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## Head injuries related to the use of baby walkers.

Fonte: PubMed
Publicador: PubMed

Tipo: Artigo de Revista Científica

Publicado em 15/09/1984
EN

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To determine what proportion of head injuries in children under 24 months of age who presented to an emergency department were related to the use of baby walkers, we reviewed the charts of 52 such children. Walkers were involved in 42% of the head injuries in the children under 12 months of age and in none of those in the children aged 12 to 24 months. All walker-related injuries, including skull fractures in three children, involved stairs (p less than 0.001). Questionnaires were also sent to all families with children aged 3 to 18 months attending a private pediatric practice to determine the prevalence of falls involving baby walkers among these children and the factors associated with such falls. Of the 152 responding families 82% reported using or having used a walker. Thirty-six percent of the families reported that their child had a fall while in a walker, with 8.8% of the falls resulting in contact with a doctor. Walker-related falls were directly associated with time spent in the walker (p less than 0.001) and with a previous fall from the walker by an older sibling (p less than 0.03). Since there is no demonstrated benefit of walkers, their use should not be encouraged, and parents should be advised of their potential danger.

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## Risks of Baby Walkers and Options for Prevention

Fonte: PubMed
Publicador: PubMed

Tipo: Artigo de Revista Científica

Publicado em /11/1985
EN

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Recent studies have reported fatal head injuries associated with baby walkers. Skull fractures and hospital admissions are significantly higher for infants who have received head injuries while using a walker. Thirty to 50% of infants regularly placed in walkers experience an accident or injury related to the device. Most injuries are minor cuts, abrasions and contusions. While there are many hazards, no benefits have been documented. The walkers do not help children learn to walk. Options for preventing injury including banning baby walkers, product design regulations, and public education about the risks. An outright ban would be difficult, because walkers are not considered inherently dangerous; they become so when parental supervision is lacking. Although design specifications will decrease some walker-related injuries, they will not prevent severe or fatal head injuries associated with falls down stairs. Public awareness of hazards from baby walkers and discouragement of their use are recommended preventive measures at this time.

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## Hydrogel Walkers with Electro-Driven Motility for Cargo Transport

Fonte: Nature Publishing Group
Publicador: Nature Publishing Group

Tipo: Artigo de Revista Científica

Publicado em 28/08/2015
EN

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In this study, soft hydrogel walkers with electro-driven motility for cargo transport have been developed via a facile mould-assisted strategy. The hydrogel walkers consisting of polyanionic poly(2-acrylamido-2-methylpropanesulfonic acid-co-acrylamide) exhibit an arc looper-like shape with two “legs” for walking. The hydrogel walkers can reversibly bend and stretch via repeated “on/off” electro-triggers in electrolyte solution. Based on such bending/stretching behaviors, the hydrogel walkers can move their two “legs” to achieve one-directional walking motion on a rough surface via repeated “on/off” electro-triggering cycles. Moreover, the hydrogel walkers loaded with very heavy cargo also exhibit excellent walking motion for cargo transport. Such hydrogel systems create new opportunities for developing electro-controlled soft systems with simple design/fabrication strategies in the soft robotic field for remote manipulation and transportation.

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## Moments of vicious walkers and M\"obius graph expansions

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

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A system of Brownian motions in one-dimension all started from the origin and
conditioned never to collide with each other in a given finite time-interval
$(0, T]$ is studied. The spatial distribution of such vicious walkers can be
described by using the repulsive eigenvalue-statistics of random Hermitian
matrices and it was shown that the present vicious walker model exhibits a
transition from the Gaussian unitary ensemble (GUE) statistics to the Gaussian
orthogonal ensemble (GOE) statistics as the time $t$ is going on from 0 to $T$.
In the present paper, we characterize this GUE-to-GOE transition by presenting
the graphical expansion formula for the moments of positions of vicious
walkers. In the GUE limit $t \to 0$, only the ribbon graphs contribute and the
problem is reduced to the classification of orientable surfaces by genus.
Following the time evolution of the vicious walkers, however, the graphs with
twisted ribbons, called M\"obius graphs, increase their contribution to our
expansion formula, and we have to deal with the topology of non-orientable
surfaces. Application of the recent exact result of dynamical correlation
functions yields closed expressions for the coefficients in the M\"obius
expansion using the Stirling numbers of the first kind.; Comment: REVTeX4...

