Novel tracking function of moving target using chaotic dynamics in a recurrent neural network model

Chaotic dynamics introduced in a recurrent neural network model is applied to controlling an object to track a moving target in two-dimensional space, which is set as an ill-posed problem. The motion increments of the object are determined by a group of motion functions calculated in real time with firing states of the neurons in the network. Several cyclic memory attractors that correspond to several simple motions of the object in two-dimensional space are embedded. Chaotic dynamics introduced in the network causes corresponding complex motions of the object in two-dimensional space. Adaptively real-time switching of control parameter results in constrained chaos (chaotic itinerancy) in the state space of the network and enables the object to track a moving target along a certain trajectory successfully. The performance of tracking is evaluated by calculating the success rate over 100 trials with respect to nine kinds of trajectories along which the target moves respectively. Computer experiments show that chaotic dynamics is useful to track a moving target. To understand the relations between these cases and chaotic dynamics, dynamical structure of chaotic dynamics is investigated from dynamical viewpoint.     

Outline of a matrix calculus for neural nets

The activity of a neural net is represented in terms of a matrix vector equation with a normalizing operator in which the matrix represents only the complete structure of the net, and the normalized vector-matrix product represents the activity of all the non-afferent neurons. The activity vectors are functions of a quantized time variable whose elements are zero (no activity) or one (activity). Certain properties of the structure matrix are discussed and the computational procedure which results from the matrix vector equation is illustrated by a specific example.     

Self-control in neural nets

This paper deals with the problem of self-controlling nets of Caianiello's type. These nets control themselves through their own elements.     

Symmetry breaking in neural nets

In this paper two well-known homogeneous models of neural nets undergoing symmetry-breaking transitions are studied in order to see if, after the transition, there is the appearance of Goldstone models. These have been found only in an approximate way; there are indications, however, that they can play a prominent role when the tissue is subjected to external inputs, constraining it to be slaved to the characteristics of those. This circumstance should be essential in explaining how a structured net can store complex inputs and give subsequently ordered outputs.     

Domain is a moving target for relational learning

The domain for relational learning was manipulated by varying the training set size for pigeons that had learned the same/different (S/D) concept. Six pigeons that had learned a S/D task with pairs of pictures with a set size of 1024 picture items had their training set size reduced to 8 items. Training on the reduced 8-item set was followed by transfer testing that was repeated four times. Transfer performance following reduction of the training set to 8 items was 9.2% less than it had been when the pigeons were trained with the 1024-item set, but 25.8% above chance. This partial abstract-concept learning remained constant over the four tests with novel stimuli. The results show that a broad domain established by a large expanding training set can once again become restricted by further training with a small training set.     

Evoked potentials in artificial neural nets

A neural net model of discrete populations of formal neurons have been constructed to study evoked potentials based on our previous simulation studies (Anninos, 1972). Some interesting results came up from the examination of our findings regarding the latencies and the period of the cyclic activity of the evoked potentials. In fact, the different successive latencies for the five identical stimuli and the different periods for each of the cyclic activities, all are consequences of inhibitory and excitatory influences from a large neuronal population. Furthermore, such behavior of the system is not only related to the unknown neuronal population but was also substantially altered by what occurred in other systems at the time of stimulus, or prior to it.Computation assistance was provided by the Health Sciences Computing Facility, UCLA, sponsored by NIH Special Research Resources Grant RR-3. Research was sponsored by NSF Grant GB 30498 and NIH Grant NS-8498.     

Cyclic modes in artificial neural nets

Artificial neural nets constructed of dicrete populations of 200–1000 formal neurons have been studied through computer simulation. Among the basic assumptions of operation of these nets are the following: a) Each neuron fires at times which are integral multiples of the synaptic delay . b) It produces the appropriate PSP's after . c) All the neurons have the same refractory period and d) temporal summation occurs without decrement, for a period less than the synaptic delay. The nets were specified by a number of parameters: fraction of inhibitory neurons in the population, average number of connections to each cell, threshold for cell firing. These parameters did not determine the detailed microscopical structures of nets which was established separately on a random basis.For the range of the parameters considered in this study it was found that neural nets are capable of supporting self-maintaining activity in the form of cycling modes, characterized by a fixed period. The period of the cycles can be altered by a steady, non-cycling external input to the net. Evidence is presented that the cycling modes depend upon the statistical parameters of the net and the stimulus characteristics rather than on the detailed structure of the net. These results suggest that non-structured nerve nets may respond in specific manner to specific stimuli.

