A Model-to-model analysis of the repeated Prisoners' Dilemma: genetic algorithms vs. evolutionary dynamics

We study the properties of the well known Replicator Dynamics when applied to a finitely repeated version of the Prisoners' Dilemma game. We characterize the behavior of such dynamics under strongly simplifying assumptions (i.e. only 3 strategies are available) and show that the basin of attraction of defection shrinks as the number of repetitions increases. After discussing the difficulties involved in trying to relax the 'strongly simplifying assumptions' above, we approach the same model by means of simulations based on genetic algorithms. The resulting simulations describe a behavior of the system very close to the one predicted by the replicator dynamics without imposing any of the assumptions of the analytical model. Our main conclusion is that analytical and computational models are good complements for research in social sciences. Indeed, while on the one hand computational models are extremely useful to extend the scope of the analysis to complex scenar

Multi-scale support vector algorithms for hot spot detection and modelling

The algorithmic approach to data modelling has developed rapidly these last years, in particular methods based on data mining and machine learning have been used in a growing number of applications. These methods follow a data-driven methodology, aiming at providing the best possible generalization and predictive abilities instead of concentrating on the properties of the data model. One of the most successful groups of such methods is known as Support Vector algorithms. Following the fruitful developments in applying Support Vector algorithms to spatial data, this paper introduces a new extension of the traditional support vector regression (SVR) algorithm. This extension allows for the simultaneous modelling of environmental data at several spatial scales. The joint influence of environmental processes presenting different patterns at different scales is here learned automatically from data, providing the optimum mixture of short and large-scale models. The method is adaptive to the spatial scale of the data. With this advantage, it can provide efficient means to model local anomalies that may typically arise in situations at an early phase of an environmental emergency. However, the proposed approach still requires some prior knowledge on the possible existence of such short-scale patterns. This is a possible limitation of the method for its implementation in early warning systems. The purpose of this paper is to present the multi-scale SVR model and to illustrate its use with an application to the mapping of Cs137 activity given the measurements taken in the region of Briansk following the Chernobyl accident.

Fast numerical algorithms for the computation of invariant tori in Hamiltonian systems

In this paper, we develop numerical algorithms that use small requirements of storage and operations for the computation of invariant tori in Hamiltonian systems (exact symplectic maps and Hamiltonian vector fields). The algorithms are based on the parameterization method and follow closely the proof of the KAM theorem given in [LGJV05] and [FLS07]. They essentially consist in solving a functional equation satisfied by the invariant tori by using a Newton method. Using some geometric identities, it is possible to perform a Newton step using little storage and few operations. In this paper we focus on the numerical issues of the algorithms (speed, storage and stability) and we refer to the mentioned papers for the rigorous results. We show how to compute efficiently both maximal invariant tori and whiskered tori, together with the associated invariant stable and unstable manifolds of whiskered tori. Moreover, we present fast algorithms for the iteration of the quasi-periodic cocycles and the computation of the invariant bundles, which is a preliminary step for the computation of invariant whiskered tori. Since quasi-periodic cocycles appear in other contexts, this section may be of independent interest. The numerical methods presented here allow to compute in a unified way primary and secondary invariant KAM tori. Secondary tori are invariant tori which can be contracted to a periodic orbit. We present some preliminary results that ensure that the methods are indeed implementable and fast. We postpone to a future paper optimized implementations and results on the breakdown of invariant tori.

On the density distribution across space: a probabilistic approach

This paper aims at providing a Bayesian parametric framework to tackle the accessibility problem across space in urban theory. Adopting continuous variables in a probabilistic setting we are able to associate with the distribution density to the Kendall's tau index and replicate the general issues related to the role of proximity in a more general context. In addition, by referring to the Beta and Gamma distribution, we are able to introduce a differentiation feature in each spatial unit without incurring in any a-priori definition of territorial units. We are also providing an empirical application of our theoretical setting to study the density distribution of the population across Massachusetts.

Bayesian Networks for Probabilistic Inference and Decision Analysis in Forensic Science

Continuing developments in science and technology mean that the amounts of information forensic scientists are able to provide for criminal investigations is ever increasing. The commensurate increase in complexity creates difficulties for scientists and lawyers with regard to evaluation and interpretation, notably with respect to issues of inference and decision. Probability theory, implemented through graphical methods, and specifically Bayesian networks, provides powerful methods to deal with this complexity. Extensions of these methods to elements of decision theory provide further support and assistance to the judicial system. Bayesian Networks for Probabilistic Inference and Decision Analysis in Forensic Science provides a unique and comprehensive introduction to the use of Bayesian decision networks for the evaluation and interpretation of scientific findings in forensic science, and for the support of decision-makers in their scientific and legal tasks. Includes self-contained introductions to probability and decision theory. Develops the characteristics of Bayesian networks, object-oriented Bayesian networks and their extension to decision models. Features implementation of the methodology with reference to commercial and academically available software. Presents standard networks and their extensions that can be easily implemented and that can assist in the reader's own analysis of real cases. Provides a technique for structuring problems and organizing data based on methods and principles of scientific reasoning. Contains a method for the construction of coherent and defensible arguments for the analysis and evaluation of scientific findings and for decisions based on them. Is written in a lucid style, suitable for forensic scientists and lawyers with minimal mathematical background. Includes a foreword by Ian Evett. The clear and accessible style of this second edition makes this book ideal for all forensic scientists, applied statisticians and graduate students wishing to evaluate forensic findings from the perspective of probability and decision analysis. It will also appeal to lawyers and other scientists and professionals interested in the evaluation and interpretation of forensic findings, including decision making based on scientific information.

