DOCSLIB.ORG

Unified Retrieval in Distributed and Heterogeneous Multimedia Information Systems Dipl. Inf. Florian Stegmaier December 18, 2013

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Unified Retrieval in Distributed and Heterogeneous Multimedia Information Systems Dipl. Inf. Florian Stegmaier December 18, 2013 University of Passau Department of Informatics and Mathematics Chair of Distributed Information Systems Doctoral Thesis Unified Retrieval in Distributed and Heterogeneous Multimedia Information Systems Dipl. Inf. Florian Stegmaier December 18, 2013 Advisor: Prof. Dr. Harald Kosch Second Advisor: Prof. Dr. Richard Chbeir In theory, there is no difference between theory and practice. But, in practice, there is. Jan L. A. van de Snepscheut (1953 – 1994). For Tamara. Abstract Multimedia retrieval is an essential part of today’s world. This situation is ob- servable in industrial domains, e.g., medical imaging, as well as in the private sector, visible by activities in manifold Social Media platforms. This trend led to the cre- ation of a huge environment of multimedia information retrieval services offering multimedia resources for almost any user requests. Indeed, the encompassed data is in general retrievable by (proprietary) APIs and query languages, but unfortu- nately a unified access is not given due to arising interoperability issues between those services. In this regard, this thesis focuses on two application scenarios, namely a medical retrieval system supporting a radiologist’s workflow, as well as an interoperable image retrieval service interconnecting diverse data silos. The scientific contribution of this dissertation is split in three different parts: the first part of this thesis improves the metadata interoperability issue. Here, major contributions to a community-driven, international standardization have been proposed leading to the specification of an API and ontology toenableaunified annotation and retrieval of media resources. The second partissuesametasearch engine especially designed for unified retrieval in distributed and heterogeneous multimedia retrieval environments. This metasearch engineiscapableofbeing operated in a federated as well as autonomous manner inside the aforementioned application scenarios. The remaining third part ensures an efficient retrieval due to the integration of optimization techniques for multimedia retrieval in the overall query execution process of the metasearch engine. Keywords: Distributed multimedia retrieval, query optimization, multimedia annotation, interoperability Kurzzusammenfassung Egal ob im industriellen Bereich oder auch im Social Media - multimediale Daten nehmen eine immer zentralere Rolle ein. Aus diesem fortlaufendem En- twicklungsprozess entwickelten sich umfangreiche Informationssysteme, die Daten für zahlreiche Bedürfnisse anbieten. Allerdings ist ein einheitlicher Zugriff auf jene verteilte und heterogene Landschaft von Informationssystemen in der Praxis nicht gewährleistet. Und dies, obwohl die Datenbestände meist über Schnittstellen abruf- bar sind. Im Detail widmet sich diese Arbeit mit der Bearbeitung zweier Anwen- dungsszenarien. Erstens, einem medizinischen System zur Diagnoseunterstützung und zweitens einer interoperablen, verteilten Bildersuche. Der wissenschaftliche Teil der vorliegenden Dissertation gliedert sich in drei Teile: Teil eins befasst sich mit dem Problem der Interoperabilitätzwischenverschiede- nen Metadatenformaten. In diesem Bereich wurden maßgebliche Beiträge für ein internationales Standardisierungsverfahren entwickelt.Zielwares,einerOntolo- gie, sowie einer Programmierschnittstelle einen vereinheitlichten Zugriff auf multi- mediale Informationen zu ermöglichen. In Teil zwei wird eineexterneMetasuch- maschine vorgestellt, die eine einheitliche Anfrageverarbeitung in