Riemannian metrics on an infinite dimensional symplectic group

The aim of this paper is the geometric study of the symplectic operators which are a perturbation of the identity by a Hilbert-Schmidt operator. This subgroup of the symplectic group was introduced in Pierre de la Harpe's classical book of Banach-Lie groups. Throughout this paper we will endow the tangent spaces with different Riemannian metrics. We will use the minimal curves of the unitary group and the positive invertible operators to compare the length of the geodesic curves in each case. Moreover we will study the completeness of the symplectic group with the geodesic distance.Comment: 18 pages. The final version of this preprint will appear in Journal of Mathematical Analysis and Application

Efficient graph-based genetic programming representation with multiple outputs

In this work, we explore and study the implication of having more than one output on a genetic programming (GP) graph-representation. This approach, called multiple interactive outputs in a single tree (MIOST), is based on two ideas. First, we defined an approach, called interactivity within an individual (IWI), which is based on a graph-GP representation. Second, we add to the individuals created with the IWI approach multiple outputs in their structures and as a result of this, we have MIOST. As a first step, we analyze the effects of IWI by using only mutations and analyze its implications (i.e., presence of neutrality). Then, we continue testing the effectiveness of IWI by allowing mutations and the standard GP crossover in the evolutionary process. Finally, we tested the effectiveness of MIOST by using mutations and crossover and conducted extensive empirical results on different evolvable problems of different complexity taken from the literature. The results reported in this paper indicate that the proposed approach has a better overall performance in terms of consistency reaching feasible solutions

Interacciones insecto-planta en una leguminosa de bosque seco tropical bajo tres coberturas con diferente perturbación Coello, Tolima, Colombia

El Bosque Seco Tropical en Colombia, ha tenido altos procesos de transformación, convirtiéndose en uno de los tres ecosistemas más amenazados y fragmentados del país con graves consecuencias sobre la biodiversidad, desconociéndose en gran medida los efectos sobre las interacciones ecológicas. Entre las interacciones más relevantes se encuentran la herbivoría, el parasitismo y la predación las cuales presentan cambios críticos a los procesos de fragmentación y pérdida de hábitat. En este estudio se determinaron los efectos de tres coberturas de Bosque Seco Tropical con diferente grado de perturbación sobre la interacción herbívoro-planta, la composición y estructura los gremios tróficos de las comunidades de insectos en Pseudosamanea guachapele (Mimosaceae). El estudio se llevó a cabo en el municipio de Coello, Tolima, se identificaron 10 árboles por cada tipo de cobertura y para cada uno se estimó el porcentaje de herbivoría foliar y tipos de daño por herbivoría. Los tipos de herbivoría variaron en respuesta a la cobertura, presentando mayor porcentaje en borde de camino. Se encontró una menor riqueza de familias en borde de camino, donde también hubo mayor abundancia de herbívoros y una disminución de parasitoides y depredadores. Parasitoides y depredadores fueron más abundantes en la vegetación secundaria alta. Estos resultados muestran una acción combinada del aumento en la abundancia de herbívoros y disminución de enemigos naturales como una causa del aumento de la herbivoría, esta última en respuesta a la pérdida de la cobertura original.The Tropical Dry Forest in Colombia has suffer high transformation processes, making it one of the three most fragmented and endangered ecosystems in the country with serious consequences for biodiversity, and largely unknown effects on ecological interactions. Herbivory, parasitism and predation are among the most relevant interactions presenting critical responses to fragmentation and loss of habitat. In this study the effects of three land cover of Tropical Dry Forest with different degrees of disturbance on plant-herbivore interactions, composition and trophic guild structure of insect communities in Pseudosamanea guachapele (Mimosaceae) were determined,In the municipality of Coello, Tolima, were identified ,and the percentage herbivory for each leaf and type of herbivory damage was estimated. Herbivory percentages varied in response to coverage, being greater on trees along the road side. Fewer family numbers, greater abundance of herbivores and lower of predators and parasitoids was also found on trees along the road side, Parasitoids and predators were more abundant in upper secondary vegetation. These results show a combined effect of the increase in the abundance of herbivores and natural enemies as a cause of increased herbivory, the latter in response to the loss of coverage.Ecólogo (a)Pregrad