Glossary

Parameters of Neural Net Model Synaptic delay - A Total number of neurons in the netlet - h Fraction of inhibitory neurons in the netlet (in % of total number of neurons) - ⁺ Average number of axon branches emanating from anexcitatory neuron - ^– Average number of axon branches emanating from an inhibitory neuron - k ⁺ Average EPSP produced by an excitatory neuron in arbitrary units of amplitude - k ^– Average IPSP produced by an inhibitory neuron in arbitrary units of amplitude - Firing threshold of neurons in the netlet - The minimum number of ESPS's necessary to trigger a neuron in the absence of inhibitory inputs - The minimum number of ESPS's necessary to trigger a neuron in the presence of inhibitory inputs. Dynamic Parameters of the Model n An integer giving the number of elapsed synaptic delays (i.e. elapsed time) - _n The activity; i.e. the fraction of active neurons in the netlet at t=n (the actual number of active cells is given by _nA) - _n={ⁱ_n} State vector of single netlet at time n This research has been supported by NIH grants NS-8012 and NS-8498, and NSF grant GB-30498. Computation assistance was provoded by the Health Sciences Computing Facility, UCLA, sponsored by NIH Special Research Resources grant RR-3.     

A benchmark for how well neural nets generalize

This paper discusses the problem of extending the domain of learning sets and introduces HERBIE, a program which achieves this through graphical procedures rather than via neural networks. It is argued that for theoretical reasons HERBIE is well-suited to serving as a benchmark for measuring generalization efficacy, and therefore to serving as a means of testing claims of emergent distributed intelligence in neural nets. The successful results of tests of HERBIE as a pattern recognizer are presented, and HERBIE's behavior is favorably compared to neural nets for several real generalization problems. Finally, applications of HERBIE independent of its serving as a generalization benchmark, particularly in the area of cognitive science, are discussed.     

A matrix calculus for neural nets: II

In a previous paper a method was given by which the efferent activity of an idealized neural net could be calculated from a given afferent pattern. Those results are extended in the present paper. Conditions are given under which nets may be considered equivalent. Rules are given for the reduction or extension of a net to an equivalent net. A procedure is given for constructing a net which has the property of converting each of a given set of afferent activity patterns into its corresponding prescribed efferent activity pattern.     

A canonical form for neural nets without circles

By “neural net” will be meant “neural net without circles.” Every neural net effects a transformation from inputs (i.e., firing patterns of the input neurons) to outputs (firing patterns of the output neurons). Two neural nets will be calledequivalent if they effect the same transformation from inputs to outputs. A canonical form is found for neural nets with respect to equivalence; i.e., a class of neural nets is defined, no two of which are equivalent, and which contains a neural net equivalent to any given neural net. This research was supported by the U.S. Air Force under Contract AF 49(638)-414 monitored by the Air Force Office of Scientific Research.     

A diffusion model of a neuron and neural nets

In the paper a diffusion model of a neuron is treated. A new, less restrictive than usually, condition of applicability of a diffusion model is presented. As a result the point-process-to-point-process model of a neuron is obtained, which produces an output signal of the same kind as the accepted input signals.     

Recognizing recurrent neural networks (rRNN): Bayesian inference for recurrent neural networks

Recurrent neural networks (RNNs) are widely used in computational neuroscience and machine learning applications. In an RNN, each neuron computes its output as a nonlinear function of its integrated input. While the importance of RNNs, especially as models of brain processing, is undisputed, it is also widely acknowledged that the computations in standard RNN models may be an over-simplification of what real neuronal networks compute. Here, we suggest that the RNN approach may be made computationally more powerful by its fusion with Bayesian inference techniques for nonlinear dynamical systems. In this scheme, we use an RNN as a generative model of dynamic input caused by the environment, e.g. of speech or kinematics. Given this generative RNN model, we derive Bayesian update equations that can decode its output. Critically, these updates define a 'recognizing RNN' (rRNN), in which neurons compute and exchange prediction and prediction error messages. The rRNN has several desirable features that a conventional RNN does not have, e.g. fast decoding of dynamic stimuli and robustness to initial conditions and noise. Furthermore, it implements a predictive coding scheme for dynamic inputs. We suggest that the Bayesian inversion of RNNs may be useful both as a model of brain function and as a machine learning tool. We illustrate the use of the rRNN by an application to the online decoding (i.e. recognition) of human kinematics.     

