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## A structure-dynamic approach to cortical organization: Number of paths and accessibility

Fonte: ELSEVIER SCIENCE BV
Publicador: ELSEVIER SCIENCE BV

Tipo: Artigo de Revista Científica

ENG

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#Cortical networks#Complex networks#Brain networks#Random walks#COMPLEX BRAIN NETWORKS#CEREBRAL-CORTEX#SMALL-WORLD#CONNECTIVITY#SYSTEM#CAT#Biochemical Research Methods

A structure-dynamic approach to cortical systems is reported which is based on the number of paths and the accessibility of each node. The latter measurement is obtained by performing self-avoiding random walks in the respective networks, so as to simulate dynamics, and then calculating the entropies of the transition probabilities for walks starting from each node. Cortical networks of three species, namely cat, macaque and humans, are studied considering structural and dynamical aspects. It is verified that the human cortical network presents the highest accessibility and number of paths (in terms of z-scores). The correlation between the number of paths and accessibility is also investigated as a mean to quantify the level of independence between paths connecting pairs of nodes in cortical networks. By comparing the cortical networks of cat, macaque and humans, it is verified that the human cortical network tends to present the largest number of independent paths of length larger than four. These results suggest that the human cortical network is potentially the most resilient to brain injures. (C) 2009 Elsevier B.V. All rights reserved.; CNPq[301303/06-1]; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq); CNPq[573583/2008-0]; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq); FAPESP[05/00587-5]; Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP); FAPESP[07/50633-9]; Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

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## Comparação de tecnicas de analise de caminhos de transferencia vibroacusticos; Comparison of techniques for vibro-acoustic transfer path analysis

Fonte: Biblioteca Digital da Unicamp
Publicador: Biblioteca Digital da Unicamp

Tipo: Dissertação de Mestrado
Formato: application/pdf

Publicado em 22/02/2006
PT

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#Acustica - Vibração#Vibração#Ruido aerodinamico#Ruido#Vibro-acoustic#Tranfer paths analysis#Noise#Vibration#Structure-borne noise#Airbone noise#Power flow

Neste trabalho é feita uma comparação de técnicas analíticas e experimentais de Análise de Caminhos de Transferência Vibroacústicos. A Análise de Caminhos de Transferência, ou TPA como é conhecida pela abreviatura em inglês, é uma ferramenta para se avaliar a contribuição de diferentes caminhos de propagação de energia vibroacústica entre uma fonte e um receptor ligados entre si por várias conexões. Uma aplicação típica de TPA é quantificar e determinar a importância relativa desses caminhos numa dada banda de freqüência, verificando-se a contribuição mais significativa para o receptor. Nessa análise, basicamente duas quantidades devem ser obtidas: as forças operacionais em cada caminho de transferência e a Função de Resposta em Freqüência desses caminhos. Essas funções podem ser obtidas tanto experimentalmente quanto analiticamente, considerando-se ou não a impedância mecânica da fonte vibroacústica. As forças operacionais podem ser diretamente obtidas de medições, usando um transdutor de forças, ou indiretamente estimadas a partir de medições auxiliares. Neste trabalho são apresentados dois métodos de obtenção indireta das forças operacionais ? o Método da Rigidez Complexa e o Método da Inversão de Matrizes ? associados com as duas possíveis configurações para determinação das Funções de Resposta em Freqüência ? incluindo e excluindo a impedância da fonte. Essas técnicas são aplicadas a dois modelos: um analítico e um experimental. avaliadas com esse modelo analítico...

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## Trajetos escolares no ensino secundário: efeitos das origens sociais e expectativas dos estudantes

Fonte: Instituto Universitário de Lisboa
Publicador: Instituto Universitário de Lisboa

Tipo: Dissertação de Mestrado

Publicado em //2012
POR

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#Trajeto escolar#Desempenho escolar#Escolhas escolares#Expectativas#School paths#School performance#School choices#Expectations

Mestrado em Sociologia e Planeamento; O presente trabalho tem como objeto de estudo os trajetos sociais e escolares de uma
amostra de 6836 jovens de 568 escolas que foram inquiridos pelo Observatório de Trajetos
dos Estudantes do Ensino Secundário (OTES) ao longo de cinco anos, através da aplicação de
três inquéritos por questionários distintos, em momentos considerados chave no seu trajeto
escolar e profissional.
Pretende-se compreender de que modo as origens sociais influenciam os trajetos vividos
e projetados dos jovens inquiridos, bem como as suas expectativas, respondendo a algumas
questões consideradas fundamentais: que elementos contribuem mais para a definição dos
trajetos escolares e profissionais, e se as representações e expectativas face ao mesmo variam
ao longo do tempo.
Ao longo do presente trabalho os trajetos serão reconstituídos e analisados, desde o
período de entrada no sistema educativo, até ao pós-secundário, sendo abrangidos os casos de
inserção profissional, e/ou no ensino superior.; This work’s main objective is to study school paths from a sample of 6836 youths from
568 schools, which participated in the first cohort of the Observatory of the Paths of
Secondary Education Students (OTES) thought five years...

