Search results for: topological data analysis

Authors: Ali Koam, Ismail Ibedou, S. E. Abbas

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In this paper, it is introduced the notion of r-fuzzy ideal separation axioms Tᵢi = 0; 1; 2 based on a fuzzy ideal I on a fuzzy topological space (X; τ). An r-fuzzy ideal connectedness related to the fuzzy ideal I is introduced which has relations with a previous r-fuzzy fuzzy connectedness. An r-fuzzy ideal compactness related to Ι is introduced which has also relations with many other types of fuzzy compactness.

Keywords: fuzzy ideal, fuzzy separation axioms, fuzzy compactness, fuzzy connectedness

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Authors: M. Marchewka

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The article is devoted to the possible optical transitions in double quantum wells system based on HgTe/HgCd(Mn)Te heterostructures. Such structures can find applications as detectors and sources of radiation in the terahertz range. The Double Quantum Wells (DQW) systems consist of two QWs separated by the transparent for electrons barrier. Such systems look promising from the point of view of the additional degrees of freedom. In the case of the topological insulator in about 6.4nm wide HgTe QW or strained 3D HgTe films at the interfaces, the topologically protected surface states appear at the interfaces/surfaces. Electrons in those edge states move along the interfaces/surfaces without backscattering due to time-reversal symmetry. Combination of the topological properties, which was already verified by the experimental way, together with the very well know properties of the DQWs, can be very interesting from the applications point of view, especially in the THz area. It is important that at the present stage, the technology makes it possible to create high-quality structures of this type, and intensive experimental and theoretical studies of their properties are already underway. The idea presented in this paper is based on the eight-band KP model, including the additional terms related to the structural inversion asymmetry, interfaces inversion asymmetry, the influence of the magnetically content, and the uniaxial strain describe the full pictures of the possible real structure. All of this term, together with the external electric field, can be sources of breaking symmetry in investigated materials. Using the 8 band KP model, we investigated the electronic shape structure with and without magnetic field from the application point of view as a THz detector in a small magnetic field (below 2T). We believe that such structures are the way to get the tunable topological insulators and the multilayer topological insulator. Using the one-dimensional electrons at the topologically protected interface states as fast and collision-free signal carriers as charge and signal carriers, the detection of the optical signal should be fast, which is very important in the high-resolution detection of signals in the THz range. The proposed engineering of the investigated structures is now one of the important steps on the way to get the proper structures with predicted properties.

Keywords: topological insulator, THz spectroscopy, KP model, II-VI compounds

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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: Shai Sarussi

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Let S be an integral domain with field of fractions F and let A be an F-algebra. An S-subalgebra R of A is called S-nice if R∩F = S and the localization of R with respect to S \{0} is A. Denoting by W the set of all S-nice subalgebras of A, and defining a notion of open sets on W, one can view W as a T0-Alexandroff space. Thus, the algebraic structure of W can be viewed from the point of view of topology. It is shown that every nonempty open subset of W has a maximal element in it, which is also a maximal element of W. Moreover, a supremum of an irreducible subset of W always exists. As a notable connection with valuation theory, one considers the case in which S is a valuation domain and A is an algebraic field extension of F; if S is indecomposed in A, then W is an irreducible topological space, and W contains a greatest element.

Keywords: integral domains, Alexandroff topology, prime spectrum of a ring, valuation domains

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Authors: Ye Wang, Ickjai Lee

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Due to the widespread of mobile sensing, there is a strong need to handle trails of moving objects, trajectories. This paper proposes three visual analytic approaches for higher order information of trajectory data sets based on the higher order Voronoi diagram data structure. Proposed approaches reveal geometrical information, topological, and directional information. Experimental results demonstrate the applicability and usefulness of proposed three approaches.

Keywords: visual analytics, higher order information, trajectory datasets, spatio-temporal data

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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: 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: Lidija R. Jevrić, Sanja O. Podunavac-Kuzmanović, Strahinja Z. Kovačević

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This study considers the selection of the most suitable in silico molecular descriptors that could be used for s-triazine pesticides characterization. Suitable descriptors among topological, geometrical and physicochemical are used for quantitative structure-retention relationships (QSRR) model establishment. Established models were obtained using linear regression (LR) and multiple linear regression (MLR) analysis. In this paper, MLR models were established avoiding multicollinearity among the selected molecular descriptors. Statistical quality of established models was evaluated by standard and cross-validation statistical parameters. For detection of similarity or dissimilarity among investigated s-triazine pesticides and their classification, principal component analysis (PCA) and hierarchical cluster analysis (HCA) were used and gave similar grouping. This study is financially supported by COST action TD1305.

