Associative memory in quaternionic Hopfield neural network

Associative memory networks based on quaternionic Hopfield neural network are investigated in this paper. These networks are composed of quaternionic neurons, and input, output, threshold, and connection weights are represented in quaternions, which is a class of hypercomplex number systems. The energy function of the network and the Hebbian rule for embedding patterns are introduced. The stable states and their basins are explored for the networks with three neurons and four neurons. It is clarified that there exist at most 16 stable states, called multiplet components, as the degenerated stored patterns, and each of these states has its basin in the quaternionic networks.     

Boolean network analysis of a neurotransmitter signaling pathway

BACKGROUND: A Boolean network is a simple computational model that may provide insight into the overall behavior of genetic networks and is represented by variables with two possible states (on/off), of the individual nodes/genes of the network. In this study, a Boolean network model has been used to simulate a molecular pathway between two neurotransmitter receptor, dopamine and glutamate receptor, systems in order to understand the consequence of using logic gate rules between nodes, which have two possible states (active and inactive). RESULTS: The dynamical properties of this Boolean network model of the biochemical pathway shows that, the pathway is stable and that, deletion/knockout of certain biologically important nodes cause significant perturbation to this network. The analysis clearly shows that in addition to the expected components dopamine and dopamine receptor 2 (DRD2), Ca(2+) ions play a critical role in maintaining stability of the pathway. CONCLUSION: So this method may be useful for the identification of potential genetic targets, whose loss of function in biochemical pathways may be responsible for disease onset. The molecular pathway considered in this study has been implicated with a complex disorder like schizophrenia, which has a complex multifactorial etiology.     

Computational functions in biochemical reaction networks.

In prior work we demonstrated the implementation of logic gates, sequential computers (universal Turing machines), and parallel computers by means of the kinetics of chemical reaction mechanisms. In the present article we develop this subject further by first investigating the computational properties of several enzymatic (single and multiple) reaction mechanisms: we show their steady states are analogous to either Boolean or fuzzy logic gates. Nearly perfect digital function is obtained only in the regime in which the enzymes are saturated with their substrates. With these enzymatic gates, we construct combinational chemical networks that execute a given truth-table. The dynamic range of a network's output is strongly affected by "input/output matching" conditions among the internal gate elements. We find a simple mechanism, similar to the interconversion of fructose-6-phosphate between its two bisphosphate forms (fructose-1,6-bisphosphate and fructose-2,6-bisphosphate), that functions analogously to an AND gate. When the simple model is supplanted with one in which the enzyme rate laws are derived from experimental data, the steady state of the mechanism functions as an asymmetric fuzzy aggregation operator with properties akin to a fuzzy AND gate. The qualitative behavior of the mechanism does not change when situated within a large model of glycolysis/gluconeogenesis and the TCA cycle. The mechanism, in this case, switches the pathway's mode from glycolysis to gluconeogenesis in response to chemical signals of low blood glucose (cAMP) and abundant fuel for the TCA cycle (acetyl coenzyme A).     

Ring-Shaped Plasmonic Logic Gates

Ring-shaped one-, two-, and three-bit plasmonic logic gate configurations and circuits have been proposed, which, besides being compact, are also versatile and can be easily cascaded, the output logic values being controlled by both the geometry of the multi-port rings and the phase of the incident beams. This latter degree of freedom, not fully exploited up to now in plasmonic circuits, offers a high degree of flexibility of logic gate configurations.

     

Efficient Universal Computing Architectures for Decoding Neural Activity

The ability to decode neural activity into meaningful control signals for prosthetic devices is critical to the development of clinically useful brain– machine interfaces (BMIs). Such systems require input from tens to hundreds of brain-implanted recording electrodes in order to deliver robust and accurate performance; in serving that primary function they should also minimize power dissipation in order to avoid damaging neural tissue; and they should transmit data wirelessly in order to minimize the risk of infection associated with chronic, transcutaneous implants. Electronic architectures for brain– machine interfaces must therefore minimize size and power consumption, while maximizing the ability to compress data to be transmitted over limited-bandwidth wireless channels. Here we present a system of extremely low computational complexity, designed for real-time decoding of neural signals, and suited for highly scalable implantable systems. Our programmable architecture is an explicit implementation of a universal computing machine emulating the dynamics of a network of integrate-and-fire neurons; it requires no arithmetic operations except for counting, and decodes neural signals using only computationally inexpensive logic operations. The simplicity of this architecture does not compromise its ability to compress raw neural data by factors greater than . We describe a set of decoding algorithms based on this computational architecture, one designed to operate within an implanted system, minimizing its power consumption and data transmission bandwidth; and a complementary set of algorithms for learning, programming the decoder, and postprocessing the decoded output, designed to operate in an external, nonimplanted unit. The implementation of the implantable portion is estimated to require fewer than 5000 operations per second. A proof-of-concept, 32-channel field-programmable gate array (FPGA) implementation of this portion is consequently energy efficient. We validate the performance of our overall system by decoding electrophysiologic data from a behaving rodent.     

