this paper are applicable to a wide variety of experimental paradigms. However, it may help to conceptualise the stimulus as for example which object, of some set, is being viewed by the experimental subject; indeed, data from such an experiment are examined later in this paper. Consider the stimuli to be taken from a discrete set S with S elements, each occurring with probability P (s). The probability of events with response r is denoted as P (r), and the joint probability distribution as P (s; r).

Numerous theories of neural processing, often motivated by experimental observations, have explored the computational properties of neural codes based on the precise or relative occurrence of spikes in a spike train. Spiking neuron models and theories however, as well as their experimental counterparts, have generally been limited to the simulation or observation of isolated neurons, isolated spike trains, or reduced neural populations. Such theories would therefore seem inappropriate to capture the properties of a neural code relying on temporal spike patterns distributed across large neuronal populations. Here we report a range of computer simulations and theoretical considerations that were designed to explore the possibilities of such a code and its relevance for visual processing. In a single, unified framework where the relation between stimulus saliency and spike asynchrony plays the central role, we describe how the ventral stream of the visual system could process natural input scenes and extract meaningful information, both rapidly and reliably. The first wave of spikes generated in the retina in response to a visual stimulation carries information explicitly in its spatio-temporal structure. This spike wave, propagating through a hierarchy of visual areas, is regenerated at each processing stage, where its temporal structure can be modified by (i) the selectivity of the cortical neurons, (ii) lateral interactions and (iii) top-down attentional influences from higher order cortical areas. The concept of temporal asynchrony within a wave of single spikes allows a unique theoretical framework to address the fundamental and complementary notions of neural information coding and representation, visual saliency and attention. 1.

Most experimental and theoretical studies of brain function assume that neurons transmit information as a rate code, but recent studies on the speed of visual processing impose temporal constraints that appear incompatible with such a coding scheme. Other coding schemes that use the pattern of spikes across a population a neurons may be much more efficient. For example, since strongly activated neurons tend to fire first, one can use the order of firing as a code. We argue that Rank Order Coding is not only very efficient, but also easy to implement in biological hardware: neurons can be made sensitive to the order of activation of their inputs by including a feed-forward shunting inhibition mechanism that progressively desensitizes the neuronal population during a wave of afferent activity. In such a case, maximum activation will only be produced when the afferent inputs are activated in the order of their synaptic weights.

The work of physicist and theoretical biologist Howard Pattee has focused on the roles that symbols and dynamics play in biological systems. Symbols, as discrete functional switching-states, are seen at the heart of all biological systems in form of genetic codes, and at the core of all neural systems in the form of informational mechanisms that switch behavior. They also appear in one form or another in all epistemic systems, from informational processes embedded in primitive organisms to individual human beings to public scientific models. Over its course, Pattee’s work has explored 1) the physical basis of informational functions (dynamical vs. rule-based descriptions, switching mechanisms, memory, symbols), 2) the functional organization of the observer (measurement, computation), 3) the means by which information can be embedded in biological organisms for purposes of self-construction and representation (as codes, modeling relations, memory, symbols), and 4) the processes by which new structures and functions can emerge over time. We discuss how these concepts can be applied to a high-level understanding of the brain. Biological organisms constantly

Time delays are ubiquitous in the nervous system. Empirical "ndings suggest that time delays are adapted when considering the synchronous activity of neurons. We introduce a framework for studying the dynamics of self-organized delay adaptation in systems which optimize coincidence of inputs. The framework comprises two families of delay adaptation mechanisms, delay shift and delay selection. For the important case of periodically modulated input we derive conditions for the existence and stability of solutions which constrain learning rules for reliable delay adaptation. Delay adaptation is also applicable in the case of several spatiotemporal neuronal input patterns. # 2000 Elsevier Science B.V. All rights reserved.

Precise temporal coding is a hallmark of the auditory system. Selective pressures to improve accuracy or encode more rapid changes have produced a suite of convergent physiological and morphological features that contribute to temporal coding. Comparative studies of temporal coding also point to shared computational strategies, and suggest how selection acts to improve coding. Both the avian cochlear nucleus angularis and the mammalian cochlear nuclei have heterogeneous cell populations, and similar responses to sound. These shared characteristics may represent convergent responses to similar selective pressures to encode features of airborne sound.

Using a delay adaptation learning rule, we model the activity-dependent development of directionally selective cells in the primary visual cortex. Based on input stimuli, a learning rule shifts delays to create synchronous arrival of spikes at cortical cells. As a result, delays become tuned creating a smooth cortical map of direction selectivity. This result demonstrates how delay adaption can serve as a powerful abstraction for modeling temporal learning in the brain.

Principle of parallel neuronal constellations..................................................................4 Principle of coherent functional group of neurons........................................................5 Population coding paradigm.........................................................................................5 Neuronal cortex as multidimensional coding “Fourier- windows “..............................6 The proposal of fractal mechanism in the cortex.........................................................7 Phase detection in the Fourier transformation...............................................................9 Is the cortex a hologram-like processor?....….............................................................10 Neuroanatomical advantages of the neuronal Fourier hologram.................................11 Basic cognitive advantage of the neuronal Fourier hologram.....................................12 Fourier hologram versus associative net neuronal models..........................................12

nalytic critique of attempts to explain regularities in behavior by invoking structures and Correspondence and requests for reprints may be addressed to John W. Donahoe, Department of Psychology, Program in Neuroscience and Behavior, University of Massachusetts, Amherst, Massachusetts 01002 (E-mail: jdonahoe@psych.umass.edu) or to Jose E. Burgos, Apartado 48276, Los Chaquaramos, Caracas, 10041, Venezuela (E-mail: jburgos@ucab.edu.ve). A compiled version of the learning algorithm and copies of the files used to simulate fixed-interval behavior are on deposit at the Cambridge Center for Behavioral Studies, 1770 Massachusetts Avenue, 123, Cambridge, Massachusetts 02140. processes that are based solely on inferences from behavior. In the case of SET, functional relations between behavioral measures (rate and choice) and time from the onsets of stimuli serve as the basis for inferring that behavior is controlled by the output of an internal pacemaker. The recourse to inferr

Abstract—Neural networks have the power to deal with information which is very hard to process using ordinary approaches, e.g. speech recognition. A recent trend in applying neural networks is to use biologically realistic neuron models. Specifically, neurons are considered which communicate with discrete pulses instead of continuous signals: spiking neurons. In this paper we investigate a small selection of properties which are found in biological neurons and investigate their effect on the general computational performance of spiking neural networks (SNN). Firstly, we investigated the way in which the internal dynamics of the neurons and delayed communication improve the ability to recognize temporal patterns. Secondly we explored an unsupervised adaptation rule which helps to distribute the work equally over all the neurons in the network, so that all neurons are involved in the task they are supposed to solve. It turned out that these biologically inspired features often improved the performance for the tasks investigated. I.