Interpretación geométrica de redes neuronales recurrentes discretas mediante grafos completos

El objetivo del presente trabajo de investigación es explorar nuevas técnicas de implementación, basadas en grafos, para las Redes de Neuronas, con el fin de simplificar y optimizar las arquitecturas y la complejidad computacional de las mismas. Hemos centrado nuestra atención en una clase de Red de Neuronas: las Redes de Neuronas Recursivas (RNR), también conocidas como redes de Hopfield. El problema de obtener la matriz sináptica asociada con una RNR imponiendo un determinado número de vectores como puntos fijos, no está en absoluto resuelto, el número de vectores prototipo que pueden ser almacenados en la red, cuando se utiliza la ley de Hebb, es bastante limitado, la red se satura rápidamente cuando se pretende almacenar nuevos prototipos. La ley de Hebb necesita, por tanto, ser revisada. Algunas aproximaciones dirigidas a solventar dicho problema, han sido ya desarrolladas. Nosotros hemos desarrollado una nueva aproximación en la forma de implementar una RNR en orden a solucionar estos problemas. La matriz sináptica es obtenida mediante la superposición de las componentes de los vectores prototipo, sobre los vértices de un Grafo, lo cual puede ser también interpretado como una coloración de dicho grafo. Cuando el periodo de entrenamiento se termina, la matriz de adyacencia del Grafo Resultante o matriz de pesos, presenta ciertas propiedades por las cuales dichas matrices serán llamadas tetraédricas. La energía asociada a cualquier estado de la red es representado por un punto (a,b) de R2. Cada uno de los puntos de energía asociados a estados que disten lo mismo del vector cero está localizado sobre la misma línea de energía de R2. El espacio de vectores de estado puede, por tanto, clasificarse en n clases correspondientes a cada una de las n diferentes distancias que puede tener cualquier vector al vector cero. La matriz (n x n) de pesos puede reducirse a un n-vector; de esta forma, tanto el tiempo de computación como el espacio de memoria requerido par almacenar los pesos, son simplificados y optimizados. En la etapa de recuperación, es introducido un vector de parámetros R2, éste es utilizado para controlar la capacidad de la red: probaremos que lo mayor es la componente a¡, lo menor es el número de puntos fijos pertenecientes a la línea de energía R¡. Una vez que la capacidad de la red ha sido controlada mediante este parámetro, introducimos otro parámetro, definido como la desviación del vector de pesos relativos, este parámetro sirve para disminuir ostensiblemente el número de parásitos. A lo largo de todo el trabajo, hemos ido desarrollando un ejemplo, el cual nos ha servido para ir corroborando los resultados teóricos, los algoritmos están escritos en un pseudocódigo, aunque a su vez han sido implamentados utilizando el paquete Mathematica 2.2., mostrándolos en un volumen suplementario al texto.---ABSTRACT---The aim of the present research is intended to explore new specifícation techniques of Neural Networks based on Graphs to be used in the optimization and simplification of Network Architectures and Computational Complexhy. We have focused our attention in a, well known, class of Neural Networks: the Recursive Neural Networks, also known as Hopfield's Neural Networks. The general problem of constructing the synaptic matrix associated with a Recursive Neural Network imposing some vectors as fixed points is fer for completery solved, the number of prototype vectors (learning patterns) which can be stored by Hebb's law is rather limited and the memory will thus quickly reach saturation if new prototypes are continuously acquired in the course of time. Hebb's law needs thus to be revised in order to allow new prototypes to be stored at the expense of the older ones. Some approaches related with this problem has been developed. We have developed a new approach of implementing a Recursive Neural Network in order to sob/e these kind of problems, the synaptic matrix is obtained superposing the components of the prototype vectors over the vértices of a Graph which may be interpreted as a coloring of the Graph. When training is finished the adjacency matrix of the Resulting Graph or matrix of weights presents certain properties for which it may be called a tetrahedral matrix The energy associated to any possible state of the net is represented as a point (a,b) in R2. Every one of the energy points associated with state-vectors having the same Hamming distance to the zero vector are located over the same energy Une in R2. The state-vector space may be then classified in n classes according to the n different possible distances firom any of the state-vectors to the zero vector The (n x n) matrix of weights may also be reduced to a n-vector of weights, in this way the computational time and the memory space required for obtaining the weights is optimized and simplified. In the recall stage, a parameter vectora is introduced, this parameter is used for controlling the capacity of the net: it may be proved that the bigger is the r, component of J, the lower is the number of fixed points located in the r¡ energy line. Once the capacity of the net has been controlled by the ex parameter, we introduced other parameter, obtained as the relative weight vector deviation parameter, in order to reduce the number of spurious states. All along the present text, we have also developed an example, which serves as a prove for the theoretical results, the algorithms are shown in a pseudocode language in the text, these algorithm so as the graphics have been developed also using the Mathematica 2.2. mathematical package which are shown in a supplementary volume of the text.