Grammars and cellular automata for evolving neural networks architectures

IEEE International Conference on Systems, Man, and Cybernetics. Nashville, TN, 8-11 October 2000The class of feedforward neural networks trained with back-propagation admits a large variety of specific architectures applicable to approximation pattern tasks. Unfortunately, the architecture design is still a human expert job. In recent years, the interest to develop automatic methods to determine the architecture of the feedforward neural network has increased, most of them based on the evolutionary computation paradigm. From this approach, some perspectives can be considered: at one extreme, every connection and node of architecture can be specified in the chromosome representation using binary bits. This kind of representation scheme is called the direct encoding scheme. In order to reduce the length of the genotype and the search space, and to make the problem more scalable, indirect encoding schemes have been introduced. An indirect scheme under a constructive algorithm, on the other hand, starts with a minimal architecture and new levels, neurons and connections are added, step by step, via some sets of rules. The rules and/or some initial conditions are codified into a chromosome of a genetic algorithm. In this work, two indirect constructive encoding schemes based on grammars and cellular automata, respectively, are proposed to find the optimal architecture of a feedforward neural network

Neural Network architectures design by Cellular Automata evolution

4th Conference of Systemics Cybernetics and Informatics. Orlando, 23-26 July 2000The design of the architecture is a crucial step in the successful application of a neural network. However, the architecture design is basically, in most cases, a human experts job. The design depends heavily on both, the expert experience and on a tedious trial-and-error process. Therefore, the development of automatic methods to determine the architecture of feedforward neural networks is a field of interest in the neural network community. These methods are generally based on search techniques, as genetic algorithms, simulated annealing or evolutionary strategies. Most of the designed methods are based on direct representation of the parameters of the network. This representation does not allow scalability, so to represent large architectures very large structures are required. In this work, an indirect constructive encoding scheme is proposed to find optimal architectures of feed-forward neural networks. This scheme is based on cellular automata representations in order to increase the scalability of the method.Publicad

Generative capacities of cellular automata codification for evolution of NN codification

Proceeding of: International Conference on Artificial Neural Networks. ICANN 2002, Madrid, Spain, August 28-30, 2002Automatic methods for designing artificial neural nets are desired to avoid the laborious and erratically human expert’s job. Evolutionary computation has been used as a search technique to find appropriate NN architectures. Direct and indirect encoding methods are used to codify the net architecture into the chromosome. A reformulation of an indirect encoding method, based on two bi-dimensional cellular automata, and its generative capacity are presented.Publicad

Evolutionary cellular configurations for designing feed-forward neural networks architectures

Proceeding of: 6th International Work-Conference on Artificial and Natural Neural Networks, IWANN 2001 Granada, Spain, June 13–15, 2001In the recent years, the interest to develop automatic methods to determine appropriate architectures of feed-forward neural networks has increased. Most of the methods are based on evolutionary computation paradigms. Some of the designed methods are based on direct representations of the parameters of the network. These representations do not allow scalability, so to represent large architectures, very large structures are required. An alternative more interesting are the indirect schemes. They codify a compact representation of the neural network. In this work, an indirect constructive encoding scheme is presented. This scheme is based on cellular automata representations in order to increase the scalability of the method

Non-Direct Encoding Method Based on Cellular Automata to Design Neural Network Architectures

Architecture design is a fundamental step in the successful application of Feed forward Neural Networks. In most cases a large number of neural networks architectures suitable to solve a problem exist and the architecture design is, unfortunately, still a human expert’s job. It depends heavily on the expert and on a tedious trial-and-error process. In the last years, many works have been focused on automatic resolution of the design of neural network architectures. Most of the methods are based on evolutionary computation paradigms. Some of the designed methods are based on direct representations of the parameters of the network. These representations do not allow scalability; thus, for representing large architectures very large structures are required. More interesting alternatives are represented by indirect schemes. They codify a compact representation of the neural network. In this work, an indirect constructive encoding scheme is proposed. This scheme is based on cellular automata representations and is inspired by the idea that only a few seeds for the initial configuration of a cellular automaton can produce a wide variety of feed forward neural networks architectures. The cellular approach is experimentally validated in different domains and compared with a direct codification scheme.Publicad