Experiment selection for the discrimination of semi-quantitative models of dynamical systems

AbstractModeling an experimental system often results in a number of alternative models that are all justified by the available experimental data. To discriminate among these models, additional experiments are needed. Existing methods for the selection of discriminatory experiments in statistics and in artificial intelligence are often based on an entropy criterion, the so-called information increment. A limitation of these methods is that they are not well-adapted to discriminating models of dynamical systems under conditions of limited measurability. Moreover, there are no generic procedures for computing the information increment of an experiment when the models are qualitative or semi-quantitative. This has motivated the development of a method for the selection of experiments to discriminate among semi-quantitative models of dynamical systems. The method has been implemented on top of existing implementations of the qualitative and semi-quantitative simulation techniques QSIM, Q2, and Q3. The applicability of the method to real-world problems is illustrated by means of an example in population biology: the discrimination of four competing models of the growth of phytoplankton in a bioreactor. The models have traditionally been considered equivalent for all practical purposes. Using our model discrimination approach and experimental data we show, however, that two of them are superior for describing phytoplankton growth under a wide range of experimental conditions

On the Papapetrou field in vacuum

In this paper we study the electromagnetic fields generated by a Killing vector field in vacuum space-times (Papapetrou fields). The motivation of this work is to provide new tools for the resolution of Maxwell's equations as well as for the search, characterization, and study of exact solutions of Einstein's equations. The first part of this paper is devoted to an algebraic study in which we give an explicit and covariant procedure to construct the principal null directions of a Papapetrou field. In the second part, we focus on the main differential properties of the principal directions, studying when they are geodesic, and in that case we compute their associated optical scalars. With this information we get the conditions that a principal direction of the Papapetrou field must satisfy in order to be aligned with a multiple principal direction of the Weyl tensor in the case of algebraically special vacuum space-times. Finally, we illustrate this study using the Kerr, Kasner and pp waves space-times.Comment: 24 pages, LaTeX2e, IOP style. To appear in Classical and Quantum Gravit

Cylindrically symmetric inhomogeneous dust collapse with a zero expansion component

We investigate a class of cylindrically symmetric inhomogeneous Λ-dust spacetimes which have a regular axis and some zero expansion component. For Λ \neq 0, we obtain new exact solutions to the Einstein equations and show that they are unique, within that class. For Λ = 0, we recover the Senovilla– Vera metric and show that it can be locally matched to an Einstein–Rosen type of exterior. Finally, we explore some consequences of the matching, such as trapped surface formation and gravitational radiation in the exterior.We thank Jose Senovilla for suggesting solutions of the form (8) and (9) and for other very useful comments which led to substancial improvements in the paper. IB and FM are supported by Portuguese Funds through Fundacao para a Cincia e Tecnologia (FCT), within the Projects UID/MAT/00013/2013 and PTDC/MAT-ANA/1275/2014. FM and NOS acknowledge a grant received from UERJ and thank the warm hospitality from Instituto de Fisica, UERJ, Rio de Janeiro, where a great part of this work was completed. MFAdaSilva acknowledges the financial support from FAPERJ (no. E-26/171.754/2000, E-26/171.533.2002, E-26/170.951/2006, E-26/110.432/2009 and E-26/111.714/2010), Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPq) Brazil (no. 450572/2009-9, 301973/2009-1 and 477268/2010-2) and Financiadora de Estudos e Projetos (FINEP) Brazil.info:eu-repo/semantics/publishedVersio

Homothetic perfect fluid space-times

A brief summary of results on homotheties in General Relativity is given, including general information about space-times admitting an r-parameter group of homothetic transformations for r>2, as well as some specific results on perfect fluids. Attention is then focussed on inhomogeneous models, in particular on those with a homothetic group $H_4$ (acting multiply transitively) and $H_3$. A classification of all possible Lie algebra structures along with (local) coordinate expressions for the metric and homothetic vectors is then provided (irrespectively of the matter content), and some new perfect fluid solutions are given and briefly discussed.Comment: 27 pages, Latex file, Submitted to Class. Quantum Gra

Researching the use of force: The background to the international project

This article provides the background to an international project on use of force by the police that was carried out in eight countries. Force is often considered to be the defining characteristic of policing and much research has been conducted on the determinants, prevalence and control of the use of force, particularly in the United States. However, little work has looked at police officers’ own views on the use of force, in particular the way in which they justify it. Using a hypothetical encounter developed for this project, researchers in each country conducted focus groups with police officers in which they were encouraged to talk about the use of force. The results show interesting similarities and differences across countries and demonstrate the value of using this kind of research focus and methodology

