroundings. For less fine grained tasks, such as navigating from one room to another in an apartment, pure grid maps are inappropriate. Grid maps are very detailed, calculating paths to navigate between rooms based on grid maps would take too long. Instead, graph-based data structures, so-called topologies, turn out to be a proper choice for such tasks. In this paper we present two methods to dynamically create topologies from grid maps. Both methods are based on non-uniform grid maps. The topologies are generated on-the-fly and can easily be modified to represent changes in the environment. This allows a hybrid approach to control mobile robots, where, depending on the situation and the current task, either the grid map or the generated topology may be used.

Keywords: robot navigation, occupancy grids, topological maps, dynamic map creation

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Authors: Jude K. Safo

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Knowledge Graphs KG) and their relation to Graph Embeddings (GE) represent a unique data structure in the landscape of machine learning (relative to image, text and acoustic data). Unlike the latter, GEs are the only data structure sufficient for representing hierarchically dense, semantic information needed for use-cases like supply chain data and protein folding where the search space exceeds the limits traditional search methods (e.g. page-rank, Dijkstra, etc.). While GEs are effective for compressing low rank tensor data, at scale, they begin to introduce a new problem of ’data retreival’ which we observe in Large Language Models. Notable attempts by transE, TransR and other prominent industry standards have shown a peak performance just north of 57% on WN18 and FB15K benchmarks, insufficient practical industry applications. They’re also limited, in scope, to next node/link predictions. Traditional linear methods like Tucker, CP, PARAFAC and CANDECOMP quickly hit memory limits on tensors exceeding 6.4 million nodes. This paper outlines a topological framework for linear mapping between concepts in KG space and GE space that preserve cardinality. Most importantly we introduce a traceable framework for composing dense linguistic strcutures. We demonstrate performance on WN18 benchmark this model hits. This model does not rely on Large Langauge Models (LLM) though the applications are certainy relevant here as well.

Keywords: representation theory, large language models, graph embeddings, applied algebraic topology, applied knot theory, combinatorics

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Authors: Nazneen Khan, Vakeel A. Khan

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In this article we introduce the Paranorm Zweier I-convergent sequence spaces, for a sequence of positive real numbers. We study some topological properties, prove the decomposition theorem and study some inclusion relations on these spaces.

Keywords: ideal, filter, I-convergence, I-nullity, paranorm

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Authors: Alan C. Lin, Tran Anh Son

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This study proposes an approach to determine the undercut regions and their releasing directions for slider design of complex parts represented by the file format of STL (STereoLithography). In order to delineate the border of undercut regions, orthogonal cutting planes are firstly employed to automatically find the inner loops of a part model. To discover the facets belonging to undercut regions, attributes are then assigned to the facets of the part model based on the topological relationship of adjacent facets of each inner loop. After that, the undercut regions are separated from other facets in the model. Through the recognized facets of the undercut regions, the concept of 'visibility map (V-map)' is further applied to determine feasible releasing directions for each of the undercut regions. The undercut regions having the same releasing direction are finally grouped to form a slider in the injection mold.

Keywords: solid model, STL data, injection mold design, visibility map

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Authors: Yusri Yusof, Chen Wong Keong

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This paper presents the implementation details of a Relational Database Management System of a STEP-technology product model repository. It is able support the implementation of any EXPRESS language schema, although it has been primarily implemented to support mechanical product life cycle applications. This database support the input of STEP part 21 file format from CAD in geometrical and topological data format and support a range of queries for mechanical product life cycle applications. This proposed relational database management system uses entity-to-table method (R1) rather than type-to-table method (R4). The two mapping methods have their own strengths and drawbacks.

Keywords: RDBMS, CAD, ISO 10303, part-21 file

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Authors: Saurabh Basu, Sudin Ganguly

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Conductance in graphene nanoribbons (GNR) in presence of magnetic (for example, Iron) and non-magnetic (for example, Gold) adatoms are explored theoretically within a Kane-Mele model for their possible spintronic applications and topologically non-trivial properties. In our work, we have considered the magnetic adatoms to induce a Rashba spin-orbit coupling (RSOC) and an exchange bias field, while the non-magnetic ones induce an RSOC and an intrinsic spin-orbit (SO) coupling. Even though RSOC is present in both, they, however, represent very different physical situations, where the magnetic adatoms do not preserve the time reversal symmetry, while the non-magnetic case does. This has important implications on the topological properties. For example, the non-magnetic adatoms, for moderately strong values of SO, the GNR denotes a quantum spin Hall insulator as evident from a 2e²/h plateau in the longitudinal conductance and presence of distinct conducting edge states with an insulating bulk. Since the edge states are protected by time reversal symmetry, the magnetic adatoms in GNR yield trivial insulators and do not possess any non-trivial topological property. However, they have greater utility than the non-magnetic adatoms from the point of view of spintronic applications. Owing to the broken spatial symmetry induced by the presence of adatoms of either type, all the x, y and z components of the spin-polarized conductance become non-zero (only the y-component survives in pristine Graphene owing to a mirror symmetry present there) and hence become suitable for spintronic applications. However, the values of the spin polarized conductances are at least two orders of magnitude larger in the case of magnetic adatoms than their non-magnetic counterpart, thereby ensuring more efficient spintronic applications. Further the applications are tunable by altering the adatom densities.

