Mechanisms of self-sustained oscillatory states in hierarchical modular networks with mixtures of electrophysiological cell types

Petar Tomov; Rodrigo F. Pena; Antonio C. Roque; Michael A. Zaks

In a network with a mixture of different electrophysiological types of neurons linked by excitatory and inhibitory connections, temporal evolution leads through repeated epochs of intensive global activity separated by intervals with low activity level. This behavior mimics ``up'' and ``down'' states, experimentally observed in cortical tissues in absence of external stimuli. We interpret global dynamical features in terms of individual dynamics of the neurons. In particular, we observe that the crucial role both in interruption and in resumption of global activity is played by distributions of the membrane recovery variable within the network. We also demonstrate that the behavior of neurons is more influenced by their presynaptic environment in the network than by their formal types, assigned in accordance with their response to constant current.

A Stochastic System with Infinite Interacting Components to Model the Time Evolution of the Membrane Potentials of a Population of Neurons

K. Yaginuma

We consider a new class of interacting particle systems with a countable number of interacting components. The system represents the time evolution of the membrane potentials of an infinite set of interacting neurons. We prove the existence and uniqueness of the process, using a perfect simulation procedure. We show that this algorithm is successful, that is, we show that the number of steps of the algorithm is almost surely finite. We also construct a perfect simulation procedure for the coupling of a process with a finite number of neurons and the process with an infinite number of neurons. As a consequence, we obtain an upper bound for the error that we make when sampling from a finite set of neurons instead of the infinite set of neurons.

A note on supersaturated set systems

Peter Frankl, Yoshiharu Kohayakawa, Vojtěch Rödl

A well-known theorem of Erdős, Ko and Rado implies that any family ℱ of k-element subsets of an n-element set with more than members must contain two members F and F' with |F∩F'| < t, as long as n is sufficiently large with respect to k and t. We investigate how many such pairs (F,F') ∈ ℱ×ℱ there must be in any such family ℱ with and α > 1.

Absolute continuity of the invariant measure in Piecewise Deterministic Markov Processes having degenerate jumps

Eva Löcherbach

We consider piecewise deterministic Markov processes with degenerate transition kernels of the "house-of-cards"-type. We use a splitting scheme based on jump times to prove the absolute continuity, as well as some regularity, of the invariant measure of the process. Finally, we obtain finer results on the regularity of the one-dimensional marginals of the invariant measure, using integration by parts with respect to the jump times.

Computationally efficient change point detection for high-dimensional regression

Florencia Leonardi, Peter Bühlmann

Large-scale sequential data is often exposed to some degree of inhomogeneity in the form of sudden changes in the parameters of the data-generating process. We consider the problem of detecting such structural changes in a high-dimensional regression setting. We propose a joint estimator of the number and the locations of the change points and of the parameters in the corresponding segments. The estimator can be computed using dynamic programming or, as we emphasize here, it can be approximated using a binary search algorithm with O(nlog(n)Lasso(n)) computational operations while still enjoying essentially the same theoretical properties; here Lasso(n) denotes the computational cost of computing the Lasso for sample size n. We establish oracle inequalities for the estimator as well as for its binary search approximation, covering also the case with a large (asymptotically growing) number of change points. We evaluate the performance of the proposed estimation algorithms on simulated data and apply the methodology to real data.

Balance Impairments after Brachial Plexus Injury as Assessed through Clinical and Posturographic Evaluation

Lidiane Souza, Thiago Lemos, Débora C. Silva, José M. de Oliveira, José F. Guedes Corrêa, Paulo L. Tavares, Laura A. Oliveira, Erika C. Rodrigues, Claudia D. Vargas

Objective: To investigate whether a sensorimotor deficit of the upper limb following a brachial plexus injury (BPI) affects the upright balance. Design: Eleven patients with a unilateral BPI and 11 healthy subjects were recruited. The balance assessment included the Berg Balance Scale (BBS), the number of feet touches on the ground while performing a 60 s single-leg stance and posturographic assessment (eyes open and feet placed hip-width apart during a single 60 s trial). The body weight distribution (BWD) between the legs was estimated from the center of pressure (COP) lateral position. The COP variability was quantified in the anterior-posterior and lateral directions. Results: BPI patients presented lower BBS scores (p = 0.048) and a higher frequency of feet touches during the single-leg stance (p = 0.042) compared with those of the healthy subjects. An asymmetric BWD toward the side opposite the affected arm was shown by 73% of BPI patients. Finally, higher COP variability was observed in BPI patients compared with healthy subjects for anterior-posterior (p = 0.020), but not for lateral direction (p = 0.818). Conclusions: This study demonstrates that upper limb sensorimotor deficits following BPI affect body balance, serving as a warning for the clinical community about the need to prevent and treat the secondary outcomes of this condition.

