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Kowalski and Sergot's (1986) Event Calculus (EC) is a simple temporal formalism that, given a set of event occurrences, derives the maximal validity intervals (MVIs) over which properties initiated or terminated by these events hold. We extend this calculus to give a semantic foundation to our Quantifiers and Connectives Event Calculus (QCEC). In particular, we extend the range of queries accepted by EC, which has so far been limited to Boolean combinations of MVI verification or computation requests, to admit arbitrary quantification over events and properties. We demonstrate the added expressive power by encoding a medical diagnosis problem as a case study. Moreover, we give a /spl lambda/Prolog implementation of this formalism and analyze the computational complexity of the extended calculus.

We consider the dynamics of a diluted mean-field spin glass model in the aging regime. The model presents a particularly rich heterogeneous behavior. In order to catch this behavior, we perform a **spin-by-spin analysis** for a **given disorder realization**. The results compare well with the outcome of a static calculation which uses the ``survey propagation'' algorithm of Mezard, Parisi, and Zecchina [Sciencexpress 10.1126/science.1073287 (2002)]. We thus confirm the connection between statics and dynamics at the level of single degrees of freedom. Moreover, working with single-site quantities, we can introduce a new response-vs-correlation plot, which clearly shows how heterogeneous degrees of freedom undergo coherent structural rearrangements. Finally we discuss the general scenario which emerges from our work and (possibly) applies to more realistic glassy models. Interestingly enough, some features of this scenario can be understood recurring to thermometric considerations., 4 pages, 5 figures (7 eps files)

The state-of-the-art error correcting codes are based on large random constructions (random graphs, random permutations, ...) and are decoded by linear-time iterative algorithms. Because of these features, they are remarkable examples of diluted mean-field spin glasses, both from the static and from the dynamic points of view. We analyze the behavior of decoding algorithms using the mapping onto statistical-physics models. This allows to understand the intrinsic (i.e. algorithm independent) features of this behavior., Comment: 40 pages, 29 eps figures

We consider a two-dimensional sigma-model with discrete icosahedral/dodecahedral symmetry. We present high-precision finite-size numerical results that show that the continuum limit of this model is different from the continuum limit of the rotationally invariant O(3) sigma-model., Lattice2001(spin), 3 pages, 4 figures

Randomized search algorithms for hard combinatorial problems exhibit a large variability of performances. We study the different types of rare events which occur in such out-of-equilibrium stochastic processes and we show how they cooperate in determining the final distribution of running times. As a by-product of our analysis we show how search algorithms are optimized by random restarts.

We consider a two-dimensional $\sigma$-model with discrete icosahedral/dodecahedral symmetry. Using the perturbative renormalization group, we argue that this model has a different continuum limit with respect to the O(3) $\sigma$ model. Such an argument is confirmed by a high-precision numerical simulation., Comment: 5 pages including 6 postscript figures. Talk given at HEP01 in Budapest, Hungary, in July 2001

Turbo codes are a very efficient method for communicating reliably through a noisy channel. There is no theoretical understanding of their effectiveness. In [1] they are mapped onto a class of disordered spin models. The analytical calculations concerning these models are reported here. We prove the existence of a no-error phase and compute its local stability threshold. As a byproduct, we gain some insight into the dynamics of the decoding algorithm., Comment: 26 pages, 3 eps figures

We consider the short-distance behaviour of the product of the Noether O(N) currents in the lattice nonlinear sigma-model. We compare the numerical results with the predictions of the operator product expansion, using one-loop perturbative renormalization-group improved Wilson coefficients. We find that, even on quite small lattices (m a \approx 1/6), the perturbative operator product expansion describes that data with an error of 5-10% in a large window 2a \ltapprox x \ltapprox m^{-1}. We present a detailed discussion of the possible systematic errors., 53 pages, 11 figures (26 eps files)

The operator product expansion is used to compute the matrix elements of composite renormalized operators on the lattice. We study the product of two fundamental fields in the two-dimensional sigma-model and discuss the possible sources of systematic errors. The key problem turns out to be the violation of asymptotic scaling., Lattice 99 (Improvement and Renormalization), 3 pages, 3 eps figures

The "turbo codes", recently proposed by Berrou et. al. are written as a disordered spin Hamiltonian. It is shown that there is a threshold Theta such that for signal to noise ratios v^2 / w^2 > Theta, the error probability per bit vanishes in the thermodynamic limit, i.e. the limit of infinitly long sequences. The value of the threshold has been computed for two particular turbo codes. It is found that it depends on the code. These results are compared with numerical simulations., 23 pages, 6 figures: Fig.2 has been replaced (in the preceding version it was identical to Fig.1)

It has been recently proposed to use the operator product expansion to evaluate the expectation values of renormalized operators without the need of a direct computation of the relevant renormalization constants. We test the viability of this idea in the two-dimensional non-linear sigma-model discussing the non-perturbative renormalization of the energy-momentum tensor., Comment: LATTICE98(matrixelement), uses espcrc2 and epsfig, 3 pages, 2 eps figures

For the O(N) sigma-model we studied the improvement program for actions with two- and four-spin interactions. An interesting example is an action which is reflection-positive, on-shell improved, and has all the coupling defined on an elementary plaquette. We show the large N solution and preliminary Monte Carlo results for N=3., Comment: Talk presented at Lattice '97 (Improvement and Renormalisation), Edinburgh (UK), July 1997. LaTeX2e, 3 pages, 2 figures, uses espcrc2 and epsfig

