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Matrix Tightness: A Linear-Algebraic Framework for Sorting by Transpositions [chapter]

Tzvika Hartman, Elad Verbin
2006 Lecture Notes in Computer Science  
These properties make it extremely useful for studying SBT. Using this model, we give a linear-algebraic framework in which SBT can be studied.  ...  We study the problems of sorting signed permutations by reversals (SBR) and sorting unsigned permutations by transpositions (SBT), which are central problems in computational molecular biology.  ...  Golumbic and the Caesarea Edmond Benjamin de Rothschild Foundation for their hospitality and for the opportunity to present preliminary results leading to this research in the France-Israel Expert Workshop  ... 
doi:10.1007/11880561_23 fatcat:77aed3ldrfcxdmeham2wqqhxd4

Signal Processing on the Permutahedron: Tight Spectral Frames for Ranked Data Analysis [article]

Yilin Chen, Jennifer DeJong, Tom Halverson, David I Shuman
2021 arXiv   pre-print
data vector lying on the permutahedron, which is a Cayley graph of the symmetric group with vertices labeled by permutations and an edge when two permutations differ by an adjacent transposition.  ...  These atoms have a more naturally interpretable structure than any known basis for signals on the permutahedron, and they form a Parseval frame, ensuring beneficial numerical properties such as energy  ...  Here, ρ γ (σ) is the matrix of the permutation σ as a linear transformation on the S ninvariant subspace V γ,i (for any i). This set {f (γ) | γ a partition of n} has a total of n!  ... 
arXiv:2103.04150v2 fatcat:vphmsjrnxzguxmrn3ml5i3f7vy

Fast Matrix Multiplication: Limitations of the Laser Method [article]

Andris Ambainis, Yuval Filmus, François Le Gall
2014 arXiv   pre-print
Until a few years ago, the fastest known matrix multiplication algorithm, due to Coppersmith and Winograd (1990), ran in time O(n^2.3755).  ...  Our framework accommodates the algorithms by Coppersmith and Winograd, Stothers, Vassilevska-Williams and Le Gall. We obtain our main result by analyzing this framework.  ...  The model In this paper is to study the complexity of matrix multiplication in the algebraic complexity model.  ... 
arXiv:1411.5414v1 fatcat:ttqt37rvxjegtendyoruhbuxx4

Sparse matrix multiplication: The distributed block-compressed sparse row library

Urban Borštnik, Joost VandeVondele, Valéry Weber, Jürg Hutter
2014 Parallel Computing  
This article presents the DBCSR (Distributed Block Compressed Sparse Row) library for scalable sparse matrix-matrix multiplication and its use in the CP2K program for linear-scaling quantum-chemical calculations  ...  Local sparse matrix multiplication is handled efficiently using a combination of techniques: blocking elements together in an application-relevant way, an autotuning library for small matrix multiplications  ...  Computer resources were provided by the Swiss National Supercomputer Centre (CSCS).  ... 
doi:10.1016/j.parco.2014.03.012 fatcat:o3yeffh4vbabzmmnm4dgjtivhu

Recursive Blocked Algorithms and Hybrid Data Structures for Dense Matrix Library Software

Erik Elmroth, Fred Gustavson, Isak Jonsson, Bo Kågström
2004 SIAM Review  
Recursion allows for efficient utilization of a memory hierarchy and generalizes existing fixed blocking by introducing automatic variable blocking that has the potential of matching every level of a deep  ...  In fact, the whole gamut of existing dense linear algebra factorization is beginning to be reexamined in view of the recursive paradigm.  ...  We are also grateful for constructive comments from James Demmel, Randy LeVeque, Margaret Wright, and an anonymous referee, who have improved on both the readability and the content of the final manuscript  ... 
doi:10.1137/s0036144503428693 fatcat:7zmqj5eee5adxk56lbccrlyq3m

Random matrix theory: Wigner-Dyson statistics and beyond. (Lecture notes of a course given at SISSA (Trieste, Italy)) [article]

V.E.Kravtsov
2012 arXiv   pre-print
This is a course on Random Matrix Theory which includes traditional as well as advanced topics presented with an extensive use of classical logarithmic plasma analogy and that of the quantum systems of  ...  The course can also be viewed as introduction to theory of localization where the (non-invariant) random matrix ensembles play a role of the toy models to illustrate functional methods based on super-vector  ...  the extended states in the tight-binding model which are the linear combinations of states localized at a given site).  ... 
arXiv:0911.0639v2 fatcat:rbbv4elzkfdmdopae25bbjupty

Topological-Like Features in Diagrammatical Quantum Circuits

Yong Zhang
2007 arXiv   pre-print
Moreover, we remark on the proposal for categorical quantum physics and information to be described by dagger ribbon categories.  ...  We perform these quantum circuits and derive characteristic equations for them with the help of topological-like operations.  ...  Furthermore, Figure 8 is presenting a suitable diagrammatical framework for unifying various sorts of descriptions for teleportation, see [8, 9] for the detail.  ... 
arXiv:quant-ph/0703196v3 fatcat:f767kou6dfa2damil3f7v3x2l4

