Showing papers in "New Mathematics and Natural Computation in 2009"

A new neutrosophic approach to image denoising

Abstract: A neutrosophic set (NS), a part of neutrosophy theory, studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. The neutrosophic set is a general formal framework that has been recently proposed. However, the neutrosophic set needs to be specified from a technical point of view. Now, we apply the neutrosophic set into image domain and define some concepts and operators for image denoising. The image G is transformed into NS domain, which is described using three membership sets: T, I and F. The entropy of the neutrosophic set is defined and employed to evaluate the indeterminancy. A new operation, γ-median-filtering operation, is proposed to decrease the set indeterminancy and remove noise. We have conducted experiments on a variety of noisy images using different types of noises with different levels. The experimental results demonstrate that the proposed approach can remove noise automatically and effectively. Especially, it can process not only noisy images with different levels of noise, but also images with different kinds of noise well without knowing the type of the noise, which is the most difficult task for image denoising.

Coherent states, fractals and brain waves

Abstract: I show that a functional representation of self-similarity (as the one occurring in fractals) is provided by squeezed coherent states. In this way, the dissipative model of brain is shown to account for the self-similarity in brain background activity suggested by power-law distributions of power spectral densities of electrocorticograms. I also briefly discuss the action-perception cycle in the dissipative model with reference to intentionality in terms of trajectories in the memory state space.

Phenomenological architecture of a mind and operational architectonics of the brain: the unified metastable continuum

Abstract: In our contribution we will observe phenomenal architecture of a mind and operational architectonics of the brain and will show their intimate connectedness within a single integrated metastable continuum. The notion of operation of different complexity is the fundamental and central one in bridging the gap between brain and mind: it is precisely by means of this notion that it is possible to identify what at the same time belongs to the phenomenal conscious level and to the neurophysiological level of brain activity organization, and what mediates between them. Implications for linguistic semantics, self-organized distributed computing algorithms, artificial machine consciousness, and diagnosis of dynamic brain diseases will be discussed briefly.

Soft ideals and generalized fuzzy ideals in semigroups

Abstract: A soft semigroup over a semigroup is a collection of subsemigroups. Similarly, a soft ideal over a semigroup is a collection of ideals of the semigroup. As a natural consequence, the idea of soft ideals of a soft semigroup originates. Soft ideals over a semigroup with a fixed set of parameters form a distributive lattice. Soft sets are a very handy tool. Soft ideals over a semigroup characterize generalized fuzzy ideals and fuzzy ideals with thresholds of S.

Creating novel goal-directed actions at criticality: a neuro-robotic experiment

Abstract: The present study examines the possible roles of cortical chaos in generating novel actions for achieving specified goals. The proposed neural network model consists of a sensory-forward model responsible for parietal lobe functions, a chaotic network model for premotor functions and prefrontal cortex model responsible for manipulating the initial state of the chaotic network. Experiments using humanoid robot were performed with the model and showed that the action plans for satisfying specific novel goals can be generated by diversely modulating and combining prior-learned behavioral patterns at critical dynamical states. Although this criticality resulted in fragile goal achievements in the physical environment of the robot, the reinforcement of the successful trials was able to provide a substantial gain with respect to the robustness. The discussion leads to the hypothesis that the consolidation of numerous sensory-motor experiences into the memory, meditating diverse imagery in the memory by cortical chaos, and repeated enaction and reinforcement of newly generated effective trials are indispensable for realizing an open-ended development of cognitive behaviors.

