Constraint handling rules. Compositional semantics and program transformation

This thesis intends to investigate two aspects of Constraint Handling Rules (CHR). It proposes a compositional semantics and a technique for program transformation. CHR is a concurrent committed-choice constraint logic programming language consisting of guarded rules, which transform multi-sets of atomic formulas (constraints) into simpler ones until exhaustion [Frü06] and it belongs to the declarative languages family. It was initially designed for writing constraint solvers but it has recently also proven to be a general purpose language, being as it is Turing equivalent [SSD05a]. Compositionality is the first CHR aspect to be considered. A trace based compositional semantics for CHR was previously defined in [DGM05]. The reference operational semantics for such a compositional model was the original operational semantics for CHR which, due to the propagation rule, admits trivial non-termination. In this thesis we extend the work of [DGM05] by introducing a more refined trace based compositional semantics which also includes the history. The use of history is a well-known technique in CHR which permits us to trace the application of propagation rules and consequently it permits trivial non-termination avoidance [Abd97, DSGdlBH04]. Naturally, the reference operational semantics, of our new compositional one, uses history to avoid trivial non-termination too. Program transformation is the second CHR aspect to be considered, with particular regard to the unfolding technique. Said technique is an appealing approach which allows us to optimize a given program and in more detail to improve run-time efficiency or spaceconsumption. Essentially it consists of a sequence of syntactic program manipulations which preserve a kind of semantic equivalence called qualified answer [Frü98], between the original program and the transformed ones. The unfolding technique is one of the basic operations which is used by most program transformation systems. It consists in the replacement of a procedure-call by its definition. In CHR every conjunction of constraints can be considered as a procedure-call, every CHR rule can be considered as a procedure and the body of said rule represents the definition of the call. While there is a large body of literature on transformation and unfolding of sequential programs, very few papers have addressed this issue for concurrent languages. We define an unfolding rule, show its correctness and discuss some conditions in which it can be used to delete an unfolded rule while preserving the meaning of the original program. Finally, confluence and termination maintenance between the original and transformed programs are shown. This thesis is organized in the following manner. Chapter 1 gives some general notion about CHR. Section 1.1 outlines the history of programming languages with particular attention to CHR and related languages. Then, Section 1.2 introduces CHR using examples. Section 1.3 gives some preliminaries which will be used during the thesis. Subsequentely, Section 1.4 introduces the syntax and the operational and declarative semantics for the first CHR language proposed. Finally, the methodologies to solve the problem of trivial non-termination related to propagation rules are discussed in Section 1.5. Chapter 2 introduces a compositional semantics for CHR where the propagation rules are considered. In particular, Section 2.1 contains the definition of the semantics. Hence, Section 2.2 presents the compositionality results. Afterwards Section 2.3 expounds upon the correctness results. Chapter 3 presents a particular program transformation known as unfolding. This transformation needs a particular syntax called annotated which is introduced in Section 3.1 and its related modified operational semantics !0t is presented in Section 3.2. Subsequently, Section 3.3 defines the unfolding rule and prove its correctness. Then, in Section 3.4 the problems related to the replacement of a rule by its unfolded version are discussed and this in turn gives a correctness condition which holds for a specific class of rules. Section 3.5 proves that confluence and termination are preserved by the program modifications introduced. Finally, Chapter 4 concludes by discussing related works and directions for future work.

Managing Interval Resources in Automated Planning

In this paper RDPPLan, a model for planning with quantitative resources specified as numerical intervals, is presented. Nearly all existing models of planning with resources require to specify exact values for updating resources modified by actions execution. In other words these models cannot deal with more realistic situations in which the resources quantities are not completely known but are bounded by intervals. The RDPPlan model allow to manage domains more tailored to real world, where preconditions and effects over quantitative resources can be specified by intervals of values, in addition mixed logical/quantitative and pure numerical goals can be posed. RDPPlan is based on non directional search over a planning graph, like DPPlan, from which it derives, it uses propagation rules which have been appropriately extended to the management of resource intervals. The propagation rules extended with resources must verify invariant properties over the planning graph which have been proven by the authors and guarantee the correctness of the approach. An implementation of the RDPPlan model is described with search strategies specifically developed for interval resources.

