Self-similarity and quasi-idempotence in neural networks and related dynamical systems

Minati, Ludovico; Winkel, Julia; Bifone, Angelo; Oświęcimka, Paweł; Jovicich, Jorge

doi:10.1063/1.4981908

Cited by 8 publications

(8 citation statements)

References 55 publications

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“…7 for two arbitrarily-chosen but representative cultures studies across stages of maturation, as well as in the complete results reported in the supplementary material. We found that, in line with previous observations showing increasing network activity and connectivity with the age of the cultures [28,29,31], the number of non-isolated nodes and of significant network links increased moving from the early to the developing and mature stages. The progression across the three stages was highlighted clearly using dMI (Fig.…”

Section: Malized Entropy)supporting

confidence: 92%

An information-theoretic framework to measure the dynamic interaction between neural spike trains

Mijatovic¹,

Antonacci²,

Lončar-Turukalo³

et al. 2020

Preprint

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Understanding the interaction patterns among simultaneous recordings of spike trains from multiple neuronal units is a key topic in neuroscience. However, an optimal approach of assessing these interactions has not been established, as existing methods either do not consider the inherent point process nature of spike trains or are based on parametric assumptions that may lead to wrong inferences if not met. This work presents a framework, grounded in the field of information dynamics, for the model-free, continuous-time estimation of both undirected (symmetric) and directed (causal) interactions between pairs of spike trains. The framework decomposes the overall information exchanged dynamically between two point processes X and Y as the sum of the dynamic mutual information (dMI) between the histories of X and Y, plus the transfer entropy (TE) along the directions X → Y and Y → X. Building on recent work which derived theoretical expressions and consistent estimators for the TE in continuous time, we develop algorithms for estimating efficiently all measures in our framework through nearest neighbor statistics. These algorithms are validated in simulations of independent and coupled spike train processes, showing the accuracy of dMI and TE in the assessment of undirected and directed interactions even for weakly coupled and short realizations, and proving the superiority of the continuous-time estimator over the discrete-time method. Then, the usefulness of the framework is illustrated in a real data scenario of recordings from in-vitro preparations of spontaneously-growing cultures of cortical neurons, where we show the ability of dMI and TE to identify how the networks of undirected and directed spike train interactions change their topology through maturation of the neuronal cultures.

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Section: Malized Entropy)supporting

confidence: 92%

An information-theoretic framework to measure the dynamic interaction between neural spike trains

Mijatovic¹,

Antonacci²,

Lončar-Turukalo³

et al. 2020

Preprint

Self Cite

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“…There is, therefore, a non-monotonic effect wherein complex dynamics effectively become ''focused'' onto the hub nodes, the most peripheral nodes remain largely independent, and the rest of the network follows more ordered dynamics compared to a corresponding ensemble of isolated oscillators. Interestingly, the effect is qualitatively reminiscent of that which iteratively squaring the adjacency matrix has on the nodal strengths [74].…”

Section: B Illustrative Examplesmentioning

confidence: 89%

“…This approach is justified by the fact that the cultures develop inhomogeneous activity, such that some nodes are noticeably more synchronized than the others, conferring to the corresponding matrices a characteristic ''striped'' appearance (Fig. 15c) [74]. As in the simulated microcircuit, the coincidence levels observed, namely up to CI ≈ 0.06, are indicative of operation in a weak synchronization regime, which represents a pervasive requirement for the maintenance of healthy neuronal dynamics [18].…”

Section: B Dissociated Neuronal Culturesmentioning

confidence: 97%

Connectivity Influences on Nonlinear Dynamics in Weakly-Synchronized Networks: Insights From Rössler Systems, Electronic Chaotic Oscillators, Model and Biological Neurons