A two dimensional field theory for motion computation

The local extraction of motion information from brightness patterns by individual movement detectors of the correlation-type is considered in the first part of the paper. A two-dimensional field theory of movement detection is developed by treating the distance between two adjacent photoreceptors as a differential. In the first approximation of the theory we only consider linear terms of the time interval between the reception of a contrast element and its delayed representation by the detector and linear terms of the spatial distances between adjacent photoreceptors. As a result we may neglect terms of higher order than quadratic in a Taylor series development of the brightness pattern. The responses of pairs of individual movement detectors are combined to a local response vector. In the first approximation of the detector field theory the response vector is proportional to the instantaneous pattern velocity vector and linearly dependent on local properties of the moving pattern. The linear dependence on pattern properties is represented by a two by two tensor consisting of elements which are nonlinear, local functional of the moving pattern. Some of the properties of the tensor elements are treated in detail. So, for instance, it is shown that the off-diagonal elements of the tensor disappear when the moving pattern consists of x- and y-dependent separable components. In the second part of the paper the tensor relation leading to the output of a movement detector pair is spatially integrated. The result of the integration is an approximation to a summation of the outputs of an array of detector pairs. The spatially integrated detector tensor relates the translatory motion vector to the resultant output vector. It is shown that the angle between the motion vector and the resultant output vector is always smaller than ±90° whereas the angle between the motion vector and local response vectors, elicited by detector pairs, may cover the entire angular range. In the discussion of the paper the limits of the field theory for motion computation as well as its higher approximations are pointed out in some detail. In a special chapter the dependence of the detector response on the pattern properties is treated and in another chapter questions connected with the so called aperture problem are discussed. Furthermore, properties for compensation of the pattern dependent deviation angle by spatial physiological integration are mentioned in the discussion.     

Computation emerges from adaptive synchronization of networking neurons

The activity of networking neurons is largely characterized by the alternation of synchronous and asynchronous spiking sequences. One of the most relevant challenges that scientists are facing today is, then, relating that evidence with the fundamental mechanisms through which the brain computes and processes information, as well as with the arousal (or progress) of a number of neurological illnesses. In other words, the problem is how to associate an organized dynamics of interacting neural assemblies to a computational task. Here we show that computation can be seen as a feature emerging from the collective dynamics of an ensemble of networking neurons, which interact by means of adaptive dynamical connections. Namely, by associating logical states to synchronous neuron's dynamics, we show how the usual Boolean logics can be fully recovered, and a universal Turing machine can be constructed. Furthermore, we show that, besides the static binary gates, a wider class of logical operations can be efficiently constructed as the fundamental computational elements interact within an adaptive network, each operation being represented by a specific motif. Our approach qualitatively differs from the past attempts to encode information and compute with complex systems, where computation was instead the consequence of the application of control loops enforcing a desired state into the specific system's dynamics. Being the result of an emergent process, the computation mechanism here described is not limited to a binary Boolean logic, but it can involve a much larger number of states. As such, our results can enlighten new concepts for the understanding of the real computing processes taking place in the brain.     

A comparison of two cell regulatory models entailing high dimensional attractors representing phenotype

Two models for mammalian cell regulation that invoke the concept of cellular phenotype represented by high dimensional dynamic attractor states are compared. In one model the attractors are derived from an experimentally determined genetic regulatory network (GRN) for the cell type. As the state space architecture within which the attractors are embedded is determined by the binding sites on proteins and the recognition sites on DNA the attractors can be described as “hard-wired” in the genome through the genomic DNA sequence. In the second model attractors arising from the interactions between active gene products (mainly proteins) and independent of the genomic sequence, are descended from a pre-cellular state from which life originated. As this model is based on the cell as an open system the attractor acts as the interface between the cell and its environment. Environmental sources of stress can serve to trigger attractor and therefore phenotypic, transitions without entailing genotypic sequence changes.It is asserted that the evidence from cell and molecular biological research and logic, favours the second model. If correct there are important implications for understanding how environmental factors impact on evolution and may be implicated in hereditary and somatic disease.     