Lyapunov spectral analysis of a nonequilibrium Ising-like transition

By simulating a nonequilibrium coupled map lattice that undergoes an Ising-like phase transition, we show that the Lyapunov spectrum and related dynamical quantities such as the dimension correlation length~$\xi_\delta$ are insensitive to the onset of long-range ferromagnetic order. As a function of lattice coupling constant~$g$ and for certain lattice maps, the Lyapunov dimension density and other dynamical order parameters go through a minimum. The occurrence of this minimum as a function of~$g$ depends on the number of nearest neighbors of a lattice point but not on the lattice symmetry, on the lattice dimensionality or on the position of the Ising-like transition. In one-space dimension, the spatial correlation length associated with magnitude fluctuations and the length~$\xi_\delta$ are approximately equal, with both varying linearly with the radius of the lattice coupling.Comment: 29 pages of text plus 15 figures, uses REVTeX macros. Submitted to Phys. Rev. E

Does brane cosmology have realistic principles?

The maximal symmetry, or Perfect Cosmological Principle(PCP), that prevents AdS type spaces from degenerating into anti-inflationary collapse is argued to be unphysical. For example, the simple requirement that brane-bulk models should be the result of having evolved from even more energetic string phenomena picks out a preferred time direction. We question whether quantum cosmological reasoning can be applied in any meaningful way to obtain, what are essentially, classical constructs . An alternative scheme is to more readily accept the PCP and allow the branes to also become eternal. A perpetually expanding and contracting brane model could be driven by the presence of charged black holes in the AdS bulk, that effectively violates the weak-energy condition as singularities are approached. This can be contrasted with the so-called Ekpyrotic universe which also closely accepts the PCP. This being broken only by occasional collisions between branes, that can then simulate a big bang cosmology.Comment: extended version and title chang

From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity

This article reviews some aspects in the current relationship between mathematical and numerical General Relativity. Focus is placed on the description of isolated systems, with a particular emphasis on recent developments in the study of black holes. Ideas concerning asymptotic flatness, the initial value problem, the constraint equations, evolution formalisms, geometric inequalities and quasi-local black hole horizons are discussed on the light of the interaction between numerical and mathematical relativists.Comment: Topical review commissioned by Classical and Quantum Gravity. Discussion inspired by the workshop "From Geometry to Numerics" (Paris, 20-24 November, 2006), part of the "General Relativity Trimester" at the Institut Henri Poincare (Fall 2006). Comments and references added. Typos corrected. Submitted to Classical and Quantum Gravit

Singularity free dilaton-driven cosmologies and pre-little-bang

There are no reasons why the singularity in the growth of the dilaton coupling should not be regularised, in a string cosmological context, by the presence of classical inhomogeneities. We discuss a class of inhomogeneous dilaton-driven models whose curvature invariants are all bounded and regular in time and space. We prove that the non-space-like geodesics of these models are all complete in the sense that none of them reaches infinity for a finite value of the affine parameter. We conclude that our examples represent truly singularity-free solutions of the low energy beta functions. We discuss some symmetries of the obtained solutions and we clarify their physical interpretation. We also give examples of solutions with spherical symmetry. In our scenario each physical quantity is everywhere defined in time and space, the big-bang singularity is replaced by a maximal curvature phase where the dilaton kinetic energy reaches its maximum. The maximal curvature is always smaller than one (in string units) and the coupling constant is also smaller than one and it grows between two regimes of constant dilaton, implying, together with the symmetries of the solutions, that higher genus and higher curvature corrections are negligible. We argue that our examples describe, in a string cosmological context, the occurrence of ``little bangs''(i.e. high curvature phases which never develop physical singularities). They also suggest the possibility of an unexplored ``pre-little-bang'' phase.Comment: 25 pages in LaTex style, 3 encapsulated figure

Artificial drainage of peatlands: hydrological and hydrochemical process and wetland restoration

Peatlands have been subject to artificial drainage for centuries. This drainage has been in response to agricultural demand, forestry, horticultural and energy properties of peat and alleviation of flood risk. However, the are several environmental problems associated with drainage of peatlands. This paper describes the nature of these problems and examines the evidence for changes in hydrological and hydrochemical processes associated with these changes. Traditional black-box water balance approaches demonstrate little about wetland dynamics and therefore the science of catchment response to peat drainage is poorly understood. It is crucial that a more process-based approach be adopted within peatland ecosystems. The environmental problems associated with peat drainage have led, in part, to a recent reversal in attitudes to peatlands and we have seen a move towards wetland restoration. However, a detailed understanding of hydrological, hydrochemical and ecological process-interactions will be fundamental if we are to adequately restore degraded peatlands, preserve those that are still intact and understand the impacts of such management actions at the catchment scale