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Approximation by neural networks and learning theory

V. Maiorov
2006 Journal of Complexity  
Consider the class of all estimators E m , that is, the class of all possible mappings h z : Z m → H . Let m ∈ N and ε > 0 be any number.  ...  Also we consider the accuracy confidence function estimator for the least-squares estimator where we calculate the estimator f z by the least-squares formula (4).  ...  This work was supported by the center for Absorption in Science, State of Israel.  ... 
doi:10.1016/j.jco.2005.09.001 fatcat:7tatjhjwe5fyzbts4gb4hjqc64

Bers and Hénon, Painlevé and Schroedinger [article]

Serge Cantat
2007 arXiv   pre-print
We shall show that the dynamics of pseudo-Anosov mapping classes resembles in many ways the dynamics of H\'enon mappings, and then apply this idea to answer open questions concerning the geometry of discrete  ...  We study the dynamics of mapping class groups on 2-dimensional character varieties.  ...  The area form Ω, which is globally defined by the formulas Ω = dx ∧ dy 2z + xy −C = dy ∧ dz 2x + yz − A = dz ∧ dx 2y + zx − B on S \ Sing(S), is almost invariant under the action of Γ * 2 , by which we  ... 
arXiv:0711.1727v2 fatcat:3tmb4dsrgjcdvlsuvys5oh3vai

Bers and Hénon, Painlevé and Schrödinger

Serge Cantat
2009 Duke mathematical journal  
We shall show that the dynamics of pseudo-Anosov mapping classes resembles in many ways the dynamics of Hénon mappings, and then apply this idea to answer open questions concerning (1) the geometry of  ...  discrete and faithful representations of free groups into SL(2, C), (2) the dynamics of Painlevé sixth equations, and (3) the spectrum of certain discrete Schrödinger operators.  ...  Since S(C) ⊂ C 3 is an affine surface, and C 3 does not contain any 1-dimensional compact subvariety, one gets a contradiction.  ... 
doi:10.1215/00127094-2009-042 fatcat:5vplftdk4jcmnikrjxuewpjfhu

Unsupervised Domain Adaptation via Discriminative Manifold Propagation

You-Wei Luo, Chuan-Xian Ren, Dao-Qing DAI, Hong Yan
2020 IEEE Transactions on Pattern Analysis and Machine Intelligence  
First, hard-assigned pseudo labels on the target domain are arbitrary and error-prone, and direct application of them may destroy the intrinsic data structure.  ...  Extensive experiments have been conducted to investigate the method and a comparative study shows the superiority of the discriminative manifold learning framework.  ...  Empirically, the dimensions of the Grassmann and affine Grassmann manifolds were set as (b s − 1) hereafter.  ... 
doi:10.1109/tpami.2020.3014218 pmid:32749963 fatcat:rghrld5levgtfgy6gcepr3kakq

Spacetime is material [article]

Luciano Combi
2021 arXiv   pre-print
We start by outlining the well-known controversy between substantivalism and relationalism and the evolution of the debate with the appearance of General Relativity.  ...  We discuss the concept of change, energy, and the ontology of spacetime events. In the last section, we review the mereology of spacetime and its relevance in cosmology.  ...  Romero for his intelectual guidance, and to Federico Lopez Armengol for many discussions on the nature of spacetime. This work was partially funded by a CONICET fellowship.  ... 
arXiv:2108.01712v1 fatcat:axdgokqcbze7jndqs6holjlnw4

Transformed Subspace Clustering [article]

Jyoti Maggu, Angshul Majumdar, Emilie Chouzenoux
2019 arXiv   pre-print
To achieve the intended goal, we embed subspace clustering techniques (locally linear manifold clustering, sparse sub-space clustering and low rank representation) into transform learning.  ...  To test the performance of the proposed techniques, benchmarking is performed on image clustering and document clustering datasets.  ...  They were further re- into subspaces, we assume that projecting them non- duced by PCA to a dimensionality of 300.  ... 
arXiv:1912.04734v1 fatcat:pfauacjv3zff5mitqo2mc7ew3e

Self-Assignment Flows for Unsupervised Data Labeling on Graphs [article]

Matthias Zisler, Artjom Zern, Stefania Petra, Christoph Schnörr
2020 arXiv   pre-print
The resulting self-assignment flow takes a pairwise data affinity matrix as input data and maximizes the correlation with a low-rank matrix that is parametrized by the variables of the assignment flow,  ...  Various experiments including the unsupervised learning of patch dictionaries using a locally invariant distance function, illustrate the properties of the approach.  ...  This work has also been stimulated by the Heidelberg Excellence Cluster STRUC-TURES, funded by the DFG under Germanys Excellence Strategy EXC-2181/1 -390900948.  ... 
arXiv:1911.03472v2 fatcat:v3hawt2svbdctowql67wemxf5u

Fourier's Method of Linear Programming and Its Dual

H. P. Williams
1986 The American mathematical monthly  
57M15 Relations with graph theory [See also 05Cxx] 57M20 Two-dimensional complexes 57M25 Knots and links in S 3 {For higher dimensions, see 57Q45} 57M27 Invariants of knots and 3-manifolds 57M30 Wild  ...  on low-dimensional manifolds 57M60 Group actions in low dimensions 57M99 None of the above, but in this section 57Nxx Topological manifolds 57N05 Topology of E 2 , 2-manifolds 57N10 Topology of general  ...  82D80 Nanostructures and nanoparticles 82D99 None of the above, but in this section 83-XX RELATIVITY AND GRAVITATIONAL THEORY 83-00 General reference works (handbooks, dictionaries, bibliographies,  ... 
doi:10.2307/2322281 fatcat:yvhgyh2epbcwdoqdhuaopkcrue

