Dynamic uniqueness for stochastic chains with unbounded memory

Christophe Gallesco, Sandro Gallo and Daniel Y. Takahashi

We say that a probability kernel exhibits dynamic uniqueness (DU) if all the stochastic chains starting from a fixed past coincide on the future tail σ-algebra. Our first theorem is a set of properties that are pairwise equivalent to DU which allow us to understand how it compares to other more classical concepts. In particular, we prove that DU is equivalent to a weak-ℓ2 summability condition on the kernel. As a corollary to this theorem, we prove that the Bramson–Kalikow and the long-range Ising models both exhibit DU if and only if their kernels are ℓ2 summable. Finally, if we weaken the condition for DU, asking for coincidence on the future σ-algebra for almost every pair of pasts, we obtain a condition that is equivalent to β-mixing (weak-Bernoullicity) of the compatible stationary chain. As a consequence, we show that a modification of the weak-ℓ2 summability condition on the kernel is equivalent to the β-mixing of the compatible stationary chain.

Post-class naps boost declarative learning in a naturalistic school setting

Thiago Cabral, Natália B. Mota, Lucia Fraga, Mauro Copelli, Mark A. McDaniel and Sidarta Ribeiro

Laboratory evidence of a positive effect of sleep on declarative memory consolidation suggests that naps can be used to boost school learning in a scalable, low-cost manner. The few direct investigations of this hypothesis have so far upheld it, but departed from the naturalistic setting by testing non-curricular contents presented by experimenters instead of teachers. Furthermore, nap and non-nap groups were composed of different children. Here we assessed the effect of post-class naps on the retention of Science and History curricular contents presented by the regular class teacher to 24 students from 5th grade. Retention was repeatedly measured 3–4 days after content learning, with weekly group randomization over 6 consecutive weeks. Contents followed by long naps (>30 min), but not short naps (

Can the Recording of Motor Potentials Evoked by Transcranial Magnetic Stimulation Be Optimized?

Marco A. C. Garcia, Victor H. Souza and Claudia D. Vargas

Transcranial magnetic stimulation (TMS) combined with surface electromyography (sEMG) has been for a long time an important non-invasive tool to investigate and better understand how brain controls the skeletal muscles. However, the present literature still lacks standardization protocols and comprehensive discussions about possible influences of sEMG electrode placement and montages on TMS evoked responses. With the advent of TMS by Barker et al. (1985), several advances have been made in basic and clinical neurophysiology (Rossini et al., 2015). In TMS, a high-intensity brief magnetic pulse applied with a coil over the subject's scalp, induces an electric field across the cortical tissue that depolarizes a group of neuronal pools. Therefore, if a single pulse is applied over a particular spot of the primary motor cortex (M1), the generated action potentials travel down the corticospinal tract reaching a specific muscle or group of muscles, which in turn can be achieved by recording their myoelectric activities. Such myoelectric activity may contain potentials varying from a few micro to millivolts and are recognized as motor evoked potentials (MEPs). MEPs can be recorded by means of sEMG with different electrode types, e.g. surface or indwelling, and montages, e.g. mono and bipolar. Most TMS applications take advantage of MEP amplitude and latency to evaluate the integrity and/or excitability of the motor corticospinal pathway to study normal and abnormal aspects of neurophysiology, including the pathophysiology of many neurological and motor disorders. Some may believe that differences in electrode arrangement for recording MEPs can offer a small impact in data quality; in this case he/she may be a victim of an ordinary pitfall. Thus, we may ask and discuss along this manuscript, what are the disadvantages and advantages of recording MEPs from different surface electrode montages? Do they provide a robust and similar comprehension of motor corticospinal excitability?