A Survey of Active Learning Algorithms for Supervised Remote Sensing Image Classification

Defining an efficient training set is one of the most delicate phases for the success of remote sensing image classification routines. The complexity of the problem, the limited temporal and financial resources, as well as the high intraclass variance can make an algorithm fail if it is trained with a suboptimal dataset. Active learning aims at building efficient training sets by iteratively improving the model performance through sampling. A user-defined heuristic ranks the unlabeled pixels according to a function of the uncertainty of their class membership and then the user is asked to provide labels for the most uncertain pixels. This paper reviews and tests the main families of active learning algorithms: committee, large margin, and posterior probability-based. For each of them, the most recent advances in the remote sensing community are discussed and some heuristics are detailed and tested. Several challenging remote sensing scenarios are considered, including very high spatial resolution and hyperspectral image classification. Finally, guidelines for choosing the good architecture are provided for new and/or unexperienced user.

DNA evidence, probabilistic evaluation and collaborative tests.

Forensic scientists working in 12 state or private laboratories participated in collaborative tests to improve the reliability of the presentation of DNA data at trial. These tests were motivated in response to the growing criticism of the power of DNA evidence. The experts' conclusions in the tests are presented and discussed in the context of the Bayesian approach to interpretation. The use of a Bayesian approach and subjective probabilities in trace evaluation permits, in an easy and intuitive manner, the integration into the decision procedure of any revision of the measure of uncertainty in the light of new information. Such an integration is especially useful with forensic evidence. Furthermore, we believe that this probabilistic model is a useful tool (a) to assist scientists in the assessment of the value of scientific evidence, (b) to help jurists in the interpretation of judicial facts and (c) to clarify the respective roles of scientists and of members of the court. Respondents to the survey were reluctant to apply this methodology in the assessment of DNA evidence.

A parameter-free approach for solving combinatorial optimization problems through biased randomization of efficient heuristics

This paper discusses the use of probabilistic or randomized algorithms for solving combinatorial optimization problems. Our approach employs non-uniform probability distributions to add a biased random behavior to classical heuristics so a large set of alternative good solutions can be quickly obtained in a natural way and without complex conguration processes. This procedure is especially useful in problems where properties such as non-smoothness or non-convexity lead to a highly irregular solution space, for which the traditional optimization methods, both of exact and approximate nature, may fail to reach their full potential. The results obtained are promising enough to suggest that randomizing classical heuristics is a powerful method that can be successfully applied in a variety of cases.

Hard instances of algorithms and proof systems

"Vegeu el resum a l'inici del document del fitxer adjunt."

Approximation algorithms for two-state anti-ferromagnetic spin systems on bounded degree graphs

In a seminal paper [10], Weitz gave a deterministic fully polynomial approximation scheme for counting exponentially weighted independent sets (which is the same as approximating the partition function of the hard-core model from statistical physics) in graphs of degree at most d, up to the critical activity for the uniqueness of the Gibbs measure on the innite d-regular tree. ore recently Sly [8] (see also [1]) showed that this is optimal in the sense that if here is an FPRAS for the hard-core partition function on graphs of maximum egree d for activities larger than the critical activity on the innite d-regular ree then NP = RP. In this paper we extend Weitz's approach to derive a deterministic fully polynomial approximation scheme for the partition function of general two-state anti-ferromagnetic spin systems on graphs of maximum degree d, up to the corresponding critical point on the d-regular tree. The main ingredient of our result is a proof that for two-state anti-ferromagnetic spin systems on the d-regular tree, weak spatial mixing implies strong spatial mixing. his in turn uses a message-decay argument which extends a similar approach proposed recently for the hard-core model by Restrepo et al [7] to the case of general two-state anti-ferromagnetic spin systems.

Extreme Precipitation Modelling Using Geostatistics and Machine Learning Algorithms

The paper presents an approach for mapping of precipitation data. The main goal is to perform spatial predictions and simulations of precipitation fields using geostatistical methods (ordinary kriging, kriging with external drift) as well as machine learning algorithms (neural networks). More practically, the objective is to reproduce simultaneously both the spatial patterns and the extreme values. This objective is best reached by models integrating geostatistics and machine learning algorithms. To demonstrate how such models work, two case studies have been considered: first, a 2-day accumulation of heavy precipitation and second, a 6-day accumulation of extreme orographic precipitation. The first example is used to compare the performance of two optimization algorithms (conjugate gradients and Levenberg-Marquardt) of a neural network for the reproduction of extreme values. Hybrid models, which combine geostatistical and machine learning algorithms, are also treated in this context. The second dataset is used to analyze the contribution of radar Doppler imagery when used as external drift or as input in the models (kriging with external drift and neural networks). Model assessment is carried out by comparing independent validation errors as well as analyzing data patterns.

MAMOT: hidden Markov modeling tool.

Hidden Markov models (HMMs) are probabilistic models that are well adapted to many tasks in bioinformatics, for example, for predicting the occurrence of specific motifs in biological sequences. MAMOT is a command-line program for Unix-like operating systems, including MacOS X, that we developed to allow scientists to apply HMMs more easily in their research. One can define the architecture and initial parameters of the model in a text file and then use MAMOT for parameter optimization on example data, decoding (like predicting motif occurrence in sequences) and the production of stochastic sequences generated according to the probabilistic model. Two examples for which models are provided are coiled-coil domains in protein sequences and protein binding sites in DNA. A wealth of useful features include the use of pseudocounts, state tying and fixing of selected parameters in learning, and the inclusion of prior probabilities in decoding. AVAILABILITY: MAMOT is implemented in C++, and is distributed under the GNU General Public Licence (GPL). The software, documentation, and example model files can be found at http://bcf.isb-sib.ch/mamot