Fluctuations for Spatially Extended Hawkes Processes

Julien Chevallier and Guilherme Ost
In a previous paper, it has been shown that the mean-field limit of spatially extended Hawkes processes is characterized as the unique solution u(t,x) of a neural field equation (NFE). The value u(t,x) represents the membrane potential at time t of a typical neuron located in position x, embedded in an infinite network of neurons. In the present paper, we complement this result by studying the fluctuations of such a stochastic system around its mean field limit u(t,x). Our first main result is a central limit theorem stating that the spatial distribution associated to these fluctuations converges to the unique solution of some stochastic differential equation driven by a Gaussian noise. In our second main result we show that the solutions of this stochastic differential equation can be well approximated by a stochastic version of the neural field equation satisfied by u(t,x). To the best of our knowledge, this result appears to be new in the literature.

Unilateral Brachial Plexus Lesion Impairs Bilateral Touch Threshold

Bia Lima Ramalho, Maria Luíza Rangel, Ana Carolina Schmaedeke, Fátima Smith Erthal and Claudia D. Vargas

Unilateral brachial plexus injury (BPI) impairs sensory and motor functions of the upper limb. This study aimed to map in detail brachial plexus sensory impairment both in the injured and the uninjured upper limb. Touch sensation was measured through Semmes-Weinstein monofilaments at the autonomous regions of the brachial plexus nerves, hereafter called points of exclusive innervation (PEIs). Seventeen BPI patients (31.35 years±6.9 SD) and 14 age-matched healthy controls (27.57 years±5.8 SD) were tested bilaterally at six selected PEIs (axillary, musculocutaneous, median, radial, ulnar, and medial antebrachial cutaneous [MABC]). As expected, the comparison between the control group and the brachial plexus patients' injured limb showed a robust difference for all PEIs (p ≤ 0.001).

Mean field limits for nonlinear spatially extended Hawkes processes with exponential memory kernels

J. Chevallier, A. Duarte, E. Löcherbach and G. Ost

We consider spatially extended systems of interacting nonlinear Hawkes processes modeling large systems of neurons placed in and study the associated mean field limits. As the total number of neurons tends to infinity, we prove that the evolution of a typical neuron, attached to a given spatial position, can be described by a nonlinear limit differential equation driven by a Poisson random measure. The limit process is described by a neural field equation. As a consequence, we provide a rigorous derivation of the neural field equation based on a thorough mean field analysis.

A Negative Slope Conductance of the Persistent Sodium Current Prolongs Subthreshold Depolarizations

Ceballos C. C., Roque A. C. and Leão R. M.

Neuronal subthreshold voltage-dependent currents determine membrane properties such as the input resistance (Rin) and the membrane time constant (τm) in the subthreshold range. In contrast with classical cable theory predictions, the persistent sodium current (INaP), a non-inactivating mode of the voltage-dependent sodium current, paradoxically increases Rin and τm when activated. Furthermore, this current amplifies and prolongs synaptic currents in the subthreshold range. Here, using a computational neuronal model, we showed that the creation of a region of negative slope conductance by INaP activation is responsible for these effects and the ability of the negative slope conductance to amplify and prolong Rin and τm relies on the fast activation of INaP. Using dynamic clamp in hippocampal CA1 pyramidal neurons in brain slices, we showed that the effects of INaP on Rin and τm can be recovered by applying an artificial INaP after blocking endogenous INaP with tetrodotoxin. Furthermore, we showed that injection of a pure negative conductance is enough to reproduce the effects of INaP on Rin and τm and is also able to prolong artificial excitatory post synaptic currents. Since both the negative slope conductance and the almost instantaneous activation are critical for producing these effects, the INaP is an ideal current for boosting the amplitude and duration of excitatory post synaptic currents near the action potential threshold.

The whole paper is available here.

Verbal Short‐Term Memory Underlies Typical Development of “Thought Organization” Measured as Speech Connectedness

Natália B. Mota, Renata Callipo, Lígia Leite, Ana R. Torres, Janaína Weissheimer, Silvia A. Bunge, Mauro Copelli and Sidarta Ribeiro

Formal thought organization obtained from free speech, a key feature for psychiatric evaluations, has been poorly investigated during typical development. Computational tools such as speech graph connectedness (LSC) currently allow for an accurate quantification in naturalistic settings. LSC's typical development is better predicted by years of education than by age. Among beginning readers, the LSC of stories composed of short‐term memory predicted reading independently from IQ. Here we set out to test a longitudinal sample (6–8 years old, n = 45, followed for 2 years) to verify whether the LSC is predictive of various memory measures, and whether such relations can explain the correlation with reading. The LSC was specifically correlated with verbal short‐term memory performance. The results support the notion that the short‐term storage of verbal information is necessary to plan a story. Given the limited sample size, the relationship of this interaction with reading remains inconclusive.

The whole paper is available here.

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