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## Applied stochastic Eigen-analysis

Fonte: Massachusetts Institute of Technology
Publicador: Massachusetts Institute of Technology

Tipo: Tese de Doutorado
Formato: 200, [3] leaves

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#Electrical Engineering and Computer Science.#/Woods Hole Oceanographic Institution. Joint Program in Applied Ocean Science and Engineering.#Woods Hole Oceanographic Institution.#Stochastic analysis#Mathematical models

The first part of the dissertation investigates the application of the theory of large random matrices to high-dimensional inference problems when the samples are drawn from a multivariate normal distribution. A longstanding problem in sensor array processing is addressed by designing an estimator for the number of signals in white noise that dramatically outperforms that proposed by Wax and Kailath. This methodology is extended to develop new parametric techniques for testing and estimation. Unlike techniques found in the literature, these exhibit robustness to high-dimensionality, sample size constraints and eigenvector misspecification. By interpreting the eigenvalues of the sample covariance matrix as an interacting particle system, the existence of a phase transition phenomenon in the largest ("signal") eigenvalue is derived using heuristic arguments. This exposes a fundamental limit on the identifiability of low-level signals due to sample size constraints when using the sample eigenvalues alone. The analysis is extended to address a problem in sensor array processing, posed by Baggeroer and Cox, on the distribution of the outputs of the Capon-MVDR beamformer when the sample covariance matrix is diagonally loaded.; (cont.) The second part of the dissertation investigates the limiting distribution of the eigenvalues and eigenvectors of a broader class of random matrices. A powerful method is proposed that expands the reach of the theory beyond the special cases of matrices with Gaussian entries; this simultaneously establishes a framework for computational (non-commutative) "free probability" theory. The class of "algebraic" random matrices is defined and the generators of this class are specified. Algebraicity of a random matrix sequence is shown to act as a certificate of the computability of the limiting eigenvalue distribution and...

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## Field computation and nonpropositional knowledge

Fonte: Monterey, California. Naval Postgraduate School
Publicador: Monterey, California. Naval Postgraduate School

Tipo: Relatório

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#STATISTICS--COMPUTER SIMULATION.#Neurocomputers, neural network? optical computers, molecular
computers, field computers, universal field computer, associative
memory, parallel processing, massive parallelism

Most current AI technology has been based on propositionally represented theoretical knowledge. It is argued that if AI is to accomplish its goals, especially in the tasks of sensory interpretation and sensorimotor coordination, then it must solve the problem of representing embodied practical knowledge. Biological evidence shows that animals use this knowledge in a way very different form digital computation. This suggests that if these problems are to be solved, then we will need a new breed of computers, which we call field computers. Examples of field computers are: neurocomputers, optical computers, molecular computers, and any kind of massively parallel analog computer. The author claims that the principle characteristic of all these computers is their massive parallelism, but we use this term in a special way. He argues that true massive parallelism comes when the number of processors is so large that it can be considered a continuous quantity. Designing and programming these computers requires a new theory of computation, one version of which is presented in this paper. Described is a universal field computer, that is, a field computer that can emulate any other field computer. It is based on a generalization of Taylor's theorem to continuous dimensional vector spaces. A number of field computations are illustrated...

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## Unification modulo a partial theory of exponentiation

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 22/12/2010
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Modular exponentiation is a common mathematical operation in modern
cryptography. This, along with modular multiplication at the base and exponent
levels (to different moduli) plays an important role in a large number of key
agreement protocols. In our earlier work, we gave many decidability as well as
undecidability results for multiple equational theories, involving various
properties of modular exponentiation. Here, we consider a partial subtheory
focussing only on exponentiation and multiplication operators. Two main results
are proved. The first result is positive, namely, that the unification problem
for the above theory (in which no additional property is assumed of the
multiplication operators) is decidable. The second result is negative: if we
assume that the two multiplication operators belong to two different abelian
groups, then the unification problem becomes undecidable.; Comment: In Proceedings UNIF 2010, arXiv:1012.4554

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## Improving circuit miniaturization and its efficiency using Rough Set Theory

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 10/12/2013
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High-speed, accuracy, meticulousness and quick response are notion of the
vital necessities for modern digital world. An efficient electronic circuit
unswervingly affects the maneuver of the whole system. Different tools are
required to unravel different types of engineering tribulations. Improving the
efficiency, accuracy and low power consumption in an electronic circuit is
always been a bottle neck problem. So the need of circuit miniaturization is
always there. It saves a lot of time and power that is wasted in switching of
gates, the wiring-crises is reduced, cross-sectional area of chip is reduced,
the number of transistors that can implemented in chip is multiplied many
folds. Therefore to trounce with this problem we have proposed an Artificial
intelligence (AI) based approach that make use of Rough Set Theory for its
implementation. Theory of rough set has been proposed by Z Pawlak in the year
1982. Rough set theory is a new mathematical tool which deals with uncertainty
and vagueness. Decisions can be generated using rough set theory by reducing
the unwanted and superfluous data. We have condensed the number of gates
without upsetting the productivity of the given circuit. This paper proposes an
approach with the help of rough set theory which basically lessens the number
of gates in the circuit...

