Well-Posed Initial-Boundary Value Problem for a Constrained Evolution System and Radiation-Controlling Constraint-Preserving Boundary Conditions

A well-posed initial-boundary value problem is formulated for the model problem of the vector wave equation subject to the divergence-free constraint. Existence, uniqueness and stability of the solution is proved by reduction to a system evolving the constraint quantity statically, i.e., the second time derivative of the constraint quantity is zero. A new set of radiation-controlling constraint-preserving boundary conditions is constructed for the free evolution problem. Comparison between the new conditions and the standard constraint-preserving boundary conditions is made using the Fourier-Laplace analysis and the power series decomposition in time. The new boundary conditions satisfy the Kreiss condition and are free from the ill-posed modes growing polynomially in time.Comment: To appear in the Journal of Hyperbolic Differential Equations. In response to the reviewers request, a theorem on well-posedness of the free evolution problem has been added, definitions clarified in Sections 4 and 5, as well as a typo was removed from Section

Stochastic Constraint

This essay reviews Power and Constraint: The Accountable Presidency After 9/11 by Jack Goldsmith (2012). With The Terror Presidency, Professor Jack Goldsmith wrote, hands down, the very best analysis of the national security issues surrounding President George W. Bush\u27s tenure. In Power and Constraint: The Accountable Presidency After 9/11, Goldsmith returns to the same set of problems, but adopts a different tack. He argues that the modern wartime Executive is constrained in new ways beyond the traditional system of checks and balances, and that these new constraints combine to create an effective system that checks executive power. Though the modern wartime Executive may disregard traditional limits on presidential power and attempt to act unilaterally, new checks from an aggressive press, a watchful and technologically enabled public, and the legalization of warfare combine to constrain the executive branch. Goldsmith argues that this system is the type of reciprocal restraint of which our Founders would have approved (p. 243). Goldsmith\u27s claim ultimately boils down to one about how presidential constraint arises from a stochastic melange produced by these newly empowered actors. But in his analysis of the constraint imposed on the modern Executive by this new system of checks and balances, Goldsmith fails to account for the values served by good process. Just as with a student\u27s four-page exam (which might reach a correct result but probably will not), the path by which the Executive is constrained matters, because it will significantly affect the substantive quality and sustainability of that end result. Goldsmith\u27s new system of accountability relies on a combination of government leaks and self-checking out of fear of reprisal, whereas the traditional system trusts [a]mbition ... to counteract ambition. The latter system--the one envisioned by the Founders--has significantly fewer side effects attached to the process of checking the Executive. In this Review, the author argues that the particular process employed to constrain the Executive has consequences beyond the mere fact of achieving some level of constraint, and the new system of checks and balances has more costs associated with it than the traditional, constitutionally envisioned system, which primarily relies on government officials. In the end, many different methods might be used to achieve constraint, broadly conceived, but the process chosen to reach that constraint has substantive implications. Part I discusses the relationship between the process used to check the Executive and the substance of the constraints imposed. It contends that, just as the Coase Theorem predicts, the initial set of entitlements will strongly influence the eventual result, and that Coasean analysis provides a helpful frame through which to assess Goldsmith\u27s claim that the new constraints he identifies can substitute for Madisonian checks and balances. Part II analyzes Goldsmith\u27s speculation that the modern cycle of permission and constraint is likely to continue, and suggests that future inquiry should examine whether particular policy solutions could be developed, in advance of the next crisis, that might break this cycle

Constraint-based sequence mining using constraint programming

The goal of constraint-based sequence mining is to find sequences of symbols that are included in a large number of input sequences and that satisfy some constraints specified by the user. Many constraints have been proposed in the literature, but a general framework is still missing. We investigate the use of constraint programming as general framework for this task. We first identify four categories of constraints that are applicable to sequence mining. We then propose two constraint programming formulations. The first formulation introduces a new global constraint called exists-embedding. This formulation is the most efficient but does not support one type of constraint. To support such constraints, we develop a second formulation that is more general but incurs more overhead. Both formulations can use the projected database technique used in specialised algorithms. Experiments demonstrate the flexibility towards constraint-based settings and compare the approach to existing methods.Comment: In Integration of AI and OR Techniques in Constraint Programming (CPAIOR), 201

Extensible Automated Constraint Modelling

In constraint solving, a critical bottleneck is the formulationof an effective constraint model of a given problem. The CONJURE system described in this paper, a substantial step forward over prototype versions of CONJURE previously reported, makes a valuable contribution to the automation of constraint modelling by automatically producing constraint models from their specifications in the abstract constraint specification language ESSENCE. A set of rules is used to refine an abstract specification into a concrete constraint model. We demonstrate that this set of rules is readily extensible to increase the space of possible constraint models CONJURE can produce. Our empirical results confirm that CONJURE can reproduce successfully the kernels of the constraint models of 32 benchmark problems found in the literature

Momentum constraint relaxation

Full relativistic simulations in three dimensions invariably develop runaway modes that grow exponentially and are accompanied by violations of the Hamiltonian and momentum constraints. Recently, we introduced a numerical method (Hamiltonian relaxation) that greatly reduces the Hamiltonian constraint violation and helps improve the quality of the numerical model. We present here a method that controls the violation of the momentum constraint. The method is based on the addition of a longitudinal component to the traceless extrinsic curvature generated by a vector potential w_i, as outlined by York. The components of w_i are relaxed to solve approximately the momentum constraint equations, pushing slowly the evolution toward the space of solutions of the constraint equations. We test this method with simulations of binary neutron stars in circular orbits and show that effectively controls the growth of the aforementioned violations. We also show that a full numerical enforcement of the constraints, as opposed to the gentle correction of the momentum relaxation scheme, results in the development of instabilities that stop the runs shortly.Comment: 17 pages, 10 figures. New numerical tests and references added. More detailed description of the algorithms are provided. Final published versio

Restricted Global Grammar Constraints

We investigate the global GRAMMAR constraint over restricted classes of context free grammars like deterministic and unambiguous context-free grammars. We show that detecting disentailment for the GRAMMAR constraint in these cases is as hard as parsing an unrestricted context free grammar.We also consider the class of linear grammars and give a propagator that runs in quadratic time. Finally, to demonstrate the use of linear grammars, we show that a weighted linear GRAMMAR constraint can efficiently encode the EDITDISTANCE constraint, and a conjunction of the EDITDISTANCE constraint and the REGULAR constraintComment: Proceedings of the 15th International Conference on Principles and Practice of Constraint Programming, Lisbon, Portugal. September 200

Stochastic Constraint Programming

To model combinatorial decision problems involving uncertainty and probability, we introduce stochastic constraint programming. Stochastic constraint programs contain both decision variables (which we can set) and stochastic variables (which follow a probability distribution). They combine together the best features of traditional constraint satisfaction, stochastic integer programming, and stochastic satisfiability. We give a semantics for stochastic constraint programs, and propose a number of complete algorithms and approximation procedures. Finally, we discuss a number of extensions of stochastic constraint programming to relax various assumptions like the independence between stochastic variables, and compare with other approaches for decision making under uncertainty.Comment: Proceedings of the 15th Eureopean Conference on Artificial Intelligenc