heterogenen und verteilten Multimediadatenbanken ermöglicht. In den Anwendungsszenarien wird zum einen auf eine föderative, als auch autonome Anfrageverarbeitung eingegan- gen. Abschließend werden in Teil drei Techniken zur Optimierung von verteilten multimedialen Anfragen präsentiert. Stichwörter: Verteilte Multimedia-Anfrageverarbeitung, Optimierung von Multimedia-Anfragen, Multimedia Annotation, Interoperabilität Acknowledgements Ihavebeenworkingonthetopicsofthisthesisformorethenfour years. Without the constant support of certain people, I surely would not have had the patience to complete it. I am not a man of many words or big explanations; however, I want to take the opportunity to express my grateful thanks: At first I want to thank my advisor Harald Kosch as well as Mario Döller for their supervision, sophisticated feedback and friendly advise. Honestly, I feel very lucky to have met so many outstanding colleagues during my period at the Chair of Distributed Information Systems (in alphabetic order): Werner Bailer, Sebastian Bayerl, Emanuel Berndl, Tobias Bürger, David Coquil, Andreas Eisenkolb, Michael Granitzer, Udo Gröbner, Thomas Kurz, Tobias Rene Mayer, Britta Meixner, Tilmann Rabl, Hatem Moussely Sergieh, Kai Schlegel, Stella Stars, Ingrid Win- ter, and Andreas Wölfl. All of you are a part of this thesis: the feedback you gave me, the ears you lent me during hard times or simply because youalwaysbrightened my day. You are all very special to me. Further, I want to thank my family: My parents Christa and Johann, who always believed in me and gave me the opportunity to study in the area of my interest. My brother Bernhard, who had really hard times in guiding my firststepsinprogram- ming Java, along with his wife Angela. My aunts and uncles Uschi and Hannes as well as Anita and Raimund. Finally my grandma Paula for being as she is. Besides, Iamblessedwithreallygreatfriends,onwhichIcanalwayscount – unfortunately Icannotenumerateeverybody,theonesIhaveinmindareawareofit. IdedicatethisthesistomybelovedwifeTamara,themostimportant person in my life. Thank you for everything. Contents List of Tables xiii List of Figures xvi List of Listings xvii IPreface 1 1 Introduction 3 1.1 Motivation ................................ 3 1.2 Contributions ............................... 5 1.3 Overview ................................. 6 II Foundations of Multimedia Information Retrieval 9 2 Multimedia Information Retrieval in a Nutshell 11 2.1 Terminology ................................ 11 2.2 Excursus: Information Retrieval .................... 12 2.3 Classification of Multimedia Information Retrieval Techniques .... 16 2.4 Multimedia Information Retrieval: An On-going Challenge ..... 17 3 Modeling Multimedia Metadata 21 3.1 Only Data about Data? ......................... 21 3.2 Classifying Metadata Schemas ...................... 25 3.3 Metamodels for Designing Metadata Schemas ............. 26 3.3.1 Representational Models ..................... 27 3.3.2 Multimedia Ontologies ...................... 29 3.4 Presence of Multimedia Metadata .................... 31 3.5 Metadata, Standardization and the Web ................ 33 4 Indexing Multimedia Resources 37 4.1 Usage of Multimedia Features During Retrieval ............ 37 4.2 Expressiveness of Features in Image Retrieval ............. 40 4.3 Similarity Measures ........................... 42 4.4 Characteristics of Similarity Query Types ............... 42 4.5 Accessing Multimedia Features ..................... 44 4.6 The Curse of Dimensionality and Beyond ............... 47 x Contents 5 Multimedia Retrieval Systems 49 5.1 Terminology & Requirements Definition ................ 49 5.2 Architectural Facets ........................... 50 5.3 Multimedia Query Languages ...................... 