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## Higher-Order Decision Theory

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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Classical decision theory models behaviour in terms of utility maximisation
where utilities represent rational preference relations over outcomes. However,
empirical evidence and theoretical considerations suggest that we need to go
beyond this framework. We propose to represent goals by higher-order functions
or operators that take other functions as arguments where the max and argmax
operators are special cases. Our higher-order functions take a context function
as their argument where a context represents a process from actions to
outcomes. By that we can define goals being dependent on the actions and the
process in addition to outcomes only. This formulation generalises outcome
based preferences to context-dependent goals. We show how to uniformly
represent within our higher-order framework classical utility maximisation but
also various other extensions that have been debated in economics.; Comment: arXiv admin note: text overlap with arXiv:1409.7411

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## A general theory of equilibrium behavior

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 04/04/2013
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Economists were content with the concept of the Nash equilibrium as game
theory's solution concept until Daskalakis, Goldberg, and Papadimitriou showed
that finding a Nash equilibrium is most likely a computationally hard problem,
a result that set off a deep scientific crisis. Motivated, in part, by their
result, in this paper, we propose a general theory of equilibrium behavior in
vector fields (and, therefore, also noncooperative games). Our line of
discourse is to show that these universal in nature mathematical objects are
endowed with significant structure, which we probe to unearth atypical,
previously unidentified, equilibrium behavior.

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## The nature of individual choice: a formalism for utility function based on set theory

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 26/10/2010
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In the theory of social choice the research is focused around the projection
of individual preference orders to the social preference order. Also, the
justification of the preference order formalism begins with the concept of
utility i.e. an alternative is preferred to another one if the utility over the
first is higher then the utility over the second. In this paper is proposed an
ideal model of measuring utilities by considering individuals and alternatives
no more as atomic concepts but as being composed by other entities. Furthermore
is proposed a formal definition of evaluation processes based on utilities.

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## Stability of Mixed-Strategy-Based Iterative Logit Quantal Response Dynamics in Game Theory

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 14/10/2013
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Using the Logit quantal response form as the response function in each step,
the original definition of static quantal response equilibrium (QRE) is
extended into an iterative evolution process. QREs remain as the fixed points
of the dynamic process. However, depending on whether such fixed points are the
long-term solutions of the dynamic process, they can be classified into stable
(SQREs) and unstable (USQREs) equilibriums. This extension resembles the
extension from static Nash equilibriums (NEs) to evolutionary stable solutions
in the framework of evolutionary game theory. The relation between SQREs and
other solution concepts of games, including NEs and QREs, is discussed. Using
experimental data from other published papers, we perform a preliminary
comparison between SQREs, NEs, QREs and the observed behavioral outcomes of
those experiments. For certain games, we determine that SQREs have better
predictive power than QREs and NEs.

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## A Decidable Theory of Skiplists of Unbounded Size and Arbitrary Height

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 18/01/2013
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This paper presents a theory of skiplists of arbitrary height, and shows
decidability of the satisfiability problem for quantifier-free formulas.
A skiplist is an imperative software data structure that implements sets by
maintaining several levels of ordered singly-linked lists in memory, where each
level is a sublist of its lower levels. Skiplists are widely used in practice
because they offer a performance comparable to balanced binary trees, and can
be implemented more efficiently. To achieve this performance, most
implementations dynamically increment the height (the number of levels).
Skiplists are difficult to reason about because of the dynamic size (number of
nodes) and the sharing between the different layers. Furthermore, reasoning
about dynamic height adds the challenge of dealing with arbitrary many levels.
The first contribution of this paper is the theory TSL that allows to express
the heap memory layout of a skiplist of arbitrary height. The second
contribution is a decision procedure for the satisfiability prob- lem of
quantifier-free TSL formulas. The last contribution is to illustrate the formal
verification of a practical skiplist implementation using this decision
procedure.; Comment: 25 pages

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## Steps towards a theory and calculus of aliasing

