Facilitated spin models: recent and new results

Facilitated or kinetically constrained spin models (KCSM) are a class of interacting particle systems reversible w.r.t. to a simple product measure. Each dynamical variable (spin) is re-sampled from its equilibrium distribution only if the surrounding configuration fulfills a simple local constraint which \emph{does not involve} the chosen variable itself. Such simple models are quite popular in the glass community since they display some of the peculiar features of glassy dynamics, in particular they can undergo a dynamical arrest reminiscent of the liquid/glass transitiom. Due to the fact that the jumps rates of the Markov process can be zero, the whole analysis of the long time behavior becomes quite delicate and, until recently, KCSM have escaped a rigorous analysis with the notable exception of the East model. In these notes we will mainly review several recent mathematical results which, besides being applicable to a wide class of KCSM, have contributed to settle some debated questions arising in numerical simulations made by physicists. We will also provide some interesting new extensions. In particular we will show how to deal with interacting models reversible w.r.t. to a high temperature Gibbs measure and we will provide a detailed analysis of the so called one spin facilitated model on a general connected graph.Comment: 30 pages, 3 figure

On the Sets of Real Numbers Recognized by Finite Automata in Multiple Bases

This article studies the expressive power of finite automata recognizing sets of real numbers encoded in positional notation. We consider Muller automata as well as the restricted class of weak deterministic automata, used as symbolic set representations in actual applications. In previous work, it has been established that the sets of numbers that are recognizable by weak deterministic automata in two bases that do not share the same set of prime factors are exactly those that are definable in the first order additive theory of real and integer numbers. This result extends Cobham's theorem, which characterizes the sets of integer numbers that are recognizable by finite automata in multiple bases. In this article, we first generalize this result to multiplicatively independent bases, which brings it closer to the original statement of Cobham's theorem. Then, we study the sets of reals recognizable by Muller automata in two bases. We show with a counterexample that, in this setting, Cobham's theorem does not generalize to multiplicatively independent bases. Finally, we prove that the sets of reals that are recognizable by Muller automata in two bases that do not share the same set of prime factors are exactly those definable in the first order additive theory of real and integer numbers. These sets are thus also recognizable by weak deterministic automata. This result leads to a precise characterization of the sets of real numbers that are recognizable in multiple bases, and provides a theoretical justification to the use of weak automata as symbolic representations of sets.Comment: 17 page

Glassy timescale divergence and anomalous coarsening in a kinetically constrained spin chain

We analyse the out of equilibrium behavior of an Ising spin chain with an asymmetric kinetic constraint after a quench to a low temperature T. In the limit T\to 0, we provide an exact solution of the resulting coarsening process. The equilibration time exhibits a `glassy' divergence \teq=\exp(const/T^2) (popular as an alternative to the Vogel-Fulcher law), while the average domain length grows with a temperature dependent exponent, \dbar ~ t^{T\ln 2}. We show that the equilibration time \teq also sets the timescale for the linear response of the system at low temperatures.Comment: 4 pages, revtex, includes two eps figures. Proof of energy barrier hierarchy added. Version to be published in Phys Rev Let

Assessment of the spectral misalignment effect (SMILE) on EarthCARE's Multi-Spectral Imager aerosol and cloud property retrievals

The Multi-Spectral Imager (MSI) on board the Earth Cloud, Aerosol and Radiation Explorer (EarthCARE) will provide horizontal information about aerosols and clouds. These measurements are needed to extend vertical cloud and aerosol property information, which is obtained from EarthCARE's active sensors, in order to obtain a full three-dimensional view of cloud and aerosol conditions. Mesoscale weather systems, in particular, will be characterized. The discovery of a non-compliance of the MSI visible–near-infrared–shortwave infrared (VNS) camera’s visible (VIS) and shortwave infrared (SWIR1) channels regarding a spectral central wavelength (CWVL) shift across-track of up to 14 nm (VIS) and 20 nm (SWIR1) led to the need for an analysis regarding its impact on MSI Level-2A aerosol and cloud products. A significant influence of the spectral misalignment effect (SMILE) on MSI retrievals is identified due to the spectral variation in gas absorption, surface reflectance, and aerosol and cloud properties within the spectral ranges of these MSI bands. For example, the VIS channel is positioned in close proximity to the red edge of green vegetation and is impacted by residual absorption of water vapor and ozone. Small central wavelength variations introduce uncertainties due to the rapid change in surface reflectance for conditions with low optical thickness. The present central wavelength shift in the VIS towards shorter wavelengths than at nadir introduces a relative error in transmission of up to 3.3 % due to the increasing influence of water vapor and ozone absorption. We found relative errors in the top-of-atmosphere (TOA) signal due to the SMILE of up to 30 % for low optical thickness over a land surface in that band. Since the magnitude of the impact strongly depends on the underlying surface and atmospheric conditions, we conclude that accounting for the SMILE in Level-2 retrievals or correcting the Level-1 signal will improve MSI aerosol and cloud product quality

Exchangeability of Qsr1p, a large ribosomal subunit protein required for subunit joining, suggests a novel translational regulatory mechanism

AbstractQsr1p is a 60S ribosomal subunit protein that is necessary for joining of large and small ribosomal subunits and is also one of the last proteins assembled onto the 60S ribosomal subunit in the cytoplasm. The finding that Qsr1p is identical to L7, a protein previously shown to cycle on and off large ribosomal subunits in the cytoplasm, suggests that the addition of Qsr1p onto the 60S ribosomal subunit could be utilized as a translational regulatory mechanism by limiting the supply of functional 60S subunits

User-definable resource bounds analysis for logic programs

We present a static analysis that infers both upper and lower bounds on the usage that a logic program makes of a set of user-definable resources. The inferred bounds will in general be functions of input data sizes. A resource in our approach is a quite general, user-defined notion which associates a basic cost function with elementary operations. The analysis then derives the related (upper- and lower-bound) resource usage functions for all predicates in the program. We also present an assertion language which is used to define both such resources and resourcerelated properties that the system can then check based on the results of the analysis. We have performed some preliminary experiments with some concrete resources such as execution steps, bytes sent or received by an application, number of files left open, number of accesses to a datábase, number of calis to a procedure, number of asserts/retracts, etc. Applications of our analysis include resource consumption verification and debugging (including for mobile code), resource control in parallel/distributed computing, and resource-oriented specialization

Integrating evolution into ecological modelling: accommodating phenotypic changes in agent based models.

PMCID: PMC3733718This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Evolutionary change is a characteristic of living organisms and forms one of the ways in which species adapt to changed conditions. However, most ecological models do not incorporate this ubiquitous phenomenon. We have developed a model that takes a 'phenotypic gambit' approach and focuses on changes in the frequency of phenotypes (which differ in timing of breeding and fecundity) within a population, using, as an example, seasonal breeding. Fitness per phenotype calculated as the individual's contribution to population growth on an annual basis coincide with the population dynamics per phenotype. Simplified model variants were explored to examine whether the complexity included in the model is justified. Outputs from the spatially implicit model underestimated the number of individuals across all phenotypes. When no phenotype transitions are included (i.e. offspring always inherit their parent's phenotype) numbers of all individuals are always underestimated. We conclude that by using a phenotypic gambit approach evolutionary dynamics can be incorporated into individual based models, and that all that is required is an understanding of the probability of offspring inheriting the parental phenotype