Keywords: chemometrics, classification analysis, molecular descriptors, pesticides, regression analysis

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Authors: Michael Gidey Gebru

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Most of Data Envelopment Analysis models operate in a static environment with input and output parameters that are chosen by deterministic data. However, due to ambiguity brought on shifting market conditions, input and output data are not always precisely gathered in real-world scenarios. Fuzzy numbers can be used to address this kind of ambiguity in input and output data. Therefore, this work aims to expand crisp Data Envelopment Analysis into Data Envelopment Analysis with fuzzy environment. In this study, the input and output data are regarded as fuzzy triangular numbers. Then, the Data Envelopment Analysis model with fuzzy environment is solved using a multi-objective method to gauge the Decision Making Units' efficiency. Finally, the developed Data Envelopment Analysis model is illustrated with an application on real data 50 educational institutions.

Keywords: efficiency, Data Envelopment Analysis, fuzzy, higher education, input, output

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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: Liang Zhao, Jili Zhang, Chongquan Zhong

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Energy consumption data, in particular those involving public buildings, are impacted by many factors: the building structure, climate/environmental parameters, construction, system operating condition, and user behavior patterns. Traditional methods for data analysis are insufficient. This paper delves into the data mining technology to determine its application in the analysis of building energy consumption data including energy consumption prediction, fault diagnosis, and optimal operation. Recent literature are reviewed and summarized, the problems faced by data mining technology in the area of energy consumption data analysis are enumerated, and research points for future studies are given.

Keywords: data mining, data analysis, prediction, optimization, building operational performance

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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: 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: 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: Jeff Chak-Fu Wong, Tony Chun Yin Yip

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The transition from secondary school to university seems exciting for many first-year students but can be more challenging than expected. Enabling instructors to know students’ learning habits and styles enhances their understanding of the students’ learning backgrounds, allows teachers to provide better support for their students, and has therefore high potential to improve teaching quality and learning, especially in any mathematics-related courses. The aim of this research is to collect students’ data using online surveys, to analyze students’ factors using learning analytics and educational data mining and to discover the characteristics of the students at risk of falling behind in their studies based on students’ previous academic backgrounds and collected data. In this paper, we use correlation-based distance methods and mutual information for measuring student factor relationships. We then develop a factor network using the Minimum Spanning Tree method and consider further study for analyzing the topological properties of these networks using social network analysis tools. Under the framework of mutual information, two graph-based feature filtering methods, i.e., unsupervised and supervised infinite feature selection algorithms, are used to analyze the results for students’ data to rank and select the appropriate subsets of features and yield effective results in identifying the factors affecting students at risk of failing. This discovered knowledge may help students as well as instructors enhance educational quality by finding out possible under-performers at the beginning of the first semester and applying more special attention to them in order to help in their learning process and improve their learning outcomes.

Keywords: students' academic performance, correlation-based distance method, social network analysis, feature selection, graph-based feature filtering method

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Authors: Bolin Hua

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In city governance, various data are involved, including city component data, demographic data, housing data and all kinds of business data. These data reflects different aspects of people, events and activities. Data generated from various systems are different in form and data source are different because they may come from different sectors. In order to reflect one or several facets of an event or rule, data from multiple sources need fusion together. Data from different sources using different ways of collection raised several issues which need to be resolved. Problem of data fusion include data update and synchronization, data exchange and sharing, file parsing and entry, duplicate data and its comparison, resource catalogue construction. Governments adopt statistical analysis, time series analysis, extrapolation, monitoring analysis, value mining, scenario prediction in order to achieve pattern discovery, law verification, root cause analysis and public opinion monitoring. The result of Multi-source data fusion is to form a uniform central database, which includes people data, location data, object data, and institution data, business data and space data. We need to use meta data to be referred to and read when application needs to access, manipulate and display the data. A uniform meta data management ensures effectiveness and consistency of data in the process of data exchange, data modeling, data cleansing, data loading, data storing, data analysis, data search and data delivery.

