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

Least costly energy management for series hybrid electric vehicles

Energy management of plug-in Hybrid Electric Vehicles (HEVs) has different challenges from non-plug-in HEVs, due to bigger batteries and grid recharging. Instead of tackling it to pursue energetic efficiency, an approach minimizing the driving cost incurred by the user - the combined costs of fuel, grid energy and battery degradation - is here proposed. A real-time approximation of the resulting optimal policy is then provided, as well as some analytic insight into its dependence on the system parameters. The advantages of the proposed formulation and the effectiveness of the real-time strategy are shown by means of a thorough simulation campaign

Hidden scaling patterns and universality in written communication

The temporal statistics exhibited by written correspondence appear to be media dependent, with features which have so far proven difficult to characterize. We explain the origin of these difficulties by disentangling the role of spontaneous activity from decision-based prioritizing processes in human dynamics, clocking all waiting times through each agent's `proper time' measured by activity. This unveils the same fundamental patterns in written communication across all media (letters, email, sms), with response times displaying truncated power-law behavior and average exponents near -3/2. When standard time is used, the response time probabilities are theoretically predicted to exhibit a bi-modal character, which is empirically borne out by our new years-long data on email. These novel perspectives on the temporal dynamics of human correspondence should aid in the analysis of interaction phenomena in general, including resource management, optimal pricing and routing, information sharing, emergency handling.Comment: 27 pages, 10 figure

Neutral dynamics with environmental noise: age-size statistics and species lifetimes

Neutral dynamics, where taxa are assumed to be demographically equivalent and their abundance is governed solely by the stochasticity of the underlying birth-death process, has proved itself as an important minimal model that accounts for many empirical datasets in genetics and ecology. However, the restriction of the model to demographic [${\cal{O}} ({\sqrt N})$] noise yields relatively slow dynamics that appears to be in conflict with both short-term and long-term characteristics of the observed systems. Here we analyze two of these problems - age size relationships and species extinction time - in the framework of a neutral theory with both demographic and environmental stochasticity. It turns out that environmentally induced variations of the demographic rates control the long-term dynamics and modify dramatically the predictions of the neutral theory with demographic noise only, yielding much better agreement with empirical data. We consider two prototypes of "zero mean" environmental noise, one which is balanced with regard to the arithmetic abundance, another balanced in the logarithmic (fitness) space, study their species lifetime statistics and discuss their relevance to realistic models of community dynamics

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

Oscillatory Behavior in a Model of Non-Markovian Mean Field Interacting Spins

We analyze a non-Markovian mean field interacting spin system, related to the Curie\u2013Weiss model. We relax the Markovianity assumption by replacing the memoryless distribution of the waiting times of a classical spin-flip dynamics with a distribution with memory. The resulting stochastic evolution for a single particle is a spin-valued renewal process, an example of a two-state semi-Markov process. We associate to the individual dynamics an equivalent Markovian description, which is the subject of our analysis. We study a corresponding interacting particle system, where a mean field interaction-depending on the magnetization of the system-is introduced as a time scaling on the waiting times between two successive particle\u2019s jumps. Via linearization arguments on the Fokker\u2013Planck mean field limit equation, we give evidence of emerging periodic behavior. Specifically, numerical analysis on the discrete spectrum of the linearized operator, characterized by the zeros of an explicit holomorphic function, suggests the presence of a Hopf bifurcation for a critical value of the temperature. The presence of a Hopf bifurcation in the limit equation matches the emergence of a periodic behavior obtained by simulating the N-particle system

Oscillatory Behavior in a Model of Non-Markovian Mean Field Interacting Spins

We analyze a non-Markovian mean field interacting spin system, related to the Curie\u2013Weiss model. We relax the Markovianity assumption by replacing the memoryless distribution of the waiting times of a classical spin-flip dynamics with a distribution with memory. The resulting stochastic evolution for a single particle is a spin-valued renewal process, an example of a two-state semi-Markov process. We associate to the individual dynamics an equivalent Markovian description, which is the subject of our analysis. We study a corresponding interacting particle system, where a mean field interaction-depending on the magnetization of the system-is introduced as a time scaling on the waiting times between two successive particle\u2019s jumps. Via linearization arguments on the Fokker\u2013Planck mean field limit equation, we give evidence of emerging periodic behavior. Specifically, numerical analysis on the discrete spectrum of the linearized operator, characterized by the zeros of an explicit holomorphic function, suggests the presence of a Hopf bifurcation for a critical value of the temperature. The presence of a Hopf bifurcation in the limit equation matches the emergence of a periodic behavior obtained by simulating the N-particle system

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