Computational methods for the detection of facial palsy

We are developing a telemedicine application which offers automated diagnosis of facial (Bell's) palsy through a Web service. We used a test data set of 43 images of facial palsy patients and 44 normal people to develop the automatic recognition algorithm. Three different image pre-processing methods were used. Machine learning techniques (support vector machine, SVM) were used to examine the difference between the two halves of the face. If there was a sufficient difference, then the SVM recognized facial palsy. Otherwise, if the halves were roughly symmetrical, the SVM classified the image as normal. It was found that the facial palsy images had a greater Hamming Distance than the normal images, indicating greater asymmetry. The median distance in the normal group was 331 (interquartile range 277-435) and the median distance in the facial palsy group was 509 (interquartile range 334-703). This difference was significant (P

Modelling the dynamics of genetic algorithms using statistical mechanics

A formalism for modelling the dynamics of Genetic Algorithms (GAs) using methods from statistical mechanics, originally due to Prugel-Bennett and Shapiro, is reviewed, generalized and improved upon. This formalism can be used to predict the averaged trajectory of macroscopic statistics describing the GA's population. These macroscopics are chosen to average well between runs, so that fluctuations from mean behaviour can often be neglected. Where necessary, non-trivial terms are determined by assuming maximum entropy with constraints on known macroscopics. Problems of realistic size are described in compact form and finite population effects are included, often proving to be of fundamental importance. The macroscopics used here are cumulants of an appropriate quantity within the population and the mean correlation (Hamming distance) within the population. Including the correlation as an explicit macroscopic provides a significant improvement over the original formulation. The formalism is applied to a number of simple optimization problems in order to determine its predictive power and to gain insight into GA dynamics. Problems which are most amenable to analysis come from the class where alleles within the genotype contribute additively to the phenotype. This class can be treated with some generality, including problems with inhomogeneous contributions from each site, non-linear or noisy fitness measures, simple diploid representations and temporally varying fitness. The results can also be applied to a simple learning problem, generalization in a binary perceptron, and a limit is identified for which the optimal training batch size can be determined for this problem. The theory is compared to averaged results from a real GA in each case, showing excellent agreement if the maximum entropy principle holds. Some situations where this approximation brakes down are identified. In order to fully test the formalism, an attempt is made on the strong sc np-hard problem of storing random patterns in a binary perceptron. Here, the relationship between the genotype and phenotype (training error) is strongly non-linear. Mutation is modelled under the assumption that perceptron configurations are typical of perceptrons with a given training error. Unfortunately, this assumption does not provide a good approximation in general. It is conjectured that perceptron configurations would have to be constrained by other statistics in order to accurately model mutation for this problem. Issues arising from this study are discussed in conclusion and some possible areas of further research are outlined.

Brain connectivity in positive and negative syndrome schizophrenia

If, as is widely believed, schizophrenia is characterized by abnormalities of brain functional connectivity, then it seems reasonable to expect that different subtypes of schizophrenia could be discriminated in the same way. However, evidence for differences in functional connectivity between the subtypes of schizophrenia is largely lacking and, where it exists, it could be accounted for by clinical differences between the patients (e.g. medication) or by the limitations of the measures used. In this study, we measured EEG functional connectivity in unmedicated male patients diagnosed with either positive or negative syndrome schizophrenia and compared them with age and sex matched healthy controls. Using new methodology (Medkour et al., 2009) based on partial coherence, brain connectivity plots were constructed for positive and negative syndrome patients and controls. Reliable differences in the pattern of functional connectivity were found with both syndromes showing not only an absence of some of the connections that were seen in controls but also the presence of connections that the controls did not show. Comparing connectivity graphs using the Hamming distance, the negative-syndrome patients were found to be more distant from the controls than were the positive syndrome patients. Bootstrap distributions of these distances were created which showed a significant difference in the mean distances that was consistent with the observation that negative-syndrome diagnosis is associated with a more severe form of schizophrenia. We conclude that schizophrenia is characterized by widespread changes in functional connectivity with negative syndrome patients showing a more extreme pattern of abnormality than positive syndrome patients.

