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Intrinsic timescales characterize dynamics of endogenous fluctuations in neural activity. Variation of intrinsic timescales across the neocortex reflects functional specialization of cortical areas, but less is known about how intrinsic timescales change during cognitive tasks. We measured intrinsic timescales of local spiking activity within columns of area V4 in male monkeys performing spatial attention tasks. The ongoing spiking activity unfolded across at least two distinct timescales, fast and slow. The slow timescale increased when monkeys attended to the receptive fields location and correlated with reaction times. By evaluating predictions of several network models, we found that spatiotemporal correlations in V4 activity were best explained by the model in which multiple timescales arise from recurrent interactions shaped by spatially arranged connectivity, and attentional modulation of timescales results from an increase in the efficacy of recurrent interactions. Our results suggest that multiple timescales may arise from the spatial connectivity in the visual cortex and flexibly change with the cognitive state due to dynamic effective interactions between neurons.

The critical brain hypothesis states that the brain can benefit from operating close to a second-order phase transition. While it has been shown that several computational aspects of sensory information processing (e. g., sensitivity to input) are optimal in this regime, it is still unclear whether these computational benefits of criticality can be leveraged by neural systems performing behaviorally relevant computations. To address this question, we investigate signatures of criticality in networks optimized to perform efficient encoding of stimuli. We consider a spike-coding network of leaky integrate-and-fire neurons with synaptic transmission delays and input noise. Previously, it was shown that the performance of such networks varies non-monotonically with the noise amplitude. Interestingly, we find that in the vicinity of the optimal noise level for efficient coding, the network dynamics exhibits signatures of criticality, namely, the distribution of avalanche sizes follows a power law. When the noise amplitude is too low or too high for efficient coding, the network appears either super-critical or sub-critical, respectively. Our work suggests that two influential, and previously disparate theories of neural processing optimization – efficient coding, and criticality – may be intimately related.

Experimental studies have shown that in cortical neurons, excitatory and inhibitory incoming currents are strongly correlated, which is hypothesized to be essential for efficient computations. Additionally, cortical neurons exhibit strong preference to particular stimuli, which combined with the co-variability of excitatory and inhibitory inputs indicates a detailed co-tuning of the corresponding populations. Such co-tuning is hypothesized to emerge during development in a self-organized manner. Indeed, theoretical studies have demonstrated that a combination of plasticity rules could lead to the emergence of E/I co-tuning in neurons driven by low noise signals from feedforward connections. However, cortical signals are very noisy and originate in highly recurrent networks, which raises a question on the ability of known plasticity mechanisms to self-organize co-tuned connectivity. We demonstrate that high noise levels combined with random recurrence destroy co-tuning. However, we demonstrate that introducing structure in the connectivity patterns of the recurrent E/I network, the recurrence does not hinder but enhances the formation of the co-tuned selectivity. We employ a combination of analytical methods and simulation-based inference to uncover constraints on the recurrent connectivity that allow E/I co-tuning to emerge. We find that stronger excitatory connectivity within similarly tuned neurons, combined with more homogeneous inhibitory connectivity enhances the ability of plasticity to produce co-tuning in an upstream population. Our results suggest that structured recurrent connectivity controls information propagation and can enhance the ability of synaptic plasticity to learn input-output relationships in higher brain areas.

In this paper, we provide a Monte Carlo method to calculate multiple stochastic integrals which is based on a.s. distributional convergence.

The article is devoted to the problem of portfolio risk management of network project interdependencies in an agricultural company, as the lack of existing methods of project portfolio risk assessment and proper consideration of interdependencies are traced. During the study, we conducted an in-depth interview with the CFO of the company to identify the pool of ongoing projects of the company, determine the types of interproject dependencies, the likelihood of the corresponding risk in the project and the level of losses in monetary terms. Using the method of expert assessments and the noisy-OR gate tool, calculations were made in the GeNIe software product to determine the overall risk of the project portfolio after identifying high-risk projects and then recommendations were given for the application of a dynamic portfolio risk management model based on the software product used in the company.

Complex systems are fascinating because their rich macroscopic properties emerge from the interaction of many simple parts. Understanding the building principles of these emergent phenomena in nature requires assessing natural complex systems experimentally. However, despite the development of large-scale data-acquisition techniques, experimental observations are often limited to a tiny fraction of the system. This spatial subsampling is particularly severe in neuroscience, where only a tiny fraction of millions or even billions of neurons can be individually recorded. Spatial subsampling may lead to significant systematic biases when inferring the collective properties of the entire system naively from a subsampled part. To overcome such biases, powerful mathematical tools have been developed in the past. In this perspective, we overview some issues arising from subsampling and review recently developed approaches to tackle the subsampling problem. These approaches enable one to assess, e.g., graph structures, collective dynamics of animals, neural network activity, or the spread of disease correctly from observing only a tiny fraction of the system. However, our current approaches are still far from having solved the subsampling problem in general, and hence we conclude by outlining what we believe are the main open challenges. Solving these challenges alongside the development of large-scale recording techniques will enable further fundamental insights into the working of complex and living systems., Comment: 20 pages, 6 figures, review article

