Publicações

Attractive regular stochastic chains: perfect simulation and phase transition

Sandro Gallo and Daniel Y. Takahashi

We prove that uniqueness of the stationary chain, or equivalently, of the g-measure, compatible with an attractive regular probability kernel is equivalent to either one of the following two assertions for this chain: (1) it is a finitary coding of an independent and identically distributed (i.i.d.) process with countable alphabet; (2) the concentration of measure holds at exponential rate. We show in particular that if a stationary chain is uniquely defined by a kernel that is continuous and attractive, then this chain can be sampled using a coupling-from-the-past algorithm. For the original Bramson–Kalikow model we further prove that there exists a unique compatible chain if and only if the chain is a finitary coding of a finite alphabet i.i.d. process. Finally, we obtain some partial results on conditions for phase transition for general chains of infinite order.

An improved upper bound on the density of universal random graphs

Domingos Dellamonica Jr., Yoshiharu Kohayakawa, Vojtěch Rödl and Andrzej Ruciński

We give a polynomial time randomized algorithm that, on receiving as input a pair (H,G) of n-vertex graphs, searches for an embedding of H into G. If H has bounded maximum degree and G is suitably dense and pseudorandom, then the algorithm succeeds with high probability. Our algorithm proves that, for every integer d ≥ 3 and a large enough constant C = Cd, as n →∞, asymptotically almost all graphs with n vertices and at least Cn2−1/d log1/d n edges contain as subgraphs all graphs with n vertices and maximum degree at most d.

Observing Grasping Actions Directed to Emotion-Laden Objects: Effects upon Corticospinal Excitability

Anaelli A. Nogueira-Campos, Ghislain Saunier, Valeria Della-Maggiore, Laura A. S. de Oliveira, Erika C. Rodrigues and Claudia D. Vargas

The motor system is recruited whenever one executes an action as well as when one observes the same action being executed by others. Although it is well established that emotion modulates the motor system, the effect of observing other individuals acting in an emotional context is particularly elusive. The main aim of this study was to investigate the effect induced by the observation of grasping directed to emotion-laden objects upon corticospinal excitability (CSE). Participants classified video-clips depicting the right-hand of an actor grasping emotion-laden objects. Twenty video-clips differing in terms of valence but balanced in arousal level were selected. Motor evoked potentials (MEPs) were then recorded from the first dorsal interosseous using transcranial magnetic stimulation (TMS) while the participants observed the selected emotional video-clips. During the video-clip presentation, TMS pulses were randomly applied at one of two different time points of grasping: (1) maximum grip aperture, and (2) object contact time. CSE was higher during the observation of grasping directed to unpleasant objects compared to pleasant ones. These results indicate that when someone observes an action of grasping directed to emotion-laden objects, the effect of the object valence promotes a specific modulation over the motor system.

Tight Hamilton cycles in random hypergraphs

Peter Allen, Julia Böttcher, Yoshiharu Kohayakawa, Yury Person

We give an algorithmic proof for the existence of tight Hamilton cycles in a random r-uniform hypergraph with edge probability p=n^{-1+eps} for every eps>0. This partly answers a question of Dudek and Frieze [Random Structures Algorithms], who used a second moment method to show that tight Hamilton cycles exist even for p=omega(n)/n (r>2) where omega(n) tends to infinity arbitrary slowly, and for p=(e+o(1))/n (r>3). The method we develop for proving our result applies to related problems as well.

