Simulated Annealing

The book contains 15 chapters presenting recent contributions of top researchers working with Simulated Annealing (SA). Although it represents a small sample of the research activity on SA, the book will certainly serve as a valuable tool for researchers interested in getting involved in this multidisciplinary field. In fact, one of the salient features is that the book is highly multidisciplinary in terms of application areas since it assembles experts from the fields of Biology, Telecommunications, Geology, Electronics and Medicine

Spatial and Temporal Prediction Models of Alaska’s 11 Species Mega-Predator Community: Towards a First State-wide Ecological Habitat, Impact, and Climate Assessment

In this study, eleven mega predators, coyote (Canis latrans), wolf (Canis lupus), fox (Vulpes vulpes), arctic fox (Vulpes lagopus), black bear (Ursus americanus), brown bear (Ursus arctos), polar bear (Ursus maritimus), wolverine (Gulo gulo), marten (Martes americana), lynx (Lynx canadensis) and golden eagle (Aquila chrysaetos) were selected to represent an Ecosystem Unit entitled “Mega Predator”. The most influential factors affecting this Ecosystem Unit were determined using a machine learning algorithm (TreeNet) and a Geographic Information System (GIS). Public available range layers were corrected for errors and detectability using occupancy model, and several ‘robust’ hotspots of the predator community were identified. Anthropogenic variables, such as proximity to railways, together with regionalized IPCC climate variables (precipitation and temperature), Alaska SNAP data and spatial variables (e.g. distance to coast) proved to be the main predictors. A second predictive TreeNet model based on climate data forecasting the next 100 years was also performed to assess the resilience of these predators. The results indicate that the Ecosystem Unit “Mega Predator” shall undergo extreme changes in the next decades, commencing in 30 years or less. The TreeNet model points to a complete shattering of the current mega predator community food chain within the next century as a direct consequence of climate change alone. Owing to the fact that IPCC models are underestimates and other factors co-occur, the findings displayed herewith are consequently underestimates. The results of the first TreeNet model and the second predictive model were used to find the optimal potential protected areas for the predator community. This prioritization search was performed with the program MARXAN. Results of the MARXAN Model indicate that the main importance of protected areas for predators lies in the Brooks Range of Northern Alaska. This study could serve as a first (digital) platform and a first step to provide a basis for landscape planners and conservationists to react properly to the upcoming impact of climate and other changes on entire ecosystems.Contents Abstract ................................................................................................. viii 1 Introduction .......................................................................................... 1 1.1 Ecological Role and Interactions of Predators .................................................. 1 1.2 Influence of Predators upon the Ecosystem ...................................................... 2 1.3 Food Web and Trophic Cascades ..................................................................... 3 1.3 Reaction of the Ecosystem to missing Apex predators ..................................... 4 1.4 Sympatric Connections of Predators in Alaska.................................................. 5 1.5 Relevant Summarized Perspectives for this Study ............................ 6 1.5.1 The Mega Predators as an Ecosystem Unit “Mega Predator” .................... 6 1.5.2 The Predator Community in Alaska ............................................................ 6 1.5.3 Assumptions for the Model ......................................................................... 8 1.6 Predator Conservation Management ................................................................ 8 1.6.1 Umbrella species ........................................................................................ 9 1.6.2 Management Indicators .............................................................................. 9 1.6.3 Focal Species ............................................................................................. 9 1.7 Science-based Conservation Management of the Mega Predator Community 10 1.8 The Mega Predator Community ...................................................................... 10 1.8.1 Canidae ........................................................................................................ 10 1.8.1.1 Coyote (Canis latrans) .............................................................................. 10 1.8.1.1.1 Distribution ....................................................................................... 11 1.8.1.1.2 Ecology ............................................................................................ 11 ii1.8.1.1.3 Home Range and Density ............................................................... 