3,070 research outputs found
The random geometry of equilibrium phases
This is a (long) survey about applications of percolation theory in
equilibrium statistical mechanics. The chapters are as follows:
1. Introduction
2. Equilibrium phases
3. Some models
4. Coupling and stochastic domination
5. Percolation
6. Random-cluster representations
7. Uniqueness and exponential mixing from non-percolation
8. Phase transition and percolation
9. Random interactions
10. Continuum modelsComment: 118 pages. Addresses: [email protected]
http://www.mathematik.uni-muenchen.de/~georgii.html [email protected]
http://www.math.chalmers.se/~olleh [email protected]
Depression and sickness behavior are Janus-faced responses to shared inflammatory pathways
It is of considerable translational importance whether depression is a form or a consequence of sickness behavior. Sickness behavior is a behavioral complex induced by infections and immune trauma and mediated by pro-inflammatory cytokines. It is an adaptive response that enhances recovery by conserving energy to combat acute inflammation. There are considerable phenomenological similarities between sickness behavior and depression, for example, behavioral inhibition, anorexia and weight loss, and melancholic (anhedonia), physio-somatic (fatigue, hyperalgesia, malaise), anxiety and neurocognitive symptoms. In clinical depression, however, a transition occurs to sensitization of immuno-inflammatory pathways, progressive damage by oxidative and nitrosative stress to lipids, proteins, and DNA, and autoimmune responses directed against self-epitopes. The latter mechanisms are the substrate of a neuroprogressive process, whereby multiple depressive episodes cause neural tissue damage and consequent functional and cognitive sequelae. Thus, shared immuno-inflammatory pathways underpin the physiology of sickness behavior and the pathophysiology of clinical depression explaining their partially overlapping phenomenology. Inflammation may provoke a Janus-faced response with a good, acute side, generating protective inflammation through sickness behavior and a bad, chronic side, for example, clinical depression, a lifelong disorder with positive feedback loops between (neuro)inflammation and (neuro)degenerative processes following less well defined triggers
Infinite volume limit of the Abelian sandpile model in dimensions d >= 3
We study the Abelian sandpile model on Z^d. In dimensions at least 3 we prove
existence of the infinite volume addition operator, almost surely with respect
to the infinite volume limit mu of the uniform measures on recurrent
configurations. We prove the existence of a Markov process with stationary
measure mu, and study ergodic properties of this process. The main techniques
we use are a connection between the statistics of waves and uniform
two-component spanning trees and results on the uniform spanning tree measure
on Z^d.Comment: First version: LaTeX; 29 pages. Revised version: LaTeX; 29 pages. The
main result of the paper has been extended to all dimensions at least 3, with
a new and simplyfied proof of finiteness of the two-component spanning tree.
Second revision: LaTeX; 32 page
Strong coupling and exceptional points in optically pumped active hyperbolic metamaterials
We investigate the interaction of light in gain-enhanced multilayered hyperbolic metamaterials in the strong interaction regime. Pumping the dye in the dielectric layers from inside the light cone, while emission occurs into the lower hyperbolic band outside the light cone, eases the problem of light incoupling. In the strong coupling regime both emission and absorption lines cause a distortion of the plasmonic modes due to Rabi splitting and a PT -symmetry broken phase, with generation of exceptional points at loss-gain compensation frequencies. We derive a semi-classical model that describes these phenomena for finite and infinite devices in detail, requiring only the overlap factor and the complex frequencies of the dye transition and the optical mode
Archimedes' law and its corrections for an active particle in a granular sea
We study the origin of buoyancy forces acting on a larger particle moving in
a granular medium subject to horizontal shaking and its corrections before
fluidization. In the fluid limit Archimedes' law is verified; before the limit
memory effects counteract buoyancy, as also found experimentally. The origin of
the friction is an excluded volume effect between active particles, which we
study more exactly for a random walker in a random environment. The same
excluded volume effect is also responsible for the mutual attraction between
bodies moving in the granular medium. Our theoretical modeling proceeds via an
asymmetric exclusion process, i.e., via a dissipative lattice gas dynamics
simulating the position degrees of freedom of a low density granular sea.Comment: 22 pages,5 figure
On the entropy production of time series with unidirectional linearity
There are non-Gaussian time series that admit a causal linear autoregressive
moving average (ARMA) model when regressing the future on the past, but not
when regressing the past on the future. The reason is that, in the latter case,
the regression residuals are only uncorrelated but not statistically
independent of the future. In previous work, we have experimentally verified
that many empirical time series indeed show such a time inversion asymmetry.
