Partner: José Amigó

Universidad Miguel Hernández-CSIC (ES)

Recent publications
1.Arnold M.M., Szczepański J., Montejo N., Amigó J.M., Wajnryb E., Sanchez-Vives M.V., Information content in cortical spike trains during brain state transitions, JOURNAL OF SLEEP RESEARCH, ISSN: 0962-1105, DOI: 10.1111/j.1365-2869.2012.01031.x, Vol.22, pp.13-21, 2013
Abstract:

Even in the absence of external stimuli there is ongoing activity in the cerebral cortex as a result of recurrent connectivity. This paper attempts to characterize one aspect of this ongoing activity by examining how the information content carried by specific neurons varies as a function of brain state. We recorded from rats chronically implanted with tetrodes in the primary visual cortex during awake and sleep periods. Electro-encephalogram and spike trains were recorded during 30-min periods, and 2–4 neuronal spikes were isolated per tetrode off-line. All the activity included in the analysis was spontaneous, being recorded from the visual cortex in the absence of visual stimuli. The brain state was determined through a combination of behavior evaluation, electroencephalogram and electromyogram analysis. Information in the spike trains was determined by using Lempel–Ziv Complexity. Complexity was used to estimate the entropy of neural discharges and thus the information content (Amigóet al. Neural Comput., 2004, 16: 717–736). The information content in spike trains (range 4–70 bits s−1) was evaluated during different brain states and particularly during the transition periods. Transitions toward states of deeper sleep coincided with a decrease of information, while transitions to the awake state resulted in an increase in information. Changes in both directions were of the same magnitude, about 30%. Information in spike trains showed a high temporal correlation between neurons, reinforcing the idea of the impact of the brain state in the information content of spike trains.

Keywords:

awake, brain states, entropy, firing rate, information, sleep, spike train

Affiliations:
Arnold M.M.-Universidad Miguel Hernández-CSIC (ES)
Szczepański J.-IPPT PAN
Montejo N.-Universidad Miguel Hernández-CSIC (ES)
Amigó J.M.-Universidad Miguel Hernández-CSIC (ES)
Wajnryb E.-IPPT PAN
Sanchez-Vives M.V.-ICREA-IDIBAPS (ES)
2.Szczepański J., Arnold M., Wajnryb E., Amigó J.M., Sanchez-Vives M.V., Mutual information and redundancy in spontaneous communication between cortical neurons, BIOLOGICAL CYBERNETICS, ISSN: 0340-1200, DOI: 10.1007/s00422-011-0425-y, Vol.104, pp.161-174, 2011
Abstract:

An important question in neural information processing is how neurons cooperate to transmit information. To study this question, we resort to the concept of redundancy in the information transmitted by a group of neurons and, at the same time, we introduce a novel concept for measuring cooperation between pairs of neurons called relative mutual information (RMI). Specifically, we studied these two parameters for spike trains generated by neighboring neurons from the primary visual cortex in the awake, freely moving rat. The spike trains studied here were spontaneously generated in the cortical network, in the absence of visual stimulation. Under these conditions, our analysis revealed that while the value of RMI oscillated slightly around an average value, the redundancy exhibited a behavior characterized by a higher variability. We conjecture that this combination of approximately constant RMI and greater variable redundancy makes information transmission more resistant to noise disturbances. Furthermore, the redundancy values suggest that neurons can cooperate in a flexible way during information transmission. This mostly occurs via a leading neuron with higher transmission rate or, less frequently, through the information rate of the whole group being higher than the sum of the individual information rates—in other words in a synergetic manner. The proposed method applies not only to the stationary, but also to locally stationary neural signals.