12 1.8.1.1.4 Feeding Habits ................................................................................ 12 1.8.1.2 Arctic Fox (Alopex lagopus) ...................................................................... 13 1.8.1.2.1 Distribution ...................................................................................... 13 1.8.1.2.2 Ecology ........................................................................................... 14 1.8.1.2.3 Habitat ............................................................................................. 14 1.8.1.2.4 Home Range ................................................................................... 14 1.8.1.2.6 Human Impact and Conservation Status ......................................... 15 1.8.1.3 Red Fox (Vulpes Vulpes) .......................................................................... 15 1.8.1.3.1 Distribution ...................................................................................... 15 1.8.1.3.2 Habitat ............................................................................................. 16 1.8.1.3.3 Feeding Habits and Home Rranges ................................................ 17 1.8.1.3.4 Human Impact and Conservation status ......................................... 17 1.8.1.3.5 Interspecific Interactions of foxes .................................................... 17 1.8.1.4 Gray Wolf (Canis lupus) ............................................................................ 18 1.8.1.4.1 Distribution ...................................................................................... 18 1.8.1.4.2 Habitat ............................................................................................. 18 1.8.1.4.3 Home Range ................................................................................... 19 1.8.1.4.4 Hunting and Diet ............................................................................. 19 1.8.1.4.5 Human Impact and Conservation Status ......................................... 19 1.8.2 Ursidae ......................................................................................................... 20 1.8.2.1 Black bear (Ursus americanus) ................................................................. 20 1.8.2.1.1 Distribution ...................................................................................... 20 iii1.8.2.1.2 Habitat ............................................................................................. 21 1.8.2.1.3 Home range and movement ............................................................ 21 1.8.2.1.4 Feeding Habits ................................................................................ 22 1.8.2.1.5 Behavior .......................................................................................... 22 1.8.2.1.6 Human Impact and Conservation Status ......................................... 22 1.8.2.2 Polar Bear (Ursus maritimus) .................................................................... 23 1.8.2.2.1 Distribution ...................................................................................... 23 1.8.2.2.2 Habitat ............................................................................................. 24 1.8.2.2.3 Feeding Habits ................................................................................ 24 1.8.2.2.4 Interspecific Interactions ................................................................. 25 1.8.2.2.5 Human Impact and Conservation Status ......................................... 25 1.8.2.3 Grizzly Bear (Ursus Arctos) ....................................................................... 25 1.8.2.3.1 Global Distribution ........................................................................... 26 1.8.2.3.2 Ecology ........................................................................................... 26 1.8.2.3.3 Home Range ................................................................................... 27 1.8.2.3.4 Feeding Habits ................................................................................ 27 1.8.2.3.5 Intraspecific Killing .......................................................................... 28 1.8.2.3.6 Human impact and Conservation status ......................................... 28 1.8.2.4 Wolverine (Gulo Gulo) ............................................................................... 29 1.8.2.4.1 Global Distribution ........................................................................... 29 1.8.2.4.2 Habitat ............................................................................................. 30 1.8.2.4.3 Feeding Habits ................................................................................ 30 1.8.2.4.4 Human Impact and Conservation .................................................... 31 iv1.8.2.5 Pine marten (Martes americana) ............................................................... 31 1.8.2.5.1 Distribution ...................................................................................... 31 1.8.2.5.2 Habitat ............................................................................................. 32 1.8.2.5.3 Density, Spatial Organization and Home Range ............................. 