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Realizability at Work: Separating Two Constructive Notions of Finiteness

2018
*
Types for Proofs and Programs
*

We elaborate in detail a

doi:10.4230/lipics.types.2016.6
dblp:conf/types/BezemC0P16
fatcat:t22m6u4wpfhjndcfqunsynckwy
*realizability*model for Martin-Löf dependent type theory with the purpose to analyze a subtle distinction between*two**constructive**notions**of**finiteness**of*a set A. ... The*two**notions*are: (1) A is Noetherian: the empty list can be*constructed*from lists over A containing duplicates by a certain inductive shortening process; (2) A is streamless: every enumeration*of*... A : U, R : A → A → U M : Noetherian R → streamless R T Y P E S 2 0 1 6 6:10*Realizability**at**Work*Proof. ...##
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Realizing anomalous anyonic symmetries at the surfaces of three-dimensional gauge theories

2017
*
Physical review B
*

In this

doi:10.1103/physrevb.96.045131
fatcat:jj62dtcfwzertau25zzrbpuae4
*work*, we find a physical*realization*for these anomalously permuting SETs as surface theories*of*certain 3d long-range entangled phases, completing our understanding*of*general anomalous SETs in ... Recently, though, it has been*realized*that symmetries, which may still be present in such systems, can give rise to a host*of*new, distinct, many-body phases, all*of*which share the same underlying topological ... Underlying our*construction*is a certain 2-complex Γ, which is just a generalization*of*the*notion**of*a graph: in addition to one dimensional links, it also contains*two*dimensional plaquettes. ...##
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Polynomial Realization of slq(2) and Fusion Rules at Exceptional Values of q

2005
*
Letters in Mathematical Physics
*

Representations

doi:10.1007/s11005-005-4381-0
fatcat:qfko5762sbdl5h2kkqmuogj5oi
*of*the sℓ_q(2) algebra are*constructed*in the space*of*polynomials*of*real (complex) variable for q^N=1. ... The spin addition rule based on eigenvalues*of*Casimir operator is illustrated on few simplest cases and conjecture for general case is formulated. ... Since we would like to*construct*a*realization*on polynomials, we introduce*two*independent variables, x and y and identify them with elements*of*the doublet representation, |↑ = y, |↓ = x. (3) Then ( ...##
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A glimpse into Thurston's work
[article]

2020
*
arXiv
*
pre-print

We present an overview

arXiv:2009.06344v2
fatcat:3m27w3h7mjgppihrpwwccry7xa
*of*some significant results*of*Thurston and their impact on mathematics. ... The final version*of*this paper will appear as Chapter 1*of*the book "In the tradition*of*Thurston: Geometry and topology", edited by K. Ohshika and A. Papadopoulos (Springer, 2020). ... He*realized**at*some point that some*of*the results he obtained were generalizations*of*results contained in*two*papers by Andreev [12, 13] . ...##
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Constructions at work or at rest?

2009
*
Cognitive Linguistics
*

I am convinced that this goal can be achieved, if only the

doi:10.1515/cogl.2009.006
fatcat:svj467t6cveqfglvxbjoockuze
*two*-linguistic and computational -strands take each other's*work*into account. ... Yet U-DOP/DOP is not the only possible computational*realization**of*CxG. ...##
###
Towards Working with Small Atomic Functions
[chapter]

2010
*
Lecture Notes in Computer Science
*

Shannon's

doi:10.1007/978-3-642-17773-6_26
fatcat:zmb45lekkfckxosvvxeammaori
*notion**of*entropy remains a benchmark reference for understanding information and data content*of*cryptosystems. ... We discuss in this paper the similar*notion**of*function entropy and examine its use on a small scale to provide perfect functional secrecy. ... It turns out that this*construction*resolves*two*classic security problems. ...##
###
Fluctuations of work from quantum subensembles: The case against quantum work-fluctuation theorems

2005
*
Physical Review E
*

A critical review is given

doi:10.1103/physreve.71.066102
pmid:16089815
fatcat:b5kpy5utyzg3pbjr6in5tegmue
*of**two*other approaches to fluctuations*of**work*proposed in the literature. ... PHYSICAL REVIEW E 71, 066102 ͑2005͒ those definitions; see, e.g., ͓16,18,27,28,30-32͔. 6 As with any exchange process, this is operationally characterized by measurements*at**two*different times. 7 Normally ... Should not one therefore restrict the definition*of*fluctuations*of**work*to this*separation*only? Answer 1. There are*at*least*two*reasons why the answer is no. ...##
###
Towards Working with Small Atomic Functions
[chapter]

