Toward an adequate mathematical model of mental space: Conscious/unconscious dynamics on m-adic trees

We try to perform geometrization of cognitive science and psychology by representing information states of cognitive systems by points of mental space given by a hierarchic m-adic tree. Associations are represented by balls and ideas by collections of balls. We consider dynamics of ideas based on lifting of dynamics of mental points. We apply our dynamical model for modeling of flows of unconscious and conscious information in the human brain. In a series of models, Models 1–3, we consider cognitive systems with increasing complexity of psychological behavior determined by structure of flows of associations and ideas.     

Probabilistic pathway representation of cognitive information

We present for mental processes the program of mathematical mapping which has been successfully realized for physical processes. We emphasize that our project is not about mathematical simulation of the brain's functioning as a complex physical system, i.e., mapping of physical and chemical processes in the brain on mathematical spaces. The project is about mapping of purely mental processes on mathematical spaces. We present various arguments--philosophic, mathematical, information, and neurophysiological--in favor of the p-adic model of mental space. p-adic spaces have structures of hierarchic trees and in our model such a tree hierarchy is considered as an image of neuronal hierarchy. Hierarchic neural pathways are considered as fundamental units of information processing. As neural pathways can go through the whole body, the mental space is produced by the whole neural system. Finally, we develop the probabilistic neural pathway model in that mental states are represented by probability distributions on mental space.     

Toward an adequate mathematical model of mental space: conscious/unconscious dynamics on m-adic trees

We try to perform geometrization of cognitive science and psychology by representing information states of cognitive systems by points of mental space given by a hierarchic m-adic tree. Associations are represented by balls and ideas by collections of balls. We consider dynamics of ideas based on lifting of dynamics of mental points. We apply our dynamical model for modeling of flows of unconscious and conscious information in the human brain. In a series of models, Models 1–3, we consider cognitive systems with increasing complexity of psychological behavior determined by structure of flows of associations and ideas.     

Quantum formalism to describe binocular rivalry

On the basis of the general character and operation of the process of perception, a formalism is sought to mathematically describe the subjective or abstract/mental process of perception. It is shown that the formalism of orthodox quantum theory of measurement, where the observer plays a key role, is a broader mathematical foundation which can be adopted to describe the dynamics of the subjective experience. The mathematical formalism describes the psychophysical dynamics of the subjective or cognitive experience as communicated to us by the subject. Subsequently, the formalism is used to describe simple perception processes and, in particular, to describe the probability distribution of dominance duration obtained from the testimony of subjects experiencing binocular rivalry. Using this theory and parameters based on known values of neuronal oscillation frequencies and firing rates, the calculated probability distribution of dominance duration of rival states in binocular rivalry under various conditions is found to be in good agreement with available experimental data. This theory naturally explains an observed marked increase in dominance duration in binocular rivalry upon periodic interruption of stimulus and yields testable predictions for the distribution of perceptual alteration in time.     

Challenging the classical notion of time in cognition: a quantum perspective

All mental representations change with time. A baseline intuition is that mental representations have specific values at different time points, which may be more or less accessible, depending on noise, forgetting processes, etc. We present a radical alternative, motivated by recent research using the mathematics from quantum theory for cognitive modelling. Such cognitive models raise the possibility that certain possibilities or events may be incompatible, so that perfect knowledge of one necessitates uncertainty for the others. In the context of time-dependence, in physics, this issue is explored with the so-called temporal Bell (TB) or Leggett–Garg inequalities. We consider in detail the theoretical and empirical challenges involved in exploring the TB inequalities in the context of cognitive systems. One interesting conclusion is that we believe the study of the TB inequalities to be empirically more constrained in psychology than in physics. Specifically, we show how the TB inequalities, as applied to cognitive systems, can be derived from two simple assumptions: cognitive realism and cognitive completeness. We discuss possible implications of putative violations of the TB inequalities for cognitive models and our understanding of time in cognition in general. Overall, this paper provides a surprising, novel direction in relation to how time should be conceptualized in cognition.     