32 1.8.3 Felidae ......................................................................................................... 33 1.8.3.1 Lynx Canadensis ....................................................................................... 33 1.8.3.1.1 Global Distribution ........................................................................... 33 1.8.3.1.2 Habitat ............................................................................................. 34 1.8.3.1.3 Home Range ................................................................................... 34 1.8.3.1.4 Hunting and Diet ............................................................................. 34 1.8.3.1.5 Impact of Humans and Conservation .............................................. 35 1.8.4. Aves ............................................................................................................ 35 1.8.4.1.1 Distribution ...................................................................................... 35 1.8.4.1.2 Habitat ............................................................................................. 36 1.8.4.1.3 Home Range ................................................................................... 36 1.8.4.1.4 Ecosystem Roles ............................................................................ 37 1.8.4.1.5 Food Habits ..................................................................................... 37 1.8.4.1.6 Predation ......................................................................................... 37 1.8.4.1.7 Conservation Status ........................................................................ 37 2. Methods ............................................................................................ 41 2.1 Software .......................................................................................... 41 2.2 Building an Occupancy Model of eleven Predators in Alaska ......................... 43 2.3 Building the Model Ecosystem Unit “Mega Predator” ...................................... 43 v2.4 Geological and Environmental Variables ......................................................... 45 2.4.1 Mean Normalized Difference Vegetation Index (NDVI) ............................. 45 2.4.2 Vegetation Classes ................................................................................... 45 2.4.3 Alaska Ecoregions Mapping ..................................................................... 46 2.4.4 Distance to roads, railways, airways, lakes, coast and towns and topographic maps .............................................................................................. 46 2.4.5 Computation of the Human Influence Index and the Human Footprint ..... 47 2.4.6 Climate layers, the General Climate Model, future Climate Prediction and Climate Change ................................................................................................. 47 2.5 Using TreeNet Algorithm for Data Mining and Climate Predictions ................. 50 2.6 Marxan Model Methods ................................................................................... 51 2.6.1 Implementing Conservation Areas for eleven Predators in Alaska ........... 51 2.6.2 Simulated annealing ................................................................................. 52 2.6.2 Questions to be answered from Marxan ................................................... 54 2.6.3 Implementation of Marxan ........................................................................ 54 2.6.4 Defining the costs for eleven Predators .................................................... 54 3 Results ............................................................................................... 56 3.1 Descriptive Maps of the Ecosystem Unit “Mega Predator” .............................. 56 3.2 Ranking of Value Importance for the Predator Community ............................. 57 3.3 Climate Predictions for the Model ................................................................... 64 3.4.1 Model Accuracy ........................................................................................ 70 3.4.2 Prediction of the Decade 2030-2039 ........................................................ 71 3.4.3 Prediction of the Decade 2060-2069 ........................................................ 72 3.4.4 Prediction of the Decade 2090-2099 ........................................................ 74 vi3.5 Near-best Solution of Protected Areas for the Eleven Mega Predator community provided by Marxan ............................................................................ 76 4.Discussion .......................................................................................... 80 4.1 Climatic Model of the Ecosystem Unit “Mega Predators of Alaska”................. 81 4.2 Potential Protected Areas ................................................................................ 83 4.3 Possible Errors of the Models ......................................................................... 85 4.4 Wildlife and Human- Influence ........................................................................ 85 5. Literature References ........................................................................ 8