A specialized subclass of interneurons mediates dopaminergic facilitation of amygdala function

The amygdala is under inhibitory control from the cortex through the activation of local GABAergic interneurons. This inhibition is greatly diminished during heightened emotional states due to dopamine release. However, dopamine excites most amygdala interneurons, suggesting that this dopaminergic gate may be mediated by an unknown subpopulation of interneurons. We hypothesized that this gate is mediated by paracapsular intercalated cells, a subset of interneurons that are innervated by both cortical and mesolimbic dopaminergic afferents. Using transgenic mice that express GFP in GABAergic interneurons, we show that paracapsular cells form a network surrounding the basolateral complex of the amygdala. We found that they provide feedforward inhibition into the basolateral and the central amygdala. Dopamine hyperpolarized paracapsular cells through D1 receptors and substantially suppressed their excitability, resulting in a disinhibition of the basolateral and central nuclei. Suppression of the paracapsular system by dopamine provides a compelling neural mechanism for the increased affective behavior observed during stress or other hyperdopaminergic states.     

Degenerate coding in neural systems

When the dimensionality of a neural circuit is substantially larger than the dimensionality of the variable it encodes, many different degenerate network states can produce the same output. In this review I will discuss three different neural systems that are linked by this theme. The pyloric network of the lobster, the song control system of the zebra finch, and the odor encoding system of the locust, while different in design, all contain degeneracies between their internal parameters and the outputs they encode. Indeed, although the dynamics of song generation and odor identification are quite different, computationally, odor recognition can be thought of as running the song generation circuitry backwards. In both of these systems, degeneracy plays a vital role in mapping a sparse neural representation devoid of correlations onto external stimuli (odors or song structure) that are strongly correlated. I argue that degeneracy between input and output states is an inherent feature of many neural systems, which can be exploited as a fault-tolerant method of reliably learning, generating, and discriminating closely related patterns.     

Stochastic radial basis functions

Stochastic signal processing can implement gaussian activation functions for radial basis function networks, using stochastic counters. The statistics of neural inputs which control the increment and decrement operations of the counter are governed by Bernoulli distributions. The transfer functions relating the input and output pulse probabilities can closely approximate gaussian activation functions which improve with the number of states in the counter. The means and variances of these gaussian approximations can be controlled by varying the output combinational logic function of the binary counter variables.     

Large-Scale Information Flow in Conscious and Unconscious States: an ECoG Study in Monkeys

Consciousness is an emergent property of the complex brain network. In order to understand how consciousness is constructed, neural interactions within this network must be elucidated. Previous studies have shown that specific neural interactions between the thalamus and frontoparietal cortices; frontal and parietal cortices; and parietal and temporal cortices are correlated with levels of consciousness. However, due to technical limitations, the network underlying consciousness has not been investigated in terms of large-scale interactions with high temporal and spectral resolution. In this study, we recorded neural activity with dense electrocorticogram (ECoG) arrays and used the spectral Granger causality to generate a more comprehensive network that relates to consciousness in monkeys. We found that neural interactions were significantly different between conscious and unconscious states in all combinations of cortical region pairs. Furthermore, the difference in neural interactions between conscious and unconscious states could be represented in 4 frequency-specific large-scale networks with unique interaction patterns: 2 networks were related to consciousness and showed peaks in alpha and beta bands, while the other 2 networks were related to unconsciousness and showed peaks in theta and gamma bands. Moreover, networks in the unconscious state were shared amongst 3 different unconscious conditions, which were induced either by ketamine and medetomidine, propofol, or sleep. Our results provide a novel picture that the difference between conscious and unconscious states is characterized by a switch in frequency-specific modes of large-scale communications across the entire cortex, rather than the cessation of interactions between specific cortical regions.     

Bulbocortical interplay in olfactory information processing via synchronous oscillations

Emergence of synchronous oscillatory activity is an inherent feature of the olfactory systems of insects, mollusks and mammals. A class of simple computational models of the mammalian olfactory system consisting of olfactory bulb and olfactory cortex is constructed to explore possible roles of the related neural circuitry in olfactory information processing via synchronous oscillations. In the models, the bulbar neural circuitry is represented by a chain of oscillators and that of cortex is analogous to an associative memory network with horizontal synaptic connections. The models incorporate the backprojection from cortical units to the bulbar oscillators in particular ways. They exhibit rapid and robust synchronous oscillations in the presence of odorant stimuli, while they show either nonoscillatory states or propagating waves in the absence of stimuli, depending on the values of model parameters. In both models, the backprojection is shown to enhance the establishment of large-scale synchrony. The results suggest that the modulation of neural activity through centrifugal inputs may play an important role at the early stage of cortical information processing.     