52 III Improving Metadata Interoperability 55 6 Unified Access to Multimedia Metadata 57 6.1 Related Work ............................... 57 6.1.1 Many Standards for Different Needs .............. 57 6.1.2 Interoperability Approaches between Metadata Schemas ... 58 6.2 Use Case & Requirements ........................ 59 6.3 A Pivot Metadata Scheme for Media Resources ............ 61 6.3.1 Ontology for Media Resources 1.0 ............... 62 6.3.2 Alignment of Metadata Formats ................ 62 6.3.3 API for Media Resources 1.0 .................. 65 7 Discussion 71 IV Distributed Multimedia Retrieval 75 8 AIR: Architecture for Interoperable Retrieval 77 8.1 Related Work ............................... 77 8.2 Application Scenarios .......................... 78 8.2.1 THESEUS: MEDICO ...................... 78 8.2.2 Interoperable Image Search ................... 79 8.3 Design Principles ............................. 81 8.4 Excursus: MPEG Query Format .................... 82 8.5 Query Execution Strategies ....................... 85 8.6 Architectural Facets ........................... 87 8.7 Distributed Query Processing ...................... 89 9 Discussion 95 VOptimizingDistributedMultimediaRetrieval 97 10 Optimization Techniques for Query Execution 99 10.1 Related Work ............................... 99 10.2 Intra-Query Optimization ........................100 10.2.1 Query Execution Planning ....................100 10.2.2 Query Processing Strategies ...................101 10.3 Inter-Query Optimization ........................104 Contents xi 10.3.1 Query Scheduler .........................104 10.3.2 Multimedia Caching System ...................104 11 Retrieval in Unfederated Multimedia Environments 109 11.1 Characterizing the Issue .........................109 11.2 Related Work ...............................110 11.3 Definitions and Notations ........................111 11.4 Algorithm Inspection & System Integration ..............117 12 Evaluation 119 12.1 Quality Measures .............................119 12.2 Evaluation of Optimization Techniques .................122 12.2.1 Evaluation Environment .....................122 12.2.2 Comparison of Intra-Query Optimization Strategies .....123 12.2.3 Results of Inter-Query Optimization ..............125 12.3 Evaluation
Load more

Recommended publications
  • Discover Linear Algebra Incomplete Preliminary Draft
    Discover Linear Algebra Incomplete Preliminary Draft Date: November 28, 2017 L´aszl´oBabai in collaboration with Noah Halford All rights reserved. Approved for instructional use only. Commercial distribution prohibited. c 2016 L´aszl´oBabai. Last updated: November 10, 2016 Preface TO BE WRITTEN. Babai: Discover Linear Algebra. ii This chapter last updated August 21, 2016 c 2016 L´aszl´oBabai. Contents Notation ix I Matrix Theory 1 Introduction to Part I 2 1 (F, R) Column Vectors 3 1.1 (F) Column vector basics . 3 1.1.1 The domain of scalars . 3 1.2 (F) Subspaces and span . 6 1.3 (F) Linear independence and the First Miracle of Linear Algebra . 8 1.4 (F) Dot product . 12 1.5 (R) Dot product over R ................................. 14 1.6 (F) Additional exercises . 14 2 (F) Matrices 15 2.1 Matrix basics . 15 2.2 Matrix multiplication . 18 2.3 Arithmetic of diagonal and triangular matrices . 22 2.4 Permutation Matrices . 24 2.5 Additional exercises . 26 3 (F) Matrix Rank 28 3.1 Column and row rank . 28 iii iv CONTENTS 3.2 Elementary operations and Gaussian elimination . 29 3.3 Invariance of column and row rank, the Second Miracle of Linear Algebra . 31 3.4 Matrix rank and invertibility . 33 3.5 Codimension (optional) . 34 3.6 Additional exercises . 35 4 (F) Theory of Systems of Linear Equations I: Qualitative Theory 38 4.1 Homogeneous systems of linear equations . 38 4.2 General systems of linear equations . 40 5 (F, R) Affine and Convex Combinations (optional) 42 5.1 (F) Affine combinations .