Active portfolio management with cardinality constraints: an application of particle swarm optimization

Abstract: This paper considers the task of forming a portfolio of assets that outperforms a benchmark index, while imposing a constraint on the tracking error volatility. We examine three alternative formulations of active portfolio management. The first one is a typical setup in which the fund manager myopically maximizes excess return. The second formulation is an attempt to set a limit on the total risk exposure of the portfolio by adding a constraint that forces a priori the risk of the portfolio to be equal to the benchmark's. In this paper, we also propose a third formulation that directly maximizes the efficiency of active portfolios, while setting a limit on the maximum tracking error variance. In determining optimal active portfolios, we incorporate additional constraints on the optimization problem, such as a limit on the maximum number of assets included in the portfolio (i.e. the cardinality of the portfolio) as well as upper and lower bounds on asset weights. From a computational point of view, the incorporation of these complex, though realistic, constraints becomes a challenge for traditional numerical optimization methods, especially when one has to assemble a portfolio from a big universe of assets. To deal properly with the complexity and the "roughness" of the solution space, we use particle swarm optimization, a population-based evolutionary technique. As an empirical application of the methodology, we select portfolios of different cardinality that actively reproduce the performance of the FTSE/ATHEX 20 Index of the Athens Stock Exchange. Our empirical study reveals important results concerning the efficiency of common practices in active portfolio management and the incorporation of cardinality constraints.

A multi-objective risk-based framework for mission capability planning

Abstract: In this paper, we propose a risk-based framework for military capability planning. Within this framework, metaheuristic techniques such as Evolutionary Algorithms are used to deal with multi-objectivity of a class of NP-hard resource investment problems, called The Mission Capability Planning Problem, under the presence of risk factors. This problem inherently has at least two conflicting objectives: minimizing the cost of investment in the resources as well as the makespan of the plans. The framework allows the addition of a risk-based objective to the problem in order to support risk assessment during the planning process. In other words, with this framework, a mechanism of progressive risk assessment is introduced to capability planning. We analyze the performance of the proposed framework under both scenarios: with and without risk. In the case of no risk, the purpose is to study several optimization-related aspects of the framework such as convergence, trade-off analysis, and its sensitivity to the algorithm parameters; while the second case is to demonstrate the ability of the framework in supporting risk assessment and also robustness analysis.

Monotonic support vector machines for credit risk rating

Abstract: Credit rating models are widely used by banking institutions to assess the creditworthiness of credit applicants and to estimate the probability of default. Several pattern classification algorithms are used for the development of such models. In contrast to other pattern classification tasks, however, credit rating models are not only expected to provide accurate predictions, but also to make clear economic sense. Within this context, the estimated probability of default is often required to be a monotone function of the independent variables. Most machine learning techniques do not take this requirement into account. In this paper, monotonicity hints are used to address this issue within the modeling framework of support vector machines (SVM), which have become increasingly popular in this field. Non-linear SVM credit rating models are developed with linear programming, taking into account the monotonicity requirement. The obtained results indicate that the introduction of monotonicity hints improves the predictive ability of the models.

The phase transition in human cognition

Abstract: This article attempts to build a bridge between cognitive psychology and computational neuroscience, perhaps allowing each group to understand the other's theoretical insights and sympathize with the other's methodological challenges. In briefly discussing a collection of conceptual demonstrations, neural network and dynamical system simulations, and human experimental results, we highlight the importance of the concept of phase transition to understand cognitive function. Our goal is to show that viewing cognition as a self-organizing process (involving phase transitions, criticality, and autocatalysis) affords a more natural explanation of these data over traditional approaches inspired by a sequence of linear filters (involving detection, recognition, and then response selection).

Modeling goal-oriented decision making through cognitive phase transitions

Abstract: Cognitive experiments indicate the presence of discontinuities in brain dynamics during high-level cognitive processing. Non-linear dynamic theory of brains pioneered by Freeman explains the experimental findings through the theory of metastability and edge-of-criticality in cognitive systems, which are key properties associated with robust operation and fast and reliable decision making. Recently, neuropercolation has been proposed to model such critical behavior. Neuropercolation is a family of probabilistic models based on the mathematical theory of bootstrap percolations on lattices and random graphs and motivated by structural and dynamical properties of neural populations in the cortex. Neuropercolation exhibits phase transitions and it provides a novel mathematical tool for studying spatio-temporal dynamics of multi-stable systems. The present work reviews the theory of cognitive phase transitions based on neuropercolation models and outlines the implications to decision making in brains and in artificial designs.