Effect of TMS coil orientation on the spatial distribution of motor evoked potentials in an intrinsic hand muscle

Souza VH, Vieira TM, Peres ASC, Garcia MAC, Vargas CD, Baffa O

Previous reports on the relationship between coil orientation and amplitude of motor evoked potential (MEP) in transcranial magnetic stimulation (TMS) did not consider the effect of electrode arrangement. Here we explore this open issue by investigating whether TMS coil orientation affects the amplitude distribution of MEPs recorded from the abductor pollicis brevis (APB) muscle with a bi-dimensional grid of 61 electrodes. Moreover, we test whether conventional mono- and bipolar montages provide representative MEPs compared to those from the grid of electrodes. Our results show that MEPs with the greatest amplitudes were elicited for 45° and 90° coil orientations, i.e. perpendicular to the central sulcus, for all electrode montages. Stimulation with the coil oriented at 135° and 315°, i.e. parallel to the central sulcus, elicited the smallest MEP amplitudes. Additionally, changes in coil orientation did not affect the spatial distribution of MEPs over the muscle extent. It has been shown that conventional electrodes with detection volume encompassing the APB belly may detect representative MEPs for optimal coil orientations. In turn, non-optimal orientations were identified only with the grid of electrodes. High-density electromyography may therefore provide new insights into the effect of coil orientation on MEPs from the APB muscle.

Reduced functional connectivity within the primary motor cortex of patients with brachial plexus injury

D. Fraiman, M. F. Miranda, F. Erthal, P. F. Buur, M. Elschot, L. Souza, S. A. R. B. Rombouts, C. A. Schimmelpenninck, D. G. Norris, M. J. A. Malessy, A. Galves and C. D. Vargas

This study aims at the effects of traumatic brachial plexus lesion with root avulsions (BPA) upon the organization of the primary motor cortex (M1). Nine right-handed patients with a right BPA in whom an intercostal to musculocutaneous (ICN-MC) nerve transfer was performed had post-operative resting state fMRI scanning. The analysis of empirical functional correlations between neighboring voxels revealed faster correlation decay as a function of distance in the M1 region corresponding to the arm in BPA patients as compared to the control group. No differences between the two groups were found in the face area. We also investigated whether such larger decay in patients could be attributed to a gray matter diminution in M1. Structural imaging analysis showed no difference in gray matter density between groups. Our findings suggest that the faster decay in neighboring functional correlations without significant gray matter diminution in BPA patients could be related to a reduced activity in intrinsic horizontal connections in M1 responsible for upper limb motor synergies.

D2 dopamine receptor regulation of learning, sleep and plasticity

A.S.C. França, B. Lobão-Soares, L. Muratori, G. Nascimento, J. Winne, C.M. Pereira, S.M.B. Jeronimo and S. Ribeiro

Dopamine and sleep have been independently linked with hippocampus-dependent learning. Since D2 dopaminergic transmission is required for the occurrence of rapid-eye-movement (REM) sleep, it is possible that dopamine affects learning by way of changes in post-acquisition REM sleep. To investigate this hypothesis, we first assessed whether D2 dopaminergic modulation in mice affects novel object preference, a hippocampus-dependent task. Animals trained in the dark period, when sleep is reduced, did not improve significantly in performance when tested 24 h after training. In contrast, animals trained in the sleep-rich light period showed significant learning after 24 h. When injected with the D2 inverse agonist haloperidol immediately after the exploration of novel objects, animals trained in the light period showed reduced novelty preference upon retesting 24 h later. Next we investigated whether haloperidol affected the protein levels of plasticity factors shown to be up-regulated in an experience-dependent manner during REM sleep. Haloperidol decreased post-exploration hippocampal protein levels at 3 h, 6 h and 12 h for phosphorylated Ca2+/calmodulin-dependent protein kinase II, at 6 h for Zif-268; and at 12 h for the brain-derived neurotrophic factor. Electrophysiological and kinematic recordings showed a significant decrease in the amount of REM sleep following haloperidol injection, while slow-wave sleep remained unaltered. Importantly, REM sleep decrease across animals was strongly correlated with deficits in novelty preference (Rho=0.56, p=0.012). Altogether, the results suggest that the dopaminergic regulation of REM sleep affects learning by modulating post-training levels of calcium-dependent plasticity factors.