    [Show full text]
  • Download Special Issue
    Scientific Programming Scientific Programming Techniques and Algorithms for Data-Intensive Engineering Environments Lead Guest Editor: Giner Alor-Hernandez Guest Editors: Jezreel Mejia-Miranda and José María Álvarez-Rodríguez Scientific Programming Techniques and Algorithms for Data-Intensive Engineering Environments Scientific Programming Scientific Programming Techniques and Algorithms for Data-Intensive Engineering Environments Lead Guest Editor: Giner Alor-Hernández Guest Editors: Jezreel Mejia-Miranda and José María Álvarez-Rodríguez Copyright © 2018 Hindawi. All rights reserved. This is a special issue published in “Scientific Programming.” All articles are open access articles distributed under the Creative Com- mons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Editorial Board M. E. Acacio Sanchez, Spain Christoph Kessler, Sweden Danilo Pianini, Italy Marco Aldinucci, Italy Harald Köstler, Germany Fabrizio Riguzzi, Italy Davide Ancona, Italy José E. Labra, Spain Michele Risi, Italy Ferruccio Damiani, Italy Thomas Leich, Germany Damian Rouson, USA Sergio Di Martino, Italy Piotr Luszczek, USA Giuseppe Scanniello, Italy Basilio B. Fraguela, Spain Tomàs Margalef, Spain Ahmet Soylu, Norway Carmine Gravino, Italy Cristian Mateos, Argentina Emiliano Tramontana, Italy Gianluigi Greco, Italy Roberto Natella, Italy Autilia Vitiello, Italy Bormin Huang, USA Francisco Ortin, Spain Jan Weglarz, Poland Chin-Yu Huang, Taiwan Can Özturan, Turkey
    [Show full text]
  • Memory Capacity of Neural Turing Machines with Matrix Representation
    Memory Capacity of Neural Turing Machines with Matrix Representation Animesh Renanse * [email protected] Department of Electronics & Electrical Engineering Indian Institute of Technology Guwahati Assam, India Rohitash Chandra * [email protected] School of Mathematics and Statistics University of New South Wales Sydney, NSW 2052, Australia Alok Sharma [email protected] Laboratory for Medical Science Mathematics RIKEN Center for Integrative Medical Sciences Yokohama, Japan *Equal contributions Editor: Abstract It is well known that recurrent neural networks (RNNs) faced limitations in learning long- term dependencies that have been addressed by memory structures in long short-term memory (LSTM) networks. Matrix neural networks feature matrix representation which inherently preserves the spatial structure of data and has the potential to provide better memory structures when compared to canonical neural networks that use vector repre- sentation. Neural Turing machines (NTMs) are novel RNNs that implement notion of programmable computers with neural network controllers to feature algorithms that have copying, sorting, and associative recall tasks. In this paper, we study augmentation of mem- arXiv:2104.07454v1 [cs.LG] 11 Apr 2021 ory capacity with matrix representation of RNNs and NTMs (MatNTMs). We investigate if matrix representation has a better memory capacity than the vector representations in conventional neural networks. We use a probabilistic model of the memory capacity us- ing Fisher information and investigate how the memory capacity for matrix representation networks are limited under various constraints, and in general, without any constraints. In the case of memory capacity without any constraints, we found that the upper bound on memory capacity to be N 2 for an N ×N state matrix.