A Resource Efficient Localized Recurrent Neural Network Architecture and Learning Algorithm

Recurrent neural networks (RNNs) are widely acknowledged as an effective tool that can be employed by a wide range of applications that store and process temporal sequences. The ability of RNNs to capture complex, nonlinear system dynamics has served as a driving motivation for their study. RNNs have the potential to be effectively used in modeling, system identification and adaptive control applications, to name a few, where other techniques fall short. Most of the proposed RNN learning algorithms rely on the calculation of error gradients with respect to the network weights. What distinguishes recurrent neural networks from static, or feedforward networks, is the fact that the gradients are time-dependent or dynamic. This implies that the current error gradient does not only depend on the current input, output and targets, but rather on its possibly infinite past. How to effectively train RNNs remains a challenging and active research topic. This thesis introduces TRTRL, an efficient, low-complexity online learning algorithm for recurrent neural networks. The approach is based on the real-time recurrent learning (RTRL) algorithm, whereby the sensitivity set of each neuron is reduced to weights associated either with its input or output links. As a consequence, storage requirements are reduced from O(N3) to O(N2) and the computational complexity is reduced from O(N4) to O(N2). Despite the radical reduction in resource requirements, it is shown through simulations results that the overall performance degradation of the truncated real-time recurrent learning (TRTRL) algorithm is minor. Moreover, the scheme lends itself to efficient hardware realization by virtue of the localized property that is inherent to the approach. The TRTRL algorithm is first implemented and evaluated using a multi-purpose CPU. Next, the framework is extended to a hardware implementation that scales to high network densities without compromising computation speed and overall performance

Neural Networks: Training and Application to Nonlinear System Identification and Control

This dissertation investigates training neural networks for system identification and classification. The research contains two main contributions as follow:1. Reducing number of hidden layer nodes using a feedforward componentThis research reduces the number of hidden layer nodes and training time of neural networks to make them more suited to online identification and control applications by adding a parallel feedforward component. Implementing the feedforward component with a wavelet neural network and an echo state network provides good models for nonlinear systems.The wavelet neural network with feedforward component along with model predictive controller can reliably identify and control a seismically isolated structure during earthquake. The network model provides the predictions for model predictive control. Simulations of a 5-story seismically isolated structure with conventional lead-rubber bearings showed significant reductions of all response amplitudes for both near-field (pulse) and far-field ground motions, including reduced deformations along with corresponding reduction in acceleration response. The controller effectively regulated the apparent stiffness at the isolation level. The approach is also applied to the online identification and control of an unmanned vehicle. Lyapunov theory is used to prove the stability of the wavelet neural network and the model predictive controller. 2. Training neural networks using trajectory based optimization approachesTraining neural networks is a nonlinear non-convex optimization problem to determine the weights of the neural network. Traditional training algorithms can be inefficient and can get trapped in local minima. Two global optimization approaches are adapted to train neural networks and avoid the local minima problem. Lyapunov theory is used to prove the stability of the proposed methodology and its convergence in the presence of measurement errors. The first approach transforms the constraint satisfaction problem into unconstrained optimization. The constraints define a quotient gradient system (QGS) whose stable equilibrium points are local minima of the unconstrained optimization. The QGS is integrated to determine local minima and the local minimum with the best generalization performance is chosen as the optimal solution. The second approach uses the QGS together with a projected gradient system (PGS). The PGS is a nonlinear dynamical system, defined based on the optimization problem that searches the components of the feasible region for solutions. Lyapunov theory is used to prove the stability of PGS and QGS and their stability under presence of measurement noise

Models for time series prediction based on neural networks. Case study : GLP sales prediction from ANCAP.

