5,741 research outputs found
On the noise-induced passage through an unstable periodic orbit II: General case
Consider a dynamical system given by a planar differential equation, which
exhibits an unstable periodic orbit surrounding a stable periodic orbit. It is
known that under random perturbations, the distribution of locations where the
system's first exit from the interior of the unstable orbit occurs, typically
displays the phenomenon of cycling: The distribution of first-exit locations is
translated along the unstable periodic orbit proportionally to the logarithm of
the noise intensity as the noise intensity goes to zero. We show that for a
large class of such systems, the cycling profile is given, up to a
model-dependent change of coordinates, by a universal function given by a
periodicised Gumbel distribution. Our techniques combine action-functional or
large-deviation results with properties of random Poincar\'e maps described by
continuous-space discrete-time Markov chains.Comment: 44 pages, 4 figure
Universality of residence-time distributions in non-adiabatic stochastic resonance
We present mathematically rigorous expressions for the residence-time and
first-passage-time distributions of a periodically forced Brownian particle in
a bistable potential. For a broad range of forcing frequencies and amplitudes,
the distributions are close to periodically modulated exponential ones.
Remarkably, the periodic modulations are governed by universal functions,
depending on a single parameter related to the forcing period. The behaviour of
the distributions and their moments is analysed, in particular in the low- and
high-frequency limits.Comment: 8 pages, 1 figure New version includes distinction between
first-passage-time and residence-time distribution
On the Rational Type 0f Moment Angle Complexes
In this note it is shown that the moment angle complexes Z(K;(D^2,,S^1))
which are rationally elliptic are a product of odd spheres and a diskComment: This version avoids the use of an incorrect result from the
literature in the proof of Theorem 1.3. There is some text overlap with
arXiv:1410.645
Metastability in Interacting Nonlinear Stochastic Differential Equations II: Large-N Behaviour
We consider the dynamics of a periodic chain of N coupled overdamped
particles under the influence of noise, in the limit of large N. Each particle
is subjected to a bistable local potential, to a linear coupling with its
nearest neighbours, and to an independent source of white noise. For strong
coupling (of the order N^2), the system synchronises, in the sense that all
oscillators assume almost the same position in their respective local potential
most of the time. In a previous paper, we showed that the transition from
strong to weak coupling involves a sequence of symmetry-breaking bifurcations
of the system's stationary configurations, and analysed in particular the
behaviour for coupling intensities slightly below the synchronisation
threshold, for arbitrary N. Here we describe the behaviour for any positive
coupling intensity \gamma of order N^2, provided the particle number N is
sufficiently large (as a function of \gamma/N^2). In particular, we determine
the transition time between synchronised states, as well as the shape of the
"critical droplet", to leading order in 1/N. Our techniques involve the control
of the exact number of periodic orbits of a near-integrable twist map, allowing
us to give a detailed description of the system's potential landscape, in which
the metastable behaviour is encoded
Beyond the Fokker-Planck equation: Pathwise control of noisy bistable systems
We introduce a new method, allowing to describe slowly time-dependent
Langevin equations through the behaviour of individual paths. This approach
yields considerably more information than the computation of the probability
density. The main idea is to show that for sufficiently small noise intensity
and slow time dependence, the vast majority of paths remain in small space-time
sets, typically in the neighbourhood of potential wells. The size of these sets
often has a power-law dependence on the small parameters, with universal
exponents. The overall probability of exceptional paths is exponentially small,
with an exponent also showing power-law behaviour. The results cover time spans
up to the maximal Kramers time of the system. We apply our method to three
phenomena characteristic for bistable systems: stochastic resonance, dynamical
hysteresis and bifurcation delay, where it yields precise bounds on transition
probabilities, and the distribution of hysteresis areas and first-exit times.