    [Show full text]
  • Noncommutative Spaces from Matrix Models Lei Lu Allen B Stern, Committee Chair Nobuchika Okada Benjamin Harms Gary Mankey Martyn
    NONCOMMUTATIVE SPACES FROM MATRIX MODELS by LEI LU ALLEN B STERN, COMMITTEE CHAIR NOBUCHIKA OKADA BENJAMIN HARMS GARY MANKEY MARTYN DIXON A DISSERTATION Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Physics and Astronomy in the Graduate School of The University of Alabama TUSCALOOSA, ALABAMA 2016 Copyright Lei Lu 2016 ALL RIGHTS RESERVED Abstract Noncommutative (NC) spaces commonly arise as solutions to matrix model equations of motion. They are natural generalizations of the ordinary commuta- tive spacetime. Such spaces may provide insights into physics close to the Planck scale, where quantum gravity becomes relevant. Although there has been much research in the literature, aspects of these NC spaces need further investigation. In this dissertation, we focus on properties of NC spaces in several different contexts. In particular, we study exact NC spaces which result from solutions to matrix model equations of motion. These spaces are associated with finite-dimensional Lie-algebras. More specifically, they are two-dimensional fuzzy spaces that arise from a three-dimensional Yang-Mills type matrix model, four-dimensional tensor- product fuzzy spaces from a tensorial matrix model, and Snyder algebra from a five-dimensional tensorial matrix model. In the first part of this dissertation, we study two-dimensional NC solutions to matrix equations of motion of extended IKKT-type matrix models in three- space-time dimensions. Perturbations around the NC solutions lead to NC field theories living on a two-dimensional space-time. The commutative limit of the solutions are smooth manifolds which can be associated with closed, open and static two-dimensional cosmologies.
    [Show full text]
  • Mathfest 2018
    Abstracts of Papers Presented at MathFest 2018 Denver, CO August 1 – 4, 2018 Published and Distributed by The Mathematical Association of America Contents Invited Addresses 1 Earle Raymond Hedrick Lecture Series by Gigliola Staffilani . 1 Nonlinear Dispersive Equations and the Beautiful Mathematics That Comes with Them Lecture 1: Thursday, August 2, 11:00–11:50 AM, Plaza Ballroom A, B, & C, Plaza Building Lecture 2: Friday, August 3, 10:30–11:20 AM, Plaza Ballroom A, B, & C, Plaza Building Lecture 3: Saturday, August 4, 10:00–10:50 AM, Plaza Ballroom A, B, & C, Plaza Building . 1 AMS-MAA Joint Invited Address . 1 Gravity’s Action on Light: A Mathematical Journey by Arlie Petters Thursday, August 2, 10:00–10:50 AM, Plaza Ballroom A, B, & C, Plaza Building . 1 MAA Invited Address . 1 Inclusion-exclusion in Mathematics: Who Stays in, Who Falls out, Why It Happens, and What We Should Do About It by Eugenia Cheng Friday, August 3, 11:30–12:20 AM, Plaza Ballroom A, B, & C, Plaza Building . 1 Snow Business: Scientific Computing in the Movies and Beyond by Joseph Teran Saturday, August 4, 11:00–11:50 AM, Plaza Ballroom A, B, & C, Plaza Building . 1 Mathematical Medicine: Modeling Disease and Treatment by Lisette de Pillis Thursday, August 2, 9:00–9:50 AM, Plaza Ballroom A, B, & C, Plaza Building . 2 MAA James R.C. Leitzel Lecture . 2 The Relationship between Culture and the Learning of Mathematics by Talitha Washington Saturday, August 4, 9:00–9:50 AM, Plaza Ballroom A, B, & C, Plaza Building .
