Information Rate of Some Classes of Non-regular Languages: An Automata-Theoretic Approach

To analyze the extent to which populations of neurons encode information in the numbers of spikes each neuron emits or in the relative time of firing of the different neurons that might reflect synchronization, we developed and analyzed the performance of an information theoretic approach. The formula quantifies the corrections to the instantaneous information rate that result from correlations in spike emission between pairs of neurons. We showed how these cross-cell terms can be separated from the correlations that occur between the spikes emitted by each neuron, the auto-cell terms in the information rate expansion. We also described a method to test whether the estimate of the amount of information contributed by stimulus-dependent synchronization is significant. With simulated data, we show that the approach can separate information arising from the number of spikes emitted by each neuron from the redundancy that can arise if neurons have common inputs and from the synergy that can arise if cells have stimulus-dependent synchronization. The usefulness of the approach is also demonstrated by showing how it helps to interpret the encoding shown by neurons in the primate inferior temporal visual cortex. When applied to a sample dataset of simultaneously recorded inferior temporal cortex neurons, the algorithm showed that most of the information is available in the number of spikes emitted by each cell; that there is typically just a small degree (approximately 12%) of redundancy between simultaneously recorded inferior temporal cortex (IT) neurons; and that there is very little gain of information that arises from stimulus-dependent synchronization effects in these neurons.

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Semisimple Synchronizing Automata and the Wedderburn-Artin Theory

International Journal of Foundations of Computer Science ◽

10.1142/s0129054116400037 ◽

2016 ◽

Vol 27 (02) ◽

pp. 127-145 ◽

Cited By ~ 3

Author(s):

Jorge Almeida ◽

Emanuele Rodaro

Keyword(s):

Upper Bound ◽

Broad Class ◽

Regular Languages ◽

Theoretic Approach ◽

Synchronizing Automata ◽

Natural Notion ◽

Strongly Connected ◽

Synchronizing Automaton ◽

Synchronizing Word ◽

Černý’S Conjecture

We present a ring theoretic approach to Černý's conjecture via the Wedderburn-Artin theory. We first introduce the radical ideal of a synchronizing automaton, and then the natural notion of semisimple synchronizing automata. This is a rather broad class since it contains simple synchronizing automata like those in Černý's series. Semisimplicity gives also the advantage of “factorizing” the problem of finding a synchronizing word into the sub-problems of finding “short” words that are zeros into the projection of the simple components in the Wedderburn-Artin decomposition. In the general case this last problem is related to the search of radical words of length at most [Formula: see text] where n is the number of states of the automaton. We show that the solution of this “Radical Conjecture” would give an upper bound [Formula: see text] for the shortest reset word in a strongly connected synchronizing automaton. Finally, we use this approach to prove the Radical Conjecture in some particular cases and Černý's conjecture for the class of strongly semisimple synchronizing automata. These are automata whose sets of synchronizing words are cyclic ideals, or equivalently, ideal regular languages that are closed under taking roots.

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An Automata Theoretic Approach to the Zero-One Law for Regular Languages: Algorithmic and Logical Aspects

Electronic Proceedings in Theoretical Computer Science ◽

10.4204/eptcs.193.13 ◽

2015 ◽

Vol 193 ◽

pp. 172-185 ◽

Cited By ~ 1

Author(s):

Ryoma Sin'ya

Keyword(s):

Regular Languages ◽

Theoretic Approach

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Ultimate resolution and information in electron microscopy

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100086787 ◽

1991 ◽

Vol 49 ◽

pp. 496-497

Author(s):

D. Van Dyck

Keyword(s):

Electron Microscopy ◽

Electron Microscope ◽

Transfer Function ◽

Information Transfer ◽

Communication Channel ◽

Structural Information ◽

Information Rate ◽

Noise Power ◽

Signal Power ◽

Imaging Device

An (electron) microscope can be considered as a communication channel that transfers structural information between an object and an observer. In electron microscopy this information is carried by electrons. According to the theory of Shannon the maximal information rate (or capacity) of a communication channel is given by C = B log2 (1 + S/N) bits/sec., where B is the band width, and S and N the average signal power, respectively noise power at the output. We will now apply to study the information transfer in an electron microscope. For simplicity we will assume the object and the image to be onedimensional (the results can straightforwardly be generalized). An imaging device can be characterized by its transfer function, which describes the magnitude with which a spatial frequency g is transferred through the device, n is the noise. Usually, the resolution of the instrument ᑭ is defined from the cut-off 1/ᑭ beyond which no spadal information is transferred.

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