Increase in hippocampal theta oscillations during spatial decision making

Hindiael Belchior, Vítor Lopes dos Santos, Adriano B. L. Tort, Sidarta Ribeiro

The processing of spatial and mnemonic information is believed to depend on hippocampal theta oscillations (5–12 Hz). However, in rats both the power and the frequency of the theta rhythm are modulated by locomotor activity, which is a major confounding factor when estimating its cognitive correlates. Previous studies have suggested that hippocampal theta oscillations support decision-making processes. In this study, we investigated to what extent spatial decision making modulates hippocampal theta oscillations when controlling for variations in locomotion speed. We recorded local field potentials from the CA1 region of rats while animals had to choose one arm to enter for reward (goal) in a four-arm radial maze. We observed prominent theta oscillations during the decision-making period of the task, which occurred in the center of the maze before animals deliberately ran through an arm toward goal location. In speed-controlled analyses, theta power and frequency were higher during the decision period when compared to either an intertrial delay period (also at the maze center), or to the period of running toward goal location. In addition, theta activity was higher during decision periods preceding correct choices than during decision periods preceding incorrect choices. Altogether, our data support a cognitive function for the hippocampal theta rhythm in spatial decision making.

Stochastic Induction of Long-Term Potentiation and Long-Term Depression

G. Antunes, A. C. Roque & F. M. Simoes-de-Souza

Long-term depression (LTD) and long-term potentiation (LTP) of granule-Purkinje cell synapses are persistent synaptic alterations induced by high and low rises of the intracellular calcium ion concentration ([Ca2+]), respectively. The occurrence of LTD involves the activation of a positive feedback loop formed by protein kinase C, phospholipase A2, and the extracellular signal-regulated protein kinase pathway, and its expression comprises the reduction of the population of synaptic AMPA receptors. Recently, a stochastic computational model of these signalling processes demonstrated that, in single synapses, LTD is probabilistic and bistable. Here, we expanded this model to simulate LTP, which requires protein phosphatases and the increase in the population of synaptic AMPA receptors. Our results indicated that, in single synapses, while LTD is bistable, LTP is gradual. Ca2+ induced both processes stochastically. The magnitudes of the Ca2+ signals and the states of the signalling network regulated the likelihood of LTP and LTD and defined dynamic macroscopic Ca2+ thresholds for the synaptic modifications in populations of synapses according to an inverse Bienenstock, Cooper and Munro (BCM) rule or a sigmoidal function. In conclusion, our model presents a unifying mechanism that explains the macroscopic properties of LTP and LTD from their dynamics in single synapses.

A stochastic version of the Potjans-Diesmann cortical column model

Vinicius L. Cordeiro, Renan O. Shimoura, Nilton L. Kamiji, Osame Kinouchi and Antonio C. Roque

Experimental evidence suggests that neurons and neural circuits display stochastic variability [1] and, therefore, it is important to have neural models that capture this stochasticity. There are basically two types of noise model for a neuron [2]: (1) spike generation is modeled deterministically and noise enters the dynamics via additional stochastic terms; or (2) spike generation is directly modeled as a stochastic process. Recently, Galves and Löcherbach [3] introduced a neural model of the latter type in which the firing of a neuron at a given time t is a random event with probability given by a monotonically increasing function of its membrane potential V. The model of Galves and Löcherbach (GL) has as one of its components a graph of interactions between neurons. In this work we consider that this graph has the structure of the Potjans and Diesmann network model of a cortical column [4]. The model of Potjans and Diesmann has four layers and two neuron types, excitatory and inhibitory, so that there are eight cell populations. The population-specific neuron densities and connectivity are taken from comprehensive anatomical and electrophysiological studies [5-6], and the model has approximately 80,000 neurons and 300,000,000 synapses. We adjusted the parameters of the firing probability of the GL model to reproduce the firing behavior of regular (excitatory) and fast (inhibitory) spiking neurons [7]. Then, we replaced the leaky integrate-and-fire neurons of the original Potjans-Diesmann model by these stochastic neurons to obtain a stochastic version of the Potjans-Diesmann model. The parameters of the model are the weights we and wi of the excitatory and inhibitory synaptic weights of the GL model [3]. We studied the firing patterns of the eight cell populations of the stochastic model in the absence of external input and characterized their behavior in the two-dimensional diagram spanned by the excitatory and inhibitory synaptic weights. For a balanced case in which the network activity is asynchronous and irregular the properties of the stochastic model are similar to the properties of the original Potjans-Diesmann model. Different neural populations have different firing rates and inhibitory neurons have higher firing rates than excitatory neurons. In particular, the stochastic model emulates the very low firing rates of layer 2/3 observed in the original model and also experimentally [4]. We also submitted the network to random input spikes applied to layers 4 and 6 to mimic thalamic inputs, as done by Potjans and Diesmann [4], and studied the propagation of activity across layers. In conclusion, the stochastic version of the Potjans-Diesmann model can be a useful replacement for the original Potjans-Diesmann model in studies that require a comparison between stochastic and deterministic models.

