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Realizability at Work: Separating Two Constructive Notions of Finiteness

Marc Bezem, Thierry Coquand, Keiko Nakata, Erik Parmann, Michael Wagner
2018 Types for Proofs and Programs  
We elaborate in detail a 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.  ... 
doi:10.4230/lipics.types.2016.6 dblp:conf/types/BezemC0P16 fatcat:t22m6u4wpfhjndcfqunsynckwy

Realizing anomalous anyonic symmetries at the surfaces of three-dimensional gauge theories

Lukasz Fidkowski, Ashvin Vishwanath
2017 Physical review B  
In this 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.  ... 
doi:10.1103/physrevb.96.045131 fatcat:jj62dtcfwzertau25zzrbpuae4

Polynomial Realization of slq(2) and Fusion Rules at Exceptional Values of q

D. Karakhanyan, Sh. Khachatryan
2005 Letters in Mathematical Physics  
Representations 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 (  ... 
doi:10.1007/s11005-005-4381-0 fatcat:qfko5762sbdl5h2kkqmuogj5oi

A glimpse into Thurston's work [article]

Ken'Ichi Ohshika, Athanase Papadopoulos
2020 arXiv   pre-print
We present an overview 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] .  ... 
arXiv:2009.06344v2 fatcat:3m27w3h7mjgppihrpwwccry7xa

Constructions at work or at rest?

Rens Bod
2009 Cognitive Linguistics  
I am convinced that this goal can be achieved, if only the 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.  ... 
doi:10.1515/cogl.2009.006 fatcat:svj467t6cveqfglvxbjoockuze

Towards Working with Small Atomic Functions [chapter]

Alec Yasinsac
2010 Lecture Notes in Computer Science  
Shannon's 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.  ... 
doi:10.1007/978-3-642-17773-6_26 fatcat:zmb45lekkfckxosvvxeammaori

Fluctuations of work from quantum subensembles: The case against quantum work-fluctuation theorems

A. E. Allahverdyan, Th. M. Nieuwenhuizen
2005 Physical Review E  
A critical review is given 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.  ... 
doi:10.1103/physreve.71.066102 pmid:16089815 fatcat:b5kpy5utyzg3pbjr6in5tegmue

Towards Working with Small Atomic Functions [chapter]

Alec Yasinsac, J. Todd McDonald
2010 Lecture Notes in Computer Science  
Shannon's 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.  ... 
doi:10.1007/978-3-642-17773-6_25 fatcat:tugmggaz4fdubm5o2qoxaciphu

The work of Peter Scholze [article]

Michael Rapoport
2019 arXiv   pre-print
To 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.  ... 
arXiv:1909.07222v1 fatcat:czywul7osneljpme4lnc75veau

On the Work of Peter Scholze

T. Wedhorn
2019 Jahresbericht der Deutschen Mathematiker-Vereinigung (Teubner)  
This is a survey article over some 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.  ... 
doi:10.1365/s13291-019-00211-y fatcat:w5ewq5dq6bfyrf3bfpu2ddxw2a

How circuits work

Johan De Kleer
1984 Artificial Intelligence  
EOL'AL. which, given a circuit topology, can 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.  ... 
doi:10.1016/0004-3702(84)90040-7 fatcat:wdjw6in7tjckjme3ftptny4fmq

How Circuits Work [chapter]

Johan De Kleer
1984 Qualitative Reasoning About Physical Systems  
EOL'AL. which, given a circuit topology, can 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.  ... 
doi:10.1016/b978-0-444-87670-6.50008-x fatcat:7hhq5m44qbfc3cs5m23vcmixlq

Felix Alexandrovich Berezin and His Work [chapter]

Alexander Karabegov, Yuri Neretin, Theodore Voronov
2012 Geometric Methods in Physics  
This is a survey 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.  ... 
doi:10.1007/978-3-0348-0448-6_1 fatcat:w62wgekwarggpnza2gmwnxpeoa

Computational Work and Time on Finite Machines

J. E. Savage
1972 Journal of the ACM  
Measures 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.  ... 
doi:10.1145/321724.321731 fatcat:4r2a4aanuvdjdj55jzlatc6dh4

On the work of Peter Scholze [article]

Torsten Wedhorn
2019 arXiv   pre-print
This is a survey article about some 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.  ... 
arXiv:1909.11510v1 fatcat:wobrtokx75byfpdw7vtkd2rygu
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