Noncommutative Geometry, the spectral standpoint [article]

Alain Connes
2019 arXiv   pre-print
2) Advances on the Baum-Connes conjecture, on coarse geometry and on higher index theory, 3) The geometrization of the pseudo-differential calculi using smooth groupoids, 4) The development of Hopf cyclic  ...  Galois group, 7) The development of quantum field theory on noncommutative spaces, 8) The discovery of a simple equation whose irreducible representations correspond to 4-dimensional spin geometries with  ...  Sullivan on Sobolev manifolds, i.e. of manifolds of dimension d where the pseudo-group underlying the atlas preserves continuous functions with one derivative in L d .  ... 
arXiv:1910.10407v1 fatcat:25i5d7urbjey3gjfx7r2tonccy

Dimensionality Reduction on SPD Manifolds: The Emergence of Geometry-Aware Methods [article]

Mehrtash Harandi, Mathieu Salzmann, Richard Hartley
2016 arXiv   pre-print
In this paper, we introduce algorithms able to handle high-dimensional SPD matrices by constructing a lower-dimensional SPD manifold.  ...  Unfortunately, computation on the Riemannian manifold of SPD matrices -especially of high-dimensional ones- comes at a high cost that limits the applicability of existing techniques.  ...  The behavior of a point close to I n for an affine invariant metric can be described by a diagonal matrix in the form Diag(exp(ν i )).  ... 
arXiv:1605.06182v1 fatcat:qjisdzihsvcz7m2shn3vmgf3cu

Small-scale Structure via Flows [chapter]

Albert M. Fisher
2004 Fractal Geometry and Stochastics III  
This is in fact true, and the resulting formula "dimension equals scenery flow entropy" unifies the formulas of Sullivan and of Bowen-Ruelle.  ...  A test is to see whether Sullivan's formula for dimension (Hausdor↵ dimension of limit set equals geodesic flow entropy) goes through for Julia sets.  ...  Note the upper and lower envelopes of the form ct d for d = log 2/ log 3, the Hausdor↵ dimension of the Cantor set.  ... 
doi:10.1007/978-3-0348-7891-3_4 fatcat:zzx5uizvaffn7mggvadnue4tem

Transfer Adaptation Learning: A Decade Survey [article]

Lei Zhang, Xinbo Gao
2020 arXiv   pre-print
This paper surveys the advances of TAL methodologies in the past decade, and the technical challenges and essential problems of TAL have been observed and discussed with deep insights and new perspectives  ...  TAL aims to build models that can perform tasks of target domain by learning knowledge from a semantic related but distribution different source domain.  ...  ACKNOWLEDGMENT The author would like to thank the pioneer researchers in transfer learning, domain adaptation and other related fields. The author would also like to thank Dr. Mingsheng Long and Dr.  ... 
arXiv:1903.04687v2 fatcat:wurprqieffalnnp6isfkhh5y5i

Instantons, black holes, and harmonic functions

Thomas Mohaupt, Kirk Waite
2009 Journal of High Energy Physics  
The geometry underlying these Lagrangians is characterized by the existence of a Hesse potential and generalizes the very special real geometry of vector multiplets.  ...  Our construction proceeds by first obtaining instanton solutions for a class of four-dimensional Euclidean sigma models, which includes those occuring for four-dimensional Euclidean N=2 vector multiplets  ...  T.M. thanks the Center for Mathematical Physics of the University of Hamburg for support and hospitality during several visits to Hamburg.  ... 
doi:10.1088/1126-6708/2009/10/058 fatcat:7gmvlpbjajgjlh3omc5ljmflzy

Geometrical and topological foundations of theoretical physics: from gauge theories to string program

Luciano Boi
2004 International Journal of Mathematics and Mathematical Sciences  
arise from the nonlocal metrical and topological structure of this manifold.  ...  We study the role of geometrical and topological concepts in the recent developments of theoretical physics, notably in non-Abelian gauge theories and superstring theory, and further we show the great  ...  During the last years, the author was also supported by the John Simon Guggenheim Memorial Foundation, the Social Science and Humanities Research Council of Canada, and the Singer-Polignac Foundation,  ... 
doi:10.1155/s0161171204304400 fatcat:f7sz43q35vf3dh7gniq6cdfgzy

A Review of Visual Descriptors and Classification Techniques Used in Leaf Species Identification

K. K. Thyagharajan, I. Kiruba Raji
2018 Archives of Computational Methods in Engineering  
Botanists easily identify plant species by discriminating between the shape of the leaf, tip, base, leaf margin and leaf vein, as well as the texture of the leaf and the arrangement of leaflets of compound  ...  As computers cannot comprehend images, they are required to be converted into features by individually analysing image shapes, colours, textures and moments.  ...  Conflict of interest: The authors declare that they have no conflict of interest.  ... 
doi:10.1007/s11831-018-9266-3 fatcat:xa4zxzfhjbgnhkv4h2xu5axhqy
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