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.

An improved silver staining procedure for schizodeme analysis in polyacrylamide gradient gels

A simple protocol is described for the silver staining of polyacrylamide gradient gels used for the separation of restriction fragments of kinetoplast DNA [schizodeme analysis of trypanosomatids (Morel et al., 1980)]. The method overcomes the problems of non-uniform staining and strong background color which are frequently encountered when conventional protocols for silver staining of linear gels. The method described has proven to be of general applicability for DNA, RNA and protein separations in gradient gels.

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.

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.

Generic optimality conditions for semi-algebraic convex programs

We consider linear optimization over a nonempty convex semi-algebraic feasible region F. Semidefinite programming is an example. If F is compact, then for almost every linear objective there is a unique optimal solution, lying on a unique \active" manifold, around which F is \partly smooth", and the second-order sufficient conditions hold. Perturbing the objective results in smooth variation of the optimal solution. The active manifold consists, locally, of these perturbed optimal solutions; it is independent of the representation of F, and is eventually identified by a variety of iterative algorithms such as proximal and projected gradient schemes. These results extend to unbounded sets F.

Wnt secretion and gradient formation.

Concentration gradients formed by the lipid-modified morphogens of the Wnt family are known for their pivotal roles during embryogenesis and adult tissue homeostasis. Wnt morphogens are also implicated in a variety of human diseases, especially cancer. Therefore, the signaling cascades triggered by Wnts have received considerable attention during recent decades. However, how Wnts are secreted and how concentration gradients are formed remains poorly understood. The use of model organisms such as Drosophila melanogaster has provided important advances in this area. For instance, we have previously shown that the lipid raft-associated reggie/flotillin proteins influence Wnt secretion and spreading in Drosophila. Our work supports the notion that producing cells secrete Wnt molecules in at least two pools: a poorly diffusible one and a reggie/flotillin-dependent highly diffusible pool which allows morphogen spreading over long distances away from its source of production. Here we revise the current views of Wnt secretion and spreading, and propose two models for the role of the reggie/flotillin proteins in these processes: (i) reggies/flotillins regulate the basolateral endocytosis of the poorly diffusible, membrane-bound Wnt pool, which is then sorted and secreted to apical compartments for long-range diffusion, and (ii) lipid rafts organized by reggies/flotillins serve as "dating points" where extracellular Wnt transiently interacts with lipoprotein receptors to allow its capture and further spreading via lipoprotein particles. We further discuss these processes in the context of human breast cancer. A better understanding of these phenomena may be relevant for identification of novel drug targets and therapeutic strategies.

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.

Liquid line of descent of a basanitic liquid at 1.5 GPa: Constraints for metasomatic vein formation

The metasomatism observed in the oceanic and continental lithosphere is generally interpreted to represent a continuous differentiation process forming anhydrous and hydrous veins plus a cryptic enrichment in the surrounding peridotite. In order to constrain the mechanisms of vein formation and potentially clarify the nature and origin of the initial metasomatic agent, we performed a series of high-pressure experiments simulating the liquid line of descent of a basanitic magma differentiating within continental or mature oceanic lithosphere. This series of experiments has been conducted in an end-loaded piston cylinder apparatus starting from an initial hydrous ne-normative basanite at 1.5 GPa and temperature varying between 1,250 and 980°C. Near-pure fractional crystallization process was achieved in a stepwise manner in 30°C temperature steps and starting compositions corresponding to the liquid composition of the previous, higher-temperature glass composition. Liquids evolve progressively from basanite to peralkaline, aluminum-rich compositions without significant SiO2 variation. The resulting cumulates are characterized by an anhydrous clinopyroxene + olivine assemblage at high temperature (1,250-1,160°C), while at lower temperature (1,130-980°C), hydrous cumulates with dominantly amphibole + minor clinopyroxene, spinel, ilmenite, titanomagnetite and apatite (1,130-980°C) are formed. This new data set supports the interpretation that anhydrous and hydrous metasomatic veins could be produced during continuous differentiation processes of primary, hydrous alkaline magmas at high pressure. However, the comparison between the cumulates generated by the fractional crystallization from an initial ne-normative liquid or from hy-normative initial compositions (hawaiite or picrobasalt) indicates that for all hydrous liquids, the different phases formed upon differentiation are mostly similar even though the proportions of hydrous versus anhydrous minerals could vary significantly. This suggests that the formation of amphibole-bearing metasomatic veins observed in the lithospheric mantle could be linked to the differentiation of initial liquids ranging from ne-normative to hy-normative in composition. The present study does not resolve the question whether the metasomatism observed in lithospheric mantle is a precursor or a consequence of alkaline magmatism; however, it confirms that the percolation and differentiation of a liquid produced by a low degree of partial melting of a source similar or slightly more enriched than depleted MORB mantle could generate hydrous metasomatic veins interpreted as a potential source for alkaline magmatism by various authors.

Heritability of renal function in hypertensive families of African descent in the Seychelles (Indian Ocean).

BACKGROUND: We estimated the heritability of three measures of glomerular filtration rate (GFR) in hypertensive families of African descent in the Seychelles (Indian Ocean). METHODS: Families with at least two hypertensive siblings and an average of two normotensive siblings were identified through a national hypertension register. Using the ASSOC program in SAGE (Statistical Analysis in Genetic Epidemiology), the age- and gender-adjusted narrow sense heritability of GFR was estimated by maximum likelihood assuming multivariate normality after power transformation. ASSOC can calculate the additive polygenic component of the variance of a trait from pedigree data in the presence of other familial correlations. The effects of body mass index (BMI), blood pressure, natriuresis, along with sodium to potassium ratio in urine and diabetes, were also tested as covariates. RESULTS: Inulin clearance, 24-hour creatinine clearance, and GFR based on the Cockcroft-Gault formula were available for 348 persons from 66 pedigrees. The age- and gender-adjusted correlations (+/- SE) were 0.51 (+/- 0.04) between inulin clearance and creatinine clearance, 0.53 (+/- 0.04) between inulin clearance and Cockcroft-Gault formula and 0.66 (+/- 0.03) between creatinine clearance and Cockcroft-Gault formula. The age- and gender-adjusted heritabilities (+/- SE) of GFR were 0.41 (+/- 0.10) for inulin clearance, 0.52 (+/- 0.13) for creatinine clearance, and 0.82 (+/- 0.09) for Cockcroft-Gault formula. Adjustment for BMI slightly lowered the correlations and heritabilities for all measurements whereas adjustment for blood pressure had virtually no effect. CONCLUSION: The significant heritability estimates of GFR in our sample of families of African descent confirm the familial aggregation of this trait and justify further analyses aimed at discovering genetic determinants of GFR.