Reservoir computing is a powerful computational framework that is particularly successful in time-series prediction tasks. It utilises a brain-inspired recurrent neural network and allows biologically plausible learning without backpropagation. Reservoir computing has relied extensively on the self-organizing properties of biological spiking neural networks. We examine the ability of a rate-based network of neural oscillators to take advantage of the self-organizing properties of synaptic plasticity. We show that such models can solve complex tasks and benefit from synaptic plasticity, which increases their performance and robustness. Our results further motivate the study of self-organizing biologically inspired computational models that do not exclusively rely on end-to-end training.

It has long been hypothesized that operating close to the critical state is beneficial for natural and artificial systems. We test this hypothesis by evolving foraging agents controlled by neural networks that can change the system's dynamical regime throughout evolution. Surprisingly, we find that all populations, regardless of their initial regime, evolve to be subcritical in simple tasks and even strongly subcritical populations can reach comparable performance. We hypothesize that the moderately subcritical regime combines the benefits of generalizability and adaptability brought by closeness to criticality with the stability of the dynamics characteristic for subcritical systems. By a resilience analysis, we find that initially critical agents maintain their fitness level even under environmental changes and degrade slowly with increasing perturbation strength. On the other hand, subcritical agents originally evolved to the same fitness, were often rendered utterly inadequate and degraded faster. We conclude that although the subcritical regime is preferable for a simple task, the optimal deviation from criticality depends on the task difficulty: for harder tasks, agents evolve closer to criticality. Furthermore, subcritical populations cannot find the path to decrease their distance to criticality. In summary, our study suggests that initializing models near criticality is important to find an optimal and flexible solution., Comment: 8 Pages, 7 Figures, Artificial Life Conference 2021

Timescales characterize the pace of change for many dynamic processes in nature. Timescales are usually estimated by fitting the exponential decay of data autocorrelation in the time or frequency domain. We show that this standard procedure often fails to recover the correct timescales due to a statistical bias arising from the finite sample size. We develop an alternative approach to estimating timescales by fitting the sample autocorrelation or power spectrum with a generative model based on a mixture of Ornstein-Uhlenbeck processes using adaptive Approximate Bayesian Computations. Our method accounts for finite sample size and noise in data and returns a posterior distribution of timescales that quantifies the estimation uncertainty and can be used for model selection. We demonstrate the accuracy of our method on synthetic data and illustrate its application to recordings from the primate cortex. We provide a customizable Python package implementing our framework with different generative models suitable for diverse applications.

The dynamic range of stimulus processing in living organisms is much larger than a single neural network can explain. For a generic, tunable spiking network we derive that while the dynamic range is maximal at criticality, the interval of discriminable intensities is very similar for any network tuning due to coalescence. Compensating coalescence enables adaptation of discriminable intervals. Thus, we can tailor an ensemble of networks optimized to the distribution of stimulus intensities, e.g., extending the dynamic range arbitrarily. We discuss potential applications in machine learning., 6 pages plus supplemental material

Spreading processes are conventionally monitored on a macroscopic level by counting the number of incidences over time. The spreading process can then be modeled either on the microscopic level, assuming an underlying interaction network, or directly on the macroscopic level, assuming that microscopic contributions are negligible. The macroscopic characteristics of both descriptions are commonly assumed to be identical. In this work, we show that these characteristics of microscopic and macroscopic descriptions can be different due to coalescence, i.e., a node being activated at the same time by multiple sources. In particular, we consider a (microscopic) branching network (probabilistic cellular automaton) with annealed connectivity disorder, record the macroscopic activity, and then approximate this activity by a (macroscopic) branching process. In this framework, we analytically calculate the effect of coalescence on the collective dynamics. We show that coalescence leads to a universal non-linear scaling function for the conditional expectation value of successive network activity. This allows us to quantify the difference between the microscopic model parameter and established macroscopic estimates. To overcome this difference, we propose a non-linear estimator that correctly infers the model branching parameter for all system sizes., 13 pages

Criticality is considered an attractive candidate state for the dynamics and function of the brain, because in models criticality maximizes a number of properties related to information transmission and computations. These include the dynamic range, the susceptibility, the sensitivity to input, the correlation length, and the pattern diversity. And indeed, numerous studies accumulated evidence that supports the criticality hypothesis. However, some observations are also contradictory. The latter might in part be explained by the fact that criticality is a “full system” property, whereas experimental neural recordings can only assess a tiny part of the full network (“subsampling problem”). Here, we first recapitulate the basic properties of a dynamical system at and around the critical point in a pedagogic manner. We show how subsampling can bias inference about the underling network dynamics, and then present two recent analytical approaches to overcome the subsampling bias, based either on neural avalanches, or on the time-series of neural activity proper. The novel approach typically allows quantify the distance to criticality from less then ten recorded neurons and a few minutes of recording only. Thereby, it offers a novel and very powerful approach to assess criticality and task-related deviations thereof.

