Classical and quantum dynamics on p-adic trees of ideas

We propose mathematical models of information processes of unconscious and conscious thinking (based on p-adic number representation of mental spaces). Unconscious thinking is described by classical cognitive mechanics (which generalizes Newton's mechanics). Conscious thinking is described by quantum cognitive mechanics (which generalizes the pilot wave model of quantum mechanics). The information state and motivation of a conscious cognitive system evolve under the action of classical information forces and a new quantum information force, namely, conscious force. Our model might provide mathematical foundations for some cognitive and psychological phenomena: collective conscious behavior, connection between physiological and mental processes in a biological organism, Freud's psychoanalysis, hypnotism, homeopathy. It may be used as the basis of a model of conscious evolution of life.     

Point process models of single-neuron discharges

In most neural systems, neurons communicate via sequences of action potentials. Contemporary models assume that the action potentials' times of occurrence rather than their waveforms convey information. The mathematical tool for describing sequences of events occurring in time and/or space is the theory of point processes. Using this theory, we show that neural discharge patterns convey time-varying information intermingled with the neuron's response characteristics. We review the basic techniques for analyzing single-neuron discharge patterns and describe what they reveal about the underlying point process model. By applying information theory and estimation theory to point processes, we describe the fundamental limits on how well information can be represented by and extracted from neural discharges. We illustrate applying these results by considering recordings from the lower auditory pathway.     

A hybrid model for the neural representation of complex mental processing in the human brain

In the present conceptual review several theoretical and empirical sources of information were integrated, and a hybrid model of the neural representation of complex mental processing in the human brain was proposed. Based on empirical evidence for strategy-related and inter-individually different task-related brain activation networks, and further based on empirical evidence for a remarkable overlap of fronto-parietal activation networks across different complex mental processes, it was concluded by the author that there might be innate and modular organized neuro-developmental starting regions, for example, in intra-parietal, and both medial and middle frontal brain regions, from which the neural organization of different kinds of complex mental processes emerge differently during individually shaped learning histories. Thus, the here proposed model provides a hybrid of both massive modular and holistic concepts of idiosyncratic brain physiological elaboration of complex mental processing. It is further concluded that 3-D information, obtained by respective methodological approaches, are not appropriate to identify the non-linear spatio-temporal dynamics of complex mental process-related brain activity in a sufficient way. How different participating network parts communicate with each other seems to be an indispensable aspect, which has to be considered in particular to improve our understanding of the neural organization of complex cognition.     

Measuring smells

Olfaction consists of a set of transforms from a physical space of odorant molecules, through a neural space of information processing, and into a perceptual space of smell. Elucidating the rules governing these transforms depends on establishing valid metrics for each of the three spaces. Here we first briefly review the perceptual and neural spaces, and then concentrate on the physical space of odorant molecules. We argue that the lack of an agreed-upon odor metric poses a significant obstacle toward understanding the neurobiology of olfaction, and suggest two alternative odor metrics as possible solutions.     

A p-Adic model for the process of thinking disturbed by physiological and information noise

We develop a model of the process of thinking in the presence of noise (which is produced by the simultaneous action of a huge number of neurons in the brain as well as by external information and internal cognitive processes). Our model is based on Freud's idea on the splitting of cognitive processes into two (closely connected) domains: consciousness and subconsciousness. We represent the process of thinking as a random dynamical process in a space of ideas endowed with a non-Euclidean geometry (which differs extremely from the ordinary Euclidean geometry of spatial location of neurons in the brain). The so-called p-adic geometry on a space of ideas describes the ability of cognitive systems to form associations. We show that random dynamical thinking systems on a p -adic space of ideas still generate only deterministic ideas. We also study positive and negative effects of noise (in particular, creativeness and stress).     

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.     

