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##
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Image and Spectrum Image Denoising under the local low Rank Assumption

2018
*
Microscopy and Microanalysis
*

Similarly, a local, patch based,

doi:10.1017/s1431927618003380
fatcat:5mfydtqx3ba4hhp5gk3hy6fj4i
*description**of*images has been found to be*effective*for denoising purposes. ... While*the*above*description**of*LLR is undeniably dense, it is also*complete*, which highlights one*of**the*advantages*of*LLR over previous patch based image denoising algorithms (e.g., BM3D or NLPCA): Apart ... Similarly, a local, patch based,*description**of*images has been found to be*effective*for denoising purposes. ...##
###
Algebraically contractible topological tensor network states

2011
*
Journal of Physics A: Mathematical and Theoretical
*

We then generalise

doi:10.1088/1751-8113/45/1/015309
fatcat:6i4ys22fargepbb4yjfntil7zy
*the*resulting*tensor*network from a spin-1/2*lattice*to a class*of*exactly contractible states on spin-S degrees*of*freedom, yielding*the*most efficient*tensor*network*description**of*... This class*of**tensor*networks is readily translated onto any*lattice*, and we differentiate between*the*physical consequences*of*bipartite and non-bipartite*lattices*on*the*properties*of**the*corresponding ... Acknowledgments DJ and SRC thank*the*National Research Foundation and*the*Ministry*of*Education*of*Singapore for support. ...##
###
Quantum information processing, operational quantum logic, convexity, and the foundations of physics
[article]

2003
*
arXiv
*
pre-print

*The*main technical content

*of*

*the*paper is in a theorem that any such theory naturally gives rise to a "weak

*effect*

*algebra*" when outcomes having

*the*same probability in all states are identified, and ... in

*the*introduction

*of*a notion

*of*"operation

*algebra*" that also takes account

*of*sequential and conditional operations. ... Acknowledgments Discussions over

*the*years with Carlton Caves, Dave Foulis, Chris Fuchs, Leonid Gurvits, Lucien Hardy, Richard Jozsa, Manny Knill, Eric Rains, Rüdiger Schack, Ben Schumacher, ...

##
###
Twenty five years of two-dimensional rational conformal field theory

2010
*
Journal of Mathematical Physics
*

In this article we try to give a condensed panoramic view

doi:10.1063/1.3277118
fatcat:qssuhm3wybgm7cfzblcaube4iq
*of**the*development*of*two-dimensional rational conformal field theory in*the*last twenty-five years. ... physics in*the**description**of*impurities, e.g. in*the*Kondo*effect*[1] . • Chiral conformal field theories describe universality classes*of*quantum Hall fluids [97] ; conformal blocks are*used*as approximate ... vertex*algebras*,*the*modular*tensor*category together with*the*value*of**the*Virasoro central charge is equivalent to*the*genus*of**the**lattice*. ...##
###
Mapping Topological to Conformal Field Theories through strange Correlators

2018
*
Physical Review Letters
*

For

doi:10.1103/physrevlett.121.177203
pmid:30411961
fatcat:km6xhjjlovgo5l62v5vjrqchru
*the*case*of*critical systems, those non-local matrix product operator symmetries are*the**lattice*remnants*of*topological conformal defects in*the*field theory*description*. ... from Ocneanu's tube*algebra*. ... Aasen for explaining his work [21, 22] , particularly*the*relevance*of*Ocneanu's tube*algebra*to topological sectors in CFTs. ...##
###
Quantum information processing, operational quantum logic, convexity, and the foundations of physics

2003
*
Studies in history and philosophy of modern physics
*

*The*main technical content

*of*

*the*paper is in a theorem that any such theory naturally gives rise to a "weak

*effect*

*algebra*" when outcomes having

*the*same probability in all states are identified, and ... in

*the*introduction

*of*a notion

*of*"operation

*algebra*" that also takes account

*of*sequential and conditional operations. ... Acknowledgments Discussions over

*the*years with Carlton Caves, Dave Foulis, Chris Fuchs, Leonid Gurvits, Lucien Hardy, Richard Jozsa, Manny Knill, Eric Rains, Rüdiger Schack, Ben Schumacher, ...

##
###
Renormalization Group Flows of Hamiltonians Using Tensor Networks

2017
*
Physical Review Letters
*

We derive

doi:10.1103/physrevlett.118.250602
pmid:28696763
fatcat:xiic5bf5jnan7hlrgkhdeetqj4
*algebraic*relations for fixed point*tensors*, calculate critical exponents, and benchmark our method on*the*Ising model and*the*six-vertex model. ... A renormalization group flow*of*Hamiltonians for two-dimensional classical partition functions is constructed*using**tensor*networks. Similar to*tensor*network renormalization ([G. Evenbly and G. ... In his treatment*of*block-spin methods on*the**lattice*, Wilson emphasized that one should be able to do precise numerical calculations*using*pure RG methods*combined*with approximations based only on locality ...##
###
Invariance of stationary and ergodic properties of a quantum source under memoryless transformations