Generalized Sznajd model for opinion propagation

In the last decade the Sznajd model has been successfully employed in modeling some properties and scale features of both proportional and majority elections. We propose a version of the Sznajd model with a generalized bounded confidence rule-a rule that limits the convincing capability of agents and that is essential to allow coexistence of opinions in the stationary state. With an appropriate choice of parameters it can be reduced to previous models. We solved this model both in a mean-field approach (for an arbitrary number of opinions) and numerically in a Barabaacutesi-Albert network (for three and four opinions), studying the transient and the possible stationary states. We built the phase portrait for the special cases of three and four opinions, defining the attractors and their basins of attraction. Through this analysis, we were able to understand and explain discrepancies between mean-field and simulation results obtained in previous works for the usual Sznajd model with bounded confidence and three opinions. Both the dynamical system approach and our generalized bounded confidence rule are quite general and we think it can be useful to the understanding of other similar models.

Analytical Study of Light Propagation in Highly Nonlinear Media

The present dissertation is devoted to the construction of exact and approximate analytical solutions of the problem of light propagation in highly nonlinear media. It is demonstrated that for many experimental conditions, the problem can be studied under the geometrical optics approximation with a sufficient accuracy. Based on the renormalization group symmetry analysis, exact analytical solutions of the eikonal equations with a higher order refractive index are constructed. A new analytical approach to the construction of approximate solutions is suggested. Based on it, approximate solutions for various boundary conditions, nonlinear refractive indices and dimensions are constructed. Exact analytical expressions for the nonlinear self-focusing positions are deduced. On the basis of the obtained solutions a general rule for the single filament intensity is derived; it is demonstrated that the scaling law (the functional dependence of the self-focusing position on the peak beam intensity) is defined by a form of the nonlinear refractive index but not the beam shape at the boundary. Comparisons of the obtained solutions with results of experiments and numerical simulations are discussed.

Fatigue crack initiation and propagation from defects in aluminium welds

Fatigue crack initiation and propagation in aluminium butt welds has been investigated. It is shown that the initiation of cracks from both buried defects and. from the weld reinforcement may be quantified by predictive laws based on either linear elastic fracture mechanics, or on Neuber's rule of stress and strain ooncentrations. The former is preferable on the grounds of theoretical models of crack tip plasticity, although either may be used as the basis of an effeotive design criteria against crack initiation. Fatigue lives fol1owing initiation were found to follow predictions based on the integration of a Paris type power law. The effect of residual stresses from the welding operation on both initiation and propagation was accounted for by a Forman type equation. This incorporated the notional stress ratio produced by the residual stresses after various heat treatments. A fracture mechanics analysis was found to be useful in describing the fatigue behaviour of the weldments at increased temperatures up to 300°C. It is pointed out, however, that the complex interaction of residual stresses, frequency, and changes in fracture mode necessitate great caution in the application of any general design criteria against crack initiation and growth at elevated. temperatures.

Dynamical models for computer viruses propagation

Nowadays, digital computer systems and networks are the main engineering tools, being used in planning, design, operation, and control of all sizes of building, transportation, machinery, business, and life maintaining devices. Consequently, computer viruses became one of the most important sources of uncertainty, contributing to decrease the reliability of vital activities. A lot of antivirus programs have been developed, but they are limited to detecting and removing infections, based on previous knowledge of the virus code. In spite of having good adaptation capability, these programs work just as vaccines against diseases and are not able to prevent new infections based on the network state. Here, a trial on modeling computer viruses propagation dynamics relates it to other notable events occurring in the network permitting to establish preventive policies in the network management. Data from three different viruses are collected in the Internet and two different identification techniques, autoregressive and Fourier analyses, are applied showing that it is possible to forecast the dynamics of a new virus propagation by using the data collected from other viruses that formerly infected the network. Copyright (c) 2008 J. R. C. Piqueira and F. B. Cesar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Rumor Propagation Model: An Equilibrium Study