Neural model of the genetic network

Many cell control processes consist of networks of interacting elements that affect the state of each other over time. Such an arrangement resembles the principles of artificial neural networks, in which the state of a particular node depends on the combination of the states of other neurons. The lambda bacteriophage lysis/lysogeny decision circuit can be represented by such a network. It is used here as a model for testing the validity of a neural approach to the analysis of genetic networks. The model considers multigenic regulation including positive and negative feedback. It is used to simulate the dynamics of the lambda phage regulatory system; the results are compared with experimental observation. The comparison proves that the neural network model describes behavior of the system in full agreement with experiments; moreover, it predicts its function in experimentally inaccessible situations and explains the experimental observations. The application of the principles of neural networks to the cell control system leads to conclusions about the stability and redundancy of genetic networks and the cell functionality. Reverse engineering of the biochemical pathways from proteomics and DNA micro array data using the suggested neural network model is discussed.     

An inhibit (INH) molecular logic gate based on 1,8-naphthalimide-sensitised europium luminescence.

A novel molecular logic gate with inhibit (INH) function has been developed, based on oxygen and a threshold europium concentration as input information and long-lived red europium luminescence as output signal.     

A biochemical logic gate using an enzyme and its inhibitor. Part II: The logic gate

Enzyme-Based Logic Gates (ENLOGs) are key components in bio-molecular systems for information processing. This report and the previous one in this series address the characterization of two bio-molecular switching elements, namely the alpha-chymotrypsin (alphaCT) derivative p-phenylazobenzoyl-alpha-chymotrypsin (PABalphaCT) and its inhibitor (proflavine), as well as their assembly into a logic gate.The experimental output of the proposed system is expressed in terms of enzymic activity and this was translated into logic output (i.e. "1" or "0") relative to a predetermined threshold value. We have found that an univalent link exists between the dominant isomers of PABalphaCT (cis or trans), the dominant form of either acridine (proflavine) or acridan and the logic output of the system. Thus, of all possible combinations, only the trans-PABalphaCT and the acridan lead to an enzymic activity that can be defined as logic output "1". The system operates under the rules of Boolean algebra and performs as an "AND" logic gate.     

Deoxyribozyme-based three-input logic gates and construction of a molecular full adder

We have developed an array of seven deoxyribozyme-based molecular logic gates that behaves as a full adder in a single solution, with three oligonucleotides as inputs and two independent fluorogenic cleavage reactions as carry and sum outputs. The sum output consisted of four new deoxyribozyme-based logic gates: an ANDAND gate and three ANDNOTANDNOT gates. These gates required the design of a generic three-input deoxyribozyme-based logic gate that can use any three-way combination of activating or inactivating inputs. This generic gate design utilizes an additional inverting element that hybridizes to convert YES logic into NOT logic and vice versa. The system represents the first solution-phase, single test tube, enzymatic full adder and shows the complexity of control over molecular scale events that can be achieved with deoxyribozyme-based logic gates. Similar systems could be applied to control autonomous therapeutic and diagnostic devices.     

Lagrange formulation of the self-organization problem of a neuronal ensemble during computation of nonlinear dissipation of energy

The Lagrange formulation for the problem of excitation of the Bresslow neural network is given to construct an arbitrary law for energy dissipation of the ensemble. The Amari assumption about neuron conductivity as a function of membrane potential allows one to admit the logistic dissipation law. It was shown that, from the viewpoint of statistics, this law is valid at coherent excitation conditions. The property of factorizing for the functioning of this ensemble was obtained.     

Exploring spike transfer through the thalamus using hybrid artificial-biological neuronal networks

We use dynamic clamp to construct "hybrid" thalamic circuits by connecting a biological neuron in situ to silicon- or software-generated "neurons" through artificial synapses. The purpose is to explore cellular sensory gating mechanisms that regulate the transfer efficiency of signals during different sleep-wake states. Hybrid technology is applied in vitro to different paradigms such as: (1) simulating interactions between biological thalamocortical neurons, artificial reticular thalamic inhibitory interneurons and a simulated sensory input, (2) grafting an artificial sensory input to a wholly biological thalamic network that generates spontaneous sleep-like oscillations, (3) injecting in thalamocortical neurons a background synaptic bombardment mimicking the activity of corticothalamic inputs. We show that the graded control of the strength of intrathalamic inhibition, combined with the membrane polarization and the fluctuating synaptic noise in thalamocortical neurons, is able to govern functional shifts between different input/output transmission states of the thalamic gate.