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- research-articleJanuary 2023
A survey on cubic fuzzy graph structure with an application in the diagnosis of brain lesions
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology (JIFS), Volume 45, Issue 22023, Pages 3513–3538https://doi.org/10.3233/JIFS-222984A cubic fuzzy graph is a fuzzy graph that simultaneously supports fuzzy membership and interval-valued fuzzy membership. This simultaneity leads to a better flexibility in modeling problems regarding uncertain variables. The cubic fuzzy graph structure, ...
- research-articleJanuary 2022
MIONet: Learning Multiple-Input Operators via Tensor Product
SIAM Journal on Scientific Computing (SISC), Volume 44, Issue 6Dec 2022, Pages A3490–A3514https://doi.org/10.1137/22M1477751As an emerging paradigm in scientific machine learning, neural operators aim to learn operators, via neural networks, that map between infinite-dimensional function spaces. Several neural operators have been recently developed. However, all the existing ...
- research-articleJanuary 2022
A Scalable and Robust Vertex-Star Relaxation for High-Order FEM
SIAM Journal on Scientific Computing (SISC), Volume 44, Issue 5Oct 2022, Pages A2991–A3017https://doi.org/10.1137/21M1444187Pavarino proved that the additive Schwarz method with vertex patches and a low-order coarse space gives a $p$-robust solver for symmetric and coercive problems [Pavanno, Numer. Math., 66 (1993), pp. 493--515]. However, for very high polynomial degree it is ...
- research-articleFebruary 2021
Sparta: high-performance, element-wise sparse tensor contraction on heterogeneous memory
PPoPP '21: Proceedings of the 26th ACM SIGPLAN Symposium on Principles and Practice of Parallel ProgrammingFebruary 2021, Pages 318–333https://doi.org/10.1145/3437801.3441581Sparse tensor contractions appear commonly in many applications. Efficiently computing a two sparse tensor product is challenging: It not only inherits the challenges from common sparse matrix-matrix multiplication (SpGEMM), i.e., indirect memory access ...
- research-articleJanuary 2019
Analysis of legendre polynomial kernel in support vector machines
International Journal of Computing Science and Mathematics (IJCSM), Volume 10, Issue 62019, Pages 580–595https://doi.org/10.1504/ijcsm.2019.104026For several types of machines learning problems, the support vector machine is a method of choice. The kernel functions are a basic ingredient in support vector machine theory. Kernels based on the concepts of orthogonal polynomials gave the great ...
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- research-articleJanuary 2019
Directional Compactly Supported Tensor Product Complex Tight Framelets with Applications to Image Denoising and Inpainting
SIAM Journal on Imaging Sciences (SJISBI), Volume 12, Issue 42019, Pages 1739–1771https://doi.org/10.1137/19M1249734Compactly supported tight framelets are of great interest and importance in both theory and application. In this paper we discuss how to construct directional compactly supported tensor product complex tight framelets having varied directionality and ...
- research-articleMarch 2017
Newtonian Program Analysis via Tensor Product
ACM Transactions on Programming Languages and Systems (TOPLAS), Volume 39, Issue 2Article No.: 9, Pages 1–72https://doi.org/10.1145/3024084Recently, Esparza et al. generalized Newton’s method—a numerical-analysis algorithm for finding roots of real-valued functions—to a method for finding fixed-points of systems of equations over semirings. Their method provides a new way to solve ...
- research-articleJanuary 2017
Product of intuitionistic fuzzy graphs and degree
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology (JIFS), Volume 32, Issue 12017, Pages 1059–1067https://doi.org/10.3233/JIFS-16348An intuitionistic fuzzy graph is an extended structure of a fuzzy graph that give more precision, flexibility and compatibility to a system when compared with the system that designed using fuzzy graphs. In this paper, we define two new operations on ...
- research-articleJanuary 2016
Newtonian program analysis via tensor product
POPL '16: Proceedings of the 43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming LanguagesJanuary 2016, Pages 663–677https://doi.org/10.1145/2837614.2837659Recently, Esparza et al. generalized Newton's method -- a numerical-analysis algorithm for finding roots of real-valued functions---to a method for finding fixed-points of systems of equations over semirings. Their method provides a new way to solve ...
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ACM SIGPLAN Notices: Volume 51 Issue 1, January 2016 - research-articleJanuary 2015
Compactly Supported Tensor Product Complex Tight Framelets with Directionality
SIAM Journal on Mathematical Analysis (SIMA), Volume 47, Issue 32015, Pages 2464–2494https://doi.org/10.1137/13092856XAlthough tensor product real-valued wavelets have been successfully applied to many high-dimensional problems, they can capture well only edge singularities along the coordinate axis directions. As an alternative and improvement of tensor product real-...