Compartmental epidemiological models have been developed since the 1920s and successfully applied to study the propagation of infectious diseases. Besides, due to their structure, in the 1960s an interesting version of these models was developed to clarify some aspects of rumor propagation, considering that spreading an infectious disease or disseminating information is analogous phenomena. Here, in an analogy with the SIR (Susceptible-Infected-Removed) epidemiological model, the ISS (Ignorant-Spreader-Stifler) rumor spreading model is studied. By using concepts from the Dynamical Systems Theory, stability of equilibrium points is established, according to propagation parameters and initial conditions. Some numerical experiments are conducted in order to validate the model.

Coexistence of interacting opinions in a generalized Sznajd model

The Sznajd model is a sociophysics model that mimics the propagation of opinions in a closed society, where the interactions favor groups of agreeing people. It is based in the Ising and Potts ferromagnetic models and, although the original model used only linear chains, it has since been adapted to general networks. This model has a very rich transient, which has been used to model several aspects of elections, but its stationary states are always consensus states. In order to model more complex behaviors, we have, in a recent work, introduced the idea of biases and prejudices to the Sznajd model by generalizing the bounded confidence rule, which is common to many continuous opinion models, to what we called confidence rules. In that work we have found that the mean field version of this model (corresponding to a complete network) allows for stationary states where noninteracting opinions survive, but never for the coexistence of interacting opinions. In the present work, we provide networks that allow for the coexistence of interacting opinions for certain confidence rules. Moreover, we show that the model does not become inactive; that is, the opinions keep changing, even in the stationary regime. This is an important result in the context of understanding how a rule that breeds local conformity is still able to sustain global diversity while avoiding a frozen stationary state. We also provide results that give some insights on how this behavior approaches the mean field behavior as the networks are changed.

Investigating Giant (Gt) Repression in the Formation of Partially Overlapping Pair-Rule Stripes

Drosophila pair-rule genes are expressed in striped patterns with a precise order of overlap between stripes of different genes. We investigated the role of Giant (Gt) in the regulation of even-skipped, hairy, runt, and fushi tarazu stripes formed in the vicinity of Gt expression domains. In gt null embryos, specific stripes of eve, h, run, and ftz are disrupted. With an ectopic expression system, we verified that stripes affected in the mutant are also repressed. Simultaneously hybridizing gt misxpressing embryos with two pair-rule gene probes, we were able to distinguish differences in the repression of pairs of stripes that overlap extensively. Together, our results showed Gt repression roles in the regulation of two groups of partially overlapping stripes and that Gt morphogen activity is part of the mechanism responsible for the differential positioning of these stripes borders. We discuss the possibility that other factors regulate Gt stripe targets as well. Developmental Dynamics 239:2989-2999, 2010. (C) 2010 Wiley-Liss, Inc.

An alternative to the Pythagorean rule? Reevaluating Problem 1 of cuneiform tablet BM 34 568

The first problem of the Seleucid mathematical cuneiform tablet BM 34 568 calculates the diagonal of a rectangle from its sides without resorting to the Pythagorean rule. For this reason, it has been a source of discussion among specialists ever since its first publication. but so far no consensus in relation to its mathematical meaning has been attained. This paper presents two new interpretations of the scribe`s procedure. based on the assumption that he was able to reduce the problem to a standard Mesopotamian question about reciprocal numbers. These new interpretations are then linked to interpretations of the Old Babylonian tablet Plimpton 322 and to the presence of Pythagorean triples in the contexts of Old Babylonian and Hellenistic mathematics. (C) 2007 Elsevier Inc. All rights reserved.

