Symbolic Knowledge Extraction from Trained Neural Networks Governed by Lukasiewicz Logics

This work describes a methodology to extract symbolic rules from trained neural networks. In our approach, patterns on the network are codified using formulas on a Lukasiewicz logic. For this we take advantage of the fact that every connective in this multi-valued logic can be evaluated by a neuron in an artificial network having, by activation function the identity truncated to zero and one. This fact simplifies symbolic rule extraction and allows the easy injection of formulas into a network architecture. We trained this type of neural network using a back-propagation algorithm based on Levenderg-Marquardt algorithm, where in each learning iteration, we restricted the knowledge dissemination in the network structure. This makes the descriptive power of produced neural networks similar to the descriptive power of Lukasiewicz logic language, minimizing the information loss on the translation between connectionist and symbolic structures. To avoid redundance on the generated network, the method simplifies them in a pruning phase, using the "Optimal Brain Surgeon" algorithm. We tested this method on the task of finding the formula used on the generation of a given truth table. For real data tests, we selected the Mushrooms data set, available on the UCI Machine Learning Repository.

Fractional dynamics in DNA

This paper addresses the DNA code analysis in the perspective of dynamics and fractional calculus. Several mathematical tools are selected to establish a quantitative method without distorting the alphabet represented by the sequence of DNA bases. The association of Gray code, Fourier transform and fractional calculus leads to a categorical representation of species and chromosomes.

Rede neural artificial para detecção de sobremortalidade atribuível à cólera no Ceará

OBJETIVO: Avaliar as redes neurais recorrentes enquanto técnica preditiva para séries temporais em saúde. MÉTODOS: O estudo foi realizado durante uma epidemia de cólera ocorrida no Estado do Ceará, em 1993 e 1994, a partir da sobremortalidade tendo como causa básica as infecções intestinais mal definidas (CID-9). O número mensal de óbitos por essa causa, referente ao período de 1979 a 1995 no Estado do Ceará, foram obtidos do Sistema de Informação de Mortalidade (SIM) do Ministério da Saúde. Estruturou-se uma rede com dois neurônios na camada de entrada, 12 na camada oculta, um neurônio na camada de saída e um na camada de memória. Todas as funções de ativação eram a função logística. O treinamento foi realizado pelo método de backpropagation, com taxa de aprendizado de 0,01 e momentum de 0,9, com dados de janeiro de 1979 a junho de 1991. O critério para fim do treinamento foi atingir 22.000 epochs. Compararam-se os resultados com os de um modelo de regressão binomial negativa. RESULTADOS: A predição da rede neural a médio prazo foi adequada, em dezembro de 1993 e novembro e dezembro de 1994. O número de óbitos registrados foi superior ao limite do intervalo de confiança. Já o modelo regressivo detectou sobremortalidade a partir de março de 1992. CONCLUSÕES: A rede neural se mostrou capaz de predição, principalmente no início do período, como também ao detectar uma alteração concomitante e posterior à ocorrência da epidemia de cólera. No entanto, foi menos precisa do que o modelo de regressão binomial, que se mostrou mais sensível para detectar aberrações concomitantes à circulação da cólera.

A marcha: a influência do Gerador de Padrão Central

A marcha é influenciada por um conjunto de factores que resultam da interacção e organização própria de sistemas neurais e mecânicos, entre os quais, da dinâmica músculo-esquelética, da modulação pelos centros nervosos superiores, pela modulação aferente e é, também, assumida como sendo controlada pelo Gerador de Padrão Central (GPC), que se define como um programa central baseado num circuito espinal geneticamente determinado, capaz de produzir um ritmo associado a cada marcha. Apresenta-se como objectivo deste trabalho abordar quais os modelos explicativos para o funcionamento do GPC e qual a evidência científica, que continua a ter muitas divergências.

Scheduling distributed energy resources in an isolated grid - an artificial neural network approach

Power Systems (PS), have been affected by substantial penetration of Distributed Generation (DG) and the operation in competitive environments. The future PS will have to deal with large-scale integration of DG and other distributed energy resources (DER), such as storage means, and provide to market agents the means to ensure a flexible and secure operation. Virtual power players (VPP) can aggregate a diversity of players, namely generators and consumers, and a diversity of energy resources, including electricity generation based on several technologies, storage and demand response. This paper proposes an artificial neural network (ANN) based methodology to support VPP resource schedule. The trained network is able to achieve good schedule results requiring modest computational means. A real data test case is presented.

