1,727 research outputs found
Return times, recurrence densities and entropy for actions of some discrete amenable groups
Results of Wyner and Ziv and of Ornstein and Weiss show that if one observes
the first k outputs of a finite-valued ergodic process, then the waiting time
until this block appears again is almost surely asymptotic to , where
is the entropy of the process. We examine this phenomenon when the allowed
return times are restricted to some subset of times, and generalize the results
to processes parameterized by other discrete amenable groups.
We also obtain a uniform density version of the waiting time results: For a
process on symbols, within a given realization, the density of the initial
-block within larger -blocks approaches , uniformly in ,
as tends to infinity. Again, similar results hold for processes with other
indexing groups.Comment: To appear in Journal d'Analyse Mathematiqu
Thermodynamic and dynamic anomalies for a three dimensional isotropic core-softened potential
Using molecular dynamics simulations and integral equations (Rogers-Young,
Percus-Yevick and hypernetted chain closures) we investigate the thermodynamic
of particles interacting with continuous core-softened intermolecular
potential. Dynamic properties are also analyzed by the simulations. We show
that, for a chosen shape of the potential, the density, at constant pressure,
has a maximum for a certain temperature. The line of temperatures of maximum
density (TMD) was determined in the pressure-temperature phase diagram.
Similarly the diffusion constant at a constant temperature, , has a maximum
at a density and a minimum at a density .
In the pressure-temperature phase-diagram the line of extrema in diffusivity is
outside of TMD line. Although in this interparticle potential lacks
directionality, this is the same behavior observed in SPC/E water.Comment: 16 page
Sharp error terms for return time statistics under mixing conditions
We describe the statistics of repetition times of a string of symbols in a
stochastic process. Denote by T(A) the time elapsed until the process spells
the finite string A and by S(A) the number of consecutive repetitions of A. We
prove that, if the length of the string grows unbondedly, (1) the distribution
of T(A), when the process starts with A, is well aproximated by a certain
mixture of the point measure at the origin and an exponential law, and (2) S(A)
is approximately geometrically distributed. We provide sharp error terms for
each of these approximations. The errors we obtain are point-wise and allow to
get also approximations for all the moments of T(A) and S(A). To obtain (1) we
assume that the process is phi-mixing while to obtain (2) we assume the
convergence of certain contidional probabilities
Shuffling cards, factoring numbers, and the quantum baker's map
It is pointed out that an exactly solvable permutation operator, viewed as
the quantization of cyclic shifts, is useful in constructing a basis in which
to study the quantum baker's map, a paradigm system of quantum chaos. In the
basis of this operator the eigenfunctions of the quantum baker's map are
compressed by factors of around five or more. We show explicitly its connection
to an operator that is closely related to the usual quantum baker's map. This
permutation operator has interesting connections to the art of shuffling cards
as well as to the quantum factoring algorithm of Shor via the quantum order
finding one. Hence we point out that this well-known quantum algorithm makes
crucial use of a quantum chaotic operator, or at least one that is close to the
quantization of the left-shift, a closeness that we also explore
quantitatively.Comment: 12 pgs. Substantially elaborated version, including a new route to
the quantum bakers map. To appear in J. Phys.