Modeling the dishabituation hierarchy: The role of the primordial hippocampus

We present a neural model for the organization and neural dynamics of the medial pallium, the toad's homolog of mammalian hippocampus. A neural mechanism, called cumulative shrinking, is proposed for mapping temporal responses from the anterior thalamus into a form of population coding referenced by spatial positions. Synaptic plasticity is modeled as an interaction of two dynamic processes which simulates acquisition and both short-term and long-term forgetting. The structure of the medial pallium model plus the plasticity model allows us to provide an account of the neural mechanisms of habituation and dishabituation. Computer simulations demonstrate a remarkable match between the model performance and the original experimental data on which the dishabituation hierarchy was based. A set of model predictions is presented, concerning mechanisms of habituation and cellular organization of the medial palliumThe research described in this paper was supported in part by grant no. 1RO1 NS 24926 from the National Institutes of Health (M.A.A., Principal Investigator)     

Reconstructing feedback representations in the ventral visual pathway with a generative adversarial autoencoder

While vision evokes a dense network of feedforward and feedback neural processes in the brain, visual processes are primarily modeled with feedforward hierarchical neural networks, leaving the computational role of feedback processes poorly understood. Here, we developed a generative autoencoder neural network model and adversarially trained it on a categorically diverse data set of images. We hypothesized that the feedback processes in the ventral visual pathway can be represented by reconstruction of the visual information performed by the generative model. We compared representational similarity of the activity patterns in the proposed model with temporal (magnetoencephalography) and spatial (functional magnetic resonance imaging) visual brain responses. The proposed generative model identified two segregated neural dynamics in the visual brain. A temporal hierarchy of processes transforming low level visual information into high level semantics in the feedforward sweep, and a temporally later dynamics of inverse processes reconstructing low level visual information from a high level latent representation in the feedback sweep. Our results append to previous studies on neural feedback processes by presenting a new insight into the algorithmic function and the information carried by the feedback processes in the ventral visual pathway.     

Memory retrieval as a p-adic dynamical system

We propose a mathematical model of the memory retrieval process based on dynamical systems over a metric space of p-adic numbers representing a configuration 'space of ideas' in which two ideas are close if they have a sufficiently long common root. Our aim is to suggest a new way of conceptualizing human memory retrieval that might be useful for simulation purposes or for the construction of artificial intelligence devices, as well as for a deeper understanding of the process itself. The dynamical system is assumed to be located in a blackbox processing unit (the 'subconscious') and controlled by an interface control unit (the 'conscious') that fixes parameters in the dynamical system and starts its iteration by sending an initial generating idea to it. We show that even simple p-adic dynamical systems admit behavioral scenarios that could explain some of the essential features of the human memory retrieval process.     

A probabilistic framework for a physiological representation of dynamically evolving sleep state

This work presents a probabilistic method for mapping human sleep electroencephalogram (EEG) signals onto a state space based on a biologically plausible mathematical model of the cortex. From a noninvasive EEG signal, this method produces physiologically meaningful pathways of the cortical state over a night of sleep. We propose ways in which these pathways offer insights into sleep-related conditions, functions, and complex pathologies. To address explicitly the noisiness of the EEG signal and the stochastic nature of the mathematical model, we use a probabilistic Bayesian framework to map each EEG epoch to a distribution of likelihoods over all model sleep states. We show that the mapping produced from human data robustly separates rapid eye movement sleep (REM) from slow wave sleep (SWS). A Hidden Markov Model (HMM) is incorporated to improve the path results using the prior knowledge that cortical physiology has temporal continuity.     

