7,687 research outputs found
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
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)
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
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 -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
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