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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#Computer Science - Software Engineering#Computer Science - Programming Languages#D.1.5#D.2.4#F.3.1#F.3.2#F.3.3#F.3.1#F.4.1

A theory, graphical notation, mathematical calculus and implementation for
finding whether two given expressions can, at execution time, denote references
attached to the same object. Intended as the basis for a comprehensive solution
to the "frame problem" and as a complement to, or even a replacement for,
separation logic, shape analysis, ownership types and dynamic frames.; Comment: Revision of original JOT paper. To appear in IJSI (International
Journal of Software and Informatics) in 2011. The original title was: The
theory and calculus of aliasing

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## On CSP and the Algebraic Theory of Effects

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 30/07/2010
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We consider CSP from the point of view of the algebraic theory of effects,
which classifies operations as effect constructors or effect deconstructors; it
also provides a link with functional programming, being a refinement of Moggi's
seminal monadic point of view. There is a natural algebraic theory of the
constructors whose free algebra functor is Moggi's monad; we illustrate this by
characterising free and initial algebras in terms of two versions of the stable
failures model of CSP, one more general than the other. Deconstructors are
dealt with as homomorphisms to (possibly non-free) algebras.
One can view CSP's action and choice operators as constructors and the rest,
such as concealment and concurrency, as deconstructors. Carrying this programme
out results in taking deterministic external choice as constructor rather than
general external choice. However, binary deconstructors, such as the CSP
concurrency operator, provide unresolved difficulties. We conclude by
presenting a combination of CSP with Moggi's computational {\lambda}-calculus,
in which the operators, including concurrency, are polymorphic. While the paper
mainly concerns CSP, it ought to be possible to carry over similar ideas to
other process calculi.

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## Homotopy limits in type theory

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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#Mathematics - Logic#Computer Science - Logic in Computer Science#Mathematics - Category Theory#03B70, 55U35#D.2.4#F.4.1

Working in homotopy type theory, we provide a systematic study of homotopy
limits of diagrams over graphs, formalized in the Coq proof assistant. We
discuss some of the challenges posed by this approach to formalizing
homotopy-theoretic material. We also compare our constructions with the more
classical approach to homotopy limits via fibration categories.; Comment: 33 pages; v3: theorem numbering changed since v2 to match journal
version

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## Theory of Programs

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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#Computer Science - Programming Languages#Computer Science - Software Engineering#D.1.4#D.1.5#D.1.3#D.2.1#D.2.4#D.3.1

A general theory of programs, programming and programming languages built up
from a few concepts of elementary set theory. Derives, as theorems, properties
treated as axioms by classic approaches to programming. Covers sequential and
concurrent computation.

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## The Euler-Poincare theory of Metamorphosis

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 04/06/2008
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In the pattern matching approach to imaging science, the process of
``metamorphosis'' is template matching with dynamical templates. Here, we
recast the metamorphosis equations of into the Euler-Poincare variational
framework of and show that the metamorphosis equations contain the equations
for a perfect complex fluid \cite{Ho2002}. This result connects the ideas
underlying the process of metamorphosis in image matching to the physical
concept of order parameter in the theory of complex fluids. After developing
the general theory, we reinterpret various examples, including point set, image
and density metamorphosis. We finally discuss the issue of matching measures
with metamorphosis, for which we provide existence theorems for the initial and
boundary value problems.

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## The Monty Hall Problem in the Game Theory Class

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 01/07/2011
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The basic Monty Hall problem is explored to introduce into the fundamental
concepts of the game theory and to give a complete Bayesian and a
(noncooperative) game-theoretic analysis of the situation. Simple combinatorial
arguments are used to exclude the holding action and to find minimax solutions.; Comment: 18 pages, 1 color figure

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## Preference aggregation theory without acyclicity: The core without majority dissatisfaction

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 03/07/2011
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#Computer Science - Computer Science and Game Theory#Mathematics - Logic#91A12, 91B14 (Primary) 91A13, 91B12 (Secondary)