Mathematical model of blood and interstitial flow and lymph production in the liver

We present a mathematical model of blood and interstitial flow in the liver. The liver is treated as a lattice of hexagonal ‘classic’ lobules, which are assumed to be long enough that end effects may be neglected and a two-dimensional problem considered. Since sinusoids and lymphatic vessels are numerous and small compared to the lobule, we use a homogenized approach, describing the sinusoidal and interstitial spaces as porous media. We model plasma filtration from sinusoids to the interstitium, lymph uptake by lymphatic ducts, and lymph outflow from the liver surface. Our results show that the effect of the liver surface only penetrates a depth of a few lobules’ thickness into the tissue. Thus, we separately consider a single lobule lying sufficiently far from all external boundaries that we may regard it as being in an infinite lattice, and also a model of the region near the liver surface. The model predicts that slightly more lymph is produced by interstitial fluid flowing through the liver surface than that taken up by the lymphatic vessels in the liver and that the non-peritonealized region of the surface of the liver results in the total lymph production (uptake by lymphatics plus fluid crossing surface) being about 5 % more than if the entire surface were covered by the Glisson–peritoneal membrane. Estimates of lymph outflow through the surface of the liver are in good agreement with experimental data. We also study the effect of non-physiological values of the controlling parameters, particularly focusing on the conditions of portal hypertension and ascites. To our knowledge, this is the first attempt to model lymph production in the liver. The model provides clinically relevant information about lymph outflow pathways and predicts the systemic response to pathological variations.     

Modeling DNA shuffling.

In vitro evolution is a new, important laboratory method to evolve molecules with desired properties. It has been used in a variety of biological studies and drug development. In this paper, we study one important mutagenesis method used in in vitro evolution experiments called DNA shuffling. We construct a mathematical model for DNA shuffling and study the properties of molecules after DNA shuffling experiments based on this model. The model for DNA shuffling consists of two parts. First we apply the Lander-Waterman model for physical mapping by fingerprinting random clones to model the distribution of regions that can be reassembled through DNA shuffling. Then we present a model for recombination between different DNA species with different mutations. We compare our theoretical results with experimental data. Finally we propose novel applications of the theoretical results to the optimal design of DNA shuffling experiments and to physical mapping using DNA shuffling.     

Quantum-like formalism for cognitive measurements

We develop a quantum formalism (Hilbert space probabilistic calculus) for measurements performed over cognitive systems. In particular, this formalism is used for mathematical modelling of the functioning of consciousness as a self-measuring quantum-like system. By using this formalism, we could predict averages of cognitive observables. Reflecting the basic idea of neurophysiological and psychological studies on a hierarchic structure of cognitive processes, we use p-adic hierarchic trees as a mathematical model of a mental space. We also briefly discuss the general problem of the choice of an adequate mental geometry.     

Models of Darwinian processes and evolutionary principles

Evolutionary processes are described as stochastic motions in a genotype space (set of sequences with a Hamming distance) and a phenotype space (vector space of phenotypic properties). Real value functions are introduced which form a landscape over these spaces; smoothness postulates are formulated. Evolution is considered as a kind of hill climbing on these adaptive landscapes. A rather simple diffusion approximation for the phenotypic processes is proposed which leads to similar mathematical problems as the Schrödinger equation for disordered potential distributions.     

Nutritional modulation of cognitive function and mental health

The important role of diet in cardiometabolic health is generally well recognised; for mental health, it is not so well understood. However, lifestyle risk factors for poor physical health are the same risk factors for mental illness, including poor diet. This is reflected by the high level of poor physical health in people with mental illness. Mediterranean, whole food diets have been associated with reduced risk for chronic disease, but very little research has investigated their mental health benefits. We provide a model for the pathways by which food components provided by a Mediterranean-style diet can facilitate healthy brain function. We then review evidence for the role of selected nutrients/food components — antioxidants, omega-3 fatty acids and B vitamins — in the brain and, hence, modulation of cognitive function and mental health. Converging evidence indicates multiple pathways by which these nutrients can assist in brain function, drawing from studies investigating them in isolation. There is very little work done on synergistic actions of nutrients and whole diets, highlighting a need for human intervention studies investigating benefits of Mediterranean-style diets for mental, as well as cardiometabolic health.     

