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String variable grammar: A logic grammar formalism for the biological language of DNA

David B. Searls
1995 The Journal of Logic Programming  
We give a number of mathematical and biological examples, and use an SVG variant to propose a new abstraction of the process of gene expression.  ...  A practical implementation called GF_~LANG is described, and some recent results in parsing genes and other high-level features of DNA sequences are summarized. <~  ...  In particular, many logic grammar systems have made free use of logic variables to copy and move constituents, as in the discontinuous grammar (DG) of Dahl and co-workers [8] .  ... 
doi:10.1016/0743-1066(95)00034-h fatcat:jzz5ibw7szhg7ef6k6ch7gc2sa

Optimal Policies for Observing Time Series and Related Restless Bandit Problems [article]

Christopher R. Dance, Tomi Silander
2017 arXiv   pre-print
of discontinuous nonlinear maps, which frequently arise in physics, control and biology.  ...  The trade-off between the cost of acquiring and processing data, and uncertainty due to a lack of data is fundamental in machine learning.  ...  Acknowledgments We thank José Niño-Mora for pointing out his work on the verification theorem and Sofia Michel for her careful reading of the manuscript.  ... 
arXiv:1703.10010v1 fatcat:sylkjxwe5jca3jq2nonuxuao44

2015 EUROPEAN SUMMER MEETING OF THE ASSOCIATION FOR SYMBOLIC LOGIC LOGIC COLLOQUIUM '15 Helsinki, Finland August 3–8, 2015

2016 Bulletin of Symbolic Logic  
The main conference topics were: Model Theory, Set Theory, Computability Theory, Proof Theory, Philosophy of Mathematics and Logic, Logic and Quantum Foundations.  ...  One of the most intriguing results on logics of dependence and independence is the tight connection between inclusion logic and the least fixed-point logic LFP.  ...  It is known that in Frege systems there are the trivial exponential upper bounds and only Ω(n 2 ) bounds of proof size and Ω(n) bounds of proof steps for tautologies with the size n [1].  ... 
doi:10.1017/bsl.2016.22 fatcat:cm4a5yyvgfajzm4qvlszviblni

Distance makes the types grow stronger

Jason Reed, Benjamin C. Pierce
2010 Proceedings of the 15th ACM SIGPLAN international conference on Functional programming - ICFP '10  
We develop examples including known differentially private algorithms, privacy-aware variants of standard functional programming idioms, and compositionality principles for differential privacy.  ...  streamline this process with a functional language whose type system automatically guarantees differential privacy, allowing the programmer to write complex privacy-safe query programs in a flexible and  ...  Acknowledgments Thanks to Helen Anderson, Jonathan Smith, Andreas Haeberlen, Adam Aviv, Daniel Wagner, Michael Hicks, Katrina Ligett, Aaron Roth, and Michael Tschantz for helpful discussions.  ... 
doi:10.1145/1863543.1863568 dblp:conf/icfp/ReedP10 fatcat:6xvioynijreq3o3wr6qlrkprru

Distance makes the types grow stronger

Jason Reed, Benjamin C. Pierce
2010 SIGPLAN notices  
We develop examples including known differentially private algorithms, privacy-aware variants of standard functional programming idioms, and compositionality principles for differential privacy.  ...  streamline this process with a functional language whose type system automatically guarantees differential privacy, allowing the programmer to write complex privacy-safe query programs in a flexible and  ...  Acknowledgments Thanks to Helen Anderson, Jonathan Smith, Andreas Haeberlen, Adam Aviv, Daniel Wagner, Michael Hicks, Katrina Ligett, Aaron Roth, and Michael Tschantz for helpful discussions.  ... 
doi:10.1145/1932681.1863568 fatcat:2vkydv6m4ffqtev5t7gdln52qu

Page 767 of Mathematical Reviews Vol. 16, Issue Index [page]

Mathematical Reviews  
Fuzzy arithmetic and fuzzy topology. Applied systems and cybernetics, Vol. I, 11, 111, IV, V, VI (Acapulco, 1980), pp. 2803-2807, Pergamon, Elmsford, N.Y., 1981.  ...  Lagrange multipliers and subderivatives of optimal value functions in nonlinear programming. Nondifferential and variational techniques in optimization (Lexington, Ky., 1980). Math. Programming Stud.  ... 