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## Normal mode paths for hydrogen exchange in the peptide ferrichrome

Fonte: PubMed
Publicador: PubMed

Tipo: Artigo de Revista Científica

Publicado em /09/1983
EN

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Possible paths for exposure to solvent and hydrogen exchange of the amide protons of ferrichrome, a cyclic hexapeptide, are examined. The paths are obtained from calculations of the vibrational normal modes of ferrichrome and correspond to low energy atomic displacements away from the local minimum in the multidimensional conformational space of the molecule. Exposure of exchangeable groups along the normal modes was determined by using the solvent accessible surface area algorithm of Lee and Richards. Three of the exchangeable protons (Gly1,2,3,) are largely exposed to solvent in the x-ray structure while the remaining three exchangeable protons of the ornithines are totally shielded from solvent. A very small number of normal mode displacements are found to expose the Orn2 and Orn3 amide groups while the Orn1 amide proton remains shielded from solvent for all the paths studied. The effective paths for exposure of Orn2 and Orn3 correspond to the lowest frequency (≈18 cm-1) motions. The paths are characterized in terms of the magnitude and energy of atomic displacements, correlated changes in dihedral angles, and the resulting changes in exposure and hydrogen bonding of exchangeable groups.

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## On Leveraging Partial Paths in Partially-Connected Networks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 21/01/2009

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Mobile wireless network research focuses on scenarios at the extremes of the
network connectivity continuum where the probability of all nodes being
connected is either close to unity, assuming connected paths between all nodes
(mobile ad hoc networks), or it is close to zero, assuming no multi-hop paths
exist at all (delay-tolerant networks). In this paper, we argue that a sizable
fraction of networks lies between these extremes and is characterized by the
existence of partial paths, i.e. multi-hop path segments that allow forwarding
data closer to the destination even when no end-to-end path is available. A
fundamental issue in such networks is dealing with disruptions of end-to-end
paths. Under a stochastic model, we compare the performance of the established
end-to-end retransmission (ignoring partial paths), against a forwarding
mechanism that leverages partial paths to forward data closer to the
destination even during disruption periods. Perhaps surprisingly, the
alternative mechanism is not necessarily superior. However, under a stochastic
monotonicity condition between current v.s. future path length, which we
demonstrate to hold in typical network models, we manage to prove superiority
of the alternative mechanism in stochastic dominance terms. We believe that
this study could serve as a foundation to design more efficient data transfer
protocols for partially-connected networks...

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## On the Groupoid Model of Computational Paths

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 08/06/2015

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The main objective of this work is to study mathematical properties of
computational paths. Originally proposed by de Queiroz & Gabbay (1994) as
`sequences or rewrites', computational paths are taken to be terms of the
identity type of Martin L\"of's Intensional Type Theory, since these paths can
be seen as the grounds on which the propositional equality between two
computational objects stand. From this perspective, this work aims to show that
one of the properties of the identity type is present on computational paths.
We are refering to the fact that that the identity type induces a groupoid
structure, as proposed by Hofmann & Streicher (1994). Using categorical
semantics, we show that computational paths induce a groupoid structure. We
also show that computational paths are capable of inducing higher categorical
structures.; Comment: 16 pages, LSFA 2015 - Preliminary Acceptance

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## Closed Light Paths in Equiangular Spiral Disks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 04/06/2013

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A new type of deformation for microscopic laser disks, the
\textit{equiangular spiral deformation} is proposed. First a short review of
the geometry of light paths in equiangular spirals in the language of real
two-dimensional geometric calculus is given. Second, the constituting equations
for \textit{closed paths} inside equiangular spirals are derived. Third, their
numerical solution is performed and found to yield two generic types of closed
light paths. \textit{Degenerate} closed paths that exist over large intervals
of the deformation parameter, and \textit{nondegenerate} closed paths which
only exist over relatively small deformation parameter intervals spanning less
than 1% of the nondegenerate intervals. Fourth, amongst the nondegenerate paths
a \textit{stable asymmetric bow-tie} shaped light trajectory was found.; Comment: 36 pages, 18 figures