Keywords:

Neurons, Shannon information, Entropy, Mutual information, Redundancy, Visual cortex, Spikes train, Spontaneous activity

Affiliations:
Szczepański J.-IPPT PAN
Arnold M.-Universidad Miguel Hernández-CSIC (ES)
Wajnryb E.-IPPT PAN
Amigó J.M.-Universidad Miguel Hernández-CSIC (ES)
Sanchez-Vives M.V.-ICREA-IDIBAPS (ES)
3.Amigó J.M., Kocarev L., Szczepański J., On some properties of the discrete Lyapunov exponent, PHYSICS LETTERS A, ISSN: 0375-9601, DOI: 10.1016/j.physleta.2008.07.076, Vol.372, pp.6265-6268, 2008
Abstract:

One of the possible by-products of discrete chaos is the application of its tools, in particular of the discrete Lyapunov exponent, to cryptography. In this Letter we explore this question in a very general setting.

Affiliations:
Amigó J.M.-Universidad Miguel Hernández-CSIC (ES)
Kocarev L.-University “Kiril i Metodij”, Skopje (MK)
Szczepański J.-IPPT PAN
4.Amigó J.M., Kocarev L., Szczepański J., Theory and practice of chaotic cryptography, PHYSICS LETTERS A, ISSN: 0375-9601, DOI: 10.1016/j.physleta.2007.02.021, Vol.366, pp.211-216, 2007
Abstract:

In this Letter we address some basic questions about chaotic cryptography, not least the very definition of chaos in discrete systems. We propose a conceptual framework and illustrate it with different examples from private and public key cryptography. We elaborate also on possible limits of chaotic cryptography.

Affiliations:
Amigó J.M.-Universidad Miguel Hernández-CSIC (ES)
Kocarev L.-University “Kiril i Metodij”, Skopje (MK)
Szczepański J.-IPPT PAN
5.Amigó J.M., Kocarev L., Szczepański J., Discrete Lyapunov exponent and resistance to differential cryptanalysis, IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS, ISSN: 1549-7747, DOI: 10.1109/TCSII.2007.901576, Vol.54, No.10, pp.882-886, 2007
Abstract:

In a recent paper, Jakimoski and Subbalakshmi provided a nice connection between the so-called discrete Lyapunov exponent of a permutation F defined on a finite lattice and its maximal differential probability, a parameter that measures the complexity of a differential cryptanalysis attack on the substitution defined by F. In this brief, we take a second look at their result to find some practical shortcomings. We also discuss more general aspects.

Keywords:

Differential cryptanalysis, discrete Lyapunov exponent (DLE), maximum differential probability (DP)

Affiliations:
Amigó J.M.-Universidad Miguel Hernández-CSIC (ES)
Kocarev L.-University “Kiril i Metodij”, Skopje (MK)
Szczepański J.-IPPT PAN
6.Kocarev L., Szczepański J., Amigó J.M., Tomovski I., Discrete chaos - I: theory, IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS, ISSN: 1549-8328, DOI: 10.1109/TCSI.2006.874181, Vol.53, No.6, pp.1300-1309, 2006
Abstract:

We propose a definition of the discrete Lyapunov exponent for an arbitrary permutation of a finite lattice. For discrete-time dynamical systems, it measures the local (between neighboring points) average spreading of the system. We justify our definition by proving that, for large classes of chaotic maps, the corresponding discrete Lyapunov exponent approaches the largest Lyapunov exponent of a chaotic map when Mrarrinfin, where M is the cardinality of the discrete phase space. In analogy with continuous systems, we say the system has discrete chaos if its discrete Lyapunov exponent tends to a positive number, when Mrarrinfin. We present several examples to illustrate the concepts being introduced.

Keywords:

Chaos, discrete chaos, Lyapunov components

Affiliations:
Kocarev L.-University “Kiril i Metodij”, Skopje (MK)
Szczepański J.-IPPT PAN
Amigó J.M.-Universidad Miguel Hernández-CSIC (ES)
Tomovski I.-other affiliation
7.Amigó J.M., Kocarev L., Szczepański J., Order patterns and chaos, PHYSICS LETTERS A, ISSN: 0375-9601, DOI: 10.1016/j.physleta.2006.01.093, Vol.355, pp.27-31, 2006
Abstract:

Chaotic maps can mimic random behavior in a quite impressive way. In particular, those possessing a generating partition can produce any symbolic sequence by properly choosing the initial state. We study in this Letter the ability of chaotic maps to generate order patterns and come to the conclusion that their performance in this respect falls short of expectations. This result reveals some basic limitation of a deterministic dynamic as compared to a random one. This being the case, we propose a non-statistical test based on ‘forbidden’ order patterns to discriminate chaotic from truly random time series with, in principle, arbitrarily high probability. Some relations with discrete chaos and chaotic cryptography are also discussed.