Nonsmooth Analysis and Optimization [article]

Christian Clason
2022 arXiv   pre-print
, and semismooth Newton methods.  ...  Treated are convex functions and subdifferentials, Fenchel duality, monotone operators and resolvents, Moreau--Yosida regularization, proximal point and (some) first-order splitting methods, Clarke subdifferentials  ...  We use the usual arithmetic on R, i.e., t < ∞ and t + ∞ = ∞ for all t ∈ R; subtraction and multiplication of negative numbers with ∞ and in particular F (x) = −∞ is not allowed, however.  ... 
arXiv:1708.04180v3 fatcat:f7aranpwzzbdvmp3bsdzexiw54

Level set methods for finding critical points of mountain pass type [article]

Adrian S. Lewis, C.H. Jeffrey Pang
2010 arXiv   pre-print
Finally, we relate critical points of mountain pass type to nonsmooth and metric critical point theory.  ...  We describe a numerical method for finding critical points that is convergent in the nonsmooth case and locally superlinearly convergent in the smooth finite dimensional case.  ...  Acknowledgments We thank Jianxin Zhou for comments on an earlier version of the manuscript, and we thank an anonymous referee for feedback, which have improved the presentation in the paper.  ... 
arXiv:0906.4466v2 fatcat:ptikyp5bivhrhdgzqbbeixrijy

Introduction to Nonsmooth Analysis and Optimization [article]

Christian Clason, Tuomo Valkonen
2020 arXiv   pre-print
Both first-order (proximal point and splitting) methods and second-order (semismooth Newton) methods are treated.  ...  They cover convex subdifferentials, Fenchel duality, monotone operators and resolvents, Moreau--Yosida regularization as well as Clarke and (briefly) limiting subdifferentials.  ...  but consists of a set of equally admissible subderivatives.  ... 
arXiv:2001.00216v3 fatcat:gs342de7v5eb3bfkxhdmxosyim

Level set methods for finding critical points of mountain pass type

Adrian S. Lewis, C.H. Jeffrey Pang
2011 Nonlinear Analysis  
Finally, we relate critical points of mountain pass type to nonsmooth and metric critical point theory.  ...  We describe a numerical method for finding critical points that is convergent in the nonsmooth case and locally superlinearly convergent in the smooth finite dimensional case.  ...  Acknowledgements We thank Jianxin Zhou for comments on an earlier version of the manuscript, and we thank an anonymous referee for feedback, which has improved the presentation in the paper.  ... 
doi:10.1016/j.na.2011.03.039 fatcat:xj2a3yj2lje7ngy33ksts2jope

Categorial Type Logics [chapter]

Michael Moortgat
1997 Handbook of Logic and Language  
All remaining errors and imperfections are my own.  ...  I am deeply indebted to Natasha Kurtonina, Dick Oehrle and Glyn Morrill: it was a pleasure to work together and exchange ideas with them over these years.  ...  *(the mathematician) whom Gottlob admired Kazimierz and Jim detested (12) DISCONTINUOUS DEPENDENCIES AND RESTRICTED COMMUTATIVITY.  ... 
doi:10.1016/b978-044481714-3/50005-9 fatcat:xseh4iz55vesfnm3daywvb7gyu

Categorial Type Logics [chapter]

Michael Moortgat
2011 Handbook of Logic and Language  
All remaining errors and imperfections are my own.  ...  I am deeply indebted to Natasha Kurtonina, Dick Oehrle and Glyn Morrill: it was a pleasure to work together and exchange ideas with them over these years.  ...  *(the mathematician) whom Gottlob admired Kazimierz and Jim detested (12) DISCONTINUOUS DEPENDENCIES AND RESTRICTED COMMUTATIVITY.  ... 
doi:10.1016/b978-0-444-53726-3.00002-5 fatcat:mg4b3coyyfhgrcztbtkglsigry

Probabilistic Constraint Logic Programming. Formal Foundations of Quantitative and Statistical Inference in Constraint-Based Natural Language Processing [article]

Stefan Riezler
2000 arXiv   pre-print
In this thesis, we present two approaches to a rigorous mathematical and algorithmic foundation of quantitative and statistical inference in constraint-based natural language processing.  ...  The first approach, called quantitative constraint logic programming, is conceptualized in a clear logical framework, and presents a sound and complete system of quantitative inference for definite clauses  ...  Claim (iii) follows by arithmetic induction.  ... 
arXiv:cs/0008036v1 fatcat:vmk2ctxzh5c3ddmoyzs2elm7e4

On the nonsmooth analysis of doubly nonlinear evolution inclusions of first and second order with applications

Aras Bacho, Technische Universität Berlin, Etienne Emmrich
2021
Evolution inclusions can be a suitable means to model such discontinuous processes mathematically.  ...  Many phenomena in nature are characterized by discontinuous processes. To describe them by suitable mathematical models is often a challenge.  ...  Evolution inclusions can be a suitable means to model such discontinuous processes mathematically.  ... 
doi:10.14279/depositonce-12327 fatcat:immye6ncgbfdjbyqvaddcinzeq

A formalisation of the theory of context-free languages in higher order logic [article]

Aditi Barthwal, University, The Australian National, University, The Australian National
2015
The mechanisation proves to be an ideal case study of how intuitive textbook proofs can blow up in size and complexity, and how details from the textbook can change during formalisation.  ...  We have mechanised classical results involving context-free grammars and pushdown automata.  ...  Acknowledgements The Little Person and the Quest for the PhD  ... 
doi:10.25911/5d6e4c3c4b543 fatcat:a55lb5rvy5a5pc2nz4uroso3uy
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