Keywords: magnetic and non-magnetic adatoms, quantum spin hall phase, spintronic applications, spin polarized conductance, time reversal symmetry

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Authors: G. De Matteis, L. Martina, V. Turco

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The work is focused on determining and comparing special nonlinear static configurations in cholesteric liquid crystals (CLCs), confined between two parallel plates and in the presence of an external static electric/magnetic field. The solutions are stabilised by topological and non-topological conservation laws since they are described in terms of integrable or partially integrable nonlinear boundary value problems. In cholesteric liquid crystals which are subject to geometric frustration; anchoring conditions at boundaries, i.e., homeotropic conditions, are incompatible with the cholesteric twist. This aspect turns out to be essential in the admissible classes of solutions, allowing also for disclination type singularities. Within the framework of Frank-Oseen theory, we study the static configurations for CLCs. First, we find numerical solutions for isolated axisymmetric states in confined CLCs with weak homeotropic anchoring at the boundaries. These solutions describe 3-dimensional modulations, namely spherulites or cholesteric bubbles, actually observed in these systems, of standard baby skyrmions. Relations with well-known nonlinear integrable systems are found and are used to explore the asymptotic behavior of the solutions. Then we turn our attention to extended periodic static configurations called Helicoids or cholesteric fingers, described by an elliptic sine-Gordon model with appropriate boundary conditions, showing how their period and energies are determined by both the thickness of the cell and the intensity of the external electric/magnetic field. We explicitly show that helicoids with π or 2π of rotations of the molecular director are different in many aspects and are not simply algebraically related. The behaviour of the solutions, their energy and the properties of the associated disclinations are discussed in detail, both analytically and numerically.

Keywords: cholesteric liquid crystals, geometric frustration, helicoids, skyrmions

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Authors: S. Vasundra, D. Venkatesh

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Wireless networks have gone through an extraordinary growth in the past few years, and will keep on playing a crucial role in future data communication. The present wireless networks aim to make communication possible anywhere and anytime. With the converging of mobile and wireless communications with Internet services, the boundary between mobile personal telecommunications and wireless computer networks is disappearing. Wireless networks of the next generation need the support of all the advances on new architectures, standards, and protocols. Since an ad hoc network may consist of a large number of mobile hosts, this imposes a significant challenge on the design of an effective and efficient routing protocol that can work well in an environment with frequent topological changes. This paper proposes improved ant colony optimization (IACO) technique. It also maintains load balancing in wireless networks. The simulation results show that the proposed IACO performs better than existing routing techniques.

Keywords: wireless networks, ant colony optimization, load balancing, architecture

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Authors: Henry Navarro, Martin Sirena, Nestor Haberkorn

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We report the electrical transport through voltage-current curves (I-V) in tunnels junction GdBa₂Cu₃O₇-d/ insulator/ GdBa₂Cu₃O₇-d, and Nb/insulator/ GdBa₂Cu₃O₇-d is analyzed using a conducting atomic force microscope (CAFM) at room temperature. The measurements were obtained on tunnel junctions with different areas (900 μm², 400 μm² and 100 μm²). Trilayers with GdBa₂Cu₃O₇-d (GBCO) as the bottom electrode, SrTiO₃ (STO) or BaTiO₃ (BTO) as the insulator barrier (thicknesses between 1.6 nm and 4 nm), and GBCO or Nb as the top electrode were grown by DC sputtering on (100) SrTiO₃ substrates. For STO and BTO barriers, asymmetric IV curves at positive and negative polarization can be obtained using electrodes with different work function. The main difference is that the BTO is a ferroelectric material, while in the STO the ferroelectricity can be produced by stress or deformation at the interfaces. In addition, hysteretic IV curves are obtained for BTO barriers, which can be ascribed to a combined effect of the FE reversal switching polarization and an oxygen vacancy migration. For GBCO/ BTO/ GBCO heterostructures, the IV curves correspond to that expected for asymmetric interfaces, which indicates that the disorder affects differently the properties at the bottom and top interfaces. Our results show the role of the interface disorder on the electrical transport of conducting/ insulator/ conduction heterostructures, which is relevant for different applications, going from resistive switching memories (at room temperature) to Josephson junctions (at low temperatures). The superconducting transition of the GBCO electrode was characterized by electrical transport using the 4-prong configuration with low density of topological defects and with Tc over liquid N₂ can be obtained for thicknesses of 16 nm, our results demonstrate that GBCO films with an average root-mean-square (RMS) smaller than 1 nm and areas (up 100 um²) free of 3-D topological defects can be obtained.