Increasing infrastructure resilience through competitive coevolution

Abstract: The world is increasingly dependent on critical infrastructures such as the electric power grid, water, gas and oil transport systems. Due to this increasing dependence and inadequate infrastructure expansion, these systems are becoming increasingly stressed. These additional stresses leave these systems less resilient to external faults, both accidental and malicious than ever before. As a result of this increased vulnerability, many critical infrastructures are becoming susceptible to cascading failures, where an initial fault caused by an external force may induce a domino-effect of further component failures. An important implication is that traditional infrastructure risk analysis methods, often relying on Monte Carlo sampling of fault scenarios, are no longer sufficient. Instead, systematic analysis based on worst-case attacks by intelligent adversaries is essential. This paper describes a coevolutionary methodology to simultaneously discover low-effort high-impact faults and corresponding means of hardening infrastructures against them. We empirically validate our methodology through an electric power transmission system case study.

The neurobiological infrastructure of natural computing: intentionality

Abstract: Brains and computers are both dynamical systems that manipulate symbols, but they differ fundamentally in their architectures and operations. Human brains do mathematics; computers do not. Computers manipulate symbols that humans put into them without grounding them in what they represent. Human brains intentionally direct the body to make symbols, and they use the symbols to represent internal states. The symbols are outside the brain. Inside the brains, the construction is effected by spatiotemporal patterns of neural activity that are operators, not symbols. The operations include formation of sequences of neural activity patterns that we observe by their electrical signs. The process is by neurodynamics, not by logical rule-driven symbol manipulation. The aim of simulating human natural computing should be to simulate the operators. In its simplest form natural computing serves for communication of meaning. Neural operators implement non-symbolic communication of internal states by all mammals, including humans, through intentional actions. The neural operators that implement symbol formation must differ, but how is unknown, so we cannot yet simulate human natural computing. Here, I propose that symbol-making operators evolved from neural mechanisms of intentional action by modification of non-symbolic operators. Both kinds of operators can be investigated by their signs of neuroelectric activity. I propose that the postulated differences should be sought by classification of the spatial textures of the signs in EEG recorded from the scalp overlying those cortical structures unique to humans in the brain that I designate as koniocortex, while the subjects are engaged in elementary arithmetic operations.

Analysis of mutation operators on quantum-behaved particle swarm optimization algorithm

Abstract: Mutation operator is one of the mechanisms of evolutionary algorithms (EAs) and it can provide diversity in the search and help to explore the undiscovered search place. Quantum-behaved particle swarm optimization (QPSO), which is inspired by fundamental theory of PSO algorithm and quantum mechanics, is a novel stochastic searching technique and it may encounter local minima problem when solving multi-modal problems just as that in PSO. A novel mutation mechanism is proposed in this paper to enhance the global search ability of QPSO and a set of different mutation operators is introduced and implemented on the QPSO. Experiments are conducted on several well-known benchmark functions. Experimental results show that QPSO with some of the mutation operators is proven to be statistically significant better than the original QPSO.

ON ASYMPTOTICALLY LACUNARY σ-STATISTICAL EQUIVALENT SEQUENCES OF FUZZY NUMBERS

Abstract: This paper presents the asymptotically lacunary σ-statistical equivalent which is a natural combination of the definition for asymptotically equivalent, invariant mean and lacunary statistical convergence of fuzzy numbers. In addition, we shall also present asymptotically lacunary σ-statistical equivalent analogs of Savas and Nuray's theorems in Ref. 8.

Fair consistency evaluation for reciprocal relations and in group decision making

Abstract: In decision-making processes, it often occurs that the decision maker is asked to pairwise compare alternatives. His/her judgements over a set of pairs of alternatives can be collected into a matrix and some relevant properties, for instance, consistency, can be estimated. Consistency is a desirable property which implies that all the pairwise comparisons respect a principle of transitivity. So far, many indices have been proposed to estimate consistency. Nevertheless, in this paper we argue that most of these indices do not fairly evaluate this property. Then, we introduce a new consistency evaluation method and we propose to use it in group decision making problems in order to fairly weigh the decision maker's preferences according to their consistency. In our analysis, we consider two families of pairwise comparison matrices: additively reciprocal pairwise comparison matrices and multiplicatively reciprocal pairwise comparison matrices.

