Automatic Probabilistic Program Verification through Random Variable Abstraction

The weakest pre-expectation calculus has been proved to be a mature theory to analyze quantitative properties of probabilistic and nondeterministic programs. We present an automatic method for proving quantitative linear properties on any denumerable state space using iterative backwards fixed point calculation in the general framework of abstract interpretation. In order to accomplish this task we present the technique of random variable abstraction (RVA) and we also postulate a sufficient condition to achieve exact fixed point computation in the abstract domain. The feasibility of our approach is shown with two examples, one obtaining the expected running time of a probabilistic program, and the other the expected gain of a gambling strategy. Our method works on general guarded probabilistic and nondeterministic transition systems instead of plain pGCL programs, allowing us to easily model a wide range of systems including distributed ones and unstructured programs. We present the operational and weakest precondition semantics for this programs and prove its equivalence

Intrinsically knotted graphs with 21 edges

We show that the 14 graphs obtained by $\nabla\mathrm{Y}$ moves on K_7 constitute a complete list of the minor minimal intrinsically knotted graphs on 21 edges. We also present evidence in support of a conjecture that the 20 graph Heawood family, obtained by a combination of $\nabla\mathrm{Y}$ and $\mathrm{Y}\nabla$ moves on K_7, is the list of graphs of size 21 that are minor minimal with respect to the property not 2--apex.Comment: 21 pages, 11 figure

The h-index as an almost-exact function of some basic statistics

As is known, the h-index, h, is an exact function of the citation pattern. At the same time, and more generally, it is recognized that h is "loosely" related to the values of some basic statistics, such as the number of publications and the number of citations. In the present study we introduce a formula that expresses the h-index as an almost-exact function of some (four) basic statistics. On the basis of an empirical study-in which we consider citation data obtained from two different lists of journals from two quite different scientific fields-we provide evidence that our ready-to-use formula is able to predict the h-index very accurately (at least for practical purposes). For comparative reasons, alternative estimators of the h-index have been considered and their performance evaluated by drawing on the same dataset. We conclude that, in addition to its own interest, as an effective proxy representation of the h-index, the formula introduced may provide new insights into "factors" determining the value of the h-index, and how they interact with each other.Web of Science11321228120

Resonant Dampers for Parametric Instabilities in Gravitational Wave Detectors

Advanced gravitational wave interferometric detectors will operate at their design sensitivity with nearly 1MW of laser power stored in the arm cavities. Such large power may lead to the uncontrolled growth of acoustic modes in the test masses due to the transfer of optical energy to the mechanical modes of the arm cavity mirrors. These parametric instabilities have the potential of significantly compromising the detector performance and control. Here we present the design of "acoustic mode dampers" that use the piezoelectric effect to reduce the coupling of optical to mechanical energy. Experimental measurements carried on an Advanced LIGO-like test mass shown a 10-fold reduction in the amplitude of several mechanical modes, thus suggesting that this technique can greatly mitigate the impact of parametric instabilities in advanced detectors

Estimating the transition matrix of a Markov chain observed at random times

In this paper we develop a statistical estimation technique to recover the transition kernel $P$ of a Markov chain $X=(X_m)_{m \in \mathbb N}$ in presence of censored data. We consider the situation where only a sub-sequence of $X$ is available and the time gaps between the observations are iid random variables. Under the assumption that neither the time gaps nor their distribution are known, we provide an estimation method which applies when some transitions in the initial Markov chain $X$ are known to be unfeasible. A consistent estimator of $P$ is derived in closed form as a solution of a minimization problem. The asymptotic performance of the estimator is then discussed in theory and through numerical simulations

Progetto di celle analogiche in tecnologia BCD6s per il pilotaggio e la lettura di flussimetri integrati

Progetto di celle analogiche in tecnologia BCD6s per il pilotaggio e la lettura di flussimetri integrat

Studio di fattibilita' per un impianto di produzione di energia elettrica tramite biomasse nel comune di Santa Luce, Pisa

Si considera il territorio comunale di Santa Luce, Pisa, come zona di produzione e sfruttamento di biomassa al fine di generare energia elettrica. Dalla disponibilità di biomassa stessa, si verifica la possibilità di alimentare un impianto di produzione di energia elettrica a fonti rinnovabili, esaminando le varie tecnologie esistenti e valutandone l'opportunità rispetto allo specifico scenario. Si pone una speciale attenzione al bilancio energetico globale, dal prelievo da campo o bosco della biomassa tal quale, all'immissione in rete dell'energia prodotta, sottolineando i passaggi necessari per un corretto ed efficiente funzionamento dell'intero impianto e filiera. Si valuta la convenienza all’utilizzo delle biomasse a fini energetici, in particolare, in riferimento alla logistica (ad esempio, costi di trasporto e stoccaggio, che tendono molto incidere sui costi del materiale alla bocca dell’impianto), ai sistemi di produzione di energia (ad esempio, il tipo e le dimensioni degli impianti e la forma del materiale di alimentazione degli stessi) e ai costi di produzione (confronto con combustibili convenzionali, in genere fossili, possibile applicazione delle varie forme di incentivo previste per le fonti energetiche rinnovabili, quali le biomasse)