2003
*
IEEE International Symposium on Information Theory, 2003. Proceedings.
*

We prove that

doi:10.1109/isit.2003.1228475
fatcat:baikal6orvdfhplgh7ukbzhpfa
*the*stationarity and*the*ergodicity*of*a quantum source {ρ [1,m] } ∞ m=1 are preserved by any trace-preserving*completely*positive linear map*of**the**tensor*product form E ⊗m , where a copy ...*of*E acts locally on each spin*lattice*site. ... We point out that such a*tensor*product map is*the*most general*description**of*a quantum memoryless channel [1] . ...##
###
What is the Mathematical Structure of Quantum Spacetime?
[article]

2007
*
arXiv
*
pre-print

In

arXiv:0706.4452v1
fatcat:rqtoecri4ncujng6dz2tvghlbu
*the*process*of*constructing a quantum topos for quantum gravity, we propose a new, operational approach to*the*problem*of**the*obervables in quantum gravity, which leads to a new mathematical point*of*... We survey indications from different branches*of*Physics that*the*fine scale structure*of*spacetime is not adequately described by a manifold. ... In this definition, × denotes*the**tensor*product*of*sup*complete**lattices*. ...##
###
Coordinating quantum agents' perspectives: convex operational theories, quantum information, and quantum foundations
[article]

2006
*
arXiv
*
pre-print

*of*

*the*perspectives within it, is

*the*key to understanding whether we may be able to achieve a unified, "objective" physical view in which quantum mechanics is

*the*appropriate

*description*for certain ... In this paper, I propose a project

*of*enlisting quantum information science as a source

*of*task-oriented axioms for

*use*in

*the*investigation

*of*operational theories in a general framework capable

*of*encompassing ... Chris Fuchs brought

*the*work

*of*Bilodeau to my attention. ...

##
###
The Equivalence of Schrödinger and Heisenberg Pictures in Quantum Cellular Automata
[article]

2019
*
arXiv
*
pre-print

*tensor*product

*algebra*(ITPA) with evolution by

*algebra*automorphism is

*the*Heisenberg template. ...

*Description*

*of*a QCA over

*the*separable Hilbert space

*of*finite, unbounded configurations (UFC Hilbert space) with unitary state evolution is

*the*Schrödinger template, and over

*the*incomplete infinite ... Acknowledgements

*The*author would like to thank David Meyer and members

*of*his research group for productive discussions. ...

##
###
The tensor algebra compiler

2017
*
Proceedings of the ACM on Programming Languages
*

This paper presents a new technique that compiles compound

doi:10.1145/3133901
dblp:journals/pacmpl/KjolstadKCLA17
fatcat:6bkwkjzqg5cxfjceuvtx5454bi
*tensor**algebra*expressions*combined*with*descriptions**of**tensor*formats into efficient loops. ...*Tensor*and linear*algebra*is pervasive in data analytics and*the*physical sciences. Often*the**tensors*, matrices or even vectors are sparse. ...*Tensor**Algebra*We assessed*the**effectiveness**of*our technique for sparse*tensor**algebra*by comparing*the*performance*of*several*tensor**algebra*kernels generated by taco with*the*same kernels implemented ...##
###
The Tensor Product as a Lattice of Regular Galois Connections
[chapter]

2006
*
Lecture Notes in Computer Science
*

*The*latter also appear as

*the*elements

*of*

*the*

*tensor*product

*of*concept

*lattices*, but it is known that not all dual bonds between two

*lattices*can be represented in this way. ... This is achieved by

*combining*methods from

*algebraic*order theory and FCA with recent results on dual bonds. ... This research was partially supported by

*the*European Commission under IST-2003-506826 "SEKT." ...

##
###
Page 730 of Mathematical Reviews Vol. , Issue 2000a
[page]

2000
*
Mathematical Reviews
*

*The*

*tensor*product

*of*

*the*

*effect*

*algebras*for two systems is

*the*

*effect*

*algebra*for

*the*

*combined*system. ...

*The*notion

*of*a o-

*effect*

*algebra*, generalizing

*the*idea

*of*a o-field, is introduced, and a corresponding o-

*tensor*product is formulated. ...

##
###
Gluon correlation functions from lattice quantum chromodynamics
[article]

2021
*
arXiv
*
pre-print

We also identified classes

arXiv:2101.06074v1
fatcat:yc5xfothtve4pc5pbvfh75nzum
*of*kinematic configurations where these deviations are minimal and*the*continuum*description**of**lattice**tensors*is improved. ...*The*first goal was to*use**lattice**tensor*representations for*the*propagator in four dimensions to understand/quantify deviations*of**the**lattice*propagator from its continuum form. ...*Completeness**of**the**tensor*bases*The*analysis*of**the*form factors alone does not offer*the*full picture for how*the**lattice*bases affect*the**description**of**the**tensor*2 . ...
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