Cortical phase transitions: properties demonstrated in continuum simulations at mesoscopic and macroscopic scales

Abstract: Continuum simulations of cortical dynamics permit consistent simulations to be performed at different spatial scales, using scale-adjusted parameter values. Properties of the simulations described here accord with Freeman's experimental and theoretical findings on gamma synchrony, phase transition, phase cones, and null spikes. State equations include effects of retrograde action potential propagation into dendritic trees, and kinetics of AMPA, GABA, and NMDA receptors. Realistic field potentials and pulse rates, gamma resonance and oscillation, and 1/f2 background activity are obtained. Zero-lag synchrony and traveling waves occur as complementary aspects of cortical transmission, and lead/lag relations between excitatory and inhibitory cell populations vary systematically around transition to autonomous gamma oscillation. Autonomous gamma is initiated by focal excitation of excitatory cells and suppressed by laterally spreading trans-cortical excitation. By implication, patches of cortex excited to gamma oscillation can mutually synchronize into larger fields, self-organized into sequences by mutual negative feedback relations, while the sequence of synchronous fields is regulated both by cortical/subcortical interactions and by traveling waves in the cortex — the latter observable as phase cones. At a critical level of cortical excitation, just before transition to autonomous gamma, patches of cortex exhibit selective sensitivity to action potential pulse trains modulated in the gamma band, while autonomous gamma releases pulse trains modulated in the same band, implying coupling of input and output modes. Transition between input and output modes may be heralded by phase slips and null spikes. Synaptic segregation by retrograde action potential propagation implies state-specific synaptic information storage.

Attractors in song

Abstract: This paper summarizes our recent attempts to integrate action and perception within a single optimization framework. We start with a statistical formulation of Helmholtz's ideas about neural energy to furnish a model of perceptual inference and learning that can explain a remarkable range of neurobiological facts. Using constructs from statistical physics it can be shown that the problems of inferring the causes of our sensory inputs and learning regularities in the sensorium can be resolved using exactly the same principles. Furthermore, inference and learning can proceed in a biologically plausible fashion. The ensuing scheme rests on Empirical Bayes and hierarchical models of how sensory information is generated. The use of hierarchical models enables the brain to construct prior expectations in a dynamic and context-sensitive fashion. This scheme provides a principled way to understand many aspects of the brain's organization and responses. We will demonstrate the brain-like dynamics that this scheme entails by using models of birdsongs that are based on chaotic attractors with autonomous dynamics. This provides a nice example of how non-linear dynamics can be exploited by the brain to represent and predict dynamics in the environment.

Novel ensemble techniques for regression with missing data

Abstract: In this paper, we consider the problem of missing data, and develop an ensemble-network model for handling the missing data. The proposed method is based on utilizing the inherent uncertainty of the missing records in generating diverse training sets for the ensemble's networks. Specifically we generate the missing values using their probability distribution function. We repeat this procedure many times thereby creating a number of complete data sets. A network is trained for each of these data sets, thereby obtaining an ensemble of networks. Several variants are proposed, and we show analytically that one of these variants is superior to the conventional mean-substitution approach for the limit of large training set. Simulation results confirm the general superiority of the proposed methods compared to the conventional approaches.

Fuzzy arrow's theorem

Abstract: In this paper, we prove a fuzzy version of Arrow's Theorem that contains the crisp version. We show that under our definitions, Arrow's Theorem remains intact even if levels of intensities of the players and levels of membership in the set of alternatives are considered.