Acyclicity of individual preferences is a minimal assumption in social choice
theory. We replace that assumption by the direct assumption that preferences
have maximal elements on a fixed agenda. We show that the core of a simple game
is nonempty for all profiles of such preferences if and only if the number of
alternatives in the agenda is less than the Nakamura number of the game. The
same is true if we replace the core by the core without majority
dissatisfaction, obtained by deleting from the agenda all the alternatives that
are non-maximal for all players in a winning coalition. Unlike the core, the
core without majority dissatisfaction depends only on the players' sets of
maximal elements and is included in the union of such sets. A result for an
extended framework gives another sense in which the core without majority
dissatisfaction behaves better than the core.; Comment: 27+3 pages

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## Theory and applications of lattice point methods for binomial ideals

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 14/09/2010
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#Mathematics - Commutative Algebra#Computer Science - Computer Science and Game Theory#Mathematics - Combinatorics#Mathematics - Dynamical Systems#Primary: 05E40, 20M25, 13F99, 20M14, 11P21, 20M15, 33C70, 91A46,
91A05, 80A30, Secondary: 52B20, 20M30, 05A15, 92E20

This survey of methods surrounding lattice point methods for binomial ideals
begins with a leisurely treatment of the geometric combinatorics of binomial
primary decomposition. It then proceeds to three independent applications whose
motivations come from outside of commutative algebra: hypergeometric systems,
combinatorial game theory, and chemical dynamics. The exposition is aimed at
students and researchers in algebra; it includes many examples, open problems,
and elementary introductions to the motivations and background from outside of
algebra.; Comment: 57 pages, 31 figures; to appear in proceedings of 2009 Abel Symposium
(Voss, Norway)

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## Multiplicative Updates in Coordination Games and the Theory of Evolution

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 15/08/2012
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#Computer Science - Computer Science and Game Theory#Quantitative Biology - Populations and Evolution#91A99#F.2.0

We study the population genetics of Evolution in the important special case
of weak selection, in which all fitness values are assumed to be close to one
another. We show that in this regime natural selection is tantamount to the
multiplicative updates game dynamics in a coordination game between genes.
Importantly, the utility maximized in this game, as well as the amount by which
each allele is boosted, is precisely the allele's mixability, or average
fitness, a quantity recently proposed in [1] as a novel concept that is crucial
in understanding natural selection under sex, thus providing a rigorous
demonstration of that insight. We also prove that the equilibria in two-person
coordination games can have large supports, and thus genetic diversity does not
suffer much at equilibrium. Establishing large supports involves answering
through a novel technique the following question: what is the probability that
for a random square matrix A both systems Ax = 1 and A^T y = 1 have positive
solutions? Both the question and the technique may be of broader interest.
[1] A. Livnat, C. Papadimitriou, J. Dushoff, and M.W. Feldman. A mixability
theory for the role of sex in evolution. Proceedings of the National Academy of
Sciences, 105(50):19803-19808...

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## Graph Theory Applications in Network Security

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 15/11/2015
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#Computer Science - Cryptography and Security#Computer Science - Networking and Internet Architecture

Graph theory has become a very critical component in many applications in the
computing field including networking and security. Unfortunately, it is also
amongst the most complex topics to understand and apply.
In this paper, we review some of the key applications of graph theory in
network security. We first cover some algorithmic aspects, then present network
coding and its relation to routing.

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## Why does Deep Learning work? - A perspective from Group Theory

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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#Computer Science - Learning#Computer Science - Neural and Evolutionary Computing#Statistics - Machine Learning

Why does Deep Learning work? What representations does it capture? How do
higher-order representations emerge? We study these questions from the
perspective of group theory, thereby opening a new approach towards a theory of
Deep learning.
One factor behind the recent resurgence of the subject is a key algorithmic
step called pre-training: first search for a good generative model for the
input samples, and repeat the process one layer at a time. We show deeper
implications of this simple principle, by establishing a connection with the
interplay of orbits and stabilizers of group actions. Although the neural
networks themselves may not form groups, we show the existence of {\em shadow}
groups whose elements serve as close approximations.
Over the shadow groups, the pre-training step, originally introduced as a
mechanism to better initialize a network, becomes equivalent to a search for
features with minimal orbits. Intuitively, these features are in a way the {\em
simplest}. Which explains why a deep learning network learns simple features
first. Next, we show how the same principle, when repeated in the deeper
layers, can capture higher order representations, and why representation
complexity increases as the layers get deeper.; Comment: 13 pages...