We study the set of solutions of random k-satisfiability formulae through the cavity method. It is known that, for an interval of the clause-to-variables ratio, this decomposes into an exponential number of pure states (clusters). We refine substantially this picture by: (i) determining the precise location of the clustering transition; (ii) uncovering a second `condensation' phase transition in the structure of the solution set for k larger or equal than 4. These results both follow from computing the large deviation rate of the internal entropy of pure states. From a technical point of view our main contributions are a simplified version of the cavity formalism for special values of the Parisi replica symmetry breaking parameter m (in particular for m=1 via a correspondence with the tree reconstruction problem) and new large-k expansions., Comment: 30 pages, 14 figures, typos corrected, discussion of appendix C expanded with a new figure

The exponent of the weight distribution of low-density parity-check (LDPC) code ensembles through a statistical physics method and a combinatorics method are computed in this paper. We show that the two approaches agree for regular LDPC codes. However, for irregular codes this is not necessarily the case.

The dasiathresholdpsila of a code ensemble can be defined as the noise level at which the block error probability curve crosses 1/2. For ensembles of low-density parity check codes used over the binary erasure channel, the behavior of the threshold for large blocklengths is known in detail. It is characterized by an asymptotic threshold value, and a finite-blocklength shift parameter. Here we present a new method for computing the shift parameter that can be applied to general binary memoryless symmetric channels, and general message passing algorithms. We check that the new approach recovers the known parameters for erasure correction.

We show that the finite-length scaling parameters for irregular LDPC codes when used over the binary erasure channel can be computed without resorting to "covariance evolution''. We provide simple expressions that can be evaluated using solely the degree distributions and the characteristics of the fixed point of density evolution.

We study the finite-size behaviour of a tree-level on-shell improved action for the N-vector model. We present numerical results for N=3 and analytic results in the large-N limit for the mass gap. We also report a perturbative computation at one loop of the mass gap for states of spatial momentum p. We present a detailed comparison of the behaviour of this action with that of other formulations, including the perfect action, and a critical discussion of the different approaches to the problem of action improvement., LaTex2e, 34 pages, 5 ps figures, uses epsf, epsfig, amsfont, cite.sty

Consider transmission over the binary erasure channel using LDPC codes. We observed in [C. Measson, et al. (2003)] a curious relationship between the resulting maximum-likelihood (ML) decoding curve and the related performance curve under iterative (IT) decoding. We interpret this as an instance of Maxwell's construction which in its original form expresses an equilibrium condition at a phase transition.

Sensor localization from only connectivity information is a highly challenging problem. To this end, our result for the first time establishes an analytic bound on the performance of the popular MDS-MAP algorithm based on multidimensional scaling. For a network consisting of n sensors positioned randomly on a unit square and a given radio range r = o(1), we show that resulting error is bounded, decreasing at a rate that is inversely proportional to r, when only connectivity information is given. The same bound holds for the range-based model, when we have an approximate measurements for the distances, and the same algorithm can be applied without any modification.

Using scaling laws, we obtain estimates of the block error probability of polar codes under successive cancellation decoding. For the binary erasure channel we present an upper and a lower bound for the scaling parameter. Numerically these two bounds match. We also present a scaling law for general binary discrete memoryless channels.

We investigate numerically the dynamics of three different spin models in the aging regime. Each of these models is meant to be representative of a distinct class of aging behavior: coarsening systems, discontinuous spin glasses, and continuous spin glasses. In order to study dynamic heterogeneities induced by quenched disorder, we consider single-spin observables for a given disorder realization. In some simple cases we are able to provide analytical predictions for single-spin response and correlation functions. The results strongly depend upon the model considered. It turns out that, by comparing the slow evolution of a few different degrees of freedom, one can distinguish between different dynamic classes. As a conclusion we present the general properties which can be induced from our results, and discuss their relation with thermometric arguments., 39 pages, 36 figures

The rate of a code is one of its most important parameters. We consider sparse graph codes and ask whether the rate of a random element of an ensemble is typically close to the design rate of the ensemble. For regular LDPC ensembles this question was answered in the affirmative in (Miller and Cohen, 2003). We start by giving an alternative proof of this statement. We then show that essentially the same type of argument applies not only to regular ensembles but also to ensembles that are derived from regular ensembles in the sense that their degree distribution is the result of applying the peeling decoder to a regular code. As an immediate consequence we prove that for regular ensembles the asymptotic MAP EXIT value coincides with the asymptotic BP EXIT value. We then give a systematic construction of ensembles for which rate and design rate differ. To accomplish this, we first show that the duality theorem (Ashikhminet al., 2004) implies that the asymptotic BP EXIT and the MAP EXIT functions are identical for any channel parameter for which the density evolution (DE) equations have a unique fixed point.

We want to extend the approximation of the error probability via a scaling approach from the BEC to general binary-input memoryless output-symmetric (BMS) channels. In particular, we consider such scaling laws for regular LDPC ensembles and message-passing (MP) decoders with a finite number of messages. We first show how to re-derive the scaling law for transmission over the BEC using an ";EXIT-like"; curve instead of the density evolution curve of the peeling decoder. The advantage of the new derivation is that the new expression of the scaling parameter a only contains quantities that can be meaningfully interpreted also for general message-passing algorithms. In particular, this expression only depends on the curvature of the EXIT-like curve as well as the variance of the messages, both taken at the critical channel parameter. We discuss how to compute these quantities for general MP algorithms and we evaluate the expressions for the specific cases of the Gallager algorithm A as well as the Decoder with Erasures and compare the resulting predictions on the error probability with simulation results.