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Parametrised bar recursion: A unifying framework for realizability interpretations of classical dependent choice [article]

Thomas Powell
2015 arXiv   pre-print
realizes a corresponding family of parametrised dependent choice principles.  ...  During the last twenty years or so a wide range of realizability interpretations of classical analysis have been developed.  ...  A computational interpretation of dependent choice We now give a parametrised realizability interpretation to the principle of countable dependent choice.  ... 
arXiv:1411.0457v2 fatcat:qheau2jvtjebpofgrk4lojwiom

Unifying Functional Interpretations: Past and Future [article]

Paulo Oliva
2014 arXiv   pre-print
This article surveys work done in the last six years on the unification of various functional interpretations including G\"odel's dialectica interpretation, its Diller-Nahm variant, Kreisel modified realizability  ...  , Stein's family of functional interpretations, functional interpretations "with truth", and bounded functional interpretations.  ...  The two main ideas behind the original unifying functional interpretation [39] are the introduction of a common notation |A|x y for such binary predicates, and a parametrised interpretation of A →  ... 
arXiv:1410.4364v1 fatcat:p2q5nxafnnarxptyj3wqlfxxh4

Why gauge? Conceptual Aspects of Gauge theories [article]

Henrique Gomes
2022 arXiv   pre-print
At its simplest, the idea of gauge is that nature is best described using a descriptively redundant language; the different descriptions are said to be related by a gauge symmetry.  ...  The over-arching question the thesis aims to answer is: how can descriptive redundancy be fruitful for physics?  ...  we have seen in §5.3.4, to a configuration space parametrised by the charges and to a choice of the Coulomb gauge for the gauge potential.  ... 
arXiv:2203.05339v1 fatcat:oilx3xv3r5htnluclqcfj3eaha

Rapid digital architecture design of orthogonal matching pursuit

Benjamin Knoop, Jochen Rust, Sebastian Schmale, Dagmar Peters-Drolshagen, Steffen Paul
2016 2016 24th European Signal Processing Conference (EUSIPCO)  
For instance, a complex-valued digital architecture for the Orthogonal Matching Pursuit (OMP) algorithm with rank-1 updating has successfully been implemented and tested, which can be utilised for the  ...  to a higher level of abstraction-the algorithmic level.  ...  The Unified CORDIC algorithm is very often the method of choice for trigonometric and transcendental functions [And98] .  ... 
doi:10.1109/eusipco.2016.7760570 dblp:conf/eusipco/KnoopRSPP16 fatcat:bo3c4fo6njeo3hjjsnwo72jbwe

Programs and Proofs: Mechanizing Mathematics with Dependent Types [article]

Ilya Sergey
2014 Zenodo  
This project contains the Coq sources, the lectures and the exercises for the course Programs and Proofs: Mechanizing Mathematics with Dependent Types.  ...  A Short Course on Interactive Proofs in Coq/Ssreflect.  ...  Hoare Type Theory In this chapter, we will consider a fairly large case study that makes use of most of Coq's features as a programming language with dependent types and as a framework to build proofs  ... 
doi:10.5281/zenodo.4996238 fatcat:34mga3vdkjhdtfksnjiwu6yknq

Herman Cappelen & Ernie Lepore , Insensitive semantics: a defense of semantic minimalism and speech act pluralism . Oxford: Blackwell, 2005. Pp. xii+219

ROBERT J. STAINTON, CATHERINE WEARING
2006 Journal of Linguistics  
FIN plays a crucial role in Roberts' attempt to make the general outlines of this classic analysis a consequence of Universal Grammar. Roberts hypothesizes that FIN must be phonologically realized.  ...  for semantic interpretation.  ...  particularly uncooperative interpretations of Chomsky (1995) .  ... 
doi:10.1017/s0022226706213835 fatcat:tpbzhdc7qffyze4dkefuj2weui

Applications of the Free Energy Principle to Machine Learning and Neuroscience [article]

Beren Millidge
2021 arXiv   pre-print
The free energy principle is a general mathematical theory of the necessary information-theoretic behaviours of systems that maintain a separation from their environment.  ...  We additionally provide a detailed mathematical understanding of the nature and origin of the information-theoretic objectives that underlie exploratory behaviour.  ...  Finally, we provide a unified mathematically principled framework for understanding and deriving many information-seeking exploration objectives through the lens of a dichotomy between 'evidence' and '  ... 
arXiv:2107.00140v1 fatcat:c6phd65xwfc2rcyq7pnth5a3pq

ON THE CONSTRUCTION OF RELATIVISTIC QUANTUM THEORY: A Progress Report [chapter]