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## Survivable Paths in Multilayer Networks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 30/04/2013

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We consider protection problems in multilayer networks. In single-layer
networks, a pair of disjoint paths can be used to provide protection for a
source-destination pair. However, this approach cannot be directly applied to
layered networks where disjoint paths may not always exist. In this paper, we
take a new approach which is based on finding a set of paths that may not be
disjoint but together will survive any single physical link failure. First, we
consider the problem of finding the minimum number of survivable paths. In
particular, we focus on two versions of this problem: one where the length of a
path is restricted, and the other where the number of paths sharing a fiber is
restricted. We prove that in general, finding the minimum survivable path set
is NP-hard, whereas both of the restricted versions of the problem can be
solved in polynomial time. We formulate the problem as Integer Linear Programs
(ILPs), and use these formulations to develop heuristics and approximation
algorithms. Next, we consider the problem of finding a set of survivable paths
that uses the minimum number of fibers. We show that this problem is NP-hard in
general, and develop heuristics and approximation algorithms with provable
approximation bounds. Finally...

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## Analytic Combinatorics of Planar Lattice Paths

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 23/04/2013

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Lattice paths effectively model phenomena in chemistry, physics and
probability theory. Asymptotic enumeration of lattice paths is linked with
entropy in the physical systems being modeled. Lattice paths restricted to
different regions of the plane are well suited to a functional equation
approach for exact and asymptotic enumeration. This thesis surveys results on
lattice paths under various restrictions, with an emphasis on lattice paths in
the quarter plane. For these paths, we develop an original systematic
combinatorial approach providing direct access to the exponential growth
factors of the asymptotic expressions.; Comment: Master's thesis of the author, 97 pages

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## Symmetries of Analytic Paths

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 21/03/2015

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#Mathematical Physics#Mathematics - Differential Geometry#58D19 (Primary) 58D05, 58D27, 53C05, 83C45

The symmetries of paths in a manifold $M$ are classified with respect to a
given pointwise proper action of a Lie group $G$ on $M$. Here, paths are
embeddings of a compact interval into $M$. There are at least two types of
symmetries: Firstly, paths that are parts of an integral curve of a fundamental
vector field on $M$ (continuous symmetry). Secondly, paths that can be
decomposed into finitely many pieces, each of which is the translate of some
free segment, where possibly the translate is cut at the two ends of the paths
(discrete symmetry). Here, a free segment is a path $e$ whose $G$-translates
either equal $e$ or intersect it in at most finitely many points. Note that all
the statements above are understood up to the parametrization of the paths. We
will show, for the category of analytic manifolds, that each path is of exactly
one of either types.
For the proof, we use that the overlap of a path $\gamma$ with one of its
translates is encoded uniquely in a mapping between subsets of $\dom\gamma$.
Running over all translates, these mappings form the so-called
reparametrization set to $\gamma$. It will turn out that, up to conjugation
with a diffeomorphism, any such set is given by the action of a Lie subgroup of
$O(2)$ on $S^1$...

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## Counting Humps in Motzkin paths

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 12/09/2011

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In this paper we study the number of humps (peaks) in Dyck, Motzkin and
Schr\"{o}der paths. Recently A. Regev noticed that the number of peaks in all
Dyck paths of order $n$ is one half of the number of super Dyck paths of order
$n$. He also computed the number of humps in Motzkin paths and found a similar
relation, and asked for bijective proofs. We give a bijection and prove these
results. Using this bijection we also give a new proof that the number of Dyck
paths of order $n$ with $k$ peaks is the Narayana number. By double counting
super Schr\"{o}der paths, we also get an identity involving products of
binomial coefficients.; Comment: 8 pages, 2 Figures

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## Symmetries of statistics on lattice paths between two boundaries

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

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We prove that on the set of lattice paths with steps N=(0,1) and E=(1,0) that
lie between two fixed boundaries T and B (which are themselves lattice paths),
the statistics `number of E steps shared with B' and `number of E steps shared
with T' have a symmetric joint distribution. To do so, we give an involution
that switches these statistics, preserves additional parameters, and
generalizes to paths that contain steps S=(0,-1) at prescribed x-coordinates.
We also show that a similar equidistribution result for path statistics follows
from the fact that the Tutte polynomial of a matroid is independent of the
order of its ground set. We extend the two theorems to k-tuples of paths
between two boundaries, and we give some applications to Dyck paths,
generalizing a result of Deutsch, to watermelon configurations, to
pattern-avoiding permutations, and to the generalized Tamari lattice. Finally,
we prove a conjecture of Nicol\'as about the distribution of degrees of k
consecutive vertices in k-triangulations of a convex n-gon. To achieve this
goal, we provide a new statistic-preserving bijection between certain k-tuples
of non-crossing paths and k-flagged semistandard Young tableaux, which is based
on local moves reminiscent of jeu de taquin.; Comment: Small typos corrected...

