Cluster algebras, quiver representations and triangulated categories

This is an introduction to some aspects of Fomin-Zelevinsky’s cluster algebras and their links with the representation theory of quivers and with Calabi-Yau triangulated categories. It is based on lectures given by the author at summer schools held in 2006 (Bavaria)and 2008 (Jerusalem). In addition to by now classical material, we present the outline of a proof of the periodicity conjecture for pairs of Dynkin diagrams (details will appear elsewhere) and recent results on the interpretation of mutations as derived equivalences.

An irreducibility criterion for group representations, with arithmetic applications

We prove a criterion for the irreducibility of an integral group representation p over the fraction field of a noetherian domain R in terms of suitably defined reductions of p at prime ideals of R. As applications, we give irreducibility results for universal deformations of residual representations, with a special attention to universal deformations of residual Galois representations associated with modular forms of weight at least 2.

Implementación y entrenamiento de un modelo clasificatorio de red neural sobre la base de datos IGBADAT para la clasificación de las rocas basálticas de acuerdo a las clases del sistema de clasificación tradicional de Yoder and Tiller.

Aquest treball vol implementar un projecte de mineria de dades en l'àrea de la petrologia ígnia, especialitat englobada dins la geologia clàssica.

Efficient learning of reactive robot behaviors with a Neural-Q_learning approach

The purpose of this paper is to propose a Neural-Q_learning approach designed for online learning of simple and reactive robot behaviors. In this approach, the Q_function is generalized by a multi-layer neural network allowing the use of continuous states and actions. The algorithm uses a database of the most recent learning samples to accelerate and guarantee the convergence. Each Neural-Q_learning function represents an independent, reactive and adaptive behavior which maps sensorial states to robot control actions. A group of these behaviors constitutes a reactive control scheme designed to fulfill simple missions. The paper centers on the description of the Neural-Q_learning based behaviors showing their performance with an underwater robot in a target following task. Real experiments demonstrate the convergence and stability of the learning system, pointing out its suitability for online robot learning. Advantages and limitations are discussed

Semi-online neural-Q_leaming for real-time robot learning

Reinforcement learning (RL) is a very suitable technique for robot learning, as it can learn in unknown environments and in real-time computation. The main difficulties in adapting classic RL algorithms to robotic systems are the generalization problem and the correct observation of the Markovian state. This paper attempts to solve the generalization problem by proposing the semi-online neural-Q_learning algorithm (SONQL). The algorithm uses the classic Q_learning technique with two modifications. First, a neural network (NN) approximates the Q_function allowing the use of continuous states and actions. Second, a database of the most representative learning samples accelerates and stabilizes the convergence. The term semi-online is referred to the fact that the algorithm uses the current but also past learning samples. However, the algorithm is able to learn in real-time while the robot is interacting with the environment. The paper shows simulated results with the "mountain-car" benchmark and, also, real results with an underwater robot in a target following behavior

Volatility smile extrapolation with an artificial neural network

I use a multi-layer feedforward perceptron, with backpropagation learning implemented via stochastic gradient descent, to extrapolate the volatility smile of Euribor derivatives over low-strikes by training the network on parametric prices.

Cannabinoid addiction: behavioral models and neural correlates

The use of cannabis sativa preparations as recreational drugs can be traced back to the earliest civilizations. However, animal models of cannabinoid addiction allowing the exploration of neural correlates of cannabinoid abuse have been developed only recently. We review these models and the role of the CB1 cannabinoid receptor, the main target of natural cannabinoids, and its interaction with opioid and dopamine transmission in reward circuits. Extensive reviews on the molecular basis of cannabinoid action are available elsewhere (Piomelli et al., 2000;Schlicker and Kathmann, 2001).

What can spike train distances tell us about the neural code?

Time scale parametric spike train distances like the Victor and the van Rossum distancesare often applied to study the neural code based on neural stimuli discrimination.Different neural coding hypotheses, such as rate or coincidence coding,can be assessed by combining a time scale parametric spike train distance with aclassifier in order to obtain the optimal discrimination performance. The time scalefor which the responses to different stimuli are distinguished best is assumed to bethe discriminative precision of the neural code. The relevance of temporal codingis evaluated by comparing the optimal discrimination performance with the oneachieved when assuming a rate code.We here characterize the measures quantifying the discrimination performance,the discriminative precision, and the relevance of temporal coding. Furthermore,we evaluate the information these quantities provide about the neural code. Weshow that the discriminative precision is too unspecific to be interpreted in termsof the time scales relevant for encoding. Accordingly, the time scale parametricnature of the distances is mainly an advantage because it allows maximizing thediscrimination performance across a whole set of measures with different sensitivitiesdetermined by the time scale parameter, but not due to the possibility toexamine the temporal properties of the neural code.