The Shortest Possible Return Time of β-Mixing Processes

Miguel Abadi; Sandro Gallo and Erika Alejandra Rada-Mora

We consider a stochastic process and a givenn-string. We study the shortestpossiblereturn time (or shortest return path) of the string over all the realizations of process starting from this string. For aβ-mixing process having complete grammar, and for each sizenof the strings, we approximate the distribution of this short return (properly re-scaled) by a non-degenerated distribution. Under mild conditions on theβcoefficients, we prove the existence of the limit of this distribution to a non-degenerated distribution. We also prove that ergodicity is not enough to guaranty this convergence. Finally, we present a connection between the shortest return and the Shannon entropy, showing that maximum of the re-scaled variables grow as the matching function of Wyner and Ziv.

Dynamics of spontaneous activity in random networks with multiple neuron subtypes and synaptic noise: Spontaneous activity in networks with synaptic noise.

Pena RFO, Zaks MA and Roque AC.

Spontaneous cortical population activity exhibits a multitude of oscillatory patterns, which often display synchrony during slow-wave sleep or under certain anesthetics and stay asynchronous during quiet wakefulness. The mechanisms behind these cortical states and transitions among them are not completely understood. Here we study spontaneous population activity patterns in random networks of spiking neurons of mixed types modeled by Izhikevich equations. Neurons are coupled by conductance-based synapses subject to synaptic noise. We localize the population activity patterns on the parameter diagram spanned by the relative inhibitory synaptic strength and the magnitude of synaptic noise. In absence of noise, networks display transient activity patterns, either oscillatory or at constant level. The effect of noise is to turn transient patterns into persistent ones: for weak noise, all activity patterns are asynchronous non-oscillatory independently of synaptic strengths; for stronger noise, patterns have oscillatory and synchrony characteristics that depend on the relative inhibitory synaptic strength. In the region of parameter space where inhibitory synaptic strength exceeds the excitatory synaptic strength and for moderate noise magnitudes networks feature intermittent switches between oscillatory and quiescent states with characteristics similar to those of synchronous and asynchronous cortical states, respectively. We explain these oscillatory and quiescent patterns by combining a phenomenological global description of the network state with local descriptions of individual neurons in their partial phase spaces. Our results point to a bridge from events at the molecular scale of synapses to the cellular scale of individual neurons to the collective scale of neuronal populations.

Physiology and assessment as low-hanging fruit for education overhaul

Sidarta Ribeiro, Natália Bezerra Mota, Valter da Rocha Fernandes, Andrea Camaz Deslandes, Guilherme Brockington and Mauro Copelli

Physiology and assessment constitute major bottlenecks of school learning among students with low socioeconomic status. The limited resources and household overcrowding typical of poverty produce deficits in nutrition, sleep, and exercise that strongly hinder physiology and hence learning. Likewise, overcrowded classrooms hamper the assessment of individual learning with enough temporal resolution to make individual interventions effective. Computational measurements of learning offer hope for low-cost, fast, scalable, and yet personalized academic evaluation. Improvement of school schedules by reducing lecture time in favor of naps, exercise, meals, and frequent automated assessments of individual performance is an easily achievable goal for education.

Discrepancy and eigenvalues of Cayley graphs

Yoshiharu Kohayakawa, Vojtěch Röd and Mathias Schacht

We consider quasirandom properties for Cayley graphs of finite abelian groups. We show that having uniform edge-distribution (i.e., small discrepancy) and having large eigenvalue gap are equivalent properties for such Cayley graphs, even if they are sparse. This affirmatively answers a question of Chung and Graham (2002) for the particular case of Cayley graphs of abelian groups, while in general the answer is negative.




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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