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## Generating Transition Paths by Langevin Bridges

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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We propose a novel stochastic method to generate paths conditioned to start
in an initial state and end in a given final state during a certain time
$t_{f}$. These paths are weighted with a probability given by the overdamped
Langevin dynamics. We show that these paths can be exactly generated by a
non-local stochastic differential equation. In the limit of short times, we
show that this complicated non-solvable equation can be simplified into an
approximate stochastic differential equation. For longer times, the paths
generated by this approximate equation can be reweighted to generate the
correct statistics. In all cases, the paths generated by this equation are
statistically independent and provide a representative sample of transition
paths. In case the reaction takes place in a solvent (e.g. protein folding in
water), the explicit solvent can be treated. The method is illustrated on the
one-dimensional quartic oscillator.

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## The Complexity of Rerouting Shortest Paths

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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The Shortest Path Reconfiguration problem has as input a graph G (with unit
edge lengths) with vertices s and t, and two shortest st-paths P and Q. The
question is whether there exists a sequence of shortest st-paths that starts
with P and ends with Q, such that subsequent paths differ in only one vertex.
This is called a rerouting sequence.
This problem is shown to be PSPACE-complete. For claw-free graphs and chordal
graphs, it is shown that the problem can be solved in polynomial time, and that
shortest rerouting sequences have linear length. For these classes, it is also
shown that deciding whether a rerouting sequence exists between all pairs of
shortest st-paths can be done in polynomial time. Finally, a polynomial time
algorithm for counting the number of isolated paths is given.; Comment: The results on claw-free graphs, chordal graphs and isolated paths
have been added in version 2 (april 2012). Version 1 (September 2010) only
contained the PSPACE-hardness result. (Version 2 has been submitted.)

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## A bag-of-paths framework for network data analysis

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 27/02/2013

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This work introduces a generic framework, called the bag-of-paths (BoP), that
can be used for link and network data analysis. The primary application of this
framework, investigated in this paper, is the definition of distance measures
between nodes enjoying some nice properties. More precisely, let us assume a
weighted directed graph G where a cost is associated to each arc. Within this
context, consider a bag containing all the possible paths between pairs of
nodes in G. Then, following, a probability distribution on this countable set
of paths through the graph is defined by minimizing the total expected cost
between all pairs of nodes while fixing the total relative entropy spread in
the graph. This results in a Boltzmann distribution on the set of paths such
that long (high-cost) paths have a low probability of being sampled from the
bag, while short (low-cost) paths have a high probability of being sampled.
Within this probabilistic framework, the BoP probabilities, P(s=i,e=j), of
drawing a path starting from node i (s=i) and ending in node j (e=j) can easily
be computed in closed form by a simple matrix inversion. Various applications
of this framework are currently investigated, e.g., the definition of distance
measures between the nodes of G...

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## Most probable paths in temporal weighted networks: An application to ocean transport

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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We consider paths in weighted and directed temporal networks, introducing
tools to compute sets of paths of high probability. We quantify the relative
importance of the most probable path between two nodes with respect to the
whole set of paths, and to a subset of highly probable paths which incorporate
most of the connection probability. These concepts are used to provide
alternative definitions of betweenness centrality. We apply our formalism to a
transport network describing surface flow in the Mediterranean sea. Despite the
full transport dynamics is described by a very large number of paths we find
that, for realistic time scales, only a very small subset of high probability
paths (or even a single most probable one) is enough to characterize global
connectivity properties of the network.