A Review of Guidelines and Models for Representation of Provenance Information from Neuroscience Experiments

Margarita Ruiz-Olazar, Evandro S. Rocha, Sueli S. Rabaça, Carlos Eduardo Ribas, Amanda S. Nascimento, Kelly R. Braghetto

To manage raw data from Neuroscience experiments we have to cope with the heterogeneity of data formats and the complexity of additional metadata, such as its provenance information, that need to be collected and stored. Although some progress has already been made toward the elaboration of a common description for Neuroscience experimental data, to the best of our knowledge, there is still no widely adopted standard model to describe this kind of data. In order to foster neurocientists to find and to use a structured and comprehensive model with a robust tracking of data provenance, we present a brief evaluation of guidelines and models for representation of raw data from Neuroscience experiments, focusing on how they support provenance tracking.

Motor planning of goal-directed action is tuned by the emotional valence of the stimulus: a kinematic study

P. O. Esteves, L. A. S. Oliveira, A. A. Nogueira-Campos, G. Saunier, T. Pozzo, J. M. Oliveira, E. C. Rodrigues, E. Volchan & C. D. Vargas

The basic underpinnings of homeostatic behavior include interacting with positive items and avoiding negative ones. As the planning aspects of goal-directed actions can be inferred from their movement features, we investigated the kinematics of interacting with emotion-laden stimuli. Participants were instructed to grasp emotion-laden stimuli and bring them toward their bodies while the kinematics of their wrist movement was measured. The results showed that the time to peak velocity increased for bringing pleasant stimuli towards the body compared to unpleasant and neutral ones, suggesting higher easiness in undertaking the task with pleasant stimuli. Furthermore, bringing unpleasant stimuli towards the body increased movement time in comparison with both pleasant and neutral ones while the time to peak velocity for unpleasant stimuli was the same as for that of neutral stimuli. There was no change in the trajectory length among emotional categories. We conclude that during the “reach-to-grasp” and “bring-to-the-body” movements, the valence of the stimuli affects the temporal but not the spatial kinematic features of motion. To the best of our knowledge, we show for the first time that the kinematic features of a goal-directed action are tuned by the emotional valence of the stimuli.

The lower tail of random quadratic forms, with applications to ordinary least squares and restricted eigenvalue properties

Roberto Imbuzeiro Oliveira

Finite sample properties of random covariance-type matrices have been the subject of much research. In this paper we focus on the "lower tail" of such a matrix, and prove that it is subgaussian under a simple fourth moment assumption on the one-dimensional marginals of the random vectors. A similar result holds for more general sums of random positive semidefinite matrices, and the (relatively simple) proof uses a variant of the so-called PAC-Bayesian method for bounding empirical processes.
We give two applications of the main result. In the first one we obtain a new finite-sample bound for ordinary least squares estimator in linear regression with random design. Our result is model-free, requires fairly weak moment assumptions and is almost optimal. Our second application is to bounding restricted eigenvalue constants of certain random ensembles with "heavy tails". These constants are important in the analysis of problems in Compressed Sensing and High Dimensional Statistics, where one recovers a sparse vector from a small umber of linear measurements. Our result implies that heavy tails still allow for the fast recovery rates found in efficient methods such as the LASSO and the Dantzig selector. Along the way we strengthen, with a fairly short argument, a recent result of Rudelson and Zhou on the restricted eigenvalue property.

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O Centro de Pesquisa, Inovação e Difusão em Neuromatemática está sediado na Universidade de São Paulo e é financiado pela FAPESP (Fundação de Amparo à Pesquisa do Estado de São Paulo).

 

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