Is the Frequency in Somatosensory Electrical Stimulation the Key Parameter in Modulating the Corticospinal Excitability of Healthy Volunteers and Stroke Patients with Spasticity?

Marco A. C. Garcia, João M. Y. Catunda, Marcio N. de Souza, Ana Paula Fontana, Sandro Sperandei, Claudia D. Vargas

Somatosensory electrical stimulation (SES) has been proposed as an approach to treat patients with sensory-motor impairment such as spasticity. However, there is still no consensus regarding which would be the adequate SES parameters to treat those deficits. Therefore, the aim of this study was to evaluate the effects of applying SES over the forearm muscles at four different frequencies of stimulation (3, 30, 150, and 300 Hz) and in two intervals of time (5′ and 30′) by means of transcranial magnetic stimulation and Hoffmann’s reflex (H-reflex) in healthy volunteers (Experiments  I and II). A group of stroke patients (Experiment  III) was also preliminary evaluated to ascertain SES effects at a low frequency (3 Hz) applied for 30′ over the forearm spastic flexors muscles by measuring the wrist joint passive torque. Motor evoked potentials and the H-reflex were collected from different forearm and hand muscles immediately before and after SES and up to 5′ (Experiment  I) and 10′ (Experiments  I and II) later. None of the investigated frequencies of SES was able to operate as a key in switching modulatory effects in the central nervous system of healthy volunteers and stroke patients with spasticity.

Bootstrap testing for cross-correlation under low firing activity

Aldana M. González-Montoro, Ricardo Cao, Nelson Espinosa, Javier Cudeiro, Jorge Mariño

A new cross-correlation synchrony index for neural activity is proposed. The index is based on the integration of the kernel estimation of the cross-correlation function. It is used to test for the dynamic synchronization levels of spontaneous neural activity under two induced brain states: sleep-like and awake-like. Two bootstrap resampling plans are proposed to approximate the distribution of the test statistics. The results of the first bootstrap method indicate that it is useful to discern significant differences in the synchronization dynamics of brain states characterized by a neural activity with low firing rate. The second bootstrap method is useful to unveil subtle differences in the synchronization levels of the awake-like state, depending on the activation pathway.

Bayesian Inference on the Memory Parameter for Gamma-Modulated Regression Models

Plinio Andrade, Laura Rifo, Soledad Torres, Francisco Torres-Avilés

In this work, we propose a Bayesian methodology to make inferences for the memory parameter and other characteristics under non-standard assumptions for a class of stochastic processes. This class generalizes the Gamma-modulated process, with trajectories that exhibit long memory behavior, as well as decreasing variability as time increases. Different values of the memory parameter influence the speed of this decrease, making this heteroscedastic model very flexible. Its properties are used to implement an approximate Bayesian computation and MCMC scheme to obtain posterior estimates. We test and validate our method through simulations and real data from the big earthquake that occurred in 2010 in Chile.

Self-Organized Near-Zero-Lag Synchronization Induced by Spike-Timing Dependent Plasticity in Cortical Populations

Fernanda S. Matias, Pedro V. Carelli, Claudio R. Mirasso, Mauro Copelli.

Several cognitive tasks related to learning and memory exhibit synchronization of macroscopic cortical areas together with synaptic plasticity at neuronal level. Therefore, there is a growing effort among computational neuroscientists to understand the underlying mechanisms relating synchrony and plasticity in the brain. Here we numerically study the interplay between spike-timing dependent plasticity (STDP) and anticipated synchronization (AS). AS emerges when a dominant flux of information from one area to another is accompanied by a negative time lag (or phase). This means that the receiver region pulses before the sender does. In this paper we study the interplay between different synchronization regimes and STDP at the level of three-neuron microcircuits as well as cortical populations. We show that STDP can promote auto-organized zero-lag synchronization in unidirectionally coupled neuronal populations. We also find synchronization regimes with negative phase difference (AS) that are stable against plasticity. Finally, we show that the interplay between negative phase difference and STDP provides limited synaptic weight distribution without the need of imposing artificial boundaries.




The Research, Innovation and Dissemination Center for Neuromathematics is hosted by the University of São Paulo and funded by FAPESP (São Paulo Research Foundation).


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