Constraint Programming viewed as Rule-based Programming

We study here a natural situation when constraint programming can be entirely reduced to rule-based programming. To this end we explain first how one can compute on constraint satisfaction problems using rules represented by simple first-order formulas. Then we consider constraint satisfaction problems that are based on predefined, explicitly given constraints. To solve them we first derive rules from these explicitly given constraints and limit the computation process to a repeated application of these rules, combined with labeling.We consider here two types of rules. The first type, that we call equality rules, leads to a new notion of local consistency, called {\em rule consistency} that turns out to be weaker than arc consistency for constraints of arbitrary arity (called hyper-arc consistency in \cite{MS98b}). For Boolean constraints rule consistency coincides with the closure under the well-known propagation rules for Boolean constraints. The second type of rules, that we call membership rules, yields a rule-based characterization of arc consistency. To show feasibility of this rule-based approach to constraint programming we show how both types of rules can be automatically generated, as {\tt CHR} rules of \cite{fruhwirth-constraint-95}. This yields an implementation of this approach to programming by means of constraint logic programming. We illustrate the usefulness of this approach to constraint programming by discussing various examples, including Boolean constraints, two typical examples of many valued logics, constraints dealing with Waltz's language for describing polyhedral scenes, and Allen's qualitative approach to temporal logic.Comment: 39 pages. To appear in Theory and Practice of Logic Programming Journa

Collective Singleton-Based Consistency for Qualitative Constraint Networks

Partial singleton closure under weak composition, or partial singleton (weak) path-consistency for short, is essential for approximating satisfiability of qualitative constraints networks. Briefly put, partial singleton path-consistency ensures that each base relation of each of the constraints of a qualitative constraint network can define a singleton relation in the corresponding partial closure of that network under weak composition, or in its corresponding partially (weak) path-consistent subnetwork for short. In particular, partial singleton path-consistency has been shown to play a crucial role in tackling the minimal labeling problem of a qualitative constraint network, which is the problem of finding the strongest implied constraints of that network. In this paper, we propose a stronger local consistency that couples partial singleton path-consistency with the idea of collectively deleting certain unfeasible base relations by exploiting singleton checks. We then propose an efficient algorithm for enforcing this consistency that, given a qualitative constraint network, performs fewer constraint checks than the respective algorithm for enforcing partial singleton path-consistency in that network. We formally prove certain properties of our new local consistency, and motivate its usefulness through demonstrative examples and a preliminary experimental evaluation with qualitative constraint networks of Interval Algebra

Consistency of holonomy-corrected scalar, vector and tensor perturbations in Loop Quantum Cosmology

Loop Quantum Cosmology yields two kinds of quantum corrections to the effective equations of motion for cosmological perturbations. Here we focus on the holonomy kind and we study the problem of the closure of the resulting algebra of constraints. Up to now, tensor, vector and scalar perturbations were studied independently, leading to different algebras of constraints. The structures of the related algebras were imposed by the requirement of anomaly freedom. In this article we show that the algebra can be modified by a very simple quantum correction, holding for all types of perturbations. This demonstrates the consistency of the theory and shows that lessons from the study of scalar perturbations should be taken into account when studying tensor modes. The Mukhanov-Sasaki equations of motion are similarly modified by a simple term.Comment: 5 page

A moment-equation-copula-closure method for nonlinear vibrational systems subjected to correlated noise

We develop a moment equation closure minimization method for the inexpensive approximation of the steady state statistical structure of nonlinear systems whose potential functions have bimodal shapes and which are subjected to correlated excitations. Our approach relies on the derivation of moment equations that describe the dynamics governing the two-time statistics. These are combined with a non-Gaussian pdf representation for the joint response-excitation statistics that has i) single time statistical structure consistent with the analytical solutions of the Fokker-Planck equation, and ii) two-time statistical structure with Gaussian characteristics. Through the adopted pdf representation, we derive a closure scheme which we formulate in terms of a consistency condition involving the second order statistics of the response, the closure constraint. A similar condition, the dynamics constraint, is also derived directly through the moment equations. These two constraints are formulated as a low-dimensional minimization problem with respect to unknown parameters of the representation, the minimization of which imposes an interplay between the dynamics and the adopted closure. The new method allows for the semi-analytical representation of the two-time, non-Gaussian structure of the solution as well as the joint statistical structure of the response-excitation over different time instants. We demonstrate its effectiveness through the application on bistable nonlinear single-degree-of-freedom energy harvesters with mechanical and electromagnetic damping, and we show that the results compare favorably with direct Monte-Carlo Simulations

A RMSM-X model for Turkey

To improve the Bank's macroeconomic modeling capabilities, a continuum of macro models referred to as RMSM-X and RMSM-XX are being developed. These models share a common accounting framework that ensures economic consistency among economic sectors. This paper shows how to specify the budget constraints and market clearing conditions in a RMSM-X model for Turkey. An overview of the system defined by the RMSM-X model, the debt module (DM) and the data base is presented, along with a detailed explanation of the theoretical model. Alternative closure rules are discussed and the debt model is presented. This paper also includes annexes which present a complete set of historical data and an explanation of how the data was constructed.Economic Theory&Research,Environmental Economics&Policies,Banks&Banking Reform,Economic Stabilization,Financial Intermediation

Gauged Double Field Theory

We find necessary and sufficient conditions for gauge invariance of the action of Double Field Theory (DFT) as well as closure of the algebra of gauge symmetries. The so-called weak and strong constraints are sufficient to satisfy them, but not necessary. We then analyze compactifications of DFT on twisted double tori satisfying the consistency conditions. The effective theory is a Gauged DFT where the gaugings come from the duality twists. The action, bracket, global symmetries, gauge symmetries and their closure are computed by twisting their analogs in the higher dimensional DFT. The non-Abelian heterotic string and lower dimensional gauged supergravities are particular examples of Gauged DFT.Comment: Minor changes, references adde