Supporting the reuse of effective CSCL learning designs through social structure representations

Distance and blended collaborative learning settings are usually characterized by different social structures defined in terms of groups' number, dimension, and composition; these structures are variable and can change within the same activity. This variability poses additional complexity to instructional designers, when they are trying to develop successful experiences from existing designs. This complexity is greatly associated with the fact that learning designs do not render explicit how social structures influenced the decisions of the original designer, and thus whether the social structures of the new setting could preclude the effectiveness of the reused design. This article proposes the usage of new representations (social structure representations, SSRs) able to support unskilled designers in reusing existing learning designs, through the explicit characterization of the social structures and constraints embedded either by the original designers or the reusing teachers, according to well-known principles of good collaborative learning practice. The article also describes an evaluation process that involved university professors, as well as the main findings derived from it. This process supported the initial assumptions about the effectiveness of SSRs, with significant evidence from both qualitative and qualitative data.

Computing congruences of modular forms and Galois representations modulo prime powers

This article starts a computational study of congruences of modular forms and modular Galoisrepresentations modulo prime powers. Algorithms are described that compute the maximum integermodulo which two monic coprime integral polynomials have a root in common in a sensethat is defined. These techniques are applied to the study of congruences of modular forms andmodular Galois representations modulo prime powers. Finally, some computational results withimplications on the (non-)liftability of modular forms modulo prime powers and possible generalisationsof level raising are presented.

Validation procedures in radiological diagnostic models. Neural network and logistic regression

The objective of this paper is to compare the performance of twopredictive radiological models, logistic regression (LR) and neural network (NN), with five different resampling methods. One hundred and sixty-seven patients with proven calvarial lesions as the only known disease were enrolled. Clinical and CT data were used for LR and NN models. Both models were developed with cross validation, leave-one-out and three different bootstrap algorithms. The final results of each model were compared with error rate and the area under receiver operating characteristic curves (Az). The neural network obtained statistically higher Az than LR with cross validation. The remaining resampling validation methods did not reveal statistically significant differences between LR and NN rules. The neural network classifier performs better than the one based on logistic regression. This advantage is well detected by three-fold cross-validation, but remains unnoticed when leave-one-out or bootstrap algorithms are used.

Galois representations, embedding problems and modular forms

To an odd irreducible 2-dimensional complex linear representation of the absolute Galois group of the field Q of rational numbers, a modular form of weight 1 is associated (modulo Artin's conjecture on the L-series of the representation in the icosahedral case). In addition, linear liftings of 2-dimensional projective Galois representations are related to solutions of certain Galois embedding problems. In this paper we present some recent results on the existence of liftings of projective representations and on the explicit resolution of embedding problems associated to orthogonal Galois representations, and explain how these results can be used to construct modular forms.

Podocalyxin is a novel polysialylated neural adhesion protein with multiple roles in neural development and synapse formation

Neural development and plasticity are regulated by neural adhesion proteins, including the polysialylated form of NCAM (PSA-NCAM). Podocalyxin (PC) is a renal PSA-containing protein that has been reported to function as an anti-adhesin in kidney podocytes. Here we show that PC is widely expressed in neurons during neural development. Neural PC interacts with the ERM protein family, and with NHERF1/2 and RhoA/G. Experiments in vitro and phenotypic analyses of podxl-deficient mice indicate that PC is involved in neurite growth, branching and axonal fasciculation, and that PC loss-of-function reduces the number of synapses in the CNS and in the neuromuscular system. We also show that whereas some of the brain PC functions require PSA, others depend on PC per se. Our results show that PC, the second highly sialylated neural adhesion protein, plays multiple roles in neural development.

Quality coding by neural populations in the early olfactory pathway: analysis using information theory

In this article, we analyze the ability of the early olfactory system to detect and discriminate different odors by means of information theory measurements applied to olfactory bulb activity images. We have studied the role that the diversity and number of receptor neuron types play in encoding chemical information. Our results show that the olfactory receptors of the biological system are low correlated and present good coverage of the input space. The coding capacity of ensembles of olfactory receptors with the same receptive range is maximized when the receptors cover half of the odor input space - a configuration that corresponds to receptors that are not particularly selective. However, the ensemble's performance slightly increases when mixing uncorrelated receptors of different receptive ranges. Our results confirm that the low correlation between sensors could be more significant than the sensor selectivity for general purpose chemo-sensory systems, whether these are biological or biomimetic.