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## Quantum Set Theory Extending the Standard Probabilistic Interpretation of Quantum Theory (Extended Abstract)

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 29/12/2014
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The notion of equality between two observables will play many important roles
in foundations of quantum theory. However, the standard probabilistic
interpretation based on the conventional Born formula does not give the
probability of equality relation for a pair of arbitrary observables, since the
Born formula gives the probability distribution only for a commuting family of
observables. In this paper, quantum set theory developed by Takeuti and the
present author is used to systematically extend the probabilistic
interpretation of quantum theory to define the probability of equality relation
for a pair of arbitrary observables. Applications of this new interpretation to
measurement theory are discussed briefly.; Comment: In Proceedings QPL 2014, arXiv:1412.8102

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## Quantum Gauge Field Theory in Cohesive Homotopy Type Theory

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 31/07/2014
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We implement in the formal language of homotopy type theory a new set of
axioms called cohesion. Then we indicate how the resulting cohesive homotopy
type theory naturally serves as a formal foundation for central concepts in
quantum gauge field theory. This is a brief survey of work by the authors
developed in detail elsewhere.; Comment: In Proceedings QPL 2012, arXiv:1407.8427

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## Ground interpolation for the theory of equality

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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Theory interpolation has found several successful applications in model
checking. We present a novel method for computing interpolants for ground
formulas in the theory of equality. The method produces interpolants from
colored congruence graphs representing derivations in that theory. These graphs
can be produced by conventional congruence closure algorithms in a
straightforward manner. By working with graphs, rather than at the level of
individual proof steps, we are able to derive interpolants that are pleasingly
simple (conjunctions of Horn clauses) and smaller than those generated by other
tools. Our interpolation method can be seen as a theory-specific implementation
of a cooperative interpolation game between two provers. We present a generic
version of the interpolation game, parametrized by the theory T, and define a
general method to extract runs of the game from proofs in T and then generate
interpolants from these runs.

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## Recognizing Speech in a Novel Accent: The Motor Theory of Speech Perception Reframed

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 20/09/2013
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#Computer Science - Computation and Language#Computer Science - Learning#Quantitative Biology - Neurons and Cognition

The motor theory of speech perception holds that we perceive the speech of
another in terms of a motor representation of that speech. However, when we
have learned to recognize a foreign accent, it seems plausible that recognition
of a word rarely involves reconstruction of the speech gestures of the speaker
rather than the listener. To better assess the motor theory and this
observation, we proceed in three stages. Part 1 places the motor theory of
speech perception in a larger framework based on our earlier models of the
adaptive formation of mirror neurons for grasping, and for viewing extensions
of that mirror system as part of a larger system for neuro-linguistic
processing, augmented by the present consideration of recognizing speech in a
novel accent. Part 2 then offers a novel computational model of how a listener
comes to understand the speech of someone speaking the listener's native
language with a foreign accent. The core tenet of the model is that the
listener uses hypotheses about the word the speaker is currently uttering to
update probabilities linking the sound produced by the speaker to phonemes in
the native language repertoire of the listener. This, on average, improves the
recognition of later words. This model is neutral regarding the nature of the
representations it uses (motor vs. auditory). It serve as a reference point for
the discussion in Part 3...

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## The equivalence of the torus and the product of two circles in homotopy type theory

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 13/10/2015
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Homotopy type theory is a new branch of mathematics which merges insights
from abstract homotopy theory and higher category theory with those of logic
and type theory. It allows us to represent a variety of mathematical objects as
basic type-theoretic constructions, higher inductive types. We present a proof
that in homotopy type theory, the torus is equivalent to the product of two
circles. This result indicates that the synthetic definition of torus as a
higher inductive type is indeed correct.

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## Inductive types in homotopy type theory

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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Homotopy type theory is an interpretation of Martin-L\"of's constructive type
theory into abstract homotopy theory. There results a link between constructive
mathematics and algebraic topology, providing topological semantics for
intensional systems of type theory as well as a computational approach to
algebraic topology via type theory-based proof assistants such as Coq.
The present work investigates inductive types in this setting. Modified rules
for inductive types, including types of well-founded trees, or W-types, are
presented, and the basic homotopical semantics of such types are determined.
Proofs of all results have been formally verified by the Coq proof assistant,
and the proof scripts for this verification form an essential component of this
research.; Comment: 19 pages; v2: added references and acknowledgements, removed appendix
with Coq README file, updated URL for Coq files. To appear in the proceedings
of LICS 2012