Using Bayesian networks with rule extraction to infer the risk of weed infestation in a corn-crop

This paper describes the modeling of a weed infestation risk inference system that implements a collaborative inference scheme based on rules extracted from two Bayesian network classifiers. The first Bayesian classifier infers a categorical variable value for the weed-crop competitiveness using as input categorical variables for the total density of weeds and corresponding proportions of narrow and broad-leaved weeds. The inferred categorical variable values for the weed-crop competitiveness along with three other categorical variables extracted from estimated maps for the weed seed production and weed coverage are then used as input for a second Bayesian network classifier to infer categorical variables values for the risk of infestation. Weed biomass and yield loss data samples are used to learn the probability relationship among the nodes of the first and second Bayesian classifiers in a supervised fashion, respectively. For comparison purposes, two types of Bayesian network structures are considered, namely an expert-based Bayesian classifier and a naive Bayes classifier. The inference system focused on the knowledge interpretation by translating a Bayesian classifier into a set of classification rules. The results obtained for the risk inference in a corn-crop field are presented and discussed. (C) 2009 Elsevier Ltd. All rights reserved.

Timoshenko versus Euler beam theory: Pitfalls of a deterministic approach

The selection criteria for Euler-Bernoulli or Timoshenko beam theories are generally given by means of some deterministic rule involving beam dimensions. The Euler-Bernoulli beam theory is used to model the behavior of flexure-dominated (or ""long"") beams. The Timoshenko theory applies for shear-dominated (or ""short"") beams. In the mid-length range, both theories should be equivalent, and some agreement between them would be expected. Indeed, it is shown in the paper that, for some mid-length beams, the deterministic displacement responses for the two theories agrees very well. However, the article points out that the behavior of the two beam models is radically different in terms of uncertainty propagation. In the paper, some beam parameters are modeled as parameterized stochastic processes. The two formulations are implemented and solved via a Monte Carlo-Galerkin scheme. It is shown that, for uncertain elasticity modulus, propagation of uncertainty to the displacement response is much larger for Timoshenko beams than for Euler-Bernoulli beams. On the other hand, propagation of the uncertainty for random beam height is much larger for Euler beam displacements. Hence, any reliability or risk analysis becomes completely dependent on the beam theory employed. The authors believe this is not widely acknowledged by the structural safety or stochastic mechanics communities. (C) 2010 Elsevier Ltd. All rights reserved.

Coupled reliability and boundary element model for probabilistic fatigue life assessment in mixed mode crack propagation

Fatigue and crack propagation are phenomena affected by high uncertainties, where deterministic methods fail to predict accurately the structural life. The present work aims at coupling reliability analysis with boundary element method. The latter has been recognized as an accurate and efficient numerical technique to deal with mixed mode propagation, which is very interesting for reliability analysis. The coupled procedure allows us to consider uncertainties during the crack growth process. In addition, it computes the probability of fatigue failure for complex structural geometry and loading. Two coupling procedures are considered: direct coupling of reliability and mechanical solvers and indirect coupling by the response surface method. Numerical applications show the performance of the proposed models in lifetime assessment under uncertainties, where the direct method has shown faster convergence than response surface method. (C) 2010 Elsevier Ltd. All rights reserved.

Non-linear boundary element formulation with tangent operator to analyse crack propagation in quasi-brittle materials

This work deals with analysis of cracked structures using BEM. Two formulations to analyse the crack growth process in quasi-brittle materials are discussed. They are based on the dual formulation of BEM where two different integral equations are employed along the opposite sides of the crack surface. The first presented formulation uses the concept of constant operator, in which the corrections of the nonlinear process are made only by applying appropriate tractions along the crack surfaces. The second presented BEM formulation to analyse crack growth problems is an implicit technique based on the use of a consistent tangent operator. This formulation is accurate, stable and always requires much less iterations to reach the equilibrium within a given load increment in comparison with the classical approach. Comparison examples of classical problem of crack growth are shown to illustrate the performance of the two formulations. (C) 2009 Elsevier Ltd. All rights reserved.