A time series is a sequence of real values that can be considered as observations of a certain system. In this work, we are interested in time series coming from dynamical systems. Such systems can be sometimes described by a set of equations that model the underlying mechanism from where the samples come. However, in several real systems, those equations are unknown, and the only information available is a set of temporal measures, that constitute a time series. On the other hand, by practical reasons it is usually required to have a prediction, v.g. to know the (approximated) value of the series in a future instant t. The goal of this thesis is to solve one of such real-world prediction problem: given historical data related with the lique ed bottled propane gas sales, predict the future gas sales, as accurately as possible. This time series prediction problem is addressed by means of neural networks, using both (dynamic) reconstruction and prediction. The problem of to dynamically reconstruct the original system consists in building a model that captures certain characteristics of it in order to have a correspondence between the long-term behavior of the model and of the system. The networks design process is basically guided by three ingredients. The dimensionality of the problem is explored by our rst ingredient, the Takens-Mañé's theorem. By means of this theorem, the optimal dimension of the (neural) network input can be investigated. Our second ingredient is a strong theorem: neural networks with a single hidden layer are universal approximators. As the third ingredient, we faced the search of the optimal size of the hidden layer by means of genetic algorithms, used to suggest the number of hidden neurons that maximizes a target tness function (related with prediction errors). These algorithms are also used to nd the most in uential networks inputs in some cases. The determination of the hidden layer size is a central (and hard) problem in the determination of the network topology. This thesis includes a state of the art of neural networks design for time series prediction, including related topics such as dynamical systems, universal approximators, gradient-descent searches and variations, as well as meta-heuristics. The survey of the related literature is intended to be extensive, for both printed material and electronic format, in order to have a landscape of the main aspects for the state of the art in time series prediction using neural networks. The material found was sometimes extremely redundant (as in the case of the back-propagation algorithm and its improvements) and scarce in others (memory structures or estimation of the signal subspace dimension in the stochastic case). The surveyed literature includes classical research works ([27], [50], [52]) as well as more recent ones ([79] , [16] or [82]), which pretends to be another contribution of this thesis. Special attention is given to the available software tools for neural networks design and time series processing. After a review of the available software packages, the most promising computational tools for both approaches are discussed. As a result, a whole framework based on mature software tools was set and used. In order to work with such dynamical systems, software intended speci cally for the analysis and processing of time series was employed, and then chaotic series were part of our focus. Since not all randomness is attributable to chaos, in order to characterize the dynamical system generating the time series, an exploration of chaotic-stochastic systems is required, as well as network models to predict a time series associated to one of them. Here we pretend to show how the knowledge of the domain, something extensively treated in the bibliography, can be someway sophisticated (such as the Lyapunov's spectrum for a series or the embedding dimension). In order to model the dynamical system generated by the time series we used the state-space model, so the time series prediction was translated in the prediction of the next system state. This state-space model, together with the delays method (delayed coordinates) have practical importance for the development of this work, speci cally, the design of the input layer in some networks (multi-layer perceptrons - MLPs) and other parameters (taps in the TFLNs). Additionally, the rest of the network components where determined in many cases through procedures traditionally used in neural networks : genetic algorithms. The criteria of model (network) selection are discussed and a trade-o between performance and network complexity is further explored, inspired in the Rissanen's minimum description length and its estimation given by the chosen software. Regarding the employed network models, the network topologies suggested from the literature as adequate for the prediction are used (TLFNs and recurrent networks) together with MLPs (a classic of arti cial neural networks) and networks committees. The e ectiveness of each method is con rmed for the proposed prediction problem. Network committees, where the predictions are a naive convex combination of predictions from individual networks, are also extensively used. The need of criteria to compare the behaviors of the model and of the real system, in the long run, for a dynamic stochastic systems, is presented and two alternatives are commented. The obtained results proof the existence of a solution to the problem of learning of the dependence Input ! Output . We also conjecture