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While "complexity science" has achieved significant successes in several interdisciplinary fields such as economics and biology, it is only a very recent observation that legal systems -- from the way legal texts are drafted and connected…

Physics and Society · Physics 2025-01-08 Pierpaolo Vivo , Daniel M. Katz , J. B. Ruhl

Verifying software correctness has always been an important and complicated task. Recently, formal proofs of critical properties of algorithms and even implementations are becoming practical. Currently, the most powerful automated proof…

Logic in Computer Science · Computer Science 2019-04-10 Michael Raskin , Christoph Welzel

Interactive proof assistants make it possible for ordinary mathematicians to write definitions and theorems in a formal proof language, like a programming language, so that a computer can parse them and check them against the rules of a…

History and Overview · Mathematics 2024-11-20 Jeremy Avigad , Johan Commelin , Heather Macbeth , Adam Topaz

A new, comprehensive approach to inhabitation problems in simply-typed lambda-calculus is shown, dealing with both decision and counting problems. This approach works by exploiting a representation of the search space generated by a given…

Logic in Computer Science · Computer Science 2017-03-14 José Espírito Santo , Ralph Matthes , Luís Pinto

We prove the finiteness of relative log pluricanonical representations in the complex analytic setting. As an application, we discuss the abundance conjecture for semi-log canonical pairs within this framework. Furthermore, we establish the…

Algebraic Geometry · Mathematics 2025-06-03 Osamu Fujino

The reconstruction of phylogenies from DNA or protein sequences is a major task of computational evolutionary biology. Common phenomena, notably variations in mutation rates across genomes and incongruences between gene lineage histories,…

Probability · Mathematics 2012-11-30 Elchanan Mossel , Sebastien Roch

There is a growing gap between the impressive results of deep image generative models and classical algorithms that offer theoretical guarantees. The former suffer from mode collapse or memorization issues, limiting their application to…

Machine Learning · Statistics 2023-06-02 Florentin Guth , Etienne Lempereur , Joan Bruna , Stéphane Mallat

We find an abundance of Cremer Julia sets of an arbitrarily high computational complexity.

Dynamical Systems · Mathematics 2019-10-08 Artem Dudko , Michael Yampolsky

In this chapter we provide an overview of computational modeling for semantic change using large and semi-large textual corpora. We aim to provide a key for the interpretation of relevant methods and evaluation techniques, and also provide…

Computation and Language · Computer Science 2023-04-14 Nina Tahmasebi , Haim Dubossarsky

Bi-clustering is a useful approach in analyzing biological data when observations come from heterogeneous groups and have a large number of features. We outline a general Bayesian approach in tackling bi-clustering problems in moderate to…

Applications · Statistics 2021-02-11 Han Yan , Jiexing Wu , Yang Li , Jun S. Liu

In this paper, we investigate the proof complexity of a wide range of substructural systems. For any proof system $\mathbf{P}$ at least as strong as Full Lambek calculus, $\mathbf{FL}$, and polynomially simulated by the extended Frege…

Logic · Mathematics 2020-08-21 Raheleh Jalali

Causal models are playing an increasingly important role in machine learning, particularly in the realm of explainable AI. We introduce a conceptualisation for generating argumentation frameworks (AFs) from causal models for the purpose of…

Artificial Intelligence · Computer Science 2022-05-25 Antonio Rago , Pietro Baroni , Francesca Toni

Computational Logic is the use of computers to establish facts in a logical formalism. Originating in 19th-century attempts to understand the nature of mathematical reasoning, the subject now comprises a wide variety of formalisms,…

Logic in Computer Science · Computer Science 2018-11-14 Lawrence C Paulson

A proof is one of the most important concepts of mathematics. However, there is a striking difference between how a proof is defined in theory and how it is used in practice. This puts the unique status of mathematics as exact science into…

In many high-dimensional problems,polynomial-time algorithms fall short of achieving the statistical limits attainable without computational constraints. A powerful approach to probe the limits of polynomial-time algorithms is to study the…

Statistics Theory · Mathematics 2025-07-11 Bertrand Even , Christophe Giraud , Nicolas Verzelen

We axiomatize the molecular-biology reasoning style, show compliance of the standard reference: Ptashne, A Genetic Switch, and present proof-theory-induced technologies to help infer phenotypes and to predict life cycles from genotypes. The…

Other Quantitative Biology · Quantitative Biology 2019-03-19 René Vestergaard , Emmanuel Pietriga

Error-correcting codes and related combinatorial constructs play an important role in several recent (and old) results in computational complexity theory. In this paper we survey results on locally-testable and locally-decodable…

Computational Complexity · Computer Science 2007-07-13 Luca Trevisan

Understanding large molecular networks consisting of entities such as genes, proteins or RNAs that interact in complex ways to drive the cellular machinery has been an active focus of systems biology. Computational approaches have played a…

Molecular Networks · Quantitative Biology 2013-04-23 Sriganesh Srihari , Mark A. Ragan

Provided that there is no theoretical frame for complex engineered systems (CES) as yet, this paper claims that bio-inspired engineering can help provide such a frame. Within CES bio-inspired systems play a key role. The disclosure from…

Other Computer Science · Computer Science 2011-10-18 Nelson Alfonso Gómez-Cruz , Carlos Eduardo Maldonado

Growth in both size and complexity of modern data challenges the applicability of traditional likelihood-based inference. Composite likelihood (CL) methods address the difficulties related to model selection and computational intractability…

Statistics Theory · Mathematics 2017-09-12 Zhendong Huang , Davide Ferrari