Scale-free networks as preasymptotic regimes of superlinear preferential attachment
We study the following paradox associated with networks growing according to
superlinear preferential attachment: superlinear preference cannot produce
scale-free networks in the thermodynamic limit, but there are superlinearly
growing network models that perfectly match the structure of some real
scale-free networks, such as the Internet. We obtain an analytic solution,
supported by extensive simulations, for the degree distribution in
superlinearly growing networks with arbitrary average degree, and confirm that
in the true thermodynamic limit these networks are indeed degenerate, i.e.,
almost all nodes have low degrees. We then show that superlinear growth has
vast preasymptotic regimes whose depths depend both on the average degree in
the network and on how superlinear the preference kernel is. We demonstrate
that a superlinearly growing network model can reproduce, in its preasymptotic
regime, the structure of a real network, if the model captures some
sufficiently strong structural constraints -- rich-club connectivity, for
example. These findings suggest that real scale-free networks of finite size
may exist in preasymptotic regimes of network evolution processes that lead to
degenerate network formations in the thermodynamic limit
Phase behavior of colloidal suspensions with critical solvents in terms of effective interactions
We study the phase behavior of colloidal suspensions the solvents of which
are considered to be binary liquid mixtures undergoing phase segregation. We
focus on the thermodynamic region close to the critical point of the
accompanying miscibility gap. There, due to the colloidal particles acting as
cavities in the critical medium, the spatial confinements of the critical
fluctuations of the corresponding order parameter result in the effective,
so-called critical Casimir forces between the colloids. Employing an approach
in terms of effective, one-component colloidal systems, we explore the
possibility of phase coexistence between two phases of colloidal suspensions,
one being rich and the other being poor in colloidal particles. The reliability
of this effective approach is discussed
Are There Sensitive Time Periods for Dementia Caregivers? The Occurrence of Behavioral and Psychological Symptoms in the Early Stages of Dementia
ABSTRACT Background: The behavioral and psychological symptoms associated with dementia (BPSD) can be burdensome to informal/family caregivers, negatively affecting mental health and expediting the institutionalization of patients. Because the dementia patient-caregiver relationship extends over long periods of time, it is useful to examine how BPSD impact caregiver depressive symptoms at varied stages of illness. The goal of this study was to assess the association of BPSD that occur during early stage dementia with subsequent caregiver depressive symptoms. Methods: Patients were followed from the early stages of dementia every six months for up to 12 years or until death (n = 160). Caregiver symptoms were assessed on average 4.5 years following patient's early dementia behaviors. A generalized estimating equation (GEE) extension of the logistic regression model was used to determine the association between informal caregiver depressive symptoms and BPSD symptoms that occurred at the earliest stages dementia, including those persistent during the first year of dementia diagnosis. Results: BPSD were common in early dementia. None of the individual symptoms observed during the first year of early stage dementia significantly impacted subsequent caregiver depressive symptoms. Only patient agitation/aggression was associated with subsequent caregiver depressive symptoms (OR = 1.76; 95% CI = 1.04-2.97) after controlling for concurrent BPSD, although not in fully adjusted models. Conclusions: Persistent agitation/aggression early in dementia diagnosis may be associated with subsequent depressive symptoms in caregivers. Future longitudinal analyses of the dementia caregiving relationship should continue to examine the negative impact of persistent agitation/aggression in the diagnosis of early stage dementia on caregivers
Structure and aggregation of colloids immersed in critical solvents
We consider an ensemble of spherical colloidal particles immersed in a
near-critical solvent such as a binary liquid mixture close to its critical
demixing point. The emerging long-ranged fluctuations of the corresponding
order parameter of the solvent drive the divergence of the correlation length.
Spatial confinements of these critical fluctuations by colloidal solute
particles, acting as cavities in the fluctuating medium, restrict and modify
the fluctuation spectrum in a way which depends on their relative
configuration. This results in effective, so-called critical Casimir forces
(CCFs) acting on the confining surfaces. Using the available knowledge about
CCFs we study the structure and stability of such colloidal suspensions by
employing an approach in terms of effective, one-component colloidal systems.
Applying the approximation of pairwise additive CCFs we calculate the radial
distribution function of the colloids, which is experimentally accessible. We
analyze colloidal aggregation due to CCFs and thus allude to previous
experimental studies which are still under debat
Multifractal properties of return time statistics
Fluctuations in the return time statistics of a dynamical system can be
described by a new spectrum of dimensions. Comparison with the usual
multifractal analysis of measures is presented, and difference between the two
corresponding sets of dimensions is established. Theoretical analysis and
numerical examples of dynamical systems in the class of Iterated Functions are
presented.Comment: 4 pages, 3 figure
On the exchange of intersection and supremum of sigma-fields in filtering theory
We construct a stationary Markov process with trivial tail sigma-field and a
nondegenerate observation process such that the corresponding nonlinear
filtering process is not uniquely ergodic. This settles in the negative a
conjecture of the author in the ergodic theory of nonlinear filters arising
from an erroneous proof in the classic paper of H. Kunita (1971), wherein an
exchange of intersection and supremum of sigma-fields is taken for granted.Comment: 20 page
- …