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

FPGA based remote code integrity verification of programs in distributed embedded systems

The explosive growth of networked embedded systems has made ubiquitous and pervasive computing a reality. However, there are still a number of new challenges to its widespread adoption that include scalability, availability, and, especially, security of software. Among the different challenges in software security, the problem of remote-code integrity verification is still waiting for efficient solutions. This paper proposes the use of reconfigurable computing to build a consistent architecture for generation of attestations (proofs) of code integrity for an executing program as well as to deliver them to the designated verification entity. Remote dynamic update of reconfigurable devices is also exploited to increase the complexity of mounting attacks in a real-word environment. The proposed solution perfectly fits embedded devices that are nowadays commonly equipped with reconfigurable hardware components that are exploited to solve different computational problems

DIFFUSION LIMIT FOR A KINETIC EQUATION WITH A THERMOSTATTED INTERFACE

International audienceWe consider a linear phonon Boltzmann equation with a reflecting/transmitting/absorbing interface. This equation appears as the Boltzmann-Grad limit for the energy density function of a harmonic chain of oscillators with inter-particle stochastic scattering in the presence of a heat bath at temperature T in contact with one oscillator at the origin. We prove that under the diffusive scaling the solutions of the phonon equation tend to the solution ρ(t, y) of a heat equation with the boundary condition ρ(t, 0) ≡ T

Diffusion limit for a kinetic equation with a thermostatted interface

We consider a linear phonon Boltzmann equation with a reflecting/transmitting/absorbing interface. This equation appears as the Boltzmann-Grad limit for the energy density function of a harmonic chain of oscillators with inter-particle stochastic scattering in the presence of a heat bath at temperature $T$ in contact with one oscillator at the origin. We prove that under the diffusive scaling the solutions of the phonon equation tend to the solution $\rho(t,y)$ of a heat equation with the boundary condition $\rho(t,0)\equiv T$

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

La gestione del dolore e della rappresentazione corporea nella sindrome dell'arto fantasma: implicazioni per la fisioterapia

INTRODUZIONE La sindrome dell’altro fantasma è un fenomeno tanto diffuso quanto talvolta poco conosciuto. L’obiettivo di questo studio è verificare, tramite la ricerca di studi reperibili nella letteratura recente, le prove di efficacia rispetto ai più diffusi trattamenti riabilitativi nella risoluzione della sintomatologia della sindrome dell’arto fantasma. La principale teoria riguardo l’eziologia e la fisiopatologia di questa sindrome sostiene che la sensazione dell’arto fantasma ed il conseguente dolore, siano dovuti ad una discrepanza tra l’intenzione motoria, la rappresentazione corticale dell’arto amputato ed i feedback soprattutto visivi (ma anche tattili e propriocettivi) che il cervello riceve successivamente all’invio dell’input motorio riferito all’arto stesso. Il trattamento per questo tipo di dolore si pone come obiettivi quello di fornire, tramite alcuni espedienti, un feedback soprattutto visivo che corrisponda all’intenzione motoria e quello di ristabilire un’immagine corporea corretta. METODI Per raggiungere l’obiettivo di questo lavoro sono stati ricercati, selezionati ed analizzati articoli ottenuti dalle principali banche dati biomedico (PubMed, PEDro, The Cochrane Library) riguardanti interventi di tipo riabilitativo fisioterapico somministrati a persone amputate di arti superiori/inferiori di qualsiasi età. RISULTATI Le proposte terapeutiche prese in analisi in questo studio sono: la Mirror Therapy, la Observation Therapy, e la terapia tramite visualizzazione mentale. La prima ha ottenuto percentuali di efficacia molto alte (in media circa l’80% dei casi ha ottenuto una diminuzione del dolore di circa il 26%). Anche la Observation Therapy ha ottenuto buoni risultati (circa il 70% di efficacia), mentre la visualizzazione mentale sembra ottenere risultati soddisfacenti solo in uno degli studi considerati. CONCLUSIONI La più efficace delle tre proposte terapeutiche sembra essere la Mirror Therapy ma dagli studi analizzati emerge il fatto che le altre due possano essere comunque delle valide alternative nei casi in cui essa non sia applicabile