We also discuss the effect of coloured noise.Comment: 37 pages, 11 figure
Прогностические факторы повторного образования полипов желудка после проведения эндоскопической полипэктомии
полипыЖЕЛУДКА БОЛЕЗНИХИРУРГИЧЕСКИЕ ОПЕРАЦИИ МАЛОИНВАЗИВНЫЕЭНДОСКОПИЯ ГАСТРОИНТЕСТИНАЛЬНАЯжелудокРЕЦИДИВполипэктоми
Criminal Law: Customer’s Permanent Exclusion From Retail Store Due to Prior Shoplifting Arrests Held Enforceable Under Criminal Trespass Statute
In interpretive research, trustworthiness has developed to become an important alternative for measuring the value of research and its effects, as well as leading the way of providing for rigour in the research process. The article develops the argument that trustworthiness plays an important role in not only effecting change in a research project’s original setting, but also that trustworthy research contributes toward building a body of knowledge that can play an important role in societal change. An essential aspect in the development of this trustworthiness is its relationship to context. To deal with the multiplicity of meanings of context, we distinguish between contexts at different levels of the research project: the domains of the researcher, the collective, and the individual participant. Furthermore, we argue that depending on the primary purpose associated with the collective learning potential, critical potential, or performative potential of phenomenographic research, developing trustworthiness may take different forms and is related to aspects of pedagogical legitimacy, social legitimacy, and epistemological legitimacy. Trustworthiness in phenomenographic research is further analysed by distinguishing between the internal horizon – the constitution of trustworthiness as it takes place within the research project – and the external horizon, which points to the impact of the phenomenographic project in the world mediated by trustworthiness
A repulsive trap for two electrons in a magnetic field
We study numerically and analytically the dynamics of two classical electrons
with Coulomb interaction in a two dimensional antidot superlattice potential in
the presence of crossed electric and magnetic fields. It is found that near one
antidot the electron pair can be trapped for a long time and the escape rate
from such a trap is proportional to the square of a weak electric field. This
is qualitatively different from the case of noninteracting electrons which are
trapped forever by the antidot. For the pair propagation in the antidot
superlattice we found a broad parameter regime for which the pair is stable and
where two repulsive electrons propagate together on an enormously large
distance.Comment: revtex, 5 pages, 6 figure
Cardiovascular and cancer mortality in relation to dietary polychlorinated biphenyls and marine polyunsaturated fatty acids: A nutritional-toxicological aspect of fish consumption
Background. Co-exposure to environmental contaminants
present in fish could mitigate the beneficial
effects of fish consumption and possibly explain
the lack of association observed for mortality in
some geographical regions.
Objective. To assess the independent associations of
dietary exposure to polychlorinated biphenyls
(PCBs) and long-chain omega-3 fish fatty acids
intake with cardiovascular and cancer mortality.
Methods. We used the prospective population-based
Swedish Mammography Cohort and the Cohort of
Swedish Men comprising 32 952 women and 36 545
men, free from cancer, cardiovascular disease and
diabetes at baseline in 1998. Validated estimates of
dietary PCBs and long-chain omega-3 fish fatty acids
[i.e. eicosapentaenoic acid (EPA) and docosahexaenoic
acid (DHA)] intake were obtained via a food
frequency questionnaire at baseline. Information on
death was ascertained through register linkage.
Results. During a mean follow-up of 15.5 years, we
ascertained 16 776 deaths. We observed for cardiovascular
mortality, comparing extreme quintiles
in multivariable models mutually adjusted for
PCBs and EPA-DHA, dose-dependent associations
for dietary PCB exposure, hazard ratio (HR) 1.31
(CI 95%: 1.08 to 1.57; P-trend 0.005) and for
dietary EPA-DHA intake, HR 0.79 (CI 95%: 0.66 to
0.95; P-trend 0.041). For cancer mortality, no clear
associations were discerned.
Conclusion. The beneficial effect of fish consumption
on the cardiovascular system seems compromised
by co-exposure to PCBs – one likely explanation for
the inconsistent associations observed between
fish consumption and mortalityThe Swedish Research Council under the grant no 2017-00822 and 2017-00644 (SIMPLER) supported the stud
Mixed-mode oscillations and interspike interval statistics in the stochastic FitzHugh-Nagumo model
We study the stochastic FitzHugh-Nagumo equations, modelling the dynamics of
neuronal action potentials, in parameter regimes characterised by mixed-mode
oscillations. The interspike time interval is related to the random number of
small-amplitude oscillations separating consecutive spikes. We prove that this
number has an asymptotically geometric distribution, whose parameter is related
to the principal eigenvalue of a substochastic Markov chain. We provide
rigorous bounds on this eigenvalue in the small-noise regime, and derive an
approximation of its dependence on the system's parameters for a large range of
noise intensities. This yields a precise description of the probability
distribution of observed mixed-mode patterns and interspike intervals.Comment: 36 page
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