H. PIERRE NOYES
2001 Series on Knots and Everything  
We construct the particulate states of quantum physics using a recursive com puter program that incorporates non-determinism by means of locally arbitrary choices.  ...  For those who wish the integers themselves to be constructed, one can follow Gefwert's approach in terms of primitive recursive functions , or follow Kilmister's foundational discussion in Appendix I where  ...  The two two-argument functions definable for the Sort are represented by + (for the "G" of T of f\ and by free choice for *J".  ... 
doi:10.1142/9789812810090_0004 fatcat:nuq33c4ptfd3la7a2lbm3bhpcm

Applications of Free Fields in 2D Current Algebra [article]

J. Rasmussen
1996 arXiv   pre-print
For higher groups an explicit Wakimoto free field realization is presented of affine current algebras based on simple Lie groups.  ...  Furthermore, a study is undertaken of primary fields in the framework of extra x variables, and screening currents of both kinds are discussed. Several new and definite results are presented.  ...  In the second identity there is a phase depending on the precise choice of the integration contour for u.  ... 
arXiv:hep-th/9610167v1 fatcat:s4tisywzyzafpacs2sdo5lotga

Scaling-up Diverse Orthogonal Convolutional Networks with a Paraunitary Framework [article]

Jiahao Su, Wonmin Byeon, Furong Huang
2021 arXiv   pre-print
Our versatile framework, for the first time, enables the study of architecture designs for deep orthogonal networks, such as choices of skip connection, initialization, stride, and dilation.  ...  standard convolutional layers and propose specific classes of their realizations.  ...  Therefore, we realize orthogonal convolutions through standard neural network optimizers on a model parameterized via our design. Interpretation of existing methods.  ... 
arXiv:2106.09121v1 fatcat:y5hrxeqv5je3pkdb57daffdgda

Lepton Flavour Symmetries [article]

Ferruccio Feruglio, Andrea Romanino
2021 arXiv   pre-print
For each type of symmetry we present several illustrative examples and we discuss specific strengths and limitations.  ...  We provide a general classification of flavour symmetries according to their interplay with the proper Poincare' and gauge groups and to their linear or nonlinear action in field space.  ...  Acknowledgments 60 ACKNOWLEDGMENTS We are grateful to Claudia Hagedorn for useful discussions and comments on a part of this manuscript.  ... 
arXiv:1912.06028v2 fatcat:pjcbmlohsbhgler6xeis6jorma

05021 Abstracts Collection – Mathematics, Algorithms, Proofs

Thierry Coquand, Henri Lombardi, Marie-Françoise Roy
2006
Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper.  ...  Depending on the choice of the two parameters one obtains well-known functional interpretations, among others Gödel's Dialectica interpretation, Diller-Nahm's variant of the Dialectica interpretation,  ...  We show that all these interpretations only dier on two basic choices, which are captured by the parameters, namely the choices of ( 1 ) "how much" of the counter-examples for A becomes witnesses for  ... 
doi:10.4230/dagsemproc.05021.1 fatcat:svvwzrh56reilgzdx2xab3rmny

Real Time Dynamics of Symmetry Breaking [article]

Zsolt Szep
2001 arXiv   pre-print
Numerical investigation were performed for out-of-equilibrium classical systems.  ...  The real time characterisation of the Goldstone effect when a condensate breaks the O(N) symmetry of the quantum and classical field theory is given.  ...  We thank Zoltán Fodor for generously providing computing resources at the Inst. for Theoretical Physics of the Eötvös University.  ... 
arXiv:hep-ph/0110024v1 fatcat:ogewpewnnrekje2on73aef4qja

Semi-classical transport theory for non-Abelian plasmas

Daniel F. Litim, Cristina Manuel
2002 Physics reports  
We review a semi-classical transport theory for non-Abelian plasmas based on a classical picture of coloured point particles.  ...  The framework permits the integrating-out of fluctuations in a systematic manner.  ...  A unified description of the different choices was given in [18] . Balachandran et al.  ... 
doi:10.1016/s0370-1573(02)00015-7 fatcat:takmk3cjyffwjcgqinxfywxnoa

The Physics of Q-balls [article]

Mitsuo I. Tsumagari
2009 arXiv   pre-print
By including quantum corrections in the scalar potentials, a naturally formed condensate in a post-inflationary era can be classically unstable and fragment into Q-balls that can be long-lived or decay  ...  In this thesis we investigate the stationary properties and formation process of a class of nontopological solitons, namely Q-balls.  ...  The reasons for this discrepancy are as before a problem with our choice of potentials. We can see that the thin-wall Q-balls for any D are both classically and absolutely stable.  ... 
arXiv:0910.3845v1 fatcat:7pjcqojahbcubo755k72vieb7a
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