Clusters and Recurrence in the Two-Dimensional Zero-Temperature Stochastic Ising Model

We analyze clustering and (local) recurrence of a standard Markov process model of spatial domain coarsening. The continuous time process, whose state space consists of assignments of +1 or -1 to each site in ${\bf Z}^2$, is the zero-temperature limit of the stochastic homogeneous Ising ferromagnet (with Glauber dynamics): the initial state is chosen uniformly at random and then each site, at rate one, polls its 4 neighbors and makes sure it agrees with the majority, or tosses a fair coin in case of a tie. Among the main results (almost sure, with respect to both the process and initial state) are: clusters (maximal domains of constant sign) are finite for times $t< \infty$, but the cluster of a fixed site diverges (in diameter) as $t \to \infty$; each of the two constant states is (positive) recurrent. We also present other results and conjectures concerning positive and null recurrence and the role of absorbing states.Comment: 16 pages, 1 figur

Monte Carlo Markov chains constrained on graphs for a target with disconnected support

This paper presents a theoretical Monte Carlo Markov chain procedure in the framework of graphs. It specifically deals with the construction of a Markov chain whose empirical distribution converges to a given reference one. The Markov chain is constrained over an underlying graph so that states are viewed as vertices, and the transition between two states can have positive probability only in the presence of an edge connecting them. The analysis focuses on the relevant case of support of the target distribution not connected in the graph. Some general arguments on the speed of convergence are also carried out

Stochastic Ising model with flipping sets of spins and fast decreasing temperature

This paper deals with the stochastic Ising model with a temperature shrinking to zero as time goes to infinity. A generalization of the Glauber dynamics is considered, on the basis of the existence of simultaneous flips of some spins. Such dynamics act on a wide class of graphs which are periodic and embedded in Rd. The interactions between couples of spins are assumed to be quenched i.i.d. random variables following a Bernoulli distribution with support {−1, +1}. The specific problem here analyzed concerns the assessment of how often (finitely or infinitely many times, almost surely) a given spin flips. Adopting the classification proposed in [14], we present conditions in order to have models of type F (any spin flips finitely many times), I (any spin flips infinitely many times) and M (a mixed case). Several examples are provided in all dimensions and for different cases of graphs. The most part of the obtained results holds true for the case of zero-temperature and some of them for the cubic lattice Ld = (Z d, Ed) as wel

Ivabradine: a preliminary observation for a new terapeutic role in patients with multiple organ dysfunction syndrome

[No abstract available

Developments in perfect simulation of Gibbs measures through a new result for the extinction of Galton-Watson-like processes

This paper deals with the problem of perfect sampling from a Gibbs measure with infinite range interactions. We present some sufficient conditions for the extinction of processes which are like supermartingales when large values are taken. This result has deep consequences on perfect simulation, showing that local modifications on the interactions of a model do not affect simulability. We also pose the question to optimize over a class of sequences of sets that influence the sufficient condition for the perfect simulation of the Gibbs measure. We completely solve this question both for the long range Ising models and for the spin models with finite range interactions.Comment: 28 page

Equivalent monopole source of the geomagnetic South Atlantic Anomaly

The South Atlantic magnetic Anomaly (SAA) is an important feature of the present geomagnetic field. In this paper we model the space-time evolution of this anomaly for the last 400 years in terms of the resultant between a decrease of a global axial dipole and an increase of a virtual local monopole source. Some characteristics of this evolution are investigated and some considerations are made on the light of a possible special state of the global geomagnetic field dynamical regime. Among the possible speculations, one is made regarding the topography of the core-mantle boundary (CMB) and its possible aspect underneath the SAA region in terms of simple sinusoidal undulations met by the monopole source during its centennial motion

Edmund Husserl between Platonism and Aristotelianism

The volume contains the first collection of essays delaying with the relations between, on the one hand, Husserl's philosophy, and, on the other, the traditions of Platonism and Aristotelianism

Anisotropic Anomalous Diffusion assessed in the human brain by scalar invariant indices

A new method to investigate anomalous diffusion in human brain is proposed. The method has been inspired by both the stretched-exponential model proposed by Hall and Barrick (HB) and DTI. Quantities extracted using HB method were able to discriminate different cerebral tissues on the basis of their complexity, expressed by the stretching exponent gamma and of the anisotropy of gamma across different directions. Nevertheless, these quantities were not defined as scalar invariants like mean diffusivity and fractional anisotropy, which are eigenvalues of the diffusion tensor. We hypotesize instead that the signal may be espressed as a simple stretched-exponential only along the principal axes of diffusion, while in a generic direction the signal is modeled as a combination of three different stretched-exponentials. In this way, we derived indices to quantify both the tissue anomalous diffusion and its anisotropy, independently of the reference frame of the experiment. We tested and compare our new method with DTI and HB approaches applying them to 10 healty subjects brain at 3T. Our experimental results show that our parameters are highly correlated to intrinsic local geometry when compared to HB indices. Moreover, they offer a different kind of contrast when compared to DTI outputs. Specifically, our indices show a higher capability to discriminate among different areas of the corpus callosum, which are known to be associated to different axonal densities.Comment: 21 pages, 6 figures, 2 table

Shannon information of the geomagnetic field for the past 7000 years

The present behaviour of the geomagnetic field as expressed by the International Geomagnetic Reference Field (IGRF) deserves special attention when compared with that shown over the past few thousands of years by two paleomagnetic/archeomagnetic models, CALS3K and CALS7K. The application of the Information theory in terms of Shannon Information and K-entropy to these models shows characteristics of an instable geomagnetic field. Although the result is mitigated when we correct the CALS7K model for its typical spectral damping, the present geomagnetic field as represented by IGRF is still rather distinct, at least for the past 4000 years, a result that is further confirmed by the CALS3K model. This is consistent with a significant global critical state started at around 1750, and still present, characterised by significant decays of the geomagnetic dipole, energy and Shannon information and high K-entropy. The details of how these characteristics may develop are not clear, since the present state could move toward an excursion or a geomagnetic polarity reversal, but we cannot exclude the possibility that the “critical” behaviour will become again more “normal”, stopping the apparent trend of the recent geomagnetic field decay

Are we going towards a global planetary magnetic change?

The dipolar part of the geomagnetic field has been decaying rapidly during the last few hundreds of years. In addition to this classical argument, from Information theory applied to geomagnetism, there are some evidences that the recent Earth magnetic field is showing characteristics typical of a reversal in progress. If this is true, many scientific and environmental questions will arise. For instance, it will be of particular interest to monitor the time-space dynamics the South Atlantic Anomaly, where the magnetic field is strongly reduced (a sort of "planetary magnetic hole"). Here we find one of the most favourite places where Low Earth Orbiting (LEO) satellites are lost or present some damages, due to the vicinity of "clouds" of electric particles (Van Allen belts) to the Earth's surface. The decay of the field will also decrease the screening effect to the solar wind and cosmic charges, so enhancing the cosmic radiation illuminating our planet: possible negative consequences are expected in terms of increase of skin cancers. Also important will be the study of the possible evolution of the core dynamics that will be generating this specific condition of the geomagnetic field