Keywords: multi-source data fusion, urban comprehensive management, information fusion, government data

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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: Semanur Soyyigit Kaya, Ercan Eren

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Energy has a prominent role for development of nations. Countries which have energy resources also have strategic power in the international trade of energy since it is essential for all stages of production in the economy. Thus, it is important for countries to analyze the weakness and strength of the system. On the other side, it is commonly believed that international trade has complex network properties. Complex network is a tool for the analysis of complex systems with heterogeneous agents and interaction between them. A complex network consists of nodes and the interactions between these nodes. Total properties which emerge as a result of these interactions are distinct from the sum of small parts (more or less) in complex systems. Thus, standard approaches to international trade are superficial to analyze these systems. Network analysis provides a new approach to analyze international trade as a network. In this network countries constitute nodes and trade relations (export or import) constitute edges. It becomes possible to analyze international trade network in terms of high degree indicators which are specific to complex systems such as connectivity, clustering, assortativity/disassortativity, centrality, etc. In this analysis, international trade of crude oil and coal which are types of fossil fuel has been analyzed from 2005 to 2014 via network analysis. First, it has been analyzed in terms of some topological parameters such as density, transitivity, clustering etc. Afterwards, fitness to Pareto distribution has been analyzed. Finally, weighted HITS algorithm has been applied to the data as a centrality measure to determine the real prominence of countries in these trade networks. Weighted HITS algorithm is a strong tool to analyze the network by ranking countries with regards to prominence of their trade partners. We have calculated both an export centrality and an import centrality by applying w-HITS algorithm to data.

Keywords: complex network approach, fossil fuel, international trade, network theory

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Authors: Jihyun Song, Kyeongjoo Kim, Minsoo Lee

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Due to the development of information technology and wireless Internet technology, various data are being generated in various fields. These data are advantageous in that they provide real-time information to the users themselves. However, when the data are accumulated and analyzed, more various information can be extracted. In addition, development and dissemination of boards such as Arduino and Raspberry Pie have made it possible to easily test various sensors, and it is possible to collect sensor data directly by using database application tools such as MySQL. These directly collected data can be used for various research and can be useful as data for data mining. However, there are many difficulties in using the board to collect data, and there are many difficulties in using it when the user is not a computer programmer, or when using it for the first time. Even if data are collected, lack of expert knowledge or experience may cause difficulties in data analysis and visualization. In this paper, we aim to construct a library for sensor data collection and analysis to overcome these problems.

Keywords: clustering, data mining, DBSCAN, k-means, k-medoids, sensor data

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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: Monica Lia

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This article presents a customer data analysis model using business intelligence tools for data modelling, transforming, data visualization and dynamic reports building. Economic organizational customer’s analysis is made based on the information from the transactional systems of the organization. The paper presents how to develop the data model starting for the data that companies have inside their own operational systems. The owned data can be transformed into useful information about customers using business intelligence tool. For a mature market, knowing the information inside the data and making forecast for strategic decision become more important. Business Intelligence tools are used in business organization as support for decision-making.

Keywords: customer analysis, business intelligence, data warehouse, data mining, decisions, self-service reports, interactive visual analysis, and dynamic dashboards, use cases diagram, process modelling, logical data model, data mart, ETL, star schema, OLAP, data universes

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Authors: Jennifer Cuellar, Angie L. Parada, Kevin N. S. Chacon, Sol M. Mejia