    [Show full text]
  • Equivariant Reduction of Matrix Gauge Theories and Emergent Chaotic Dynamics a Thesis Submitted to the Graduate School of Natura
    EQUIVARIANT REDUCTION OF MATRIX GAUGE THEORIES AND EMERGENT CHAOTIC DYNAMICS A THESIS SUBMITTED TO THE GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES OF MIDDLE EAST TECHNICAL UNIVERSITY BY GÖKSU CAN TOGA˘ IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN PHYSICS JULY 2018 Approval of the thesis: EQUIVARIANT REDUCTION OF MATRIX GAUGE THEORIES AND EMERGENT CHAOTIC DYNAMICS submitted by GÖKSU CAN TOGA˘ in partial fulfillment of the requirements for the degree of Master of Science in Physics Department, Middle East Technical Uni- versity by, Prof. Dr. Halil Kalıpçılar Dean, Graduate School of Natural and Applied Sciences Prof. Dr. Altug˘ Özpineci Head of Department, Physics Prof. Dr. Seçkin Kürkçüoglu˘ Supervisor, Physics Department, METU Examining Committee Members: Prof. Dr. Ali Ulvi Yılmazer Physics Engineering Department, Ankara University Prof. Dr. Seçkin Kürkçüoglu˘ Physics Department, METU Assoc. Prof. Dr. Yusuf Ipeko˙ glu˘ Physics Department, METU Prof. Dr. Ismail˙ Turan Physics Department, METU Prof. Dr. Sadi Turgut Physics Department, METU Date: I hereby declare that all information in this document has been obtained and presented in accordance with academic rules and ethical conduct. I also declare that, as required by these rules and conduct, I have fully cited and referenced all material and results that are not original to this work. Name, Last Name: GÖKSU CAN TOGA˘ Signature : iv ABSTRACT EQUIVARIANT REDUCTION OF MATRIX GAUGE THEORIES AND EMERGENT CHAOTIC DYNAMICS Toga,˘ Göksu Can M.S., Department of Physics Supervisor : Prof. Dr. Seçkin Kürkçüoglu˘ July 2018, 74 pages In this thesis we focus on a massive deformation of a Yang-Mills matrix gauge the- ory.
    [Show full text]
  • Pattern Classification and Associative Recall by Neural Networks
    PATTERN CLASSIFICATION AND ASSOCIATIVE RECALL BY NEURAL NETWORKS Thesis by Tzi-Dar Chiueh In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 1989 (Submitted May 24, 1989) -u- To MY BELOVED PARENTS A D MY DEAREST VVIFE -iii- Acknowledgements The author would like to express his gratitude to Professor Rodney M. Goodman for his guidance and interest in this work. Many helpful a.nd stimulating discussions with Amir Atiya a.nd John Miller are a.lso acknowledged. Tha.nks are a.lso due to Patrick Smythe, Sean Coffey, Kathleen Kramer, and Chi-Cha.o Cha.o. The author acknowledges fina.ncia.l support of two teaching assistantships a.nd various research assistantships from the Institute. Last, but not least, the author wishes to gratefully acknowledge his parents Mr. C. M. Chiueh a.nd Ms. Y. J . W. Chiueh, a.nd his wife Jill J . H. Wang for their encouragement and support during his period of residence at the Institute. -IV- Abstract The first part of this dissertation discusses a new classifier based on a multilayer feed-forward network architecture. The main idea is to map irregularly-distributed pro­ totypes in a classification problem to codewords that are organized in some way. Then the pattern classification problem is transformed into a threshold decoding problem, which is easily solved using simple hard-limiter neurons. At first we propose the new model and introduce two families of good "internal representation" codes. Then some analyses and software simulation concerning the storage capacity of this new model are done.
    [Show full text]
  • Discover Linear Algebra Incomplete Preliminary Draft
    Discover Linear Algebra Incomplete Preliminary Draft Date: November 28, 2017 L´aszl´oBabai in collaboration with Noah Halford All rights reserved. Approved for instructional use only. Commercial distribution prohibited. c 2016 L´aszl´oBabai. Last updated: November 10, 2016 Preface TO BE WRITTEN. Babai: Discover Linear Algebra. ii This chapter last updated August 21, 2016 c 2016 L´aszl´oBabai. Contents Notation ix I Matrix Theory 1 Introduction to Part I 2 1 (F, R) Column Vectors 3 1.1 (F) Column vector basics . 3 1.1.1 The domain of scalars . 4 1.2 (F) Subspaces and span . 8 1.3 (F) Linear independence and the First Miracle of Linear Algebra . 11 1.4 (F) Dot product . 16 1.5 (R) Dot product over R ................................. 18 1.6 (F) Additional exercises . 19 2 (F) Matrices 20 2.1 Matrix basics . 20 2.2 Matrix multiplication . 24 2.3 Arithmetic of diagonal and triangular matrices . 31 2.4 Permutation Matrices . 33 2.5 Additional exercises . 36 3 (F) Matrix Rank 39 3.1 Column and row rank . 39 iii iv CONTENTS 3.2 Elementary operations and Gaussian elimination . 40 3.3 Invariance of column and row rank, the Second Miracle of Linear Algebra . 43 3.4 Matrix rank and invertibility . 45 3.5 Codimension (optional) . 47 3.6 Additional exercises . 48 4 (F) Theory of Systems of Linear Equations I: Qualitative Theory 51 4.1 Homogeneous systems of linear equations . 51 4.2 General systems of linear equations . 54 5 (F, R) Affine and Convex Combinations (optional) 56 5.1 (F) Affine combinations .