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## Vicious accelerating walkers

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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A vicious walker system consists of N random walkers on a line with any two
walkers annihilating each other upon meeting. We study a system of N vicious
accelerating walkers with the velocity undergoing Gaussian fluctuations, as
opposed to the position. We numerically compute the survival probability
exponent, {\alpha}, for this system, which characterizes the probability for
any two walkers not to meet. For example, for N = 3, {\alpha} = 0.71 \pm 0.01.
Based on our numerical data, we conjecture that 1/8N(N - 1) is an upper bound
on {\alpha}. We also numerically study N vicious Levy flights and find, for
instance, for N = 3 and a Levy index {\mu} = 1 that {\alpha} = 1.31 \pm 0.03.
Vicious accelerating walkers relate to no-crossing configurations of
semiflexible polymer brushes and may prove relevant for a non-Markovian
extension of Dyson's Brownian motion model.; Comment: 7.5 pages, 5 figures

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## Vicious walkers, friendly walkers and Young tableaux II: With a wall

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

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#Condensed Matter - Statistical Mechanics#High Energy Physics - Lattice#High Energy Physics - Theory#Mathematical Physics#Mathematics - Combinatorics#17B20 (Primary) 05A15 05E05 05E10 82B20 82B23 (Secondary)

We derive new results for the number of star and watermelon configurations of
vicious walkers in the presence of an impenetrable wall by showing that these
follow from standard results in the theory of Young tableaux, and combinatorial
descriptions of symmetric functions. For the problem of $n$-friendly walkers,
we derive exact asymptotics for the number of stars and watermelons both in the
absence of a wall and in the presence of a wall.; Comment: 35 pages, AmS-LaTeX; Definitions of n-friendly walkers clarified; the
statement of Theorem 4 and its proof were corrected

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## Vicious Walkers in a Potential

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 08/03/2004

Relevância na Pesquisa

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We consider N vicious walkers moving in one dimension in a one-body potential
v(x). Using the backward Fokker-Planck equation we derive exact results for the
asymptotic form of the survival probability Q(x,t) of vicious walkers initially
located at (x_1,...,x_N) = x, when v(x) is an arbitrary attractive potential.
Explicit results are given for a square-well potential with absorbing or
reflecting boundary conditions at the walls, and for a harmonic potential with
an absorbing or reflecting boundary at the origin and the walkers starting on
the positive half line. By mapping the problem of N vicious walkers in zero
potential onto the harmonic potential problem, we rederive the results of
Fisher [J. Stat. Phys. 34, 667 (1984)] and Krattenthaler et al. [J. Phys. A
33}, 8835 (2000)] respectively for vicious walkers on an infinite line and on a
semi-infinite line with an absorbing wall at the origin. This mapping also
gives a new result for vicious walkers on a semi-infinite line with a
reflecting boundary at the origin: Q(x,t) \sim t^{-N(N-1)/2}.; Comment: 5 pages

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## A Reflection Principle for Three Vicious Walkers

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 10/08/2008

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We establish a reflection principle for three lattice walkers and use this
principle to reduce the enumeration of the configurations of three vicious
walkers to that of configurations of two vicious walkers. In the combinatorial
treatment of two vicious walkers, we make connections to two-chain watermelons
and to the classical ballot problem. Precisely, the reflection principle leads
to a bijection between three walks $(L_1, L_2, L_3)$ such that $L_2$ intersects
both $L_1$ and $L_3$ and three walks $(L_1, L_2, L_3)$ such that $L_1$
intersects $L_3$. Hence we find a combinatorial interpretation of the formula
for the generating function for the number of configurations of three vicious
walkers, originally derived by Bousquet-M\'elou by using the kernel method, and
independently by Gessel by using tableaux and symmetric functions.; Comment: 12 pages, 5 figures

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## Random walk on a population of random walkers

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 17/12/2007

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We consider a population of $N$ labeled random walkers moving on a substrate,
and an excitation jumping among the walkers upon contact. The label
$\mathcal{X}(t)$ of the walker carrying the excitation at time $t$ can be
viewed as a stochastic process, where the transition probabilities are a
stochastic process themselves. Upon mapping onto two simpler processes, the
quantities characterizing $\mathcal{X}(t)$ can be calculated in the limit of
long times and low walkers density. The results are compared with numerical
simulations. Several different topologies for the substrate underlying
diffusion are considered.; Comment: 16 pages, 9 figures

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## Exact distributions of the number of distinct and common sites visited by N independent random walkers

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 11/02/2013

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#Condensed Matter - Statistical Mechanics#Condensed Matter - Disordered Systems and Neural Networks#Mathematics - Probability

