Type systems for distributed programs: session communication

Distributed systems are everywhere around us and guaranteeing their correctness is of paramount importance. It is natural to expect that these systems interact and communicate among them to achieve a common task. In this work, we develop techniques based on types and type systems for the verification of correctness, consistency and safety properties related to communication in complex distributed systems. We study advanced safety properties related to communication, like deadlock or lock freedom and progress. We study session types in the pi-calculus describing distributed systems and communication-centric computation. Most importantly, we de- fine an encoding of the session pi-calculus into the standard typed pi-calculus in order to understand the expressive power of these concurrent calculi. We show how to derive in the session pi-calculus basic properties, like type safety or complex ones, like progress, by exploiting this encoding

A Differentiable Homotopy to Compute Nash Equilibria of n-Person Games

The literature on the computation of Nash equilibria in n-person games is dominated by simplicial methods. This paper is the first to introduce a globally convergent algorithm that fully exploits the differentiability present in the problem. It presents an everywhere differentiable homotopy to do the computations. The homotopy path can therefore be followed by several numerical techniques. Moreover, instead of computing some Nash equilibrium, the algorithm is constructed in such a way that it computes the Nash equilibrium selected by the tracing procedure of Harsanyi and Selten. As a by-product of our proofs it follows that for a generic game the tracing procedure defines an unique feasible path. The numerical performance of the algorithm is illustrated by means of several examples.microeconomics ;

Attracting and repelling Lagrangian coherent structures from a single computation

Hyperbolic Lagrangian Coherent Structures (LCSs) are locally most repelling or most attracting material surfaces in a finite-time dynamical system. To identify both types of hyperbolic LCSs at the same time instance, the standard practice has been to compute repelling LCSs from future data and attracting LCSs from past data. This approach tacitly assumes that coherent structures in the flow are fundamentally recurrent, and hence gives inconsistent results for temporally aperiodic systems. Here we resolve this inconsistency by showing how both repelling and attracting LCSs are computable at the same time instance from a single forward or a single backward run. These LCSs are obtained as surfaces normal to the weakest and strongest eigenvectors of the Cauchy-Green strain tensor.Comment: Under consideration for publication in Chaos/AI

Models of everywhere revisited: a technological perspective

The concept ‘models of everywhere’ was first introduced in the mid 2000s as a means of reasoning about the environmental science of a place, changing the nature of the underlying modelling process, from one in which general model structures are used to one in which modelling becomes a learning process about specific places, in particular capturing the idiosyncrasies of that place. At one level, this is a straightforward concept, but at another it is a rich multi-dimensional conceptual framework involving the following key dimensions: models of everywhere, models of everything and models at all times, being constantly re-evaluated against the most current evidence. This is a compelling approach with the potential to deal with epistemic uncertainties and nonlinearities. However, the approach has, as yet, not been fully utilised or explored. This paper examines the concept of models of everywhere in the light of recent advances in technology. The paper argues that, when first proposed, technology was a limiting factor but now, with advances in areas such as Internet of Things, cloud computing and data analytics, many of the barriers have been alleviated. Consequently, it is timely to look again at the concept of models of everywhere in practical conditions as part of a trans-disciplinary effort to tackle the remaining research questions. The paper concludes by identifying the key elements of a research agenda that should underpin such experimentation and deployment

Binary black holes in circular orbits. II. Numerical methods and first results

We present the first results from a new method for computing spacetimes representing corotating binary black holes in circular orbits. The method is based on the assumption of exact equilibrium. It uses the standard 3+1 decomposition of Einstein equations and conformal flatness approximation for the 3-metric. Contrary to previous numerical approaches to this problem, we do not solve only the constraint equations but rather a set of five equations for the lapse function, the conformal factor and the shift vector. The orbital velocity is unambiguously determined by imposing that, at infinity, the metric behaves like the Schwarzschild one, a requirement which is equivalent to the virial theorem. The numerical scheme has been implemented using multi-domain spectral methods and passed numerous tests. A sequence of corotating black holes of equal mass is calculated. Defining the sequence by requiring that the ADM mass decrease is equal to the angular momentum decrease multiplied by the orbital angular velocity, it is found that the area of the apparent horizons is constant along the sequence. We also find a turning point in the ADM mass and angular momentum curves, which may be interpreted as an innermost stable circular orbit (ISCO). The values of the global quantities at the ISCO, especially the orbital velocity, are in much better agreement with those from third post-Newtonian calculations than with those resulting from previous numerical approaches.Comment: 27 pages, 20 PostScript figures, improved presentation of the regularization procedure for the shift vector, new section devoted to the check of the momentum constraint, references added + minor corrections, accepted for publication in Phys. Rev.

On Factorization of Molecular Wavefunctions

Recently there has been a renewed interest in the chemical physics literature of factorization of the position representation eigenfunctions \{$\Phi$\} of the molecular Schr\"odinger equation as originally proposed by Hunter in the 1970s. The idea is to represent $\Phi$ in the form $\varphi\chi$ where $\chi$ is \textit{purely} a function of the nuclear coordinates, while $\varphi$ must depend on both electron and nuclear position variables in the problem. This is a generalization of the approximate factorization originally proposed by Born and Oppenheimer, the hope being that an `exact' representation of $\Phi$ can be achieved in this form with $\varphi$ and $\chi$ interpretable as `electronic' and `nuclear' wavefunctions respectively. We offer a mathematical analysis of these proposals that identifies ambiguities stemming mainly from the singularities in the Coulomb potential energy.Comment: Manuscript submitted to Journal of Physics A: Mathematical and Theoretical, May 2015. Accepted for Publication August 24 201