Quantum-like brain: "Interference of minds"

We present a contextualist statistical realistic model for quantum-like representations in physics, cognitive science, and psychology. We apply this model to describe cognitive experiments to check quantum-like structures of mental processes. The crucial role is played by interference of probabilities for mental observables. Recently one such experiment based on recognition of images was performed. This experiment confirmed our prediction on the quantum-like behavior of mind. In our approach "quantumness of mind" has no direct relation to the fact that the brain (as any physical body) is composed of quantum particles. We invented a new terminology "quantum-like (QL) mind." Cognitive QL-behavior is characterized by a nonzero coefficient of interference lambda. This coefficient can be found on the basis of statistical data. There are predicted not only cos theta-interference of probabilities, but also hyperbolic cosh theta-interference. This interference was never observed for physical systems, but we could not exclude this possibility for cognitive systems. We propose a model of brain functioning as a QL-computer (there is a discussion on the difference between quantum and QL computers).     

The role of parental investments for cognitive and noncognitive skill formation—Evidence for the first 11 years of life

This paper examines the impact of parental investments on the development of cognitive, mental and emotional skills during childhood using data from a longitudinal study, the Mannheim Study of Children at Risk, starting at birth. Our work offers three important innovations. First, we use reliable measures of the child's cognitive, mental and emotional skills as well as accurate measures of parental investments. The observed investments include parental health behaviour, playing and talking with the child, play materials, leisure activities and others. Second, we estimate latent factor models to account for unobserved characteristics of children. Third, we examine the skill development for girls and boys separately, as well as for children who were born with either organic or psychosocial risk. We find a decreasing impact of parental investments on cognitive and mental skills over time, while emotional skills seem to be unaffected by parental investments in childhood. Thus, inequality at birth persists during childhood. Since families are the main sources of education during the first years of life, our results have important implications for the quality of the parent-child relationship. Improving maternal health during pregnancy and parental investments in infancy can yield large benefits for cognitive and mental development later in childhood.     

Development of gaze following abilities in wolves (Canis lupus)

The ability to coordinate with others' head and eye orientation to look in the same direction is considered a key step towards an understanding of others mental states like attention and intention. Here, we investigated the ontogeny and habituation patterns of gaze following into distant space and behind barriers in nine hand-raised wolves. We found that these wolves could use conspecific as well as human gaze cues even in the barrier task, which is thought to be more cognitively advanced than gazing into distant space. Moreover, while gaze following into distant space was already present at the age of 14 weeks and subjects did not habituate to repeated cues, gazing around a barrier developed considerably later and animals quickly habituated, supporting the hypothesis that different cognitive mechanisms may underlie the two gaze following modalities. More importantly, this study demonstrated that following another individuals' gaze around a barrier is not restricted to primates and corvids but is also present in canines, with remarkable between-group similarities in the ontogeny of this behaviour. This sheds new light on the evolutionary origins of and selective pressures on gaze following abilities as well as on the sensitivity of domestic dogs towards human communicative cues.     

Review and application of group theory to molecular systems biology

In this paper we provide a review of selected mathematical ideas that can help us better understand the boundary between living and non-living systems. We focus on group theory and abstract algebra applied to molecular systems biology. Throughout this paper we briefly describe possible open problems. In connection with the genetic code we propose that it may be possible to use perturbation theory to explore the adjacent possibilities in the 64-dimensional space-time manifold of the evolving genome. With regards to algebraic graph theory, there are several minor open problems we discuss. In relation to network dynamics and groupoid formalism we suggest that the network graph might not be the main focus for understanding the phenotype but rather the phase space of the network dynamics. We show a simple case of a C ₆ network and its phase space network. We envision that the molecular network of a cell is actually a complex network of hypercycles and feedback circuits that could be better represented in a higher-dimensional space. We conjecture that targeting nodes in the molecular network that have key roles in the phase space, as revealed by analysis of the automorphism decomposition, might be a better way to drug discovery and treatment of cancer.     