Neurodynamics of category learning: towards understanding the creation of meaning in the brain

Abstract: Category learning, the formation and use of categories (equivalence classes of meaning), is an elemental function of cognition. We report our approach to study the physiological mechanisms underlying category learning using high-density multi-channel recordings of electrocorticograms in rodents. These data suggest the coexistence of separate coding principles for representing physical stimulus attributes ("stimulus representation") and subjectively relevant information (meaning) about stimuli, respectively. The implications of these findings for the construction of interactive cortical sensory neuroprostheses are discussed.

On critical State Transitions between different levels in Neural Systems

Abstract: The framework of "Modern Theory of Critical State Transitions"1,2 considers the relation between different levels of organization in complex systems in terms of critical state transitions. A state transition between levels entails changes of scale of observables and, concurrently, new formats of description at reduced dimensionality. It is suggested that this principle can be applied to the hierarchic structure of the nervous system, whereby the relations between different levels of its functional organization can be viewed as successions of state transitions: upon state transition, the 'lower' level presents to the 'higher' level an abstraction of itself, at reduced dimensionality and at a coarser scale. The re-scaling in the state transitions is associated with new objects of description, displays new properties and obeys new laws, commensurate to the new scale. To illustrate this process, some aspects of the neural events thought to be associated with cognition and consciousness are discussed. However, the intent is also more general in that state transitions between all levels of organization are proposed as the mechanisms by which successively higher levels of organization "emerge" from lower levels.

Catalysis, perception, and consciousness

Abstract: This paper describes and provides support for a non-representational theory of perception called the Fractal Catalytic theory, which proposes that perception is a catalytic type of process that occurs at multiple scales.1 Enzyme catalysis involves a vibratory facilitation of a reaction. A catalytic model for smell at the molecular level is supported by evidence that smell involves a vibratory process.2 This type of facilitation can be generalized to the neural level, where many neuroscientists have observed vibratory neural patterns. At the level of the organism, we describe research with blind individuals who experience a visuo-spatial world through patterns of sounds or tactile vibrations. Such research argues against the standard theory that people are representing objects and events, and supports the view that experience arises as an organism mediates (catalyzes) the transitions in its surround. The theory relates to the biologically-grounded theory of Autopoiesis3 as well as proposals that catalysis is central in biological evolution. We examine the implications of this theory for the nature of consciousness.

Can ants predict bankruptcy? a comparison of ant colony systems to other state-of-the-art computational methods

Abstract: In the current work, we consider the applicability of Ant Colony Systems (ACS) to the bankruptcy prediction problem. ACS are nature-based algorithms that mimic the functions of live organisms to find the best performing solution. In our work, ACS are used for the extraction of classification rules for bankruptcy prediction. An experimental study was conducted in order to evaluate the performance of the system and identify well performing parameters. Results were compared to the performance obtained by state-of-the-art methods for classification, namely the Artificial Neural Networks, the Support Vector Machines, the Partial Decision Trees and the Fuzzy Lattice Reasoning. Comparison indicates the high performance of the ACS which is further supported by their ability to extract classification rules, thus offering interpretation of the prediction results. The latter is of great importance in the field of corporate distress where no unified theory on distress prediction exists. Most studies with distress prediction have focused on increasing the accuracy of the model and have not always paid attention to the model interpretation.

Emotion recognition based on the analysis of facial expresions: a survey

Abstract: Face expression recognition is an active area of research with several fields of applications, ranging from emotion recognition for advanced human computer interaction to avatar animation for the movie industry. This paper presents a review of the state-of-the-art emotion recognition based on the visual analysis of facial expressions. We cover the main technical approaches and discuss the issues related to the gathering of data for the validation of the proposed systems.

Hierarchical spatio-temporal dynamics of a chaotic neural network for multistable binocular rivalry

Abstract: Binocular rivalry is perceptual alternation that occurs when different visual images are presented to each eye. Despite the intensive studies, the mechanism of binocular rivalry still remains unclear. In multistable binocular rivalry, which is a special case of binocular rivalry, it is known that the perceptual alternation between paired patterns is more frequent than that between unpaired patterns. This result suggests that perceptual transition in binocular rivalry is not a simple random process, and the memories stored in the brain can play an important role in the perceptual transition. In this study, we propose a hierarchical chaotic neural network model for multistable binocular rivalry and show that our model reproduces some characteristic features observed in multistable binocular rivalry.