that the system is dynamic-stochastic but not chaotic, because we only have a realization of the random process corresponding to the sales. As a non-chaotic system, the mean of the predictions of the sales would improve as the available data increase, although the probability of a prediction with a big error is always non-null due to the randomness present. This solution is found in a constructive and exhaustive way. The exhaustiveness can be deduced from the next ve statements: the design of a neural network requires knowing the input and output dimension,the number of the hidden layers and of the neurons in each of them. the use of the Takens-Mañé's theorem allows to derive the dimension of the input data by theorems such as the Kolmogorov's and Cybenko's ones the use of multi-layer perceptrons with only one hidden layer is justi ed so several of such models were tested the number of neurons in the hidden layer is determined many times heuristically using genetic algorithms a neuron in the output gives the desired prediction As we said, two tasks are carried out: the development of a time series prediction model and the analysis of a feasible model for the dynamic reconstruction of the system. With the best predictive model, obtained by an ensemble of two networks, an acceptable average error was obtained when the week to be predicted is not adjacent to the training set (7.04% for the week 46/2011). We believe that these results are acceptable provided the quantity of information available, and represent an additional validation that neural networks are useful for time series prediction coming from dynamical systems, no matter whether they are stochastic or not. Finally, the results con rmed several already known facts (such as that adding noise to the inputs and outputs of the training values can improve the results; that recurrent networks trained with the back-propagation algorithm don't have the problem of vanishing gradients in short periods and that the use of committees - which can be seen as a very basic of distributed arti cial intelligence - allows to improve signi cantly the predictions).Una serie temporal es una secuencia de valores reales que pueden ser considerados como observaciones de un cierto sistema. En este trabajo, estamos interesados en series temporales provenientes de sistemas dinámicos. Tales sistemas pueden ser algunas veces descriptos por un conjunto de ecuaciones que modelan el mecanismo subyacente que genera las muestras. sin embargo, en muchos sistemas reales, esas ecuaciones son desconocidas, y la única información disponible es un conjunto de medidas en el tiempo, que constituyen la serie temporal. Por otra parte, por razones prácticas es generalmente requerida una predicción, es decir, conocer el valor (aproximado) de la serie en un instante futuro t. La meta de esta tesis es resolver un problema de predicción del mundo real: dados los datos históricos relacionados con las ventas de gas propano licuado, predecir las ventas futuras, tan aproximadamente como sea posible. Este problema de predicción de series temporales es abordado por medio de redes neuronales, tanto para la reconstrucción como para la predicción. El problema de reconstruir dinámicamente el sistema original consiste en construir un modelo que capture ciertas características de él de forma de tener una correspondencia entre el comportamiento a largo plazo del modelo y del sistema. El proceso de diseño de las redes es guiado básicamente por tres ingredientes. La dimensionalidad del problema es explorada por nuestro primer ingrediente, el teorema de Takens-Mañé. Por medio de este teorema, la dimensión óptima de la entrada de la red neuronal puede ser investigada. Nuestro segundo ingrediente es un teorema muy fuerte: las redes neuronales con una sola capa oculta son un aproximador universal. Como tercer ingrediente, encaramos la búsqueda del tamaño oculta de la capa oculta por medio de algoritmos genéticos, usados para sugerir el número de neuronas ocultas que maximizan una función objetivo (relacionada con los errores de predicción). Estos algoritmos se usan además para encontrar las entradas a la red que influyen más en la salida en algunos casos. La determinación del tamaño de la capa oculta es un problema central (y duro) en la determinación de la topología de la red. Esta tesis incluye un estado del arte del diseño de redes neuronales para la predicción de series temporales, incluyendo tópicos relacionados tales como sistemas dinámicos, aproximadores universales, búsquedas basadas en el gradiente y sus variaciones, así como meta-heurísticas. El relevamiento de la literatura relacionada busca ser extenso, para tanto el material impreso como para el que esta en formato electrónico, de forma de tener un panorama de los principales aspectos del estado del arte en la predicción de series temporales usando redes neuronales. El material hallado fue algunas veces extremadamente redundante (como en el caso del algoritmo de retropropagación y sus mejoras) y escaso en otros (estructuras de memoria o estimación de la dimensión del sub-espacio de señal en el caso estocástico). La literatura consultada incluye trabajos de investigación clásicos ( ([27], [50], [52])' así