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## Model Theory of Ultrafinitism I: Fuzzy Initial Segments of Arithmetics

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 20/11/2006
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This article is the first of an intended series of works on the model theory
of Ultrafinitism. It is roughly divided into two parts. The first one addresses
some of the issues related to ultrafinitistic programs, as well as some of the
core ideas proposed thus far. The second part of the paper presents a model of
ultrafinitistic arithmetics based on the notion of fuzzy initial segments of
the standard natural numbers series. We also introduce a proof theory and a
semantics for ultrafinitism through which feasibly consistent theories can be
treated on the same footing as their classically consistent counterparts. We
conclude with a brief sketch of a foundational program, that aims at
reproducing the transfinite within the finite realm.; Comment: 31 pages, Tennenbaum Memorial invited talk

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## Ioco Theory for Probabilistic Automata

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 09/04/2015
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Model-based testing (MBT) is a well-known technology, which allows for
automatic test case generation, execution and evaluation. To test
non-functional properties, a number of test MBT frameworks have been developed
to test systems with real-time, continuous behaviour, symbolic data and
quantitative system aspects. Notably, a lot of these frameworks are based on
Tretmans' classical input/output conformance (ioco) framework. However, a
model-based test theory handling probabilistic behaviour does not exist yet.
Probability plays a role in many different systems: unreliable communication
channels, randomized algorithms and communication protocols, service level
agreements pinning down up-time percentages, etc. Therefore, a probabilistic
test theory is of great practical importance. We present the ingredients for a
probabilistic variant of ioco and define the {\pi}oco relation, show that it
conservatively extends ioco and define the concepts of test case, execution and
evaluation.; Comment: In Proceedings MBT 2015, arXiv:1504.01928

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## Categories of relations as models of quantum theory

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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Categories of relations over a regular category form a family of models of
quantum theory. Using regular logic, many properties of relations over sets
lift to these models, including the correspondence between Frobenius structures
and internal groupoids. Over compact Hausdorff spaces, this lifting gives
continuous symmetric encryption. Over a regular Mal'cev category, this
correspondence gives a characterization of categories of completely positive
maps, enabling the formulation of quantum features. These models are closer to
Hilbert spaces than relations over sets in several respects: Heisenberg
uncertainty, impossibility of broadcasting, and behavedness of rank one
morphisms.; Comment: In Proceedings QPL 2015, arXiv:1511.01181

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## Elements of Game Theory - Part I: Foundations, acts and mechanisms

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 16/06/2015
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In this paper, a gentle introduction to Game Theory is presented in the form
of basic concepts and examples. Minimax and Nash's theorem are introduced as
the formal definitions for optimal strategies and equilibria in zero-sum and
nonzero-sum games. Several elements of cooperative gaming, coalitions, voting
ensembles, voting power and collective efficiency are described in brief.
Analytical (matrix) and extended (tree-graph) forms of game representation is
illustrated as the basic tools for identifying optimal strategies and
"solutions" in games of any kind. Next, a typology of four standard nonzero-sum
games is investigated, analyzing the Nash equilibria and the optimal strategies
in each case. Signaling, stance and third-party intermediates are described as
very important properties when analyzing strategic moves, while credibility and
reputation is described as crucial factors when signaling promises or threats.
Utility is introduced as a generalization of typical cost/gain functions and it
is used to explain the incentives of irrational players under the scope of
"rational irrationality". Finally, a brief reference is presented for several
other more advanced concepts of gaming, including emergence of cooperation,
evolutionary stable strategies...

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