    [Show full text]
  • On Equivalence of Matrices
    On Equivalence of Matrices ⋆ Daizhan Cheng Key Laboratory of Systems and Control, AMSS, Chinese Academy of Sciences, Beijing 100190, P.R.China Abstract A new matrix product, called the semi-tensor product (STP), is briefly reviewed. The STP extends the classical matrix product to two arbitrary matrices. Under STP the set of matrices becomes a monoid (semi-group with identity). Some related structures and properties are investigated. Then the generalized matrix addition is also introduced, which extends the classical matrix addition to a class of two matrices with different dimensions. Motivated by STP of matrices, two kinds of equivalences of matrices (including vectors) are introduced, which are called matrix equivalence (M-equivalence) and vector equivalence (V-equivalence) respectively. The lattice structure has been es- tablished for each equivalence. Under each equivalence, the corresponding quotient space becomes a vector space. Under M- equivalence, many algebraic, geometric, and analytic structures have been posed to the quotient space, which include (i) lattice structure; (ii) inner product and norm (distance); (iii) topology; (iv) a fiber bundle structure, called the discrete bundle; (v) bundled differential manifold; (vi) bundled Lie group and Lie algebra. Under V-equivalence, vectors of different dimensions form a vector space V, and a matrix A of arbitrary dimension is considered as an operator (linear mapping) on V. When A is a bounded operator (not necessarily square but includes square matrices as a special case), the generalized characteristic function, eigenvalue and eigenvector etc. are defined. In one word, this new matrix theory overcomes the dimensional barrier in certain sense. It provides much more freedom for using matrix approach to practical problems.
    [Show full text]
  • Synthesis of Hopfield Type Associative Memories
    On the EXISTENCE OF HOPFIELD NEURAL NETWORKS: SYNTHESIS OF HOPFIELD TYPE ASSOCIATIVE MEMORIES: Garimella Rama Murthy* and Moncef Gabbouj** *International Institute of Information Technology, Hyderabad, India **Tampere University of Technology, Tampere, Finland ABSTRACT In this research paper, the problem of existence of the associative memory synthesized by Hopfield is addressed and solved. Using Hadamard matrix of suitable dimension, an algorithm to synthesize real valued Hopfield neural network is discussed. The problem of existence and synthesis of a certain complex Hopfield neural network is addressed and solved. Also, synthesis of real and complex Hopfield type associative memories is discussed. Novel Complex Hadamard matrices are defined and studied. Using such matrices Novel Complex Hadamard transform is proposed. Also complex Walsh functions are proposed. Certain interesting distance measures are defined. 1. INTRODUCTION : In the progress of Science and Technology, homosapiens attempted mathematical model of natural ( physical / chemical / biological ) systems. Specifically, there were attempts to model the biological neural network. McCulloch and Pitts proposed a model of artificial neuron. Using that model of neuron and its variations, researchers comprehensively built the theory of Artificial Neural Networks (ANNs). In this theory, some important milestones were Single Layer Perceptron (SLP) and Multi Layer Perceptron (MLP). Multi Layer Perceptron is an example of feedforward neural network that received considerable attention and many applications continue to utilize such a neural network. Researchers were naturally motivated to investigate feedback neural networks. Hopfield effectively succeeded in proposing a feedback neural network model that acts as an associative memory. Hopfield neural network model led to intense research activity on various types of associative memories such as the Bi-directional Associative Memory (BAM ).
