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

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

Thermal conductivity of the Toda lattice with conservative noise

We study the thermal conductivity of the one dimensional Toda lattice perturbed by a stochastic dynamics preserving energy and momentum. The strength of the stochastic noise is controlled by a parameter $\gamma$. We show that heat transport is anomalous, and that the thermal conductivity diverges with the length $n$ of the chain according to $\kappa(n) \sim n^\alpha$, with $0 < \alpha \leq 1/2$. In particular, the ballistic heat conduction of the unperturbed Toda chain is destroyed. Besides, the exponent $\alpha$ of the divergence depends on $\gamma$

Co-construction of a Data Collection Tool: A Case Study with Atikamekw Women

Gendered knowledge, roles and responsibilities in Indigenous cultures have historically been based on reciprocity and complementarity. By excluding Indigenous women from decision-making, colonial policies have reduced the knowledge base on which decisions are made. Indigenous women’s voices have also been largely excluded from research, and researchers have played a substantial role in their marginalization. It is within this context, and in a research decolonization effort, that we present a case study of the process of co-constructing a data collection tool with Atikamekw women. While preparing a research project on Indigenous women’s roles in the governance of land and natural resources, we worked with three Atikamekw women who gave particularly high importance to the process of obtaining participant consent. We designed the consent form together, so that it would address their concerns about trust, transparency, and community involvement throughout the research process. If research is to be decolonized, research tools should not be developed within university offices, but through meaningful collaboration with research participants