2010
*
Lecture Notes in Computer Science
*

Shannon's

doi:10.1007/978-3-642-17773-6_25
fatcat:tugmggaz4fdubm5o2qoxaciphu
*notion**of*entropy remains a benchmark reference for understanding information and data content*of*cryptosystems. ... We discuss in this paper the similar*notion**of*function entropy and examine its use on a small scale to provide perfect functional secrecy. ... It turns out that this*construction*resolves*two*classic security problems. ...##
###
The work of Peter Scholze
[article]

2019
*
arXiv
*
pre-print

To

arXiv:1909.07222v1
fatcat:czywul7osneljpme4lnc75veau
*work*with the pro-étale topology, Scholze introduces the*notion**of*a totally disconnected perfectoid space: this is a (quasi-compact and quasi-*separated*) perfectoid space X that is as close as possible ... Here the*two*copies*of*the prime number p have to be thought*of*as*two*independent variables. ...##
###
On the Work of Peter Scholze

2019
*
Jahresbericht der Deutschen Mathematiker-Vereinigung (Teubner)
*

This is a survey article over some

doi:10.1365/s13291-019-00211-y
fatcat:w5ewq5dq6bfyrf3bfpu2ddxw2a
*of*the*work**of*Peter Scholze. No originality is claimed. ... But it is easy to define the*notion**of*a*finite*étale morphism. ... Perfectoid Spaces We can now give the definition*of*one*of*the central*notions*in Scholze's*work*. ...##
###
How circuits work

1984
*
Artificial Intelligence
*

EOL'AL. which, given a circuit topology, can

doi:10.1016/0004-3702(84)90040-7
fatcat:wdjw6in7tjckjme3ftptny4fmq
*construct*by qualitative causal analysis a description*of*the mechanism by which the circuit operates. ... Another aspect*of*the theory. teleological analysis, describes how the*notion*that the system has a purpose can be used to structure and aid this causal analysis. ... As changes in these fields propagate*at**finite*speeds, this process takes a certain amount*of*time. ...##
###
How Circuits Work
[chapter]

1984
*
Qualitative Reasoning About Physical Systems
*

EOL'AL. which, given a circuit topology, can

doi:10.1016/b978-0-444-87670-6.50008-x
fatcat:7hhq5m44qbfc3cs5m23vcmixlq
*construct*by qualitative causal analysis a description*of*the mechanism by which the circuit operates. ... Another aspect*of*the theory. teleological analysis, describes how the*notion*that the system has a purpose can be used to structure and aid this causal analysis. ... As changes in these fields propagate*at**finite*speeds, this process takes a certain amount*of*time. ...##
###
Felix Alexandrovich Berezin and His Work
[chapter]

2012
*
Geometric Methods in Physics
*

This is a survey

doi:10.1007/978-3-0348-0448-6_1
fatcat:w62wgekwarggpnza2gmwnxpeoa
*of*Berezin's*work*focused on three topics: representation theory, general concept*of*quantization, and supermathematics. ... Neretin's*work*was also partially supported by the FWF grant, Project 22122. ... In [19] and [37] , Berezin*constructed**finite*approximations*of*Feynman path integrals with the use*of*operator symbols. See also Berezin and M. A. ...##
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Computational Work and Time on Finite Machines

1972
*
Journal of the ACM
*

Measures

doi:10.1145/321724.321731
fatcat:4r2a4aanuvdjdj55jzlatc6dh4
*of*the computational*work*and computational delay required by ms chines to compute functions are given. ... KEY WORDS AND PHRASES: computational*work*,*finite*machines, automata, memor: hierarchies, general purpose computer, computational efficiency, functional complexity ... Here we let AE be the minimum*separation*between energy levels and let*At*be the minimum time to determine which*of**two*levels an input to a logic element is in. ...##
###
On the work of Peter Scholze
[article]

2019
*
arXiv
*
pre-print

This is a survey article about some

arXiv:1909.11510v1
fatcat:wobrtokx75byfpdw7vtkd2rygu
*of*the*work**of*Peter Scholze for the Jahresbericht der DMV. No originality is claimed. ... It is hoped that it can serve as a guideline to an exciting and increasingly large edifice*of*theory. ... Perfectoid spaces We can now give the definition*of*one*of*the central*notions*in Scholze's*work*. Definition 3.3. ...
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