Topological-Like Features in Diagrammatical Quantum Circuits

Yong Zhang, Louis H. Kauffman
2007 Quantum Information Processing  
Moreover, we remark on the proposal for categorical quantum physics and information to be described by dagger ribbon categories. 1 This manuscript is a formal written version of Y.  ...  We perform these quantum circuits and derive characteristic equations for them with the help of topological-like operations.  ...  Griffiths for critical comments on the early draft, and he especially thanks Y.-S. Wu for stimulating discussions.  ... 
doi:10.1007/s11128-007-0067-0 fatcat:hyqtc36qw5aihni5nb4q7ggq5q

Move Schedules: Fast persistence computations in coarse dynamic settings [article]

Matthew Piekenbrock, Jose A. Perea
2021 arXiv   pre-print
Our first result is an analysis of a simple linear-time strategy which reduces the number of column operations needed to simulate persistence across a fixed homotopy by at most a factor of 2.  ...  The standard procedure for computing the persistent homology of a filtered simplicial complex is the matrix reduction algorithm.  ...  For example, while sorting by transpositions and reversals is NP-hard, and sorting by prefix transpositions (i.e., when i = 1 always) is unknown, there are polynomial time algorithms for sorting by block  ... 
arXiv:2104.12285v2 fatcat:qxqlzgw7bjfs3eshd3pvn5kchq

Homomorphic Sensing [article]

Manolis C. Tsakiris, Liangzu Peng
2019 arXiv   pre-print
Given a linear subspace and a finite set of linear transformations we develop an algebraic theory which establishes conditions guaranteeing that points in the subspace are uniquely determined from their  ...  As a special case, we recover known conditions for unlabeled sensing, as well as new results and extensions.  ...  Aldo Conca for first noting and sharing the phenomenon of Lemmas 2 and 3. We also thank Dr. Laurent Kneip for suggesting the case study of image registration under general affine transformations.  ... 
arXiv:1901.07852v3 fatcat:55himfjobnha3ienq3nowrjpyq

Online order basis algorithm and its impact on the block Wiedemann algorithm

Pascal Giorgi, Romain Lebreton
2014 Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation - ISSAC '14  
Order bases are a fundamental tool for linear algebra with polynomial coefficients.  ...  Using this algorithm inside block Wiedemann methods leads to an improvement of their practical performance by a constant factor.  ...  This work has been supported by the French ANR under the grants HPAC (ANR-11-BS02-013), CATREL (ANR-12-BS02-001).  ... 
doi:10.1145/2608628.2608647 dblp:conf/issac/GiorgiL14 fatcat:fszr5bjjb5du3jx5va6iji2mg4

Network Coding Theory: A Survey

Riccardo Bassoli, Hugo Marques, Jonathan Rodriguez, Kenneth W. Shum, Rahim Tafazolli
2013 IEEE Communications Surveys and Tutorials  
in those networks by avoiding non-linear network coding.  ...  Next, in some scenarios, scalar linear network coding is not enough to solve the network and non-linear network coding is necessary; actually, vector network coding represents a way to achieve solvability  ...  A generator matrix G for a linear code is a k by n matrix for which the rows are a basis of the code.  ... 
doi:10.1109/surv.2013.013013.00104 fatcat:jgnf4i7rczfqrcyv7tygrydtxm

Diversity-Multiplexing Tradeoff in Selective-Fading MIMO Channels

Pedro Coronel, Helmut Bolcskei
2007 2007 IEEE International Symposium on Information Theory  
We establish the optimal diversity-multiplexing (DM) tradeoff of coherent time, frequency and time-frequency selective-fading MIMO channels and provide a code design criterion for DM-tradeoff optimality  ...  Finally, as a consequence of our results, we find that the classical rank criterion for space-time code design (in selective-fading MIMO channels) ensures optimality in the sense of the DM-tradeoff.  ...  The eigenvalues of the n × n Hermitian matrix A, sorted in ascending order, are denoted by λ k (A), k = 1, 2, . . . , n.  ... 
doi:10.1109/isit.2007.4557649 dblp:conf/isit/CoronelB07 fatcat:kb3khcjqezempaay5htwiibq7a

Diversity-Multiplexing Tradeoff in Selective-Fading MIMO Channels [article]

Pedro Coronel, Helmut Bölcskei
2007 arXiv   pre-print
We establish the optimal diversity-multiplexing (DM) tradeoff of coherent time, frequency and time-frequency selective-fading MIMO channels and provide a code design criterion for DM-tradeoff optimality  ...  Finally, as a consequence of our results, we find that the classical rank criterion for space-time code design (in selective-fading MIMO channels) ensures optimality in the sense of the DM-tradeoff.  ...  The eigenvalues of the n × n Hermitian matrix A, sorted in ascending order, are denoted by λ k (A), k = 1, 2, . . . , n.  ... 
arXiv:0704.3402v1 fatcat:qe6yulmdv5g5nltxxtddao4x7a

Memoryless computation: New results, constructions, and extensions

Maximilien Gadouleau, Søren Riis
2015 Theoretical Computer Science  
, or not-for-prot purposes provided that: • a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text  ...  Second, we show that allowing programs to use memory is also incorporated in the memoryless computation framework.  ...  Cameron, Ben Fairbairn, Peter Keevash and Rasmus Petersen for stimulating discussions.  ... 
doi:10.1016/j.tcs.2014.09.040 fatcat:42brbrzdhbf2fibo5su5vh5s4i
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