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## Particles in RSOS paths

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

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#High Energy Physics - Theory#Condensed Matter - Statistical Mechanics#Mathematical Physics#Mathematics - Combinatorics

We introduce a new representation of the paths of the Forrester-Baxter RSOS
models which represents the states of the irreducible modules of the minimal
models M(p',p). This representation is obtained by transforming the RSOS paths,
for the cases p> 2p'-2, to new paths for which horizontal edges are allowed at
certain heights. These new paths are much simpler in that their weight is
nothing but the sum of the position of the peaks. This description paves the
way for the interpretation of the RSOS paths in terms of fermi-type charged
particles out of which the fermionic characters could be obtained
constructively. The derivation of the fermionic character for p'=2 and p=kp'+/-
1 is outlined. Finally, the particles of the RSOS paths are put in relation
with the kinks and the breathers of the restricted sine-Gordon model.; Comment: 15 pages, few typos corrected, version published

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## Minimum-Link Paths Revisited

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 13/02/2013

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A path or a polygonal domain is C-oriented if the orientations of its edges
belong to a set of C given orientations; this is a generalization of the
notable rectilinear case (C = 2). We study exact and approximation algorithms
for minimum-link C-oriented paths and paths with unrestricted orientations,
both in C-oriented and in general domains. Our two main algorithms are as
follows:
A subquadratic-time algorithm with a non-trivial approximation guarantee for
general (unrestricted-orientation) minimum-link paths in general domains.
An algorithm to find a minimum-link C-oriented path in a C-oriented domain.
Our algorithm is simpler and more time-space efficient than the prior
algorithm.
We also obtain several related results:
- 3SUM-hardness of determining the link distance with unrestricted
orientations (even in a rectilinear domain).
- An optimal algorithm for finding a minimum-link rectilinear path in a
rectilinear domain. The algorithm and its analysis are simpler than the
existing ones.
- An extension of our methods to find a C-oriented minimum-link path in a
general (not necessarily C-oriented) domain.
- A more efficient algorithm to compute a 2-approximate C-oriented
minimum-link path.
- A notion of "robust" paths. We show how minimum-link C-oriented paths
approximate the robust paths with unrestricted orientations to within an
additive error of 1.; Comment: 29 pages...

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## Natural selection of paths in networks

Fonte: Universidade Autônoma de Barcelona
Publicador: Universidade Autônoma de Barcelona

Tipo: info:eu-repo/semantics/article; info:eu-repo/semantics/submittedVersion
Formato: application/pdf

Publicado em //2011
ENG

Relevância na Pesquisa

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#Evolution#Natural selection#Network dynamics#Neural computation#Neuronal replicator hypothesis#Path evolution

We present a novel algorithm that exhibits natural selection of paths in a network. If each node and weighted directed edge has a unique identifier, a path in the network is defined as an ordered list of these unique identifiers. We take a population perspective and view each path as a genotype. If each node has a node phenotype then a path phenotype is defined as the list of node phenotypes in order of traversal. We show that given appropriate path traversal, weight change and structural plasticity rules, a path is a unit of evolution because it can exhibit multiplicative growth (i.e. change it’s probability of being traversed), and have variation and heredity. Thus, a unit of evolution need not be a spatially distinct physical individual. The total set of paths in a network consists of all possible paths from the start node to a finish node. Each path phenotype is associated with a reward that determines whether the edges of that path will be multiplicatively strengthened (or weakened). A pair-wise tournament selection algorithm is implemented which compares the reward obtained by two paths. The directed edges of the winning path are strengthened, whilst the directed edges of the losing path are weakened. Edges shared by both paths are not changed (or weakened if diversity is desired). Each time a node is activated there is a probability that the path will mutate...

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## Natural Selection of Paths in Networks

Fonte: Nature Preceedings
Publicador: Nature Preceedings

Tipo: Manuscript

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We present a novel algorithm that exhibits natural selection of paths in a network. If each node and weighted directed edge has a unique identifier, a path in the network is defined as an ordered list of these unique identifiers. We take a population perspective and view each path as a genotype. If each node has a node phenotype then a path phenotype is defined as the list of node phenotypes in order of traversal. We show that given appropriate path traversal, weight change and structural plasticity rules, a path is a unit of evolution because it can exhibit multiplicative growth (i.e. change it’s probability of being traversed), and have variation and heredity. Thus, a unit of evolution need not be a spatially distinct physical individual. The total set of paths in a network consists of all possible paths from the start node to a finish node. Each path phenotype is associated with a reward that determines whether the edges of that path will be multiplicatively strengthened (or weakened). A pair-wise tournament selection algorithm is implemented which compares the reward obtained by two paths. The directed edges of the winning path are strengthened, whilst the directed edges of the losing path are weakened. Edges shared by both paths are not changed (or weakened if diversity is desired). Each time a node is activated there is a probability that the path will mutate...

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