Fuzzy inclusion and fuzzy similarity with gödel fuzzy implicator

Abstract: Fuzzy inclusion and fuzzy similarity are introduced as mappings which produce fuzzy sets constructed with the help of Godel implicator. The properties of resulting fuzzy sets of inclusion and similarity are studied in detail. Some axiomatic characteristics for being fuzzy orders and fuzzy equivalence relations are also included.

Neurodynamic correlates of higher cognition and consciousness — editorial

Abstract: In spite of the explosive growth of experimental research in basic neurobiology and neurophysiology of brain components in the past decade, understanding the integrated functioning of the brain remains a significant scientific challenge Essential for understanding human brain function is the detailed knowledge concerning the spatio-temporal dynamics of neuronal populations and their intricate interactions during cognitive functions The aim of the present issue is to examine brain dynamics and cognitive functions from a multidisciplinary perspective and to introduce the most recent results in this research frontier Topics relevant to the special issue include: (i) Modeling brain dynamics at the mesoscopic and macroscopic scales, including dynamical systems with distributed parameters; (ii) Applying tools of discrete mathematics, statistical and quantum physics, network science to describe the dynamics of brains; (iii) Experimental research on brain dynamics from various aspects, including fundamental neurobiology, evoked potentials, functional brain imaging, and cognitive functions; (iv) Clinical neuroscience issues for improved diagnosis of dynamic brain diseases and their potential therapies This special issue is dedicated to Professor Walter J Freeman on the occasion of his 80th birthday Dr Freeman produced breakthrough contributions to research on brain dynamics over the past five decades The present issue covers all aspects of neurodynamics, starting from neural populations of high-level cognition and consciousness, as well as philosophical aspects and practical implementations on digital computers and hardware designs

Large-scale cortical network coordination: a proposal for the neural substrate of expectancy

Abstract: Optimal human behavior depends on the expectancy of future events based on perceptual analysis of an individual's present situation using knowledge gained from past experience. This article explores the proposition that the neural processes underlying perceptual analysis, knowledge retrieval, and expectancy are all integrated through the coordination of large-scale networks of the cerebral cortex. It is proposed that expectancy is created when local networks expressing knowledge of the likely future events associated with an individual's present situation are coordinated as part of large-scale networks expressing the totality of knowledge relations concerning the situation.

Rate and gamma modulation in attentional tasks

Abstract: Experimental and theoretical work has related rate modulation and gamma synchronization modulation to visual attention. Here, we review briefly some of the influential experiments and our modeling work on the subject. We show that attentional modulation generally gets stronger along the visual pathway and that rate and gamma synchronization can vary independently of each other. Moreover, we show that in a model system, reaction times are faster in the presence of gamma synchronization. This suggests behavioral relevance for gamma synchronization.

Prediction of elephant movement in a game reserve using neural networks

Abstract: A large number of South Africa's elephants can be found on small wildlife reserves. The large nutritional demands and destructive foraging behavior of elephants can threaten rare species of vegetation. If conservation management is to protect threatened species of vegetation, knowing how long elephants will stay in one area of a reserve as well as which area they will move to next could be useful. The goal of this study was to train a recurrent neural network to predict an elephant herd's next position in the Pongola Game Reserve. Accurate predictions would provide a useful tool in assessing future impact of elephant populations on different areas of the reserve. Particle swarm optimization (PSO), PSO initialized backpropagation (PSO-BP) and PSO initialized backpropagation through time (PSO-BPTT) algorithms are used to adapt the recurrent neural network's weights. The effectiveness of PSO, PSO-BP and PSO-BPTT for training a recurrent neural network for elephant migration prediction is compared and PSO-BPTT produces the most accurate predictions at the expense of more computational cost.