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## Teaching Wireless Sensor Networks: An Holistic Approach Bridging Theory and Practice at the Master Level

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 09/10/2013
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Wireless Sensor Networks (WSNs) are a new technology that has received a
substantial attention from several academic research fields in the last years.
There are many applications of WSNs, including environmental monitoring,
industrial automation, intelligent transportation systems, healthcare and
wellbeing, smart energy, to mention a few. Courses have been introduced both at
the PhD and at the Master levels. However, these existing courses focus on
particular aspects of WSNs (Networking, or Signal Processing, or Embedded
Software), whereas WSNs encompass disciplines traditionally separated in
Electrical Engineering and Computer Sciences. This paper gives two original
contributions: the essential knowledge that should be brought in a WSNs course
is characterized, and a course structure with an harmonious holistic approach
is proposed. A method based on both theory and experiments is illustrated for
the design of this course, whereby the students have hands-on to implement,
understand, and develop in practice the implications of theoretical concepts.
Theory and applications are thus considered all together. Ultimately, the
objective of this paper is to design a new course, to use innovative hands-on
experiments to illustrate the theoretical concepts in the course...

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## Morphoid Type Theory

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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Morphoid type theory is a typed foundation for mathematics in which each type
is associated with an equality relation in correspondence with the standard
notions of isomorphism in mathematics. The main result is an abstraction
theorem stating that isomorphic objects are substitutable in well typed
contexts. A corollary is "Voldemort's theorem" stating that a non-canonical
object, like a point on a circle, or an isomorphism between a finite
dimensional vector space and its dual, cannot be named by a well typed
expression.
Morphoid type theory seems different from the recently developed homotopy
type theory (HOTT). Morphoid type theory is classical and extensional while
HOTT is constructive and intensional. Morphoid type theory does not involve
homotopy theory. Morphoids are technically quite different from the infinity
groupoids of HOTT.

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## Higher-Order Termination: from Kruskal to Computability

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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Termination is a major question in both logic and computer science. In logic,
termination is at the heart of proof theory where it is usually called strong
normalization (of cut elimination). In computer science, termination has always
been an important issue for showing programs correct. In the early days of
logic, strong normalization was usually shown by assigning ordinals to
expressions in such a way that eliminating a cut would yield an expression with
a smaller ordinal. In the early days of verification, computer scientists used
similar ideas, interpreting the arguments of a program call by a natural
number, such as their size. Showing the size of the arguments to decrease for
each recursive call gives a termination proof of the program, which is however
rather weak since it can only yield quite small ordinals. In the sixties, Tait
invented a new method for showing cut elimination of natural deduction, based
on a predicate over the set of terms, such that the membership of an expression
to the predicate implied the strong normalization property for that expression.
The predicate being defined by induction on types, or even as a fixpoint, this
method could yield much larger ordinals. Later generalized by Girard under the
name of reducibility or computability candidates...

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## A Theory of Computation Based on Quantum Logic (I)

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 29/03/2004
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The (meta)logic underlying classical theory of computation is Boolean
(two-valued) logic. Quantum logic was proposed by Birkhoff and von Neumann as a
logic of quantum mechanics more than sixty years ago. The major difference
between Boolean logic and quantum logic is that the latter does not enjoy
distributivity in general. The rapid development of quantum computation in
recent years stimulates us to establish a theory of computation based on
quantum logic. The present paper is the first step toward such a new theory and
it focuses on the simplest models of computation, namely finite automata. It is
found that the universal validity of many properties of automata depend heavily
upon the distributivity of the underlying logic. This indicates that these
properties does not universally hold in the realm of quantum logic. On the
other hand, we show that a local validity of them can be recovered by imposing
a certain commutativity to the (atomic) statements about the automata under
consideration. This reveals an essential difference between the classical
theory of computation and the computation theory based on quantum logic.

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## Negotiating over Bundles and Prices Using Aggregate Knowledge

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 23/12/2004
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Combining two or more items and selling them as one good, a practice called
bundling, can be a very effective strategy for reducing the costs of producing,
marketing, and selling goods. In this paper, we consider a form of multi-issue
negotiation where a shop negotiates both the contents and the price of bundles
of goods with his customers. We present some key insights about, as well as a
technique for, locating mutually beneficial alternatives to the bundle
currently under negotiation. The essence of our approach lies in combining
historical sales data, condensed into aggregate knowledge, with current data
about the ongoing negotiation process, to exploit these insights. In
particular, when negotiating a given bundle of goods with a customer, the shop
analyzes the sequence of the customer's offers to determine the progress in the
negotiation process. In addition, it uses aggregate knowledge concerning
customers' valuations of goods in general. We show how the shop can use these
two sources of data to locate promising alternatives to the current bundle.
When the current negotiation's progress slows down, the shop may suggest the
most promising of those alternatives and, depending on the customer's response,
continue negotiating about the alternative bundle...