We study the number of distinct sites S_N(t) and common sites W_N(t) visited
by N independent one dimensional random walkers, all starting at the origin,
after t time steps. We show that these two random variables can be mapped onto
extreme value quantities associated to N independent random walkers. Using this
mapping, we compute exactly their probability distributions P_N^d(S,t) and
P_N^d(W,t) for any value of N in the limit of large time t, where the random
walkers can be described by Brownian motions. In the large N limit one finds
that S_N(t)/\sqrt{t} \propto 2 \sqrt{\log N} + \widetilde{s}/(2 \sqrt{\log N})
and W_N(t)/\sqrt{t} \propto \widetilde{w}/N where \widetilde{s} and
\widetilde{w} are random variables whose probability density functions (pdfs)
are computed exactly and are found to be non trivial. We verify our results
through direct numerical simulations.; Comment: 5 pages, 3 figures

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## Maximum Distance Between the Leader and the Laggard for Three Brownian Walkers

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 30/06/2010

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We consider three independent Brownian walkers moving on a line. The process
terminates when the left-most walker (the `Leader') meets either of the other
two walkers. For arbitrary values of the diffusion constants D_1 (the Leader),
D_2 and D_3 of the three walkers, we compute the probability distribution
P(m|y_2,y_3) of the maximum distance m between the Leader and the current
right-most particle (the `Laggard') during the process, where y_2 and y_3 are
the initial distances between the leader and the other two walkers. The result
has, for large m, the form P(m|y_2,y_3) \sim A(y_2,y_3) m^{-\delta}, where
\delta = (2\pi-\theta)/(\pi-\theta) and \theta =
cos^{-1}(D_1/\sqrt{(D_1+D_2)(D_1+D_3)}. The amplitude A(y_2,y_3) is also
determined exactly.

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## Arrival statistics and exploration properties of mortal walkers

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 09/08/2013

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We study some of the salient features of the arrival statistics and explo-
ration properties of mortal random walkers, that is, walkers that may die as
they move, or as they wait to move. Such evanescence or death events have
profound consequences for quantities such as the number of distinct sites
visited which are relevant for the computation of encounter- controlled rates
in chemical kinetics. We exploit the observation that well-known methods
developed decades ago for immortal walkers are widely applicable to mortal
walkers. The particular cases of exponential and power-law evanescence are
considered in detail. Finally, we discuss the relevance of our results to the
target problem with mortal traps and a particular application thereof, namely,
the defect di?usion model. Evanescence of defects is postulated as a possible
complementary contri- bution or perhaps even an alternative to anomalous
di?usion to explain observed stretched exponential relaxation behavior.

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## Exact encounter times for many random walkers on regular and complex networks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 03/06/2009

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The exact mean time between encounters of a given particle in a system
consisting of many particles undergoing random walks in discrete time is
calculated, on both regular and complex networks. Analytical results are
obtained both for independent walkers, where any number of walkers can occupy
the same site, and for walkers with an exclusion interaction, when no site can
contain more than one walker. These analytical results are then compared with
numerical simulations, showing very good agreement.; Comment: 11 pages, 4 figures. Submitted for publication

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## Caught Active Walkers

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 13/05/2000

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A discrete implementation on a lattice of the Active Walker Model is
presented. After the model's validity is shown in simple simulations, more
complex simulations of walkers passing consecutively a lattice from an
arbitrary starting point at the left border to a random destination on the
right border are presented. It is found that walkers may be caught at a certain
position by bouncing back and forth between two contiguous lattice sites. The
statistical characteristics of this catchment effect are being studied. The
probability distribution of the number of walkers having passed the lattice
before the catchment occurred shows a exponential decrease to higher numbers.
Furthermore, the influence of some parameters of the model on the catchment
phenomenon is discussed. Position and height of the maxima of these
distributions show a linear dependency on a parameter.; Comment: 8 pages, 10 figures

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## Vicious Random Walkers and a Discretization of Gaussian Random Matrix Ensembles

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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The vicious random walker problem on a one dimensional lattice is considered.
Many walkers take simultaneous steps on the lattice and the configurations in
which two of them arrive at the same site are prohibited. It is known that the
probability distribution of N walkers after M steps can be written in a
determinant form. Using an integration technique borrowed from the theory of
random matrices, we show that arbitrary k-th order correlation functions of the
walkers can be expressed as quaternion determinants whose elements are
compactly expressed in terms of symmetric Hahn polynomials.; Comment: LaTeX, 15 pages, 1 figure, minor corrections made before publication
in Nucl. Phys. B

