From a kinetic equation to a diffusion under an anomalous scaling

A linear Boltzmann equation is interpreted as the forward equation for the probability density of a Markov process (K(t), i(t), Y(t)), where (K(t), i(t)) is an autonomous reversible jump process, with waiting times between two jumps with finite expectation value but infinite variance, and Y(t) is an additive functional of K(t). We prove that under an anomalous rescaling Y converges in distribution to a two-dimensional Brownian motion. As a consequence, the appropriately rescaled solution of the Boltzmann equation converges to a diffusion equation

Long time, large scale limit of the Wigner transform for a system of linear oscillators in one dimension

We consider the long time, large scale behavior of the Wigner transform W_\eps(t,x,k) of the wave function corresponding to a discrete wave equation on a 1-d integer lattice, with a weak multiplicative noise. This model has been introduced in Basile, Bernardin, and Olla to describe a system of interacting linear oscillators with a weak noise that conserves locally the kinetic energy and the momentum. The kinetic limit for the Wigner transform has been shown in Basile, Olla, and Spohn. In the present paper we prove that in the unpinned case there exists $\gamma_0>0$ such that for any $\gamma\in(0,\gamma_0]$ the weak limit of W_\eps(t/\eps^{3/2\gamma},x/\eps^{\gamma},k), as \eps\ll1, satisfies a one dimensional fractional heat equation $\partial_t W(t,x)=-\hat c(-\partial_x^2)^{3/4}W(t,x)$ with $\hat c>0$. In the pinned case an analogous result can be claimed for W_\eps(t/\eps^{2\gamma},x/\eps^{\gamma},k) but the limit satisfies then the usual heat equation

Asymptotics of the solutions of the stochastic lattice wave equation

We consider the long time limit theorems for the solutions of a discrete wave equation with a weak stochastic forcing. The multiplicative noise conserves the energy and the momentum. We obtain a time-inhomogeneous Ornstein-Uhlenbeck equation for the limit wave function that holds both for square integrable and statistically homogeneous initial data. The limit is understood in the point-wise sense in the former case, and in the weak sense in the latter. On the other hand, the weak limit for square integrable initial data is deterministic

Superintendent Relations: Impact of Leadership on Student Learning

Since the implementation of No Child Left Behind school systems across America have been searching for the answer to increasing student achievement. Researchers have found many methods of increasing achievement through leadership behaviors, however others have found that superintendents have a very small impact on achievement and proficiency. The purpose of this study was to investigate the correlation between superintendent leadership behaviors and student proficiency rates in school districts in rural West Virginia. This quantitative, correlational study specifically sought to discover how accurately school proficiency rates could be predicted from a linear combination of superintendent instructional leadership behaviors. Fifty-five school districts in rural West Virginia were the target for this study. Of the 55 districts, a convenience sample of 41 superintendents were used for this study. Superintendents self-ranked their level of emphasis placed on leadership behaviors in the Superintendent Instructional Leadership Survey (SILS) using a five-point Likert Scale. A multiple regression was conducted to determine the correlation between the independent variable (superintendent leadership behaviors) and dependent variable (student proficiency) and found a high level of prediction, R=.962, p \u3c .001

Superdiffusion of energy in Hamiltonian systems perturbed by a conservative noise

We review some recent results on the anomalous diffusion of energy in systems of 1D coupled oscillators and we revisit the role of momentum conservation.Comment: Proceedings of the conference PSPDE 2012 https://sites.google.com/site/meetingpspde

Thermal conductivity in harmonic lattices with random collisions

We review recent rigorous mathematical results about the macroscopic behaviour of harmonic chains with the dynamics perturbed by a random exchange of velocities between nearest neighbor particles. The random exchange models the effects of nonlinearities of anharmonic chains and the resulting dynamics have similar macroscopic behaviour. In particular there is a superdiffusion of energy for unpinned acoustic chains. The corresponding evolution of the temperature profile is governed by a fractional heat equation. In non-acoustic chains we have normal diffusivity, even if momentum is conserved.Comment: Review paper, to appear in the Springer Lecture Notes in Physics volume "Thermal transport in low dimensions: from statistical physics to nanoscale heat transfer" (S. Lepri ed.

Online and offline security policy assessment

Network architectures and applications are becoming increasingly complex. Several approaches to automatically enforce configurations on devices, applications and services have been proposed, such as Policy-Based Network Management (PBNM). However, the management of enforced configurations in production environments (e.g. data center) is a crucial and complex task. For example, updates on firewall configuration to change a set of rules. Although this task is fundamental for complex systems, few effective solutions have been proposed for monitoring and managing enforced configurations. This work proposes a novel approach to monitor and manage enforced configurations in production environments. The main contributions of this paper are a formal model to identify/generate traffic flows and to verify the enforced configurations, and a slim and transparent framework to perform the policy assessment. We have implemented and validated our approach in a virtual environment in order to evaluate different scenarios. The results demonstrate that the prototype is effective and has good performance, therefore our model can be effectively used to analyse several types of IT infrastructures. A further interesting result is that our approach is complementary to PBNM

UNVEIL (Understanding Vulnerability to Expand Insight on Local units)

Recent crises have exposed rooted inequalities across territories, which have unveiled their different levels of vulnerability and,consequently, their different capacity to resist and react to challenges. A territory’s level of exposure to challenges and the featuresthat can heighten the impact of crises is commonly referred to as Vulnerability. Describing and monitoring territories’ patterns ofvulnerability is key to understanding their strengths and weaknesses, in order to identify the tailor-made actions that would makepolitical interventions effective and efficient. Measuring vulnerability, however, requires disentangling the concept across several dimensions, which might not be limited to socio-economic or environmental factors. In this respect, the often neglected political-institutional dimension of vulnerability stands out, since it determines a territory’s ability to effectively deliver policies and provide timely responses to crises through effective and democratic institutions (EC, SFR 2020). Vulnerability assessments are usually carried out at the supranational (e.g, the European Union), or country level. Subnational levels, and especially the smallest local units, are seldom included in the measurement efforts, despite often being the first bulwark of resistance against challenges, as the outbreak of the COVID-19 pandemic proved (CoR 2020; 2021). Against this background, the UNVEIL project undertakes the challenge of systematically embedding the measurement of the vulnerability of the local units into policymaking. It will do so by providing an encompassing conceptualization of vulnerability, across three main dimensions (Environmental, Socio-economic, Political-Institutional), on which developing an aggregate index (ESPIV index) for the measurement and monitoring of vulnerability of local units, and then provide policy-makers the knowledge to enact appropriate strategies. To empirically test the ESPIV index, UNVEIL will foreground Italy’s municipalities, which provide a heterogeneous sample of territories with different magnitudes of vulnerability and thus a sound starting point for future comparative research. UNVEIL has the ambition to have both scientific and practical relevance. Scientifically, it will contribute by adopting a multidisciplinary approach for the conceptualization and operationalization of vulnerability. UNVEIL will build on a combination of comparative, statistical, and case-study research design, and make use of both quantitative (descriptive and explanatory analyses of a large-N dataset, factor-analysis) and qualitative (literature review, semi-structured interviews, archive research) analysis to triangulate on data. The practical relevance of the UNVEIL project relies on the development of the ESPIV index, which can be used by policymakers to understand their territory’s vulnerability and thus devise and enact the most appropriate, tailor-made, and evidence-based strategies of action