Egalitarian state-transition systems (extended version)

We argue that considering transitions at the same level as states, as first-class citizens, is advantageous in many cases. Namely, the use of atomic propositions on transitions, as well as on states, allows temporal formulas and strategies to be more powerful, general, and meaningful. We define egalitarian structures and logics, and show how they generalize well-known state-based, event-based, and mixed ones. We present translations from egalitarian to non-egalitarian settings that, in particular, allow the model checking of LTLR formulas using Maude’s LTL model checker. We have implemented these translations as a prototype in Maude itself.

A Replacement Technique to Maximize Task Reuse in Reconfigurable Systems

Dynamically reconfigurable hardware is a promising technology that combines in the same device both the high performance and the flexibility that many recent applications demand. However, one of its main drawbacks is the reconfiguration overhead, which involves important delays in the task execution, usually in the order of hundreds of milliseconds, as well as high energy consumption. One of the most powerful ways to tackle this problem is configuration reuse, since reusing a task does not involve any reconfiguration overhead. In this paper we propose a configuration replacement policy for reconfigurable systems that maximizes task reuse in highly dynamic environments. We have integrated this policy in an external taskgraph execution manager that applies task prefetch by loading and executing the tasks as soon as possible (ASAP). However, we have also modified this ASAP technique in order to make the replacements more flexible, by taking into account the mobility of the tasks and delaying some of the reconfigurations. In addition, this replacement policy is a hybrid design-time/run-time approach, which performs the bulk of the computations at design time in order to save run-time computations. Our results illustrate that the proposed strategy outperforms other state-ofthe-art replacement policies in terms of reuse rates and achieves near-optimal reconfiguration overhead reductions. In addition, by performing the bulk of the computations at design time, we reduce the execution time of the replacement technique by 10 times with respect to an equivalent purely run-time one.

Auctioning versus grandfathering in cap-and-trade systems with market power and incomplete information

We compare auctioning and grandfathering as allocation mechanisms of emission permits when there is a secondary market with market power and firms have private information on their own abatement technologies. Based on real-life cases such as the EU ETS, we consider a multi-unit, multi-bid uniform auction. At the auction, each firm anticipates its role in the secondary market, either as a leader or a follower. This role affects each firms’ valuation of the permits (which are not common across firms) as well as their bidding strategies and it precludes the auction from generating a cost-effective allocation of permits, as it occurs in simpler auction models. Auctioning tends to be more cost-effective than grandfathering when the firms’ abatement cost functions are sufficiently different from one another, especially if the follower has lower abatement costs than the leader and the dispersion of the marginal costs is large enough.

Standardized environmental management systems as an internal management tool

In a principal-agent model we analyze the firm’s decision to adopt an informal or a standardized Environmental Management System (EMS). Our results are consistent with empirical evidence in several respects. A standardized EMS increases the internal control at the cost of introducing some degree of rigidity that entails an endogenous setup cost. Standardized systems are more prone to be adopted by big and well established firms and under tougher environmental policies. Firms with standardized EMS tend to devote more effort to abatement although this effort results in lower pollution only if public incentives are strong enough, suggesting a complementarity relationship between standardized EMS and public policies. Emission charges have both a marginal effect on abatement and a qualitative effect on the adoption decision that may induce a conflict between private and public interests. As a result of the combination of these two effects it can be optimal for the government to distort the tax in a specific way in order to push the firm to choose the socially optimal EMS. The introduction of standardized systems can result in win-win situations where firms, society and the environment get better off.

Multivariate orthogonal polynomials and integrable systems

Multivariate orthogonal polynomials in D real dimensions are considered from the perspective of the Cholesky factorization of a moment matrix. The approach allows for the construction of corresponding multivariate orthogonal polynomials, associated second kind functions, Jacobi type matrices and associated three term relations and also Christoffel-Darboux formulae. The multivariate orthogonal polynomials, their second kind functions and the corresponding Christoffel-Darboux kernels are shown to be quasi-determinants as well as Schur complements of bordered truncations of the moment matrix; quasi-tau functions are introduced. It is proven that the second kind functions are multivariate Cauchy transforms of the multivariate orthogonal polynomials. Discrete and continuous deformations of the measure lead to Toda type integrable hierarchy, being the corresponding flows described through Lax and Zakharov-Shabat equations; bilinear equations are found. Varying size matrix nonlinear partial difference and differential equations of the 2D Toda lattice type are shown to be solved by matrix coefficients of the multivariate orthogonal polynomials. The discrete flows, which are shown to be connected with a Gauss-Borel factorization of the Jacobi type matrices and its quasi-determinants, lead to expressions for the multivariate orthogonal polynomials and their second kind functions in terms of shifted quasi-tau matrices, which generalize to the multidimensional realm, those that relate the Baker and adjoint Baker functions to ratios of Miwa shifted tau-functions in the 1D scenario. In this context, the multivariate extension of the elementary Darboux transformation is given in terms of quasi-determinants of matrices built up by the evaluation, at a poised set of nodes lying in an appropriate hyperplane in R^D, of the multivariate orthogonal polynomials. The multivariate Christoffel formula for the iteration of m elementary Darboux transformations is given as a quasi-determinant. It is shown, using congruences in the space of semi-infinite matrices, that the discrete and continuous flows are intimately connected and determine nonlinear partial difference-differential equations that involve only one site in the integrable lattice behaving as a Kadomstev-Petviashvili type system. Finally, a brief discussion of measures with a particular linear isometry invariance and some of its consequences for the corresponding multivariate polynomials is given. In particular, it is shown that the Toda times that preserve the invariance condition lay in a secant variety of the Veronese variety of the fixed point set of the linear isometry.