153 research outputs found
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
Artificial Intelligence for Science in Quantum, Atomistic, and Continuum Systems
Advances in artificial intelligence (AI) are fueling a new paradigm of
discoveries in natural sciences. Today, AI has started to advance natural
sciences by improving, accelerating, and enabling our understanding of natural
phenomena at a wide range of spatial and temporal scales, giving rise to a new
area of research known as AI for science (AI4Science). Being an emerging
research paradigm, AI4Science is unique in that it is an enormous and highly
interdisciplinary area. Thus, a unified and technical treatment of this field
is needed yet challenging. This work aims to provide a technically thorough
account of a subarea of AI4Science; namely, AI for quantum, atomistic, and
continuum systems. These areas aim at understanding the physical world from the
subatomic (wavefunctions and electron density), atomic (molecules, proteins,
materials, and interactions), to macro (fluids, climate, and subsurface) scales
and form an important subarea of AI4Science. A unique advantage of focusing on
these areas is that they largely share a common set of challenges, thereby
allowing a unified and foundational treatment. A key common challenge is how to
capture physics first principles, especially symmetries, in natural systems by
deep learning methods. We provide an in-depth yet intuitive account of
techniques to achieve equivariance to symmetry transformations. We also discuss
other common technical challenges, including explainability,
out-of-distribution generalization, knowledge transfer with foundation and
large language models, and uncertainty quantification. To facilitate learning
and education, we provide categorized lists of resources that we found to be
useful. We strive to be thorough and unified and hope this initial effort may
trigger more community interests and efforts to further advance AI4Science
Fibonacci primes, primes of the form and beyond
We speculate on the distribution of primes in exponentially growing, linear
recurrence sequences in the integers. By tweaking a heuristic
which is successfully used to predict the number of prime values of
polynomials, we guess that either there are only finitely many primes , or
else there exists a constant (which we can give good approximations to)
such that there are primes with , as . We compare our conjecture to the limited amount of data that we can
compile.Comment: v2; replace earlier draft inadvertently submitted as v
Security and Privacy for the Modern World
The world is organized around technology that does not respect its users. As a precondition of participation in digital life, users cede control of their data to third-parties with murky motivations, and cannot ensure this control is not mishandled or abused. In this work, we create secure, privacy-respecting computing for the average user by giving them the tools to guarantee their data is shielded from prying eyes. We first uncover the side channels present when outsourcing scientific computation to the cloud, and address them by building a data-oblivious virtual environment capable of efficiently handling these workloads. Then, we explore stronger privacy protections for interpersonal communication through practical steganography, using it to hide sensitive messages in realistic cover distributions like English text. Finally, we discuss at-home cryptography, and leverage it to bind a user’s access to their online services and important files to a secure location, such as their smart home. This line of research represents a new model of digital life, one that is both full-featured and protected against the security and privacy threats of the modern world
A Stochastic Analysis Approach to Tensor Field Theories
We present two different arguments using stochastic analysis to construct
super-renormalizable tensor field theories, namely the and
models. The first approach is the construction of a Langevin
dynamic combined with a PDE energy estimate while the second is an application
of the variational approach of Barashkov and Gubinelli. By leveraging the
melonic structure of divergences, regularising properties of non-local
products, and controlling certain random operators, we demonstrate that for
tensor field theories these arguments can be significantly simplified in
comparison to what is required for models
Essence and Necessity
What is the relation between metaphysical necessity and essence? This paper defends
the view that the relation is one of identity: metaphysical necessity is a special case
of essence. My argument consists in showing that the best joint theory of essence and
metaphysical necessity is one in which metaphysical necessity is just a special case of
essence. The argument is made against the backdrop of a novel, higher-order logic of
essence (HLE), whose core features are introduced in the first part of the paper. The
second part investigates the relation between metaphysical necessity and essence in the
context of HLE. Reductive hypotheses are among the most natural hypotheses to be
explored in the context of HLE. But they also have to be weighed against their nonreductive
rivals. I investigate three different reductive hypotheses and argue that two
of them fare better than their non-reductive rivals: they are simpler, more natural, and
more systematic. Specifically, I argue that one candidate reduction, according to which