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The purification of bio-ethanol through distillation methods is an unresolved issue at the biofuel industry because of the ethanol-water azeotrope formation, which increases the steps of the purification process and subsequently increases the production costs. Therefore, understanding the mixture nature at the molecular level could provide new insights for improving the current methods and/or designing new and more efficient purification methods. For that reason, the present study focuses on the evaluation and analysis of (ethanol)₉-water heterodecamers, as the systems with the minimum molecular proportion that represents the azeotropic concentration (96 %m/m in ethanol). The computational modelling was carried out with B3LYP-D3/6-311++G(d,p) in Gaussian 09. Initial explorations of the potential energy surface were done through two methods: annealing simulated runs and molecular dynamics trajectories besides intuitive structures obtained from smaller (ethanol)n-water heteroclusters, n = 7, 8 and 9. The energetic order of the seven stable heterodecamers determines the most stable heterodecamer (Hdec-1) as a structure forming a bicyclic geometry with the O-H---O hydrogen bonds (HBs) where the water is a double proton donor molecule. Hdec-1 combines 1 water molecule and the same quantity of every ethanol conformer; this is, 3 trans, 3 gauche 1 and 3 gauche 2; its abundance is 89%, its decamerization energy is -80.4 kcal/mol, i.e. 13 kcal/mol most stable than the less stable heterodecamer. Besides, a way to understand why methanol does not form an azeotropic mixture with water, analogous systems ((ethanol)10, (methanol)10, and (methanol)9-water)) were optimized. Topologic analysis of the electron density reveals that Hec-1 forms 33 weak interactions in total: 11 O-H---O, 8 C-H---O, 2 C-H---C hydrogen bonds and 12 H---H interactions. The strength and abundance of the most unconventional interactions (H---H, C-H---O and C-H---O) seem to explain the preference of the ethanol for forming heteroclusters instead of clusters. Besides, O-H---O HBs present a significant covalent character according to topologic parameters as the Laplacian of electron density and the relationship between potential and kinetic energy densities evaluated at the bond critical points; obtaining negatives values and values between 1 and 2, for those two topological parameters, respectively.

Keywords: ADMP, DFT, ethanol-water azeotrope, Grimme dispersion correction, simulated annealing, weak interactions

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Authors: Ameur Abdelkader, Abed Bouarfa Hafida

Abstract:

Since its inception, predictive analysis has revolutionized the IT industry through its robustness and decision-making facilities. It involves the application of a set of data processing techniques and algorithms in order to create predictive models. Its principle is based on finding relationships between explanatory variables and the predicted variables. Past occurrences are exploited to predict and to derive the unknown outcome. With the advent of big data, many studies have suggested the use of predictive analytics in order to process and analyze big data. Nevertheless, they have been curbed by the limits of classical methods of predictive analysis in case of a large amount of data. In fact, because of their volumes, their nature (semi or unstructured) and their variety, it is impossible to analyze efficiently big data via classical methods of predictive analysis. The authors attribute this weakness to the fact that predictive analysis algorithms do not allow the parallelization and distribution of calculation. In this paper, we propose to extend the predictive analysis algorithm, Classification And Regression Trees (CART), in order to adapt it for big data analysis. The major changes of this algorithm are presented and then a version of the extended algorithm is defined in order to make it applicable for a huge quantity of data.

Keywords: predictive analysis, big data, predictive analysis algorithms, CART algorithm

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Authors: Minh Quang Le, Dane Taylor

Abstract:

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: Ji Eun Shin, Byung Ho Jung, Dong Hoon Lim

Abstract:

It is almost impossible to store or analyze big data increasing exponentially with traditional technologies. Hadoop is a new technology to make that possible. R programming language is by far the most popular statistical tool for big data analysis based on distributed processing with Hadoop technology. With RHadoop that integrates R and Hadoop environment, we implemented parallel multiple regression analysis with different sizes of actual data. Experimental results showed our RHadoop system was much faster as the number of data nodes increases. We also compared the performance of our RHadoop with lm function and big lm packages available on big memory. The results showed that our RHadoop was faster than other packages owing to paralleling processing with increasing the number of map tasks as the size of data increases.

Keywords: big data, Hadoop, parallel regression analysis, R, RHadoop

Procedia PDF Downloads 407

Authors: Takahiro Nishigaki, Katsumi Nitta, Takashi Onoda

Abstract:

In this paper, we present a method of applying Independent Topic Analysis (ITA) to increasing the number of document data. The number of document data has been increasing since the spread of the Internet. ITA was presented as one method to analyze the document data. ITA is a method for extracting the independent topics from the document data by using the Independent Component Analysis (ICA). ICA is a technique in the signal processing; however, it is difficult to apply the ITA to increasing number of document data. Because ITA must use the all document data so temporal and spatial cost is very high. Therefore, we present Incremental ITA which extracts the independent topics from increasing number of document data. Incremental ITA is a method of updating the independent topics when the document data is added after extracted the independent topics from a just previous the data. In addition, Incremental ITA updates the independent topics when the document data is added. And we show the result applied Incremental ITA to benchmark datasets.

Keywords: text mining, topic extraction, independent, incremental, independent component analysis

Procedia PDF Downloads 276