Correlation between pre-treatment quasispecies complexity and treatment outcome in chronic HCV genotype 3a

Pre-treatment HCV quasispecies complexity and diversity may predict response to interferon based anti-viral therapy. The objective of this study was to retrospectively (1) examine temporal changes in quasispecies prior to the start of therapy and (2) investigate extensively quasispecies evolution in a group of 10 chronically infected patients with genotype 3a, treated with pegylated alpha 2a-Interferon and ribavirin. The degree of sequence heterogeneity within the hypervariable region 1 was assessed by analyzing 20-30 individual clones in serial serum samples. Genetic parameters, including amino acid Shannon entropy, Hamming distance and genetic distance were calculated for each sample. Treatment outcome was divided into (1) sustained virological responders (SVR) and (2) treatment failure (TF).Our results indicate, (1) quasispecies complexity and diversity are lower in the SVR group, (2) quasispecies vary temporally and (3) genetic heterogeneity at baseline can be used to predict treatment outcome. We discuss the results from the perspective of replicative homeostasis. We discuss the results from the perspective of replicative homeostasis.

Efficient Image and Video Representations for Retrieval

Image (Video) retrieval is an interesting problem of retrieving images (videos) similar to the query. Images (Videos) are represented in an input (feature) space and similar images (videos) are obtained by finding nearest neighbors in the input representation space. Numerous input representations both in real valued and binary space have been proposed for conducting faster retrieval. In this thesis, we present techniques that obtain improved input representations for retrieval in both supervised and unsupervised settings for images and videos. Supervised retrieval is a well known problem of retrieving same class images of the query. We address the practical aspects of achieving faster retrieval with binary codes as input representations for the supervised setting in the first part, where binary codes are used as addresses into hash tables. In practice, using binary codes as addresses does not guarantee fast retrieval, as similar images are not mapped to the same binary code (address). We address this problem by presenting an efficient supervised hashing (binary encoding) method that aims to explicitly map all the images of the same class ideally to a unique binary code. We refer to the binary codes of the images as `Semantic Binary Codes' and the unique code for all same class images as `Class Binary Code'. We also propose a new class­ based Hamming metric that dramatically reduces the retrieval times for larger databases, where only hamming distance is computed to the class binary codes. We also propose a Deep semantic binary code model, by replacing the output layer of a popular convolutional Neural Network (AlexNet) with the class binary codes and show that the hashing functions learned in this way outperforms the state­ of ­the art, and at the same time provide fast retrieval times. In the second part, we also address the problem of supervised retrieval by taking into account the relationship between classes. For a given query image, we want to retrieve images that preserve the relative order i.e. we want to retrieve all same class images first and then, the related classes images before different class images. We learn such relationship aware binary codes by minimizing the similarity between inner product of the binary codes and the similarity between the classes. We calculate the similarity between classes using output embedding vectors, which are vector representations of classes. Our method deviates from the other supervised binary encoding schemes as it is the first to use output embeddings for learning hashing functions. We also introduce new performance metrics that take into account the related class retrieval results and show significant gains over the state­ of­ the art. High Dimensional descriptors like Fisher Vectors or Vector of Locally Aggregated Descriptors have shown to improve the performance of many computer vision applications including retrieval. In the third part, we will discuss an unsupervised technique for compressing high dimensional vectors into high dimensional binary codes, to reduce storage complexity. In this approach, we deviate from adopting traditional hyperplane hashing functions and instead learn hyperspherical hashing functions. The proposed method overcomes the computational challenges of directly applying the spherical hashing algorithm that is intractable for compressing high dimensional vectors. A practical hierarchical model that utilizes divide and conquer techniques using the Random Select and Adjust (RSA) procedure to compress such high dimensional vectors is presented. We show that our proposed high dimensional binary codes outperform the binary codes obtained using traditional hyperplane methods for higher compression ratios. In the last part of the thesis, we propose a retrieval based solution to the Zero shot event classification problem - a setting where no training videos are available for the event. To do this, we learn a generic set of concept detectors and represent both videos and query events in the concept space. We then compute similarity between the query event and the video in the concept space and videos similar to the query event are classified as the videos belonging to the event. We show that we significantly boost the performance using concept features from other modalities.