Quantum-like model of processing of information in the brain based on classical electromagnetic field

We propose a model of quantum-like (QL) processing of mental information. This model is based on quantum information theory. However, in contrast to models of "quantum physical brain" reducing mental activity (at least at the highest level) to quantum physical phenomena in the brain, our model matches well with the basic neuronal paradigm of the cognitive science. QL information processing is based (surprisingly) on classical electromagnetic signals induced by joint activity of neurons. This novel approach to quantum information is based on representation of quantum mechanics as a version of classical signal theory which was recently elaborated by the author. The brain uses the QL representation (QLR) for working with abstract concepts; concrete images are described by classical information theory. Two processes, classical and QL, are performed parallely. Moreover, information is actively transmitted from one representation to another. A QL concept given in our model by a density operator can generate a variety of concrete images given by temporal realizations of the corresponding (Gaussian) random signal. This signal has the covariance operator coinciding with the density operator encoding the abstract concept under consideration. The presence of various temporal scales in the brain plays the crucial role in creation of QLR in the brain. Moreover, in our model electromagnetic noise produced by neurons is a source of superstrong QL correlations between processes in different spatial domains in the brain; the binding problem is solved on the QL level, but with the aid of the classical background fluctuations.     

The mystery of structure and function of sensory processing areas of the neocortex: a resolution

Many different neural models have been proposed to account for major characteristics of the memory phenomenon family in primates. However, in spite of the large body of neurophysiological, anatomical and behavioral data, there is no direct evidence for supporting one model while falsifying the others. And yet, we can discriminate models based on their complexity and/or their predictive power. In this paper we present a computational framework with our basic assumption that neural information processing is performed by generative networks. A complex architecture is 'derived' by using information-theoretic principles. We find that our approach seems to uncover possible relations among the functional memory units (declarative and implicit memory) and the process of information encoding in primates. The architecture can also be related to the entorhinal-hippocampal loop. An effort is made to form a prototype of this computational architecture and to map it onto the functional units of the neocortex. This mapping leads us to claim that one may gain a better understanding by considering that anatomical and functional layers of the cortex differ. Philosophical consequences regarding the homunculus fallacy are also considered.     

Metacognition and mentalizing are associated with distinct neural representations of decision uncertainty

Metacognition and mentalizing are both associated with meta-level mental state representations. Conventionally, metacognition refers to monitoring one’s own cognitive processes, while mentalizing refers to monitoring others’ cognitive processes. However, this self-other dichotomy is insufficient to delineate the 2 high-level mental processes. We here used functional magnetic resonance imaging (fMRI) to systematically investigate the neural representations of different levels of decision uncertainty in monitoring different targets (the current self, the past self [PS], and others) performing a perceptual decision-making task. Our results reveal diverse formats of internal mental state representations of decision uncertainty in mentalizing, separate from the associations with external cue information. External cue information was commonly represented in the right inferior parietal lobe (IPL) across the mentalizing tasks. However, the internal mental states of decision uncertainty attributed to others were uniquely represented in the dorsomedial prefrontal cortex (dmPFC), rather than the temporoparietal junction (TPJ) that also represented the object-level mental states of decision inaccuracy attributed to others. Further, the object-level and meta-level mental states of decision uncertainty, when attributed to the PS, were represented in the precuneus and the lateral frontopolar cortex (lFPC), respectively. In contrast, the dorsal anterior cingulate cortex (dACC) represented currently experienced decision uncertainty in metacognition, and also uncertainty about the estimated decision uncertainty (estimate uncertainty), but not the estimated decision uncertainty per se in mentalizing. Hence, our findings identify neural signatures to clearly delineate metacognition and mentalizing and further imply distinct neural computations on internal mental states of decision uncertainty during metacognition and mentalizing.

The relationship between metacognition and mentalizing is still a matter of debate, as both are associated with meta-representations. This study adapts a task paradigm used in metacognition to apply in mentalizing and compares the neural representations of decision uncertainty in metacognition and mentalizing.