The nervous system can be represented as a multiscale network comprised by single cells or ensembles that are linked by physical or functional connections. Groups of morphologically and physiologically diverse neurons are wired as connectivity patterns with a certain degree of universality across species and individual variability. Thereby, community detection approaches are often used to characterize how neural units cluster into such densely interconnected groups. However, the communities may possess deeper structural features that remain undetected by current algorithms. We present a scheme for refined parcellation of neuronal networks, by identifying local integrator units (LU) that are contained in network communities. An LU is defined as a connected subnetwork in which all neuronal connections are constrained within this unit, and can be formed for instance by a set of interneurons. Our method uses the Louvain algorithm to detect communities and participation coefficients to discriminate local neurons from global hubs. The sensitivity of the algorithm for discovering LUs with respect to the choice of community detection algorithm and network parameters was tested by simulations of different synthetic networks. The appropriateness of the algorithm for real-world scenarios was demonstrated on weighted and binary Caenorhabditis elegans connectomes. The detected LUs are distinctly localized within the worm body and clearly define functional groups. This approach provides a robust, observer-independent parcellation strategy that is useful for functional structure confirmation and potentially contributes to the current efforts in quantitative whole-brain architectonics of different species as well as the analysis of functional connectivity networks.

To study the reaction of an early-ripening soybean variety to the formation of plant reproductive organs under the influence of different length of daylight hours, studies of 2 sowing periods in a growing house with a new early-ripening variety Sentyabrinka of the FSBSI FRC VNII of Soybean were conducted. Artificial reduction of the daylight duration to 8 hours was established from the phase of the 3rd triple leaf with alternating day and night periods in each variant 7 times during the growing season. The control was plants whose growth and development took place in natural light conditions. According to the research results, it was found that the change in the daylight duration during the vegetation period had a significant impact on the duration of the phases of plant growth and development, the growing season as a whole. When sowing soybeans on May 28 with a natural daylight, the height of plants and their seed productivity were higher than those of plants with a shortened daylight. At this sowing period, the highest productivity was obtained from one plant – 9.3 g, which is 1.0 g more compared to soybean plants with a sowing period of June 3. The growth of plants, the formation of reproductive organs and the seed productivity of the early-repining variety Sentyabrinka depended on the duration of daylight, which can be regulated by the sowing period.

The avalanche transformation as a model for avalanches in neural dynamics was introduced in [8] in 2008. Here we discuss this transformation in terms of group actions, random dynamics and skew products with a finite invariant measure. The results are based on [8]. Some open problems are mentioned. Read More: http://www.worldscientific.com/doi/10.1142/S0219493716600054

How a complex network is connected crucially impacts its dynamics and function. Percolation, the transition to extensive connectedness on gradual addition of links, was long believed to be continuous, but recent numerical evidence of ‘explosive percolation’ suggests that it might also be discontinuous if links compete for addition. Here we analyse the microscopic mechanisms underlying discontinuous percolation processes and reveal a strong impact of single-link additions. We show that in generic competitive percolation processes, including those showing explosive percolation, single links do not induce a discontinuous gap in the largest cluster size in the thermodynamic limit. Nevertheless, our results highlight that for large finite systems single links may still induce substantial gaps, because gap sizes scale weakly algebraically with system size. Several essentially macroscopic clusters coexist immediately before the transition, announcing discontinuous percolation. These results explain how single links may drastically change macroscopic connectivity in networks where links add competitively.

The limit as N → ∞ of the eigenvalue correlation function is studied in a neighborhood of zero for N × N Hermitian matrices chosen at random from the Hilbert-Schmidt sphere of an appropriate radius. Dyson’s famous sin π(t1 − t2)/π(t1 − t2)-kernel asymptotic is extended to this class of matrix ensembles. Bibliography: 9 titles.

In many studies of self-organized criticality (SOC), branching processes were used to model the dynamics of the activity of the system during avalanches. This mathematical simplification was also adopted when investigating systems with a complicated connection topology including recurrent and subthreshold interactions. However, none of these studies really analyzed whether this convenient approximation was indeed applicable. In present paper we study the correspondences between avalanches generated by branching processes and by a fully connected neural network. The benefit from the analysis is not only the justification of such correspondence but also a simple learning rule, which allows self-organization of the network towards a critical state as recently observed in slice experiments.