Diffusion in Fluctuating Media: The Resonant Activation Problem

We present a one-dimensional model for diffusion in a fluctuating lattice; that is a lattice which can be in two or more states. Transitions between the lattice states are induced by a combination of two processes: one periodic deterministic and the other stochastic. We study the dynamics of a system of particles moving in that medium, and characterize the problem from different points of view: mean first passage time (MFPT), probability of return to a given site ($P_{s_0}$), and the total length displacement or number of visited lattice sites ($\Lambda$). We observe a double {\it resonant activation}-like phenomenon when we plot the MFPT and $P_{s_0}$ as functions of the intensity of the transition rate stochastic component.Comment: RevTex, 15 pgs, 8 figures, submitted to Eur.Phys.J.

FIG: The Finite Improbability Generator

This paper introduces the statistical model checker FIGV, that estimates transient and steady-state reachability properties in stochastic automata. This software tool specialises in Rare Event Simulation via importance splitting, and implements the algorithms RESTART and Fixed Effort. FIG is push-button automatic since the user need not define an importance function: this function is derived from the model specification plus the property query. The tool operates with Input/Output Stochastic Automata with Urgency, aka IOSA models, described either in the native syntax or in the JANI exchange format. The theory backing FIG has demonstrated good efficiency, comparable to optimal importance splitting implemented ad hoc for specific models. Written in C++, FIG can outperform other state-of-the-art tools for Rare Event Simulation.</p

Bulk Mediated Surface Diffusion: The Infinite System Case

An analytical soluble model based on a Continuous Time Random Walk (CTRW) scheme for the adsorption-desorption processes at interfaces, called bulk-mediated surface diffusion, is presented. The time evolution of the effective probability distribution width on the surface is calculated and analyzed within an anomalous diffusion framework. The asymptotic behavior for large times shows a sub-diffusive regime for the effective surface diffusion but, depending on the observed range of time, other regimes may be obtained. Montecarlo simulations show excellent agreement with analytical results. As an important byproduct of the indicated approach, we present the evaluation of the time for the first visit to the surface.Comment: 15 pages, 7 figure

Bulk Mediated Surface Diffusion: Finite System Case

We address the dynamics of adsorbed molecules (a fundamental issue in surface physics) within the framework of a Master Equation scheme, and study the diffusion of particles in a finite cubic lattice whose boundaries are at the $z=1$ and the $z=L$ planes where $L = 2,3,4,...$, while the $x$ and $y$ directions are unbounded. As we are interested in the effective diffusion process at the interface $z = 1$, we calculate analytically the conditional probability for finding the system on the $z=1$ plane as well as the surface dispersion as a function of time and compare these results with Monte Carlo simulations finding an excellent agreement.Comment: 19 pages, 8 figure

Narrow-escape-time problem: the imperfect trapping case

We present a master equation approach to the \emph{narrow escape time} (NET) problem, i.e. the time needed for a particle contained in a confining domain with a single narrow opening, to exit the domain for the first time. We introduce a finite transition probability, $\nu$, at the narrow escape window allowing the study of the imperfect trapping case. Ranging from 0 to $\infty$, $\nu$ allowed the study of both extremes of the trapping process: that of a highly deficient capture, and situations where escape is certain ("perfect trapping" case). We have obtained analytic results for the basic quantity studied in the NET problem, the \emph{mean escape time} (MET), and we have studied its dependence in terms of the transition (desorption) probability over (from) the surface boundary, the confining domain dimensions, and the finite transition probability at the escape window. Particularly we show that the existence of a global minimum in the NET depends on the `imperfection' of the trapping process. In addition to our analytical approach, we have implemented Monte Carlo simulations, finding excellent agreement between the theoretical results and simulations.Comment: 9 page

Efficient Algorithms for Quantitative Attack Tree Analysis

Numerous analysis methods for quantitative attack tree analysis have been proposed. These algorithms compute relevant security metrics, i.e. performance indicators that quantify how good the security of a system is, such as the most likely attack, the cheapest, or the most damaging one. This paper classifies attack trees in two dimensions: proper trees vs. directed acyclic graphs (i.e. with shared subtrees); and static vs. dynamic gates. For each class, we propose novel algorithms that work over a generic attribute domain, encompassing a large number of concrete security metrics defined on the attack tree semantics. We also analyse the computational complexity of our methods

Efficient Algorithms for Quantitative Attack Tree Analysis

Numerous analysis methods for quantitative attack tree analysis have been proposed. These algorithms compute relevant security metrics, i.e. performance indicators that quantify how good the security of a system is, such as the most likely attack, the cheapest, or the most damaging one. This paper classifies attack trees in two dimensions: proper trees vs. directed acyclic graphs (i.e. with shared subtrees); and static vs. dynamic gates. For each class, we propose novel algorithms that work over a generic attribute domain, encompassing a large number of concrete security metrics defined on the attack tree semantics. We also analyse the computational complexity of our methods

Primary Blast Traumatic Brain Injury in the Rat: Relating Diffusion Tensor Imaging and Behavior

The incidence of traumatic brain injury (TBI) among military personnel is at its highest point in U.S. history. Experimental animal models of blast have provided a wealth of insight into blast injury. The mechanisms of neurotrauma caused by blast, however, are still under debate. Specifically, it is unclear whether the blast shockwave in the absence of head motion is sufficient to induce brain trauma. In this study, the consequences of blast injury were investigated in a rat model of primary blast TBI. Animals were exposed to blast shockwaves with peak reflected overpressures of either 100 or 450 kPa (39 and 110 kPa incident pressure, respectively) and subsequently underwent a battery of behavioral tests. Diffusion tensor imaging (DTI), a promising method to detect blast injury in humans, was performed on fixed brains to detect and visualize the spatial dependence of blast injury. Blast TBI caused significant deficits in memory function as evidenced by the Morris Water Maze, but limited emotional deficits as evidenced by the Open Field Test and Elevated Plus Maze. Fractional anisotropy, a metric derived from DTI, revealed significant brain abnormalities in blast-exposed animals. A significant relationship between memory deficits and brain microstructure was evident in the hippocampus, consistent with its role in memory function. The results provide fundamental insight into the neurological consequences of blast TBI, including the evolution of injury during the sub-acute phase and the spatially dependent pattern of injury. The relationship between memory dysfunction and microstructural brain abnormalities may provide insight into the persistent cognitive difficulties experienced by soldiers exposed to blast neurotrauma and may be important to guide therapeutic and rehabilitative efforts