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## Vicious walkers, friendly walkers and Young tableaux III: Between two walls

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

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#Condensed Matter - Statistical Mechanics#Mathematics - Combinatorics#82B23 (Primary) 05A15 05E05 82B20 (Secondary)

We derive exact and asymptotic results for the number of star and watermelon
configurations of vicious walkers confined to lie between two impenetrable
walls, as well as for the analogous problem for $\infty$-friendly walkers. Our
proofs make use of results from symmetric function theory and the theory of
basic hypergeometric series.; Comment: 15 pages, LaTeX; several typos in Section 3 corrected

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## Quantum Walk-based Generation of Entanglement Between Two Walkers

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 25/01/2009

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Quantum walks can be used either as tools for quantum algorithm development
or as entanglement generators, potentially useful to test quantum hardware. We
present a novel algorithm based on a discrete Hadamard quantum walk on a line
with one coin and two walkers whose purpose is to generate entanglement between
walkers. We provide several classical computer simulations of our quantum
algorithm in which we show that, although the asymptotical amount of
entanglement generated between walkers does not reach the highest degree of
entanglement possible at each step for either coin measurement outcome, the
entanglement ratio (entanglement generated/highest value of entanglement
possible, for each step) tends to converge, and the actual convergence value
depends on the coin initial state and on the coin measurement outcome.
Furthermore, our numerical simulations show that, for the quantum walks used in
our algorithm, the value towards which entanglement ratio converges also
depends on the position probability distribution symmetry of a quantum walk
computed with one single walker and the same coin initial state employed in the
corresponding quantum walk with two walkers.; Comment: 8 pages, 15 figures

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## Scaling Limit of Vicious Walkers, Schur Function, and Gaussian Random Matrix Ensemble

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 12/10/2001

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We consider the diffusion scaling limit of the vicious walkers and derive the
time-dependent spatial-distribution function of walkers. The dependence on
initial configurations of walkers is generally described by using the symmetric
polynomials called the Schur functions. In the special case in the scaling
limit that all walkers are started from the origin, the probability density is
simplified and it shows that the positions of walkers on the real axis at time
one is identically distributed with the eigenvalues of random matrices in the
Gaussian orthogonal ensemble. Since the diffusion scaling limit makes the
vicious walkers converge to the nonintersecting Brownian motions in
distribution, the present study will provide a new method to analyze
intersection problems of Brownian motions in one-dimension.; Comment: 4 pages,revtex,no figures

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## Fraction of uninfected walkers in the one-dimensional Potts model

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

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The dynamics of the one-dimensional q-state Potts model, in the zero
temperature limit, can be formulated through the motion of random walkers which
either annihilate (A + A -> 0) or coalesce (A + A -> A) with a q-dependent
probability. We consider all of the walkers in this model to be mutually
infectious. Whenever two walkers meet, they experience mutual contamination.
Walkers which avoid an encounter with another random walker up to time t remain
uninfected. The fraction of uninfected walkers is investigated numerically and
found to decay algebraically, U(t) \sim t^{-\phi(q)}, with a nontrivial
exponent \phi(q). Our study is extended to include the coupled
diffusion-limited reaction A+A -> B, B+B -> A in one dimension with equal
initial densities of A and B particles. We find that the density of walkers
decays in this model as \rho(t) \sim t^{-1/2}. The fraction of sites unvisited
by either an A or a B particle is found to obey a power law, P(t) \sim
t^{-\theta} with \theta \simeq 1.33. We discuss these exponents within the
context of the q-state Potts model and present numerical evidence that the
fraction of walkers which remain uninfected decays as U(t) \sim t^{-\phi},
where \phi \simeq 1.13 when infection occurs between like particles only...

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## Time walkers and spatial dynamics of ageing information

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

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The distribution of information is essential for living system's ability to
coordinate and adapt. Random walkers are often used to model this distribution
process and, in doing so, one effectively assumes that information maintains
its relevance over time. But the value of information in social and biological
systems often decay and must continuously be updated. To capture the spatial
dynamics of ageing information, we introduce time walkers. A time walker moves
like a random walker, but interacts with traces left by other walkers, some
representing older information, some newer. The traces forms a navigable
information landscape. We quantify the dynamical properties of time walkers
moving on a two-dimensional lattice and the quality of the information
landscape generated by their movements. We visualise the self-similar landscape
as a river network, and show that searching in this landscape is superior to
random searching and scales as the length of loop-erased random walks.

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