Autoinhibition of TBCB regulates EB1-mediated microtubule dynamics

Tubulin cofactors (TBCs) participate in the folding, dimerization, and dissociation pathways of the tubulin dimer. Among them, TBCB and TBCE are two CAP-Gly domain-containing proteins that together efficiently interact with and dissociate the tubulin dimer. In the study reported here we showed that TBCB localizes at spindle and midzone microtubules during mitosis. Furthermore, the motif DEI/M-COO− present in TBCB, which is similar to the EEY/F-COO− element characteristic of EB proteins, CLIP-170, and α-tubulin, is required for TBCE–TBCB heterodimer formation and thus for tubulin dimer dissociation. This motif is responsible for TBCB autoinhibition, and our analysis suggests that TBCB is a monomer in solution. Mutants of TBCB lacking this motif are derepressed and induce microtubule depolymerization through an interaction with EB1 associated with microtubule tips. TBCB is also able to bind to the chaperonin complex CCT containing α-tubulin, suggesting that it could escort tubulin to facilitate its folding and dimerization, recycling or degradation.

A marcha: a influência do Gerador de Padrão Central

A marcha é influenciada por um conjunto de factores que resultam da interacção e organização própria de sistemas neurais e mecânicos, entre os quais, da dinâmica músculo-esquelética, da modulação pelos centros nervosos superiores, pela modulação aferente e é, também, assumida como sendo controlada pelo Gerador de Padrão Central (GPC), que se define como um programa central baseado num circuito espinal geneticamente determinado, capaz de produzir um ritmo associado a cada marcha. Apresenta-se como objectivo deste trabalho abordar quais os modelos explicativos para o funcionamento do GPC e qual a evidência científica, que continua a ter muitas divergências.

Symbolic dynamics and renormalization of non-autonomous k periodic dynamical systems

The purpose of this paper was to introduce the symbolic formalism based on kneading theory, which allows us to study the renormalization of non-autonomous periodic dynamical systems.

An Extension of Gompertzian Growth Dynamics Weibull and Frechet Models

In this work a new probabilistic and dynamical approach to an extension of the Gompertz law is proposed. A generalized family of probability density functions, designated by Beta* (p, q), which is proportional to the right hand side of the Tsoularis-Wallace model, is studied. In particular, for p = 2, the investigation is extended to the extreme value models of Weibull and Frechet type. These models, described by differential equations, are proportional to the hyper-Gompertz growth model. It is proved that the Beta* (2, q) densities are a power of betas mixture, and that its dynamics are determined by a non-linear coupling of probabilities. The dynamical analysis is performed using techniques of symbolic dynamics and the system complexity is measured using topological entropy. Generally, the natural history of a malignant tumour is reflected through bifurcation diagrams, in which are identified regions of regression, stability, bifurcation, chaos and terminus.

Topological Complexity and Predictability in the Dynamics of a Tumor Growth Model with Shilnikov's Chaos

Dynamical systems modeling tumor growth have been investigated to determine the dynamics between tumor and healthy cells. Recent theoretical investigations indicate that these interactions may lead to different dynamical outcomes, in particular to homoclinic chaos. In the present study, we analyze both topological and dynamical properties of a recently characterized chaotic attractor governing the dynamics of tumor cells interacting with healthy tissue cells and effector cells of the immune system. By using the theory of symbolic dynamics, we first characterize the topological entropy and the parameter space ordering of kneading sequences from one-dimensional iterated maps identified in the dynamics, focusing on the effects of inactivation interactions between both effector and tumor cells. The previous analyses are complemented with the computation of the spectrum of Lyapunov exponents, the fractal dimension and the predictability of the chaotic attractors. Our results show that the inactivation rate of effector cells by the tumor cells has an important effect on the dynamics of the system. The increase of effector cells inactivation involves an inverse Feigenbaum (i.e. period-halving bifurcation) scenario, which results in the stabilization of the dynamics and in an increase of dynamics predictability. Our analyses also reveal that, at low inactivation rates of effector cells, tumor cells undergo strong, chaotic fluctuations, with the dynamics being highly unpredictable. Our findings are discussed in the context of tumor cells potential viability.

Strong and weak Allee effects and chaotic dynamics in Richards' growths

In this paper we define and investigate generalized Richards' growth models with strong and weak Allee effects and no Allee effect. We prove the transition from strong Allee effect to no Allee effect, passing through the weak Allee effect, depending on the implicit conditions, which involve the several parameters considered in the models. New classes of functions describing the existence or not of Allee effect are introduced, a new dynamical approach to Richards' populational growth equation is established. These families of generalized Richards' functions are proportional to the right hand side of the generalized Richards' growth models proposed. Subclasses of strong and weak Allee functions and functions with no Allee effect are characterized. The study of their bifurcation structure is presented in detail, this analysis is done based on the configurations of bifurcation curves and symbolic dynamics techniques. Generically, the dynamics of these functions are classified in the following types: extinction, semi-stability, stability, period doubling, chaos, chaotic semistability and essential extinction. We obtain conditions on the parameter plane for the existence of a weak Allee effect region related to the appearance of cusp points. To support our results, we present fold and flip bifurcations curves and numerical simulations of several bifurcation diagrams.