Keywords: thin film, sputtering, conductive atomic force microscopy, tunnel junctions

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Authors: Jana Andzane, Gunta Kunakova, Margarita Baitimirova, Mikelis Marnauza, Floriana Lombardi, Donats Erts

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Bismuth selenide (Bi₂Se₃) is known as a narrow band gap semiconductor with pronounced thermoelectric (TE) and topological insulator (TI) properties. Unique TI properties offer exciting possibilities for fundamental research as observing the exciton condensate and Majorana fermions, as well as practical application in spintronic and quantum information. In turn, TE properties of this material can be applied for wide range of thermoelectric applications, as well as for broadband photodetectors and near-infrared sensors. Nanostructuring of this material results in improvement of TI properties due to suppression of the bulk conductivity, and enhancement of TE properties because of increased phonon scattering at the nanoscale grains and interfaces. Regarding TE properties, crystallographic growth direction, as well as orientation of the nanostructures relative to the growth substrate, play significant role in improvement of TE performance of nanostructured material. For instance, Bi₂Se₃ layers consisting of randomly oriented nanostructures and/or of combination of them with planar nanostructures show significantly enhanced in comparison with bulk and only planar Bi₂Se₃ nanostructures TE properties. In this work, a catalyst-free vapour-solid deposition technique was applied for controlled obtaining of different types of Bi₂Se₃ nanostructures and continuous nanostructured layers for targeted applications. For example, separated Bi₂Se₃ nanoplates, nanobelts and nanowires can be used for investigations of TI properties; consisting from merged planar and/or randomly oriented nanostructures Bi₂Se₃ layers are useful for applications in heat-to-power conversion devices and infrared detectors. The vapour-solid deposition was carried out using quartz tube furnace (MTI Corp), equipped with an inert gas supply and pressure/temperature control system. Bi₂Se₃ nanostructures/nanostructured layers of desired type were obtained by adjustment of synthesis parameters (process temperature, deposition time, pressure, carrier gas flow) and selection of deposition substrate (glass, quartz, mica, indium-tin-oxide, graphene and carbon nanotubes). Morphology, structure and composition of obtained Bi₂Se₃ nanostructures and nanostructured layers were inspected using SEM, AFM, EDX and HRTEM techniques, as well as home-build experimental setup for thermoelectric measurements. It was found that introducing of temporary carrier gas flow into the process tube during the synthesis and deposition substrate choice significantly influence nanostructures formation mechanism. Electrical, thermoelectric, and topological insulator properties of different types of deposited Bi₂Se₃ nanostructures and nanostructured coatings are characterized as a function of thickness and discussed.

Keywords: bismuth seleinde, nanostructures, topological insulator, vapour-solid deposition

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Authors: Lijuan Zhou, Mengqi Wu, Changyong Niu

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Attributed graph clustering can utilize the graph topology and node attributes to uncover hidden community structures and patterns in complex networks, aiding in the understanding and analysis of complex systems. Utilizing contrastive learning for attributed graph clustering can effectively exploit meaningful implicit relationships between data. However, existing attributed graph clustering methods based on contrastive learning suffer from the following drawbacks: 1) Complex data augmentation increases computational cost, and inappropriate data augmentation may lead to semantic drift. 2) The selection of positive and negative samples neglects the intrinsic cluster structure learned from graph topology and node attributes. Therefore, this paper proposes a method called self-supervised Attributed Graph Clustering with Dual Contrastive Loss constraints (AGC-DCL). Firstly, Siamese Multilayer Perceptron (MLP) encoders are employed to generate two views separately to avoid complex data augmentation. Secondly, the neighborhood contrastive loss is introduced to constrain node representation using local topological structure while effectively embedding attribute information through attribute reconstruction. Additionally, clustering-oriented contrastive loss is applied to fully utilize clustering information in global semantics for discriminative node representations, regarding the cluster centers from two views as negative samples to fully leverage effective clustering information from different views. Comparative clustering results with existing attributed graph clustering algorithms on six datasets demonstrate the superiority of the proposed method.

Keywords: attributed graph clustering, contrastive learning, clustering-oriented, self-supervised learning

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Authors: Minh Quang Le, Dane Taylor

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Convection is a well-studied topic in fluid dynamics, yet it is less understood in the context of networks flows. Here, we incorporate techniques from topological data analysis (namely, persistent homology) to automate the detection and characterization of convective/cyclic/chiral flows over networks, particularly those that arise for irreversible Markov chains (MCs). As two applications, we study convection cycles arising under the PageRank algorithm, and we investigate chiral edges flows for a stochastic model of a bi-monomer's configuration dynamics. Our experiments highlight how system parameters---e.g., the teleportation rate for PageRank and the transition rates of external and internal state changes for a monomer---can act as homology regularizers of convection, which we summarize with persistence barcodes and homological bifurcation diagrams. Our approach establishes a new connection between the study of convection cycles and homology, the branch of mathematics that formally studies cycles, which has diverse potential applications throughout the sciences and engineering.

Keywords: homology, persistent homolgy, markov chains, convection cycles, filtration

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Authors: Ayşe Dilek Maden

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For a given a simple connected graph, we present some new bounds via a new approach for a special topological index given by the sum of the real number power of the non-zero normalized Laplacian eigenvalues. To use this approach presents an advantage not only to derive old and new bounds on this topic but also gives an idea how some previous results in similar area can be developed.

Keywords: degree Kirchhoff index, normalized Laplacian eigenvalue, spanning tree, simple connected graph

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