    [Show full text]
  • On Multimatrix Models Motivated by Random Noncommutative Geometry Ii: a Yang-Mills–Higgs Matrix Model
    ON MULTIMATRIX MODELS MOTIVATED BY RANDOM NONCOMMUTATIVE GEOMETRY II: A YANG-MILLS–HIGGS MATRIX MODEL CARLOS I. PEREZ-SANCHEZ Abstract. We continue the study of fuzzy geometries inside Connes’ spectral formalism and their relation to multimatrix models. In this companion paper to [arXiv:2007:10914, Ann. Henri Poincaré, 2021] we propose a gauge theory setting based on noncommuta- tive geometry, which—just as the traditional formulation in terms of almost-commutative manifolds—has the ability to also accommodate a Higgs field. However, in contrast to ‘almost-commutative manifolds’, the present framework employs only finite dimensional algebras. In a path-integral quantization approach to the Spectral Action, this allows to state Yang-Mills–Higgs theory (on four-dimensional Euclidean fuzzy space) as an explicit random multimatrix model obtained here, whose matrix fields exactly mirror those of the Yang-Mills–Higgs theory on a smooth manifold. 1. Introduction The approximation of smooth manifolds by finite geometries (or geometries de- scribed by finite dimensional algebras) has been treated in noncommutative ge- ometry (NCG) some time ago [LLS01] and often experiences a regain of interest; in [DLM14, CvS20], for instance, these arise from truncations of space to a finite resolution. In an ideologically similar vein but from a technically different view- point, this paper addresses gauge theories derived from the Spectral Formalism of NCG, using exclusively finite-dimensional algebras, also for the description of the space(time). This allows one to make precise sense of path integrals over noncom- mutative geometries. Although this formulation is valid at the moment only for a small class of geometries, the present method might shed light on the general problem of quantization of NCG, already tackled using von Neumann’s information theoretic entropy in [CCvS19] and [DKvS19], by fermionic and bosonic-fermionic second quantization, respectively.
    [Show full text]
  • Deep Quantum Geometry of Matrices
    Deep Quantum Geometry of Matrices Xizhi Han and Sean A. Hartnoll Department of Physics, Stanford University, Stanford, CA 94305-4060, USA Abstract We employ machine learning techniques to provide accurate variational wavefunc- tions for matrix quantum mechanics, with multiple bosonic and fermionic matrices. Variational quantum Monte Carlo is implemented with deep generative flows to search for gauge invariant low energy states. The ground state, and also long-lived metastable states, of an SU(N) matrix quantum mechanics with three bosonic matrices, as well as its supersymmetric ‘mini-BMN’ extension, are studied as a function of coupling and N. Known semiclassical fuzzy sphere states are recovered, and the collapse of these geome- tries in more strongly quantum regimes is probed using the variational wavefunction. We then describe a factorization of the quantum mechanical Hilbert space that corre- sponds to a spatial partition of the emergent geometry. Under this partition, the fuzzy sphere states show a boundary-law entanglement entropy in the large N limit. arXiv:1906.08781v2 [hep-th] 5 Jan 2020 1 Contents 1 Introduction3 2 The mini-BMN model5 2.1 Representation of the fermion wavefunction...................6 2.2 Gauge invariance and gauge fixing........................7 3 Architecture design for matrix quantum mechanics8 3.1 Parametrizing and sampling the gauge invariant wavefunction.........9 3.2 Benchmarking the architecture.......................... 10 4 The emergence of geometry 13 4.1 Numerical results, bosonic sector......................... 13 4.2 Semiclassical analysis of the fuzzy sphere..................... 15 4.3 Numerical results, supersymmetric sector..................... 18 5 Entanglement on the fuzzy sphere 21 5.1 Free field with an angular momentum cutoff..................
    [Show full text]