- research-articleJanuary 2014
Tensor Product Complex Tight Framelets with Increasing Directionality
SIAM Journal on Imaging Sciences (SJISBI), Volume 7, Issue 22014, Pages 997–1034https://doi.org/10.1137/130928558Tensor product real-valued wavelets have been employed in many applications such as image processing with impressive performance. Edge singularities are ubiquitous and play a fundamental role in image processing and many other two-dimensional problems. ...
- research-articleAugust 2013
Fast and scalable polynomial kernels via explicit feature maps
KDD '13: Proceedings of the 19th ACM SIGKDD international conference on Knowledge discovery and data miningAugust 2013, Pages 239–247https://doi.org/10.1145/2487575.2487591Approximation of non-linear kernels using random feature mapping has been successfully employed in large-scale data analysis applications, accelerating the training of kernel machines. While previous random feature mappings run in O(ndD) time for $n$ ...
- chapterJanuary 2013
Multiparty communication complexity of vector---valued and sum---type functions
Information Theory, Combinatorics, and Search TheoryJanuary 2013, Pages 451–462Rudolf Ahlswede's work on communication complexity dealt with functions defined on direct sums: vector---valued functions and sum---type functions. He was interested in single---letter characterizations and provided several lower bound techniques to ...
- research-articleJanuary 2013
Linear Maps Preserving Ky Fan Norms and Schatten Norms of Tensor Products of Matrices
SIAM Journal on Matrix Analysis and Applications (SIMAX), Volume 34, Issue 22013, Pages 673–685https://doi.org/10.1137/120891794For a positive integer $n$, let $M_n$ be the set of $n\times n$ complex matrices. Suppose $\|\cdot\|$ is the Ky Fan $k$-norm with $1 \le k \le mn$ or the Schatten $p$-norm with $1 \le p \le \infty$ ($p\ne 2$) on $M_{mn}$, where $m,n\ge 2$ are positive ...
- ArticleMarch 2012
On revealing replicating structures in multiway data: a novel tensor decomposition approach
LVA/ICA'12: Proceedings of the 10th international conference on Latent Variable Analysis and Signal SeparationMarch 2012, Pages 297–305https://doi.org/10.1007/978-3-642-28551-6_37A novel tensor decomposition is proposed to make it possible to identify replicating structures in complex data, such as textures and patterns in music spectrograms. In order to establish a computational framework for this paradigm, we adopt a multiway (...
- ArticleMarch 2012
A low rank tensorial approximations method of computation of singular values and singular vectors for SVD problem
ASM'12: Proceedings of the 6th international conference on Applied Mathematics, Simulation, ModellingMarch 2012, Pages 49–53A new method of computation of singular values and left and right singular vectors of arbitrary nonsquare matrices has been proposed. The method permits to avoid solutions of high rank systems of linear equations of singular value decomposition problem, ...
- ArticleJune 2011
Contextual image annotation via projection and quantum theory inspired measurement for integration of text and visual features
QI'11: Proceedings of the 5th international conference on Quantum interactionJune 2011, Pages 217–222Multimedia information retrieval suffers from the semantic gap, a difference between human perception and machine representation of images. In order to reduce the gap, a quantum theory inspired theoretical framework for integration of text and visual ...
- ArticleJune 2011
A compositional distributional semantics, two concrete constructions, and some experimental evaluations
QI'11: Proceedings of the 5th international conference on Quantum interactionJune 2011, Pages 35–47We provide an overview of the hybrid compositional distributional model of meaning, developed in [6], which is based on the categorical methods also applied to the analysis of information flow in quantum protocols. The mathematical setting stipulates ...
- ArticleMay 2011
The Tensor PMV-algebra of an MV-algebra
ISMVL '11: Proceedings of the 2011 41st IEEE International Symposium on Multiple-Valued LogicMay 2011, Pages 274–276https://doi.org/10.1109/ISMVL.2011.37The classical construction of tensor algebra is done in the context of MV-algebras. We construct the tensor PMV-algebra of an MV-algebra, which yields an adjunction between the category of MV-algebras and the category of PMV-algebras. In particular, for ...
- ArticleAugust 2009
Two Dimensional Tensor Product B-spline Wavelet Scaling Functions for Solution of Two-Dimensional Steady Navier-Stokes (NS) Equations
IHMSC '09: Proceedings of the 2009 International Conference on Intelligent Human-Machine Systems and Cybernetics - Volume 02August 2009, Pages 7–10https://doi.org/10.1109/IHMSC.2009.128In order to introduce a new numerical method based on wavelet analysis for solution of Navier-Stokes(NS) equations which has lots of application in the fields of Ocean and Navigation, for the Steady viscous fluid flow in Parallel-Plate, the fourth-order ...