The Impact of Symbolic and Non-Symbolic Quantity on Spatial Learning

An implicit mapping of number to space via a “mental number line” occurs automatically in adulthood. Here, we systematically explore the influence of differing representations of quantity (no quantity, non-symbolic magnitudes, and symbolic numbers) and directional flow of stimuli (random flow, left-to-right, or right-to-left) on learning and attention via a match-to-sample working memory task. When recalling a cognitively demanding string of spatial locations, subjects performed best when information was presented right-to-left. When non-symbolic or symbolic numerical arrays were embedded in these spatial locations, and mental number line congruency prompted, this effect was attenuated and in some cases reversed. In particular, low-performing female participants who viewed increasing non-symbolic number arrays paired with the spatial locations exhibited better recall for left-to-right directional flow information relative to right-to-left, and better processing for the left side of space relative to the right side of space. The presence of symbolic number during spatial learning enhanced recall to a greater degree than non-symbolic number—especially for female participants, and especially when cognitive load is high—and this difference was independent of directional flow of information. We conclude that quantity representations have the potential to scaffold spatial memory, but this potential is subtle, and mediated by the nature of the quantity and the gender and performance level of the learner.     

Molecular neurobiology of human cognition

Recent studies into human mental retardation syndromes have given new insights into the molecular underpinnings of human cognitive processing, in particular into mechanisms likely to contribute to learning and memory. In this minireview, we present an overview of one signal transduction cascade that has garnered attention of late in this context, the ras/ERK/CREB pathway. We focus on this cascade because of recent exciting discoveries concerning the basis of neurofibromatosis type 1 (NF1) mental retardation, which link cognitive defects in this syndrome to disruptions of ras and its intracellular targets.     

Quantum-like model of brain's functioning: decision making from decoherence

We present a quantum-like model of decision making in games of the Prisoner's Dilemma type. By this model the brain processes information by using representation of mental states in a complex Hilbert space. Driven by the master equation the mental state of a player, say Alice, approaches an equilibrium point in the space of density matrices (representing mental states). This equilibrium state determines Alice's mixed (i.e., probabilistic) strategy. We use a master equation in which quantum physics describes the process of decoherence as the result of interaction with environment. Thus our model is a model of thinking through decoherence of the initially pure mental state. Decoherence is induced by the interaction with memory and the external mental environment. We study (numerically) the dynamics of quantum entropy of Alice's mental state in the process of decision making. We also consider classical entropy corresponding to Alice's choices. We introduce a measure of Alice's diffidence as the difference between classical and quantum entropies of Alice's mental state. We see that (at least in our model example) diffidence decreases (approaching zero) in the process of decision making. Finally, we discuss the problem of neuronal realization of quantum-like dynamics in the brain; especially roles played by lateral prefrontal cortex or/and orbitofrontal cortex.     

Your Space or Mine? Mapping Self in Time

While humans are capable of mentally transcending the here and now, this faculty for mental time travel (MTT) is dependent upon an underlying cognitive representation of time. To this end, linguistic, cognitive and behavioral evidence has revealed that people understand abstract temporal constructs by mapping them to concrete spatial domains (e.g. past = backward, future = forward). However, very little research has investigated factors that may determine the topographical characteristics of these spatiotemporal maps. Guided by the imperative role of episodic content for retrospective and prospective thought (i.e., MTT), here we explored the possibility that the spatialization of time is influenced by the amount of episodic detail a temporal unit contains. In two experiments, participants mapped temporal events along mediolateral (Experiment 1) and anterioposterior (Experiment 2) spatial planes. Importantly, the temporal units varied in self-relevance as they pertained to temporally proximal or distal events in the participant’s own life, the life of a best friend or the life of an unfamiliar other. Converging evidence from both experiments revealed that the amount of space used to represent time varied as a function of target (self, best friend or unfamiliar other) and temporal distance. Specifically, self-time was represented as occupying more space than time pertaining to other targets, but only for temporally proximal events. These results demonstrate the malleability of space-time mapping and suggest that there is a self-specific conceptualization of time that may influence MTT as well as other temporally relevant cognitive phenomena.     