et al. 2019

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Natural and engineered networks, such as interconnected neurons, ecological and social networks, coupled oscillators, wireless terminals and power loads, are characterized by an appreciable heterogeneity in the local connectivity around each node. For instance, in both elementary structures such as stars and complex graphs having scale-free topology, a minority of elements are linked to the rest of the network disproportionately strongly. While the effect of the arrangement of structural connections on the emergent synchronization pattern has been studied extensively, considerably less is known about its influence on the temporal dynamics unfolding within each node. Here, we present a comprehensive investigation across diverse simulated and experimental systems, encompassing star and complex networks of Rössler systems, coupled hysteresis-based electronic oscillators, microcircuits of leaky integrate-and-fire model neurons, and finally recordings from in-vitro cultures of spontaneously-growing neuronal networks. We systematically consider a range of dynamical measures, including the correlation dimension, nonlinear prediction error, permutation entropy, and other information-theoretical indices. The empirical evidence gathered reveals that under situations of weak synchronization, wherein rather than a collective behavior one observes significantly differentiated dynamics, denser connectivity tends to locally promote the emergence of stronger signatures of nonlinear dynamics. In deterministic systems, transition to chaos and generation of higher-dimensional signals were observed; however, when the coupling is stronger, this relationship may be lost or even inverted. In systems with a strong stochastic component, the generation of more temporally-organized activity could be induced. These observations have many potential implications across diverse fields of basic and applied science, for example, in the design of distributed sensing systems based on wireless coupled oscillators, in network identification and control, as well as in the interpretation of neuroscientific and other dynamical data.

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“…This is suitable for cases where the complexity of the phenomenon under consideration is so high that the use of different non-equivalent models is necessary 2 (see ( [6], pp. [64][65][66][67][68][69][70][71][72][73][74][75] and there is need for logical openness [12,34,42].…”

Section: Constructivist Approachmentioning

confidence: 99%

“…A further line of research may consider the compatibilities, equivalences among fuzzy profiles, semantic fuzzy profiles, and their properties during networking by considering variable idempotence (when M ≈ c + kM 2 as in [73]), as well as other matrix properties M(t) that represent the networks and random matrices that allow for possible mathematics-specific descriptions.…”

Section: Further Researchmentioning

confidence: 99%

Big Data: From Forecasting to Mesoscopic Understanding. Meta-Profiling as Complex Systems

Minati¹

2019

Systems

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We consider Big Data as a phenomenon with acquired properties, similar to collective behaviours, that establishes virtual collective beings. We consider the occurrence of ongoing non-equivalent multiple properties in the conceptual framework of structural dynamics given by sequences of structures and not only by different values assumed by the same structure. We consider the difference between modelling and profiling in a constructivist way, as De Finetti intended probability to exist, depending on the configuration taken into consideration. The past has little or no influence, while events and their configurations are not memorised. Any configuration of events is new, and the probabilistic values to be considered are reset. As for collective behaviours, we introduce methodological and conceptual proposals using mesoscopic variables and their property profiles and meta-profile Big Data and non-computable profiles which were inspired by the use of natural computing to deal with cyber-ecosystems. The focus is on ongoing profiles, in which the arising properties trace trajectories, rather than assuming that we can foresee them based on the past.We assume that dealing with Big Data as a phenomenon contains not only traces of past events, but also the assumption of having properties that are independent from the original event, when studied as a virtual collective being [6]. Thus, we consider the occurrence of ongoing, non-equivalent, multiple properties with any initial temporal beginning, duration, and variable combination in conceptual correspondence with the nature of quasi-systems, which occur when a system is not always the same system and or even a system at all [7,8].We then mention the criticality of the level of description, as well as the scalarity assumed to detect the properties as well as the conceptual ineffectiveness of increasing the quantity of data available. Before proposing new approaches allowed by the conceptual 'definitions' mentioned above, we consider the differences between models and profiles. Models (especially ideal) are expected to support understanding, while profiling is intended to represent non-ideal, data-driven models, and their emergent, ongoing properties, for example, correlations and coherences [9]. Another differentiation considered is between forecasting and understanding. Forecasting is based on the importance of the past, is based on analogies and repetitiveness, and takes some contextual conditions into account. Understanding is considered to be the ability to conjecture, hypothesise, speculate, and, finally, realise the nature of the phenomenon under study, for instance, chaotic, hosting bifurcations, fluctuations, and the presence of multiple dynamic coherences.We specify that the differences introduced above should be considered in a constructivist conceptual framework in which, instead of trying to find how a phenomenon 'really' is, one looks for the most effective way to think of it (multiple modelling) [10]. For instance, we consider the conceptual framework of the t...

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Self-similarity and quasi-idempotence in neural networks and related dynamical systems

Cited by 8 publications

References 55 publications

An information-theoretic framework to measure the dynamic interaction between neural spike trains

An information-theoretic framework to measure the dynamic interaction between neural spike trains

Connectivity Influences on Nonlinear Dynamics in Weakly-Synchronized Networks: Insights From Rössler Systems, Electronic Chaotic Oscillators, Model and Biological Neurons

Big Data: From Forecasting to Mesoscopic Understanding. Meta-Profiling as Complex Systems

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