Continuity properties of a factor of Markov chains

Walter A. F. de Carvalho, Sandro Gallo and Nancy L. Garcia

Starting from a Markov chain with a finite or a countable infinite alphabet, we consider the chain obtained when all but one symbol are indistinguishable for the practitioner. We study conditions on the transition matrix of the Markov chain ensuring that the image chain has continuous or discontinuous transition probabilities with respect to the past.

Stochastic Ising model with plastic interactions

Eugene Pechersky, Guillem Via and Anatoly Yambartsev

We propose a new model based on the Ising model with the aim to study synaptic plasticity phenomena in neural networks. It is today well established in biology that the synapses or connections between certain types of neurons are strengthened when the neurons are co-active, a form of the so called synaptic plasticity. Such mechanism is believed to mediate the formation and maintenance of memories. The proposed model describes some features from that phenomenon. Together with the spin-flip dynamics, in our model the coupling constants are also subject to stochastic dynamics, so that they interact with each other. The evolution of the system is described by a continuous-time Markov jump process.

Phase transitions and self-organized criticality in networks of stochastic spiking neurons

Ludmila Brochini, Ariadne de Andrade Costa, Miguel Abadi, Antônio C. Roque, Jorge Stolfi and Osame Kinouchi

Phase transitions and critical behavior are crucial issues both in theoretical and experimental neuroscience. We report analytic and computational results about phase transitions and self-organized criticality (SOC) in networks with general stochastic neurons. The stochastic neuron has a firing probability given by a smooth monotonic function Φ(V) of the membrane potential V, rather than a sharp firing threshold. We find that such networks can operate in several dynamic regimes (phases) depending on the average synaptic weight and the shape of the firing function Φ. In particular, we encounter both continuous and discontinuous phase transitions to absorbing states. At the continuous transition critical boundary, neuronal avalanches occur whose distributions of size and duration are given by power laws, as observed in biological neural networks. We also propose and test a new mechanism to produce SOC: the use of dynamic neuronal gains – a form of short-term plasticity probably located at the axon initial segment (AIS) – instead of depressing synapses at the dendrites (as previously studied in the literature). The new self-organization mechanism produces a slightly supercritical state, that we called SOSC, in accord to some intuitions of Alan Turing.

Motor Coordination Correlates with Academic Achievement and Cognitive Function in Children

Valter R. Fernandes, Michelle L. Scipião Ribeiro, Thais Melo, Paulo de Tarso Maciel-Pinheiro, Thiago T. Guimarães, Narahyana B. Araújo, Sidarta Ribeiro and Andréa C. Deslandes

The relationship between exercise and cognition is an important topic of research that only recently began to unravel. Here, we set out to investigate the relation between motor skills, cognitive function, and school performance in 45 students from 8 to 14 years of age. We used a cross-sectional design to evaluate motor coordination (Touch Test Disc), agility (Shuttle Run Speed—running back and forth), school performance (Academic Achievement Test), the Stroop test, and six sub-tests of the Wechsler Intelligence Scale for Children-IV (WISC-IV). We found, that the Touch Test Disc was the best predictor of school performance (R2 = 0.20). Significant correlations were also observed between motor coordination and several indices of cognitive function, such as the total score of the Academic Achievement Test (AAT; Spearman's rho = 0.536; p ≤ 0.001), as well as two WISC-IV sub-tests: block design (R = −0.438; p = 0.003) and cancelation (rho = −0.471; p = 0.001). All the other cognitive variables pointed in the same direction, and even correlated with agility, but did not reach statistical significance. Altogether, the data indicate that visual motor coordination and visual selective attention, but not agility, may influence academic achievement and cognitive function. The results highlight the importance of investigating the correlation between physical skills and different aspects of cognition.

