3,018 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
Relating the Cosmological Constant and Supersymmetry Breaking in Warped Compactifications of IIB String Theory
It has been suggested that the observed value of the cosmological constant is
related to the supersymmetry breaking scale M_{susy} through the formula Lambda
\sim M_p^4 (M_{susy}/M_p)^8. We point out that a similar relation naturally
arises in the codimension two solutions of warped space-time varying
compactifications of string theory in which non-isotropic stringy moduli induce
a small but positive cosmological constant.Comment: 7 pages, LaTeX, references added and minor changes made, (v3) map
between deSitter and global cosmic brane solutions clarified, supersymmetry
breaking discussion improved and references adde
Generalized Green-Schwarz mechanism in F theory
We derive the anomaly 8-form of 6-dimensional gauge theories arising in F
theory compactifications on elliptic Calabi-Yau threefolds. The result allows
to determine the matter content of certain such theories in terms of
intersection numbers on the base of elliptic fibration. We also discuss gauge
theories on 7-branes with double point singularities on the worldvolume.
Applications to Type II compactifications on Hirzebruch surfaces and are
outlined.Comment: 11 pages, harvmac. Normalization of (tr R^2)^2 term correcte
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
The Regulation of Commodity Options
To outline further genetic mechanisms of transformation from follicular lymphoma (FL) to diffuse large B-cell lymphoma (DLBCL), we have performed whole genome array-CGH in 81 tumors from 60 patients [29 de novo DLBCL (dnDLBCL), 31 transformed DLBCL (tDLBCL), and 21 antecedent FL]. In 15 patients, paired tumor samples (primary FL and a subsequent tDLBCL) were available, among which three possessed more than two subsequent tumors, allowing us to follow specific genetic alterations acquired before, during, and after the transformation. Gain of 2p15-16.1 encompassing, among others, the REL, BCL11A, USP34, COMMD1, and OTX1 genes was found to be more common in the tDLBCL compared with dnDLBCL (P < 0.001). Furthermore, a high-level amplification of 2p15-16.1 was also detected in the FL stage prior to transformation, indicating its importance during the transformation event. Quantitative real-time PCR showed a higher level of amplification of REL, USP34, and COMMD1 (all involved in the NF kappa B-pathway) compared with BCL11A, which indicates that the altered genes disrupting the NF kappa B pathway may be the driver genes of transformation rather than the previously suggested BCL11A. Moreover, a 17q21.33 amplification was exclusively found in tDLBCL, never in FL (P < 0.04) or dnDLBCL, indicating an upregulation of genes of importance during the later phase of transformation. Taken together, our study demonstrates potential genomic markers for disease progression to clinically more aggressive forms. We also confirm the importance of the TP53-, CDKN2A-, and NF kappa B-pathways for the transformation from FL to DLBCL
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
Integrability and Ergodicity of Classical Billiards in a Magnetic Field
We consider classical billiards in plane, connected, but not necessarily
bounded domains. The charged billiard ball is immersed in a homogeneous,
stationary magnetic field perpendicular to the plane. The part of dynamics
which is not trivially integrable can be described by a "bouncing map". We
compute a general expression for the Jacobian matrix of this map, which allows
to determine stability and bifurcation values of specific periodic orbits. In
some cases, the bouncing map is a twist map and admits a generating function
which is useful to do perturbative calculations and to classify periodic
orbits. We prove that billiards in convex domains with sufficiently smooth
boundaries possess invariant tori corresponding to skipping trajectories.
Moreover, in strong field we construct adiabatic invariants over exponentially
large times. On the other hand, we present evidence that the billiard in a
square is ergodic for some large enough values of the magnetic field. A
numerical study reveals that the scattering on two circles is essentially
chaotic.Comment: Explanations added in Section 5, Section 6 enlarged, small errors
corrected; Large figures have been bitmapped; 40 pages LaTeX, 15 figures,
uuencoded tar.gz. file. To appear in J. Stat. Phys. 8
A mathematical framework for critical transitions: normal forms, variance and applications
Critical transitions occur in a wide variety of applications including
mathematical biology, climate change, human physiology and economics. Therefore
it is highly desirable to find early-warning signs. We show that it is possible
to classify critical transitions by using bifurcation theory and normal forms
in the singular limit. Based on this elementary classification, we analyze
stochastic fluctuations and calculate scaling laws of the variance of
stochastic sample paths near critical transitions for fast subsystem
bifurcations up to codimension two. The theory is applied to several models:
the Stommel-Cessi box model for the thermohaline circulation from geoscience,
an epidemic-spreading model on an adaptive network, an activator-inhibitor
switch from systems biology, a predator-prey system from ecology and to the
Euler buckling problem from classical mechanics. For the Stommel-Cessi model we
compare different detrending techniques to calculate early-warning signs. In
the epidemics model we show that link densities could be better variables for
prediction than population densities. The activator-inhibitor switch
demonstrates effects in three time-scale systems and points out that excitable
cells and molecular units have information for subthreshold prediction. In the
predator-prey model explosive population growth near a codimension two
bifurcation is investigated and we show that early-warnings from normal forms
can be misleading in this context. In the biomechanical model we demonstrate
that early-warning signs for buckling depend crucially on the control strategy
near the instability which illustrates the effect of multiplicative noise.Comment: minor corrections to previous versio
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