Distance Distributions and Energy of Designs in Hamming Spaces

We obtain new combinatorial upper and lower bounds for the potential energy of designs in q-ary Hamming space. Combined with results on reducing the number of all feasible distance distributions of such designs this gives reasonable good bounds. We compute and compare our lower bounds to recently obtained universal lower bounds. Some examples in the binary case are considered.

WEAK ISOMETRIES OF HAMMING SPACES

In this thesis we study weak isometries of Hamming spaces. These are permutations of a Hamming space that preserve some but not necessarily all distances. We wish to find conditions under which a weak isometry is in fact an isometry. This type of problem was first posed by Beckman and Quarles for Rn. In chapter 2 we give definitions pertinent to our research. The 3rd chapter focuses on some known results in this area with special emphasis on papers by V. Krasin as well as S. De Winter and M. Korb who solved this problem for the Boolean cube, that is, the binary Hamming space. We attempted to generalize some of their methods to the non-boolean case. The 4th chapter has our new results and is split into two major contributions. Our first contribution shows if n=p or p < n2, then every weak isometry of Hnq that preserves distance p is an isometry. Our second contribution gives a possible method to check if a weak isometry is an isometry using linear algebra and graph theory.

Comparison of high-speed videokeratoscopy and ultrasound distance sensing for measuring the longitudinal corneal apex movements

Two different methods to measure binocular longitudinal corneal apex movements were synchronously applied. High-speed videokeratoscopy at a sampling frequency of 15 Hz and a customdesigned ultrasound distance sensor at 100 Hz were used for the left and the right eye, respectively. Four healthy subjects participated in the study. Simultaneously, cardiac electric cycle (ECG) was registered for each subject at 100 Hz. Each measurement took 20 s. Subjects were asked to suppress blinking during the measurements. A rigid headrest and a bite-bar were used to minimize undesirable head movements. Time, frequency and time-frequency representations of the acquired signals were obtained to establish their temporal and spectral contents. Coherence analysis was used to estimate the correlation between the measured signals. The results showed close correlation between both corneal apex movements and the cardiopulmonary system. Unraveling these relationships could lead to better understanding of interactions between ocular biomechanics and vision. The advantages and disadvantages of the two methods in the context of measuring longitudinal movements of the corneal apex are outlined.

Closing the cultural distance gap: managing value-based knowledge in MNC by using MEP

Today more than ever, generating and managing knowledge is an essential source of competitive advantage for every organization, and particularly for Multinational corporations (MNC). However, despite the undisputed agreement about the importance of creating and managing knowledge, there are still a large number of corporations that act unethically or illegally. Clearly, there is a lack of attention in gaining more knowledge about the management of ethical knowledge in organizations. This paper refers to value-based knowledge, as the process of recognise and manage those values that stand at the heart of decision-making and action in organizations. In order to support MNCs in implementing value-based knowledge process, the managerial ethical profile (MEP) has been presented as a valuable tool to facilitate knowledge management process at both the intra-organizational network level and at the inter-organizational network level.

ePortfolios and preservice teachers : governing at a distance through non-human actors

This chapter seeks to develop an analysis of the contemporary use of the ePortfolio (Electronic Portfolio) in education practices. Unlike other explorations of this new technology which are deterministic in their approach, the authors seek to reveal the techniques and practices of government which underpin the implementation of the e-portfolio. By interrogating a specific case study example from a large Australian university’s preservice teacher program, the authors find that the e-portfolio is represented as eLearning technology but serves to govern students via autonomization and self responsibilization. Using policy data and other key documents, they are able to reveal the e-portfolio as a delegated authority in the governance of preservice teachers. However, despite this ongoing trend, they suggest that like other practices of government, the e-portfolio will eventually fail. This however the authors conclude opens up space for critical thought and engagement which is not afforded presently.

Distance Education and the Integration of E-learning in a Graduate Program

Historically, distance education consisted of a combination of face-to-face blocks of time and surface mailed packages. However, advances in information technology literacy and the abundance of personal computers has placed e-learning in increased demand. The authors describe the planning, implementation, and evaluation of the blending of e-learning with face-to-face education in the postgraduate nursing forum. Experiences of this particular student group are also discussed.