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## Evolutionary Socioeconomics: a Schumpeterian Computer Simulation

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 23/04/2006
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#Computer Science - Computer Science and Game Theory#Computer Science - Computers and Society#K.4.0#J.4#I.6.3

The following note contains a computer simulation concerning the struggle
between two companies: the first one is "the biggest zaibatsu of all", while
the second one is "small, fast, ruthless". The model is based on a
neo-Schumpeterian framework operating in a Darwinian evolutionary environment.
After running the program a large number of times, two characteristics stand
out: -- There is always a winner which takes it all, while the loser
disappears. -- The key to success is the ability to employ efficiently the
technological innovations. The topic of the present paper is strictly related
with the content of the following notes: Michele Tucci, Evolution and
Gravitation: a Computer Simulation of a Non-Walrasian Equilibrium Model;
Michele Tucci, Oligopolistic Competition in an Evolutionary Environment: a
Computer Simulation. The texts can be downloaded respectively at the following
addresses: http://arxiv.org/abs/cs.CY/0209017
http://arxiv.org/abs/cs.CY/0501037 These references include some preliminary
considerations regarding the comparison between the evolutionary and the
gravitational paradigms and the evaluation of approaches belonging to rival
schools of economic thought.; Comment: PDF, 15 pages, 5 graphs

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## A Proposal To Support Wellbeing in People With Borderline Personality Disorder: Applying Reminiscent Theory in a Mobile App

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 21/02/2013
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In this paper the research draws upon reminiscence therapy, which is used in
treating dementia, as an applied theory to promote well being in people who
experience low moods. The application proposed here aims to promote wellbeing
for people suffering from mood disorders and dementia but could potentially be
used to enhance wellbeing for many types of users. Use of the application is
anticipated to improve mood in a group of users where severe emotional problems
are prevalent. The research aims to evaluate the effectiveness of a
reminiscence based application in promoting well being in people specifically
with Borderline Personality Disorder (BPD). The long term objective of this
research is to establish the effectiveness of reminiscence theory on user
groups aside from dementia, particularly other mental illnesses. The research
advocates involving end users within the design process both to inform and
evaluate the development of a mobile and tablet application.; Comment: Conference paper

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## 2006: Celebrating 75 years of AI - History and Outlook: the Next 25 Years

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 31/08/2007
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When Kurt Goedel layed the foundations of theoretical computer science in
1931, he also introduced essential concepts of the theory of Artificial
Intelligence (AI). Although much of subsequent AI research has focused on
heuristics, which still play a major role in many practical AI applications, in
the new millennium AI theory has finally become a full-fledged formal science,
with important optimality results for embodied agents living in unknown
environments, obtained through a combination of theory a la Goedel and
probability theory. Here we look back at important milestones of AI history,
mention essential recent results, and speculate about what we may expect from
the next 25 years, emphasizing the significance of the ongoing dramatic
hardware speedups, and discussing Goedel-inspired, self-referential,
self-improving universal problem solvers.; Comment: 14 pages; preprint of invited contribution to the Proceedings of the
``50th Anniversary Summit of Artificial Intelligence'' at Monte Verita,
Ascona, Switzerland, 9-14 July 2006

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## Models and termination of proof-reduction in the $\lambda$$\Pi$-calculus modulo theory

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 26/01/2015
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We define a notion of model for the $\lambda \Pi$-calculus modulo theory, a
notion of super-consistent theory, and prove that proof-reduction terminates in
the $\lambda \Pi$-calculus modulo a super-consistent theory. We prove this way
the termination of proof-reduction in two theories in the $\lambda
\Pi$-calculus modulo theory, and their consistency: an embedding of Simple type
theory and an embedding of the Calculus of constructions.

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## The selection monad as a CPS transformation

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 20/03/2015
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A computation in the continuation monad returns a final result given a
continuation, ie. it is a function with type $(X \to R) \to R$. If we instead
return the intermediate result at $X$ then our computation is called a
selection function. Selection functions appear in diverse areas of mathematics
and computer science (especially game theory, proof theory and topology) but
the existing literature does not heavily emphasise the fact that the selection
monad is a CPS translation. In particular it has so far gone unnoticed that the
selection monad has a call/cc-like operator with interesting similarities and
differences to the usual call/cc, which we explore experimentally using
Haskell.
Selection functions can be used whenever we find the intermediate result more
interesting than the final result. For example a SAT solver computes an
assignment to a boolean function, and then its continuation decides whether it
is a satisfying assignment, and we find the assignment itself more interesting
than the fact that it is or is not satisfying. In game theory we find the move
chosen by a player more interesting than the outcome that results from that
move. The author and collaborators are developing a theory of games in which
selection functions are viewed as generalised notions of rationality...

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