Psychosis and the Control of Lucid Dreaming

Natália B. Mota, Adara Resende, Sérgio A. Mota-Rolim, Mauro Copelli and Sidarta Ribeiro

Dreaming and psychosis share important features, such as intrinsic sense perceptions independent of external stimulation, and a general lack of criticism that is associated with reduced frontal cerebral activity. Awareness of dreaming while a dream is happening defines lucid dreaming (LD), a state in which the prefrontal cortex is more active than during regular dreaming. For this reason, LD has been proposed to be potentially therapeutic for psychotic patients. According to this view, psychotic patients would be expected to report LD less frequently, and with lower control ability, than healthy subjects. Furthermore, psychotic patients able to experience LD should present milder psychiatric symptoms, in comparison with psychotic patients unable to experience LD. To test these hypotheses, we investigated LD features (occurrence, control abilities, frequency, and affective valence) and psychiatric symptoms (measure by PANSS, BPRS, and automated speech analysis) in 45 subjects with psychotic symptoms [25 with Schizophrenia (S) and 20 with Bipolar Disorder (B) diagnosis] versus 28 non-psychotic control (C) subjects. Psychotic lucid dreamers reported control of their dreams more frequently (67% of S and 73% of B) than non-psychotic lucid dreamers (only 23% of C; S > C with p = 0.0283, B > C with p = 0.0150). Importantly, there was no clinical advantage for lucid dreamers among psychotic patients, even for the diagnostic question specifically related to lack of judgment and insight. Despite some limitations (e.g., transversal design, large variation of medications), these preliminary results support the notion that LD is associated with psychosis, but falsify the hypotheses that we set out to test. A possible explanation is that psychosis enhances the experience of internal reality in detriment of external reality, and therefore lucid dreamers with psychotic symptoms would be more able to control their internal reality than non-psychotic lucid dreamers. Training dream lucidity is likely to produce safe psychological strengthening in a non-psychotic population, but in a psychotic population LD practice may further empower deliria and hallucinations, giving internal reality the appearance of external reality.

Retrieving a context tree from EEG data

A. Duarte, R. Fraiman, A. Galves, G. Ost, C. Vargas

It has been repeatedly conjectured that the brain retrieves statistical regularities from stimuli, so that their structural features are separated from noise. Here we present a new statistical approach allowing to address this conjecture. This approach is based on a new class of stochastic processes driven by context tree models. Also, it associates to a new experimental protocol in which structured auditory sequences are presented to volunteers while electroencephalographic signals are recorded from their scalp. A statistical model selection procedure for functional data is presented to analyze the electrophysiological signals. This procedure is proved to be consistent. Applied to samples of electrophysiological trajectories collected during structured auditory stimuli presentation, it produces results supporting the conjecture that the brain effectively identifies the context tree characterizing the source.

Computational Tracking of Mental Health in Youth

Mota N., Copelli M., Ribeiro S.

The early onset of mental disorders can lead to serious cognitive damage, and timely interventions are needed in order to prevent them. In patients of low socioeconomic status, as is common in Latin America, it can be hard to identify children at risk. Here, we briefly introduce the problem by reviewing the scarce epidemiological data from Latin America regarding the onset of mental disorders, and discussing the difficulties associated with early diagnosis. Then we present computational psychiatry, a new field to which we and other Latin American researchers have contributed methods particularly relevant for the quantitative investigation of psychopathologies manifested during childhood. We focus on new technologies that help to identify mental disease and provide prodromal evaluation, so as to promote early differential diagnosis and intervention. To conclude, we discuss the application of these methods to clinical and educational practice. A comprehensive and quantitative characterization of verbal behavior in children, from hospitals and laboratories to homes and schools, may lead to more effective pedagogical and medical intervention.

Machine Learning Algorithms for Automatic Classification of Marmoset Vocalizations

Hjalmar K. Turesson, Sidarta Ribeiro, Danillo R. Pereira, João P. Papa, Victor Hugo C. de Albuquerque

Automatic classification of vocalization type could potentially become a useful tool for acoustic the monitoring of captive colonies of highly vocal primates. However, for classification to be useful in practice, a reliable algorithm that can be successfully trained on small datasets is necessary. In this work, we consider seven different classification algorithms with the goal of finding a robust classifier that can be successfully trained on small datasets. We found good classification performance (accuracy > 0.83 and F1-score > 0.84) using the Optimum Path Forest classifier. Dataset and algorithms are made publicly available.

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.




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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