metaphysical necessity is truth in virtue of the nature of all propositions, is superior to the
others, including one proposed by Kit Fine, according to which metaphysical necessity is
truth in virtue of the nature of all objects. The paper concludes by offering some reasons
to think that the best joint theory of essence and metaphysical necessity is one in which
the logic of metaphysical necessity includes S4, but not S5
LIPIcs, Volume 248, ISAAC 2022, Complete Volume
LIPIcs, Volume 248, ISAAC 2022, Complete Volum
Logic, ontology, and arithmetic : a study of the development of Bertrand Russell’s Mathematical Philosophy from The Principles of Mathematics to Principia Mathematica
O presente trabalho tem por objeto de análise o desenvolvimento da Filosofia Matemática de Bertrand Russell desde os Principles of Mathematics até e inlcuindo a primeira edição de Principia Mathematica, tendo como fio condutor as mudanças no pensamento de Russell com respeito a três tópicos interligados, a saber: (1) a concepção de Russell da Lógica enquanto uma ciência (2) os compromissos ontológicos da Lógica e (3) a tese Russelliana de que a Matemática Pura a Aritmética particular é nada mais do que um ramo da Lógica. Esses três tópicos interligados formam um fio condutor que seguimos na tese para avaliar qual interpretação fornece o melhor relato da evidência textual disponível em Principia Mathematica e nos manuscritos produzidos por Russell no período relevante. A posição geral defendida é que a interpretação de Gregory Landini apresenta argumentos decisivos contra a ortodoxia de comentadores que atribuem à Principia uma hierarquia de tipos ramificada de entidades confusamente formulada, e mostramos que os três pontos apontados acima que formam o fio condutor da tese corroboram fortemente a interpretação de Landini. Os resultados que apontam para a conclusão geral de nossa investigação estão apresentados na tese dividida em duas partes. A primeira parte discute o desenvolvimento da lógica de concepção de Russell e do projeto Logicista desde sua gênese e nos Principles of Mathematics até Principia Mathematica. Esta primeira parte define o contexto para a segunda, que discute a Lógica Russeliana e o Logicismo em sua versão madura apresentada em Principia. Mostramos que, ao fim e ao cabo, o a teoria Lógica e a forma da tese Logicista apresentada em Principia é o resultado do longo processo iniciado com descoberta da Teoria dos Símbolos Incompletos que levou Russell a gradualmente reduzir os compromissos ontológicos de sua concepção da Lógica enquanto uma ciência, culminando na teoria apresentada na Introdução de Principia, na qual ele procura formular uma hierarquia dos tipos que evita o compromisso ontológico com classes, proposições e também com as assim chamadas funções proposicionais e que esse mesmo processo levou Russell a uma concepção da tese de Logicista de acordo com a qual a Matemática é uma ciência cujos compromissos ontológicos não incluem qualquer espécie de objetos (no sentido Fregeano) sejam eles particulares concretos ou abstratos.The present work has as its object of analysis the development of Bertrand Russell’s Mathematical Philosophy from the Principles of Mathematics up to and including the first edition of Principia Mathematica, having as a guiding thread the changes in Russell’s thought with respect to three interconnected topics, namely: (1) Russell’s conception of Logic as a science (2) the ontological commitments of Logic and (3) Russell’s thesis that Pure Mathematics in particular Arithmetic is nothing more than a branch of Logic. These three interconnected topics form a common thread that we follow in the dissertation to assess which interpretation offers the best account of the available textual evidence in Principia Mathematica and in the manuscripts produced by Russell in the relevant period. The general position held is that Gregory Landini’s interpretation presents decisive arguments against the orthodoxy of commentators who attribute to Principia a confusingly formulated hierarchy of ramfified types of entities, and we show that the three points indicated out above that form the main thread of the thesis strongly corroborate Landini’s interpretation. The results that point to the general conclusion of our investigation are stated in the dissertation divided into two parts. The first part discusses the development of Russell’s conception of Logic and the of Logicist project from its genesis and in Principles of Mathematics up to Principia Mathematica. This first part sets the context for a second, which discusses a Russellian Logic and Logicism in its mature version presented in Principia. We show that, in the end, the Logic theory and the form of the Logicist thesis presented in Principia is the result of a long process that started with the discovery of the theory of Incomplete Symbols which led Russell to reduce the ontological commitments of his conception of Logic as a science, culminating in the theory of types presented in Principia’s Introduction, in which Russell seeks to formulate a hierarchy of types that avoids the ontological commitment to classes, propositions and also with socalled propositional functions, and that this same process led Russell to a conception of the Logicist thesis according to Mathematics is a science with no ontological commitments to any kind of objects (in the Fregean sense) whether these are conceived as concrete or abstract particulars
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