Andrzej Lozowski

Complex-valued multistate neural associative memory

A model of a multivalued associative memory is presented. This memory has the form of a fully connected attractor neural network composed of multistate complex-valued neurons. Such a network is able to perform the task of storing and recalling gray-scale images. It is also shown that the complex-valued fully connected neural network may be considered as a generalization of a Hopfield network containing real-valued neurons. A computational energy function is introduced and evaluated in order to prove network stability for asynchronous dynamics. Storage capacity as related to the number of accessible neuron states is also estimated.

Synchronization and control in a cellular neural network of chaotic units by local pinnings

We present a new technique for controlling the behaviour of a large system composed of chaotic units by using only a few control units referred to as pinnings. Our model can be regarded as an extension of cellular neural networks to chaotic cells, in this paper described by Lorenz equations, locally coupled by identical connections. The network is of moderate size, 27 × 27. By tuning the connection strength D, a large variety of global behaviours can be obtained: from fully turbulent to fully coherent spatiotemporal states. In between the system exhibits unstable partial synchronization. We show that by using one (or only a few) unit(s) controlled on a chosen unstable periodic orbit by the standard method of Ott, Grebogi and Yorke (OGY), the global dynamics can be substantially changed: all units tend to obey periodic dynamics. By appropriate placement of pinnings the spatiotemporal state of the network can be ordered and shaped.

Signal Processing with temporal sequences in olfactory systems

The olfactory system is a very efficient biological setup capable of odor information processing with neural signals. The nature of neural signals restricts the information representation to multidimensional temporal sequences of spikes. The information is contained in the interspike intervals within each individual neural signal and interspike intervals between multiple signals. A mechanism of interactions between random excitations evoked by odorants in the olfactory receptors of the epithelium and deterministic operation of the olfactory bulb is proposed in this paper. Inverse Frobenius-Perron models of the bulbs temporal sequences are fitted to the interspike distributions of temporally modulated receptor signals. Ultimately, such pattern matching results in ability to recognize odors and offer a hypothetic model for signal processing occurring in the primary stage of the olfactory system.

Synchronization and anti-synchronization of Chua's oscillators via a piecewise linear coupling circuit

A chaotic associative memory may be constructed by coupling a network of Chuas circuits via piecewise linear conductances. Synchronization and anti-synchronization states are used to represent binary memory patterns. The chaotic network dynamics enable the memory to wander among patterns which have non-zero correlations with the input pattern. This paper describes two discrete circuits which may be used as the basis for implementing the coupling element as proposed in Jankowski et al. (1995). Initial coupling experiments support the proposed design approaches,.

Synchronization and association in a large network of coupled Chua's circuits

This work presents the results of simulation of the fully connected networks of Chuas circuits mutually coupled by nonlinear conductances derived using the Hebbian learning rule. The network can be regarded as a generalization of the Hopfield neural network built up of chaotic units. Due to the space-time synchronization of units, the studied network exhibits the ability of pattern retrieval and decorrelation of complex input patterns.

Invariant Recognition of Spatio-Temporal Patterns in The Olfactory System Model

This paper presents a model of a network of integrate-and-fire neurons with time delay weights, capable of invariant spatio-temporal pattern recognition. Spatio-temporal patterns are formed by spikes according to the encoding principle that the phase shifts of the spikes encode the input stimulus intensity which corresponds to the concentration of constituent molecules of an odor. We applied the Hopfields phase shift encoding principle at the output level for spatio-temporal pattern recognition: Firing of an output neuron indicates that corresponding odor is recognized and phase shift of its firing encodes the concentration of the recognized odor. The temporal structure of the model provides the base for the modeling of higher level tasks, where temporal correlation is involved, such as feature binding and segmentation, object recognition, etc.

High-frequency Chua's circuit

An implementation of Chuas chaotic oscillator with a tunnel diode is proposed. The tunnel diode replaces Chuas piece-wise nonlinear element. This enables an oscillation frequency much higher than the original implementations. Numerical simulation of the oscillator dynamics indicates the existence of a double-scroll chaotic attractor in the phase space.

Synchronization phenomena in 2D chaotic CNN

Complex pattern formation in two-dimensional cellular network of chaotic oscillators is presented in the paper. The patterns are related to unstable periodic orbits of the network chaotic dynamics and may be formed in the synchronization process obtained by means of chaos suppression. This effect can be considered as transition from turbulent phase to partially synchronized phase in the network.<<ETX>>

Bifurcation-based neural computation

Quadratic logistic map (QLM) is proposed as a generalized form of an artificial neuron (AN). Dynamics of the QLM not only exhibits computational abilities, but also has certain common features with the one of the modified Hodgkin-Huxley models of a neuron. The rest state of the QLM neuron is wandering within a chaotic attractor. Applied input is an additional bifurcation parameter of the system. Input of a certain range induces emergence of corresponding stable orbit. An arbitrary large number of attractors can be stored in a single QLM neuron. We explore the computational abilities of the QLM dynamics and argue that it may reflect certain aspects of dynamics of biological neurons.

Temporal-to-spatial dynamic mapping, flexible recognition, and temporal correlations in an olfactory cortex model.

Abstract. This paper proposes temporal-to-spatial dynamic mapping inspired by neural dynamics of the olfactory cortex. In our model the temporal structure of olfactory-bulb patterns is mapped to the spatial dynamics of the ensemble of cortical neurons. This mapping is based on the following biological mechanism: while anterior part of piriform cortex can be excited by the afferent input alone, the posterior areas require both afferent and association signals, which are temporally correlated in a specific way. One of the functional types of the neurons in our model corresponds to the cortical spatial dynamics and encodes odor components, and another represents temporal activity of association-fiber signals, which, we suggest, may be relevant to the encoding of odor concentrations. The temporal-to-spatial mapping and distributed representation of the model enable simultaneous rough cluster classification and fine recognition of patterns within a cluster as parts of the same dynamic process. The model is able to extract and segment the components of complex odor patterns which are spatiotemporal sequences of neural activity.