Begin, After, and Later: a Maximal Decidable Interval Temporal Logic

Interval temporal logics (ITLs) are logics for reasoning about temporal statements expressed over intervals, i.e., periods of time. The most famous ITL studied so far is Halpern and Shoham's HS, which is the logic of the thirteen Allen's interval relations. Unfortunately, HS and most of its fragments have an undecidable satisfiability problem. This discouraged the research in this area until recently, when a number non-trivial decidable ITLs have been discovered. This paper is a contribution towards the complete classification of all different fragments of HS. We consider different combinations of the interval relations Begins, After, Later and their inverses Abar, Bbar, and Lbar. We know from previous works that the combination ABBbarAbar is decidable only when finite domains are considered (and undecidable elsewhere), and that ABBbar is decidable over the natural numbers. We extend these results by showing that decidability of ABBar can be further extended to capture the language ABBbarLbar, which lays in between ABBar and ABBbarAbar, and that turns out to be maximal w.r.t decidability over strongly discrete linear orders (e.g. finite orders, the naturals, the integers). We also prove that the proposed decision procedure is optimal with respect to the complexity class

Basic properties of nonsmooth Hormander's vector fields and Poincare's inequality

We consider a family of vector fields defined in some bounded domain of R^p, and we assume that they satisfy Hormander's rank condition of some step r, and that their coefficients have r-1 continuous derivatives. We extend to this nonsmooth context some results which are well-known for smooth Hormander's vector fields, namely: some basic properties of the distance induced by the vector fields, the doubling condition, Chow's connectivity theorem, and, under the stronger assumption that the coefficients belong to C^{r-1,1}, Poincare's inequality. By known results, these facts also imply a Sobolev embedding. All these tools allow to draw some consequences about second order differential operators modeled on these nonsmooth Hormander's vector fields.Comment: 60 pages, LaTeX; Section 6 added and Section 7 (6 in the previous version) changed. Some references adde

Bluecat: A Local Uncertainty Estimator for Deterministic Simulations and Predictions

We present a new method for simulating and predicting hydrologic variables with uncertainty assessment and provide example applications to river flows. The method is identified with the acronym “Bluecat” and is based on the use of a deterministic model which is subsequently converted to a stochastic formulation. The latter provides an adjustment on statistical basis of the deterministic prediction along with its confidence limits. The distinguishing features of the proposed approach are the ability to infer the probability distribution of the prediction without requiring strong hypotheses on the statistical characterization of the prediction error (e.g., normality, homoscedasticity), and its transparent and intuitive use of the observations. Bluecat makes use of a rigorous theory to estimate the probability distribution of the predictand conditioned by the deterministic model output, by inferring the conditional statistics of observations. Therefore Bluecat bridges the gaps between deterministic (possibly physically based, or deep learning-based) and stochastic models, as well as between rigorous theory and transparent use of data with an innovative and user oriented approach. We present two examples of application to the case studies of the Arno river at Subbiano and Sieve river at Fornacina. The results confirm the distinguishing features of the method along with its technical soundness. We provide an open software working in the R environment, along with help facilities and detailed instructions to reproduce the case studies presented here

Climate Extrapolations in Hydrology: The Expanded Bluecat Methodology

Bluecat is a recently proposed methodology to upgrade a deterministic model (D-model) into a stochastic one (S-model), based on the hypothesis that the information contained in a time series of observations and the concurrent predictions made by the D-model is sufficient to support this upgrade. The prominent characteristics of the methodology are its simplicity and transparency, which allow its easy use in practical applications, without sophisticated computational means. In this paper, we utilize the Bluecat methodology and expand it in order to be combined with climate model outputs, which often require extrapolation out of the range of values covered by observations. We apply the expanded methodology to the precipitation and temperature processes in a large area, namely the entire territory of Italy. The results showcase the appropriateness of the method for hydroclimatic studies, as regards the assessment of the performance of the climate projections, as well as their stochastic conversion with simultaneous bias correction and uncertainty quantification

Generalized Jacobi identities and ball-box theorem for horizontally regular vector fields

We consider a family of vector fields and we assume a horizontal regularity on their derivatives. We discuss the notion of commutator showing that different definitions agree. We apply our results to the proof of a ball-box theorem and Poincar\'e inequality for nonsmooth H\"ormander vector fields.Comment: arXiv admin note: material from arXiv:1106.2410v1, now three separate articles arXiv:1106.2410v2, arXiv:1201.5228, arXiv:1201.520

Analytic determination of dynamical and mosaic length scales in a Kac glass model

We consider a disordered spin model with multi-spin interactions undergoing a glass transition. We introduce a dynamic and a static length scales and compute them in the Kac limit (long--but--finite range interactions). They diverge at the dynamic and static phase transition with exponents (respectively) -1/4 and -1. The two length scales are approximately equal well above the mode coupling transition. Their discrepancy increases rapidly as this transition is approached. We argue that this signals a crossover from mode coupling to activated dynamics.Comment: 4 pages, 4 eps figures. New version conform to the published on

Replicated Bethe Free Energy: A Variational Principle behind Survey Propagation

A scheme to provide various mean-field-type approximation algorithms is presented by employing the Bethe free energy formalism to a family of replicated systems in conjunction with analytical continuation with respect to the number of replicas. In the scheme, survey propagation (SP), which is an efficient algorithm developed recently for analyzing the microscopic properties of glassy states for a fixed sample of disordered systems, can be reproduced by assuming the simplest replica symmetry on stationary points of the replicated Bethe free energy. Belief propagation and generalized SP can also be offered in the identical framework under assumptions of the highest and broken replica symmetries, respectively.Comment: appeared in Journal of the Physical Society of Japan 74, 2133-2136 (2005

The effect of voltage distortion on ageing acceleration of insulation systems under partial discharge activity

The features of harmonic distortion which may affect significantly the reliability of typical ac-power network equipment, such as low-voltage self-healing capacitors used for reactive power and harmonic compensation are investigated. Moreover, the effect of high-frequency pulse-like voltage generated by adjustable speed drives (ASD) on electrical machine insulation is also investigated, resorting to life tests carried out on different insulating materials of the standard and "corona resistant" type, at electrical field levels able to incept partial discharges (PD)

Error-correcting code on a cactus: a solvable model

An exact solution to a family of parity check error-correcting codes is provided by mapping the problem onto a Husimi cactus. The solution obtained in the thermodynamic limit recovers the replica symmetric theory results and provides a very good approximation to finite systems of moderate size. The probability propagation decoding algorithm emerges naturally from the analysis. A phase transition between decoding success and failure phases is found to coincide with an information-theoretic upper bound. The method is employed to compare Gallager and MN codes.Comment: 7 pages, 3 figures, with minor correction

On Spin-Glass Complexity

We study the quenched complexity in spin-glass mean-field models satisfying the Becchi-Rouet-Stora-Tyutin supersymmetry. The outcome of such study, consistent with recent numerical results, allows, in principle, to conjecture the absence of any supersymmetric contribution to the complexity in the Sherrington-Kirkpatrick model. The same analysis can be applied to any model with a Full Replica Symmetry Breaking phase, e.g. the Ising $p$-spin model below the Gardner temperature. The existence of different solutions, breaking the supersymmetry, is also discussed.Comment: 4 pages, 2 figures; Text changed in some parts, typos corrected, Refs. [17],[21] and [22] added, two Refs. remove