On the Purity of the free boundary condition Potts measure on random trees

We consider the free boundary condition Gibbs measure of the Potts model on a random tree. We provide an explicit temperature interval below the ferromagnetic transition temperature for which this measure is extremal, improving older bounds of Mossel and Peres. In information theoretic language extremality of the Gibbs measure corresponds to non-reconstructability for symmetric q-ary channels. The bounds are optimal for the Ising model and appear to be close to what we conjecture to be the true values up to a factor of 0.0150 in the case q = 3 and 0.0365 for q = 4. Our proof uses an iteration of random boundary entropies from the outside of the tree to the inside, along with a symmetrization argument.Comment: 14 page

A symmetric entropy bound on the non-reconstruction regime of Markov chains on Galton-Watson trees

We give a criterion of the form Q(d)c(M)<1 for the non-reconstructability of tree-indexed q-state Markov chains obtained by broadcasting a signal from the root with a given transition matrix M. Here c(M) is an explicit function, which is convex over the set of M's with a given invariant distribution, that is defined in terms of a (q-1)-dimensional variational problem over symmetric entropies. Further Q(d) is the expected number of offspring on the Galton-Watson tree. This result is equivalent to proving the extremality of the free boundary condition-Gibbs measure within the corresponding Gibbs-simplex. Our theorem holds for possibly non-reversible M and its proof is based on a general Recursion Formula for expectations of a symmetrized relative entropy function, which invites their use as a Lyapunov function. In the case of the Potts model, the present theorem reproduces earlier results of the authors, with a simplified proof, in the case of the symmetric Ising model (where the argument becomes similar to the approach of Pemantle and Peres) the method produces the correct reconstruction threshold), in the case of the (strongly) asymmetric Ising model where the Kesten-Stigum bound is known to be not sharp the method provides improved numerical bounds.Comment: 10 page

Zoo-technical application of Ground Source Heat Pumps: a pilot case study

Ground Source Heat Pumps are energy-efficient HVAC systems usually adopted in residential and commercial buildings. However the control of the thermal environment is required not only in spaces occupied by people, but also in intensive breeding farms, in order to maintain healthy conditions and to increase productivity. In the Italian livestock breedings, heating is usually provided by means of gas or Diesel burners directly installed in the stable. An important part of the heating load is due to the large ventilation rates required for the livestock wellbeing. Cooling is either absent or achieved by evaporative systems that also increase the humidity level in the stables, thus requiring even larger ventilation rates. Therefore the applicability of geothermal heating and cooling in breeding farms was analysed in a research project co-funded by the Lombardy Region and the Italian Ministry of Research and Education. A pilot system for heating, cooling and ventilation was designed and installed in a piglets room at the Experimental and Didactic Zoo-technical Center of the University of Milan. Five Borehole Heat Exchangers (BHEs), installed down to a depth of 60 meters into an alluvial aquifer, were coupled with a Ground Source Heat Pump. The heat pump provides heating and cooling to an Air Handling Unit, including a Heat Recovery system. A monitoring system was installed in order to measure comfort conditions in the piglet room, operating conditions and energy consumption of the HVAC system, together with the spreading of the thermal plume in the ground. In this paper the results of a monitoring campaign carried out in a typical winter period are presented and discussed. The overall energy efficiency of the system, expressed in terms of a COP, results to be equal to 4.04. A comparison between the pilot HVAC system and a traditional one is also carried out, showing that the proposed solution can provide over 40% primary energy saving. Following, cost savings in energy bills for farmers are found, although the ratio between electricity cost and fuel cost is a key parameter

Metastates in mean-field models with random external fields generated by Markov chains

We extend the construction by Kuelske and Iacobelli of metastates in finite-state mean-field models in independent disorder to situations where the local disorder terms are are a sample of an external ergodic Markov chain in equilibrium. We show that for non-degenerate Markov chains, the structure of the theorems is analogous to the case of i.i.d. variables when the limiting weights in the metastate are expressed with the aid of a CLT for the occupation time measure of the chain. As a new phenomenon we also show in a Potts example that, for a degenerate non-reversible chain this CLT approximation is not enough and the metastate can have less symmetry than the symmetry of the interaction and a Gaussian approximation of disorder fluctuations would suggest.Comment: 20 pages, 2 figure

Heart Rate Turbulence Predicts Survival Independently From Severity of Liver Dysfunction in Patients With Cirrhosis

Background: Reduced heart rate variability (HRV) is an independent predictor of mortality in patients with cirrhosis. However, conventional HRV indices can only be interpreted in individuals with normal sinus rhythm. In patients with recurrent premature ventricular complexes (PVCs), the predictive capacity of conventional HRV indices is compromised. Heart Rate Turbulence (HRT) represents the biphasic change of the heart rate after PVCs. This study was aimed to define whether HRT parameters could predict mortality in cirrhotic patients. Materials and Methods: 24 h electrocardiogram recordings were collected from 40 cirrhotic patients. Turbulence Onset was calculated as HRT indices. The enrolled patients were followed up for 12 months after the recruitment in relation to survival and/or transplantation. Results: During the follow-up period, 21 patients (52.5%) survived, 12 patients (30%) died and 7 patients (17.5%) had liver transplantation. Turbulence Onset was found to be strongly linked with mortality on Cox regression (Hazard ratio = 1.351, p < 0.05). Moreover, Turbulence Onset predicted mortality independently of MELD and Child-Pugh's Score. Conclusion: This study provides further evidence of autonomic dysfunction in cirrhosis and suggests that HRT is reliable alternative to HRV in patients with PVCs

MicroMotility: State of the art, recent accomplishments and perspectives on the mathematical modeling of bio-motility at microscopic scales

Mathematical modeling and quantitative study of biological motility (in particular, of motility at microscopic scales) is producing new biophysical insight and is offering opportunities for new discoveries at the level of both fundamental science and technology. These range from the explanation of how complex behavior at the level of a single organism emerges from body architecture, to the understanding of collective phenomena in groups of organisms and tissues, and of how these forms of swarm intelligence can be controlled and harnessed in engineering applications, to the elucidation of processes of fundamental biological relevance at the cellular and sub-cellular level. In this paper, some of the most exciting new developments in the fields of locomotion of unicellular organisms, of soft adhesive locomotion across scales, of the study of pore translocation properties of knotted DNA, of the development of synthetic active solid sheets, of the mechanics of the unjamming transition in dense cell collectives, of the mechanics of cell sheet folding in volvocalean algae, and of the self-propulsion of topological defects in active matter are discussed. For each of these topics, we provide a brief state of the art, an example of recent achievements, and some directions for future research

MODELLING WAVE-STRUCTURE INTERACTION WITH A NEW COMPRESSIBLE TWO-PHASE FLOW SOLVER

This contribution presents and investigates the effects of the air entrainment and air compressibility on the shape and magnitude of the wave impacts occurring at crown walls on top of sea defenses. To this purpose, a new solver, developed in the OpenFoam environment to represent the wave interactions with impermeable and porous coastal structures, accounting for the fluid compressibility, is checked against recent laboratory tests of wave overtopping and wave impacts. By comparing the first results of this new code to the ones obtained with the native solver dealing with incompressible fluids exclusively, significant advances in the representation of the pressure signals and peaks at the walls seem to be achieved