como de los más reciente ([79] , [16] or [82]). Se presta especial atención a las herramientas de software disponibles para el diseño de redes neuronales y el procesamiento de series temporales. Luego de una revisión de los paquetes de software disponibles, las herramientas más promisiorias para ambas tareas son discutidas. Como resultado, un entorno de trabajo completo basado en herramientas de software maduras fue definido y usado. Para trabajar con los mencionados sistemas dinámicos, software especializado en el análisis y proceso de las series temporales fue empleado, y entonces las series caóticas fueron estudiadas. Ya que no toda la aleatoriedad es atribuible al caos, para caracterizar al sistema dinámico que genera la serie temporal se requiere una exploración de los sistemas caóticos-estocásticos, así como de los modelos de red para predecir una serie temporal asociada a uno de ellos. Aquí se pretende mostrar cómo el conocimiento del dominio, algo extensamente tratado en la literatura, puede ser de alguna manera sofisticado (tal como el espectro de Lyapunov de la serie o la dimensión del sub-espacio de señal). Para modelar el sistema dinámico generado por la serie temporal se usa el modelo de espacio de estados, por lo que la predicción de la serie temporal es traducida en la predicción del siguiente estado del sistema. Este modelo de espacio de estados, junto con el método de los delays (coordenadas demoradas) tiene importancia práctica en el desarrollo de este trabajo, específicamente, en el diseño de la capa de entrada en algunas redes (los perceptrones multicapa) y otros parámetros (los taps de las redes TLFN). Adicionalmente, el resto de los componentes de la red con determinados en varios casos a través de procedimientos tradicionalmente usados en las redes neuronales: los algoritmos genéticos. Los criterios para la selección de modelo (red) son discutidos y un balance entre performance y complejidad de la red es explorado luego, inspirado en el minimum description length de Rissanen y su estimación dada por el software elegido. Con respecto a los modelos de red empleados, las topologóas de sugeridas en la literatura como adecuadas para la predicción son usadas (TLFNs y redes recurrentes) junto con perceptrones multicapa (un clásico de las redes neuronales) y comités de redes. La efectividad de cada método es confirmada por el problema de predicción propuesto. Los comités de redes, donde las predicciones son una combinación convexa de las predicciones dadas por las redes individuales, son también usados extensamente. La necesidad de criterios para comparar el comportamiento del modelo con el del sistema real, a largo plazo, para un sistema dinámico estocástico, es presentada y dos alternativas son comentadas. Los resultados obtenidos prueban la existencia de una solución al problema del aprendizaje de la dependencia Entrada - Salida . Conjeturamos además que el sistema generador de serie de las ventas es dinámico-estocástico pero no caótico, ya que sólo tenemos una realización del proceso aleatorio correspondiente a las ventas. Al ser un sistema no caótico, la media de las predicciones de las ventas debería mejorar a medida que los datos disponibles aumentan, aunque la probabilidad de una predicción con un gran error es siempre no nula debido a la aleatoriedad presente. Esta solución es encontrada en una forma constructiva y exhaustiva. La exhaustividad puede deducirse de las siguiente cinco afirmaciones : el diseño de una red neuronal requiere conocer la dimensión de la entrada y de la salida, el número de capas ocultas y las neuronas en cada una de ellas el uso del teorema de takens-Mañé permite derivar la dimensión de la entrada por teoremas tales como los de Kolmogorov y Cybenko el uso de perceptrones con solo una capa oculta es justificado, por lo que varios de tales modelos son probados el número de neuronas en la capa oculta es determinada varias veces heurísticamente a través de algoritmos genéticos una sola neurona de salida da la predicción deseada. Como se dijo, dos tareas son llevadas a cabo: el desarrollo de un modelo para la predicción de la serie temporal y el análisis de un modelo factible para la reconstrucción dinámica del sistema. Con el mejor modelo predictivo, obtenido por el comité de dos redes se logró obtener un error aceptable en la predicción de una semana no contigua al conjunto de entrenamiento (7.04% para la semana 46/2011). Creemos que este es un resultado aceptable dada la cantidad de información disponible y representa una validación adicional de que las redes neuronales son útiles para la predicción de series temporales provenientes de sistemas dinámicos, sin importar si son estocásticos o no. Finalmente, los resultados experimentales confirmaron algunos hechos ya conocidos (tales como que agregar ruido a los datos de entrada y de salida de los valores de entrenamiento puede mejorar los resultados: que las redes recurrentes entrenadas con el algoritmo de retropropagación no presentan el problema del gradiente evanescente en periodos cortos y que el uso de de comités - que puede ser visto como una forma muy básica de inteligencia artificial distribuida - permite mejorar significativamente las predicciones)