Keywords:

Chaotic maps, Order patterns, Permutation entropy, Discrete Lyapunov exponent, Chaotic cryptography

Affiliations:
Amigó J.M.-Universidad Miguel Hernández-CSIC (ES)
Kocarev L.-University “Kiril i Metodij”, Skopje (MK)
Szczepański J.-IPPT PAN
8.Szczepański J., Amigó J.M., Michałek T., Kocarev L., Cryptographically secure substitutions based on the approximation of mixing maps, IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS, ISSN: 1549-8328, DOI: 10.1109/TCSI.2004.841602, Vol.52, No.2, pp.443-453, 2005
Abstract:

In this paper, we explore, following Shannon’s suggestion that diffusion should be one of the ingredients of resistant block ciphers, the feasibility of designing cryptographically secure substitutions (think of S-boxes, say) via approximation of mixing maps by periodic transformations. The expectation behind this approach is, of course, that the nice diffusion properties of such maps will be inherited by their approximations, at least if the convergence rate is appropriate and the associated partitions are sufficiently fine. Our results show that this is indeed the case and that, in principle, block ciphers with close-to-optimal immunity to linear and differential cryptanalysis (as measured by the linear and differential approximation probabilities) can be designed along these guidelines. We provide also practical examples and numerical evidence for this approximation philosophy.

Keywords:

Black cipher, differential cryptanalysis, linear cryptanalysis, mixing dynamical system, periodic approximation, S box

Affiliations:
Szczepański J.-IPPT PAN
Amigó J.M.-Universidad Miguel Hernández-CSIC (ES)
Michałek T.-IPPT PAN
Kocarev L.-University “Kiril i Metodij”, Skopje (MK)
9.Amigó J.M., Szczepański J., Kocarev L., A chaos-based approach to the design of cryptographically secure substitutions, PHYSICS LETTERS A, ISSN: 0375-9601, DOI: 10.1016/j.physleta.2005.05.057, Vol.343, pp.55-60, 2005
Abstract:

We show that chaotic maps may be used for designing so-called substitution boxes for ciphers resistant to linear and differential cryptanalysis, providing an alternative to the algebraic methods. Our approach is based on the approximation of mixing maps by periodic transformations. The expectation behind is, of course, that the nice chaotic properties of such maps will be inherited by their approximations, at least if the convergence rate is appropriate and the associated partitions are sufficiently fine. We show that this is indeed the case and that, in principle, substitutions with close-to-optimal immunity to linear and differential cryptanalysis can be designed along these guidelines. We provide also practical examples and numerical evidence for this approximation philosophy

Keywords:

Chaotic maps, Periodic approximations, Bit permutations, Cryptanalysis

Affiliations:
Amigó J.M.-Universidad Miguel Hernández-CSIC (ES)
Szczepański J.-IPPT PAN
Kocarev L.-University “Kiril i Metodij”, Skopje (MK)
10.Amigó J.M., Szczepański J., A Conceptual Guide to Chaos Theory, Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.9, pp.1-43, 1999

Conference abstracts
1.Szczepański J., Sanchez-Vives M.V., Arnold M.M., Montejo N., Paprocki B., Pręgowska A., Amigó J.M., Wajnryb E., Analyzing Neuroscience Signals using Information Theory and Complexity Shannon Communication Approach, 12th INCF, 12th INCF Workshop on Node Communication and Collaborative Neuroinformatics, 2015-04-16/04-17, Warszawa (PL), pp.1-32, 2015