Reproductive dynamics of Sterna hirundinacea Lesson, 1831 in Ilha dos Cardos, Santa Catarina, Brazil

In this work, we intend to describe the reproductive dynamics of Sterna hirundinacea in an island fromSouth Brazil.We studied the reproductive biology of this species in its natural environment and provide data on their growth, survival, and reproductive success in Ilha dosCardos, SantaCatarina, South Brazil. Samplingswere carried out daily on the island throughout the reproductive seasons of 2003, 2005, and 2006 and the different stages of development of the chicks were characterized according to age, length of the beak, and plumage characteristics.We provide a basic equation Lm = 167.91 (1 – e −0.062t−(−0.23)) to determine the approximate age of individuals using their body mass. The main cause of chick mortality on the island was natural (63.17% in 2003, 81.41% in 2005, and 79.96% in 2006), whereas predation contributed to mortality in a proportion of 38.83% in 2003, 18.59% in 2005, and 20.04% in 2006.The absence in the area of the chicks’ main predator, Kelp gull (Larus dominicanus), the large number of chicks that reached the final stages of development, and their reproductive success demonstrate that Ilha dos Cardos is an important breeding site for the species in southern Brazil.

FMRI 3D registration based on Fourier space subsets using neural networks

In this work, we present a neural network (NN) based method designed for 3D rigid-body registration of FMRI time series, which relies on a limited number of Fourier coefficients of the images to be aligned. These coefficients, which are comprised in a small cubic neighborhood located at the first octant of a 3D Fourier space (including the DC component), are then fed into six NN during the learning stage. Each NN yields the estimates of a registration parameter. The proposed method was assessed for 3D rigid-body transformations, using DC neighborhoods of different sizes. The mean absolute registration errors are of approximately 0.030 mm in translations and 0.030 deg in rotations, for the typical motion amplitudes encountered in FMRI studies. The construction of the training set and the learning stage are fast requiring, respectively, 90 s and 1 to 12 s, depending on the number of input and hidden units of the NN. We believe that NN-based approaches to the problem of FMRI registration can be of great interest in the future. For instance, NN relying on limited K-space data (possibly in navigation echoes) can be a valid solution to the problem of prospective (in frame) FMRI registration.

Imported and autochthonous cases in the dynamics of dengue epidemics in Brazil

OBJECTIVE: To estimate the basic reproduction number (R0) of dengue fever including both imported and autochthonous cases. METHODS: The study was conducted based on epidemiological data of the 2003 dengue epidemic in Brasília, Brazil. The basic reproduction number is estimated from the epidemic curve, fitting linearly the increase of initial cases. Aiming at simulating an epidemic with both autochthonous and imported cases, a "susceptible-infectious-resistant" compartmental model was designed, in which the imported cases were considered as an external forcing. The ratio between R0 of imported versus autochthonous cases was used as an estimator of real R0. RESULTS: The comparison of both reproduction numbers (only autochthonous versus all cases) showed that considering all cases as autochthonous yielded a R0 above one, although the real R0 was below one. The same results were seen when the method was applied on simulated epidemics with fixed R0. This method was also compared to some previous proposed methods by other authors and showed that the latter underestimated R0 values. CONCLUSIONS: It was shown that the inclusion of both imported and autochthonous cases is crucial for the modeling of the epidemic dynamics, and thus provides critical information for decision makers in charge of prevention and control of this disease.

Efeito da fortificação alimentar com ácido fólico na prevalência de defeitos do tubo neural

OBJETIVO:Analisar o efeito de alimentos fortificados com ácido fólico na prevalência de defeitos de fechamento do tubo neural entre nascidos vivos. MÉTODOS: Estudo longitudinal de nascidos vivos do município de Recife (PE) entre 2000 e 2006. Os dados pesquisados foram obtidos do Sistema Nacional de Informações de Nascidos Vivos. Os defeitos de fechamento do tubo neural foram definidos de acordo com o Código Internacional de Doenças-10ª Revisão: anencefalia, encefalocele e espinha bífida. Compararam-se as prevalências nos períodos anterior (2000-2004) e posterior (2005-2006) ao período mandatório à fortificação. Analisou-se a tendência temporal das prevalências trimestrais de defeitos do fechamento do tubo neural pelos testes de Mann-Kendall e Sen's Slope. RESULTADOS: Não se identificou tendência de redução na ocorrência do desfecho (Teste de Mann-Kendall; p= 0,270; Sen's Slope =-0,008) no período estudado. Não houve diferença estatisticamente significativa entre as prevalências de defeitos do fechamento do tubo neural nos períodos anterior e posterior à fortificação dos alimentos com acido fólico de acordo com as características maternas. CONCLUSÕES: Embora não tenha sido observada redução dos defeitos do fechamento do tubo neural após o período mandatório de fortificação de alimentos com ácido fólico, os resultados encontrados não permitem descartar o seu benefício na prevenção desta malformação. São necessários estudos avaliando maior período e considerando o nível de consumo dos produtos fortificados pelas mulheres em idade fértil.