Inference reasoning on fishers' knowledge using Bayesian causal maps

Scientists and managers are not the only holders of knowledge regarding environmental issues: other stakeholders such as farmers or fishers do have empirical and relevant knowledge. Thus, new approaches for knowledge representation in the case of multiple knowledge sources, but still enabling reasoning, are needed. Cognitive maps and Bayesian networks constitute some useful formalisms to address knowledge representations. Cognitive maps are powerful graphical models for knowledge gathering or displaying. If they offer an easy means to express individual judgments, drawing inferences in cognitive maps remains a difficult task. Bayesian networks are widely used for decision making processes that face uncertain information or diagnosis. But they are difficult to elicitate. To take advantage of each formalism and to overcome their drawbacks, Bayesian causal maps have been developed. In this approach, cognitive maps are used to build the network and obtain conditional probability tables. We propose here a complete framework applied on a real problem. From the different views of a group of shellfish dredgers about their activity, we derive a decision facilitating tool, enabling scenarios testing for fisheries management.     

A dynamic over games drives selfish agents to win–win outcomes

Understanding human institutions, animal cultures and other social systems requires flexible formalisms that describe how their members change them from within. We introduce a framework for modelling how agents change the games they participate in. We contrast this between-game ‘institutional evolution’ with the more familiar within-game ‘behavioural evolution’. We model institutional change by following small numbers of persistent agents as they select and play a changing series of games. Starting from an initial game, a group of agents trace trajectories through game space by navigating to increasingly preferable games until they converge on ‘attractor’ games. Agents use their ‘institutional preferences'' for game features (such as stability, fairness and efficiency) to choose between neighbouring games. We use this framework to pose a pressing question: what kinds of games does institutional evolution select for; what is in the attractors? After computing institutional change trajectories over the two-player space, we find that attractors have disproportionately fair outcomes, even though the agents who produce them are strictly self-interested and indifferent to fairness. This seems to occur because game fairness co-occurs with the self-serving features these agents do actually prefer. We thus present institutional evolution as a mechanism for encouraging the spontaneous emergence of cooperation among small groups of inherently selfish agents, without space, reputation, repetition, or other more familiar mechanisms. Game space trajectories provide a flexible, testable formalism for modelling the interdependencies of behavioural and institutional evolutionary processes, as well as a mechanism for the evolution of cooperation.     

Espaces de représentation et psychopathologie

A subjective world can be conceptualized as a “representational space” — that is, as a universe displayed from memory, in which the subject “is sailing”. Recent cognitive theory provides some conceptual tools for describing such a space in a relevant way for clinical purposes. The construction of a representational space is based on mental representations: (a) analogical representations, which display a content in working memory; (b) symbolic representations, which code and link up analogical representations to form a represented world. The dynamics of representations and affects is ruled by a principle of unification of representational space. The topology of a representational space depends on objective and subjective constraints which cause some “folds” and limit the display of such a space. The interaction between an event and a subjective memory can be analyzed within this framework, so that the concepts of trauma and defence processes can be defined. Clinical syndromes are defensive configurations that tend to close the representational space.     

AUTOMATIC ACOUSTIC IDENTIFICATION OF SINGING INSECTS

ABSTRACT

We report on our research efforts towards developing efficient equipment for the automatic recognition of insects using only the acoustic modality. Specifically, we deal with three groups of insects, namely the crickets, cicadas and katydids. Inspired by well-documented tactics of speech processing, the signal processing employed in the present work is elaborated further with respect to the sound production mechanisms of insects. In order to improve the practical efficacy of our equipment, we adopt a score-level fusion of classifiers with non-parametric (probabilistic neural network) and parametric (Gaussian mixture models) estimation of the probability density function. An efficient hierarchic classification scheme is introduced, where the identification of unlabelled input takes place at various levels of hierarchy, such as suborder, family, subfamily, genus and species. We evaluate the practical significance of our approach on a large and well-documented catalogue of recordings of crickets, cicadas and katydids. For the hierarchic classification scheme, we report identification accuracy that exceeds 99% at suborder and family levels. In the straight classification scheme, we report accuracy of 90% for 307 species.