Conditions for periodic and aperiodic behavior of formal neural nets

Formal neural networks (FNN) can display dynamical behaviours, more or less different from each other depending on their units, the functions attributed to these units, interconnections, parameters, state spaces and initial states, etc. Whatever is 'chaos' - of which several practical and more exact definitions exist -, it used to be emerging at special conditions. Its prediction most often requires an individual analysis of the dynamical system (DS) in question. A study of such conditions is usually necessary in order to reach suitable control, which now seems to become a new trend in chaos theory. In chaos control tasks quick commands and at least short-term foresight of trends are required. It is a primary question also to define in advance what is regarded to be a controlled case of chaos. Possible importance of these general considerations at molecular scale is also discussed, avoiding not well-founded speculations.     

Thermodynamics energy for both supervised and unsupervised learning neural nets at a constant temperature

Unified Lyaponov function is given for the first time to prove the learning methodologies convergence of artificial neural network (ANN), both supervised and unsupervised, from the viewpoint of the minimization of the Helmholtz free energy at the constant temperature. Early in 1982, Hopfield has proven the supervised learning by the energy minimization principle. Recently in 1996, Bell & Sejnowski has algorithmically demonstrated Independent Component Analyses (ICA) generalizing the Principal Component Analyses (PCA) that the continuing reduction of early vision redundancy happens towards the "sparse edge maps" by maximization of the ANN output entropy. We explore the combination of both as Lyaponov function of which the proven convergence gives both learning methodologies. The unification is possible because of the thermodynamics Helmholtz free energy at a constant temperature. The blind de-mixing condition for more than two objects using two sensor measurement. We design two smart cameras with short term working memory to do better image de-mixing of more than two objects. We consider channel communication application that we can efficiently mix four images using matrices [AO] and [Al] to send through two channels.     

CYLD deubiquitinase as a recurrent target in oncogenic processes

CYLD deubiquitinase has been originally defined as a tumor suppressor based exclusively on genetic findings. Indeed, inactivation of CYLD in humans results in familial cylindromatosis and multiple trichoepithelioma, two pathologies characterized by the development of tumors originating specifically from the skin appendages. A set of recent publications has revealed that recurrent inactivation of CYLD occurs through diverse mechanisms in several forms of cancer, unequivocally confirming its tumor suppressor function. This property is associated with the critical role played by CYLD in negatively regulating several signaling pathway, among them the NF-κB signaling pathway.     

On a recurrent neural network producing oscillations

A recurrent two-node neural network producing oscillations is analyzed. The network has no true inputs and the outputs from the network exhibit a circular phase portrait. The weight configuration of the network is investigated, resulting in analytical weight expressions, which are compared with numerical weight estimates obtained by training the network on the desired trajectories. The values predicted by the analytical expressions agree well with the findings from the numerical study, and can also explain the asymptotic properties of the networks studied.     

Mitochondrial tRNA valine as a recurrent target for mutations involved in mitochondrial cardiomyopathies

The aim of this study was to identify the genetic defect in two patients having cardiac dysfunction accompanied by neurological symptoms, and in one case MRI evidence of cortical and cerebellar atrophy with hyperintensities in the basal ganglia. Muscle biopsies from each patient revealed single and combined mitochondrial respiratory chain deficiency. The complete mtDNA sequencing of both patients revealed two transitions in the mitochondrial tRNA(Val) gene (MT-TV) (m.1628C>T in Patient 1, and m.1644G>A in Patient 2). The functional and molecular analyses reported here suggest that the MT-TV gene should be routinely considered in the diagnosis of mitochondrial cardiomyopathies.