For various physical systems, it is known that time-inversion asymmetries are
linked to the thermodynamic entropy production in non-equilibrium states. Here
we show that such a link also exists for the above unidirectional linearity.
We study the dynamical evolution of a physical toy system with linear
coupling to an infinite environment and show that the linearity of the dynamics
is inherited to the forward-time conditional probabilities, but not to the
backward-time conditionals. The reason for this asymmetry between past and
future is that the environment permanently provides particles that are in a
product state before they interact with the system, but show statistical
dependencies afterwards. From a coarse-grained perspective, the interaction
thus generates entropy. We quantitatively relate the strength of the
non-linearity of the backward conditionals to the minimal amount of entropy
generation.Comment: 16 page
Network representations of non-equilibrium steady states: Cycle decompositions, symmetries and dominant paths
Non-equilibrium steady states (NESS) of Markov processes give rise to
non-trivial cyclic probability fluxes. Cycle decompositions of the steady state
offer an effective description of such fluxes. Here, we present an iterative
cycle decomposition exhibiting a natural dynamics on the space of cycles that
satisfies detailed balance. Expectation values of observables can be expressed
as cycle "averages", resembling the cycle representation of expectation values
in dynamical systems. We illustrate our approach in terms of an analogy to a
simple model of mass transit dynamics. Symmetries are reflected in our approach
by a reduction of the minimal number of cycles needed in the decomposition.
These features are demonstrated by discussing a variant of an asymmetric
exclusion process (TASEP). Intriguingly, a continuous change of dominant flow
paths in the network results in a change of the structure of cycles as well as
in discontinuous jumps in cycle weights.Comment: 3 figures, 4 table
Cognitively-inspired Agent-based Service Composition for Mobile & Pervasive Computing
Automatic service composition in mobile and pervasive computing faces many
challenges due to the complex and highly dynamic nature of the environment.
Common approaches consider service composition as a decision problem whose
solution is usually addressed from optimization perspectives which are not
feasible in practice due to the intractability of the problem, limited
computational resources of smart devices, service host's mobility, and time
constraints to tailor composition plans. Thus, our main contribution is the
development of a cognitively-inspired agent-based service composition model
focused on bounded rationality rather than optimality, which allows the system
to compensate for limited resources by selectively filtering out continuous
streams of data. Our approach exhibits features such as distributedness,
modularity, emergent global functionality, and robustness, which endow it with
capabilities to perform decentralized service composition by orchestrating
manifold service providers and conflicting goals from multiple users. The
evaluation of our approach shows promising results when compared against
state-of-the-art service composition models.Comment: This paper will appear on AIMS'19 (International Conference on
Artificial Intelligence and Mobile Services) on June 2
Partially ordered models
We provide a formal definition and study the basic properties of partially
ordered chains (POC). These systems were proposed to model textures in image
processing and to represent independence relations between random variables in
statistics (in the later case they are known as Bayesian networks). Our chains
are a generalization of probabilistic cellular automata (PCA) and their theory
has features intermediate between that of discrete-time processes and the
theory of statistical mechanical lattice fields. Its proper definition is based
on the notion of partially ordered specification (POS), in close analogy to the
theory of Gibbs measure. This paper contains two types of results. First, we
present the basic elements of the general theory of POCs: basic geometrical
issues, definition in terms of conditional probability kernels, extremal
decomposition, extremality and triviality, reconstruction starting from
single-site kernels, relations between POM and Gibbs fields. Second, we prove
three uniqueness criteria that correspond to the criteria known as bounded
uniformity, Dobrushin and disagreement percolation in the theory of Gibbs
measures.Comment: 54 pages, 11 figures, 6 simulations. Submited to Journal of Stat.
Phy
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