Undersampled Critical Branching Processes on Small-World and Random Networks Fail to Reproduce the Statistics of Spike Avalanches

The power-law size distributions obtained experimentally for neuronal avalanches are an important evidence of criticality in the brain. This evidence is supported by the fact that a critical branching process exhibits the same exponent t~3=2. Models at criticality have been employed to mimic avalanche propagation and explain the statistics observed experimentally. However, a crucial aspect of neuronal recordings has been almost completely neglected in the models: undersampling. While in a typical multielectrode array hundreds of neurons are recorded, in the same area of neuronal tissue tens of thousands of neurons can be found. Here we investigate the consequences of undersampling in models with three different topologies (two-dimensional, small-world and random network) and three different dynamical regimes (subcritical, critical and supercritical). We found that undersampling modifies avalanche size distributions, extinguishing the power laws observed in critical systems. Distributions from subcritical systems are also modified, but the shape of the undersampled distributions is more similar to that of a fully sampled system. Undersampled supercritical systems can recover the general characteristics of the fully sampled version, provided that enough neurons are measured. Undersampling in two-dimensional and small-world networks leads to similar effects, while the random network is insensitive to sampling density due to the lack of a well-defined neighborhood. We conjecture that neuronal avalanches recorded from local field potentials avoid undersampling effects due to the nature of this signal, but the same does not hold for spike avalanches. We conclude that undersampled branching-process-like models in these topologies fail to reproduce the statistics of spike avalanches.

Undersampled Critical Branching Processes on Small-World and Random Networks Fail to Reproduce the Statistics of Spike Avalanches

The power-law size distributions obtained experimentally for neuronal avalanches are an important evidence of criticality in the brain. This evidence is supported by the fact that a critical branching process exhibits the same exponent t~3=2. Models at criticality have been employed to mimic avalanche propagation and explain the statistics observed experimentally. However, a crucial aspect of neuronal recordings has been almost completely neglected in the models: undersampling. While in a typical multielectrode array hundreds of neurons are recorded, in the same area of neuronal tissue tens of thousands of neurons can be found. Here we investigate the consequences of undersampling in models with three different topologies (two-dimensional, small-world and random network) and three different dynamical regimes (subcritical, critical and supercritical). We found that undersampling modifies avalanche size distributions, extinguishing the power laws observed in critical systems. Distributions from subcritical systems are also modified, but the shape of the undersampled distributions is more similar to that of a fully sampled system. Undersampled supercritical systems can recover the general characteristics of the fully sampled version, provided that enough neurons are measured. Undersampling in two-dimensional and small-world networks leads to similar effects, while the random network is insensitive to sampling density due to the lack of a well-defined neighborhood. We conjecture that neuronal avalanches recorded from local field potentials avoid undersampling effects due to the nature of this signal, but the same does not hold for spike avalanches. We conclude that undersampled branching-process-like models in these topologies fail to reproduce the statistics of spike avalanches.

Controle adaptativo por modelo de referencia e estrutura variável discreto no tempo

With the technology progess, embedded systems using adaptive techniques are being used frequently. One of these techniques is the Variable Structure Model- Reference Adaptive Control (VS-MRAC). The implementation of this technique in embedded systems, requires consideration of a sampling period which if not taken into consideration, can adversely affect system performance and even takes the system to instability. This work proposes a stability analysis of a discrete-time VS-MRAC accomplished for SISO linear time-invariant plants with relative degree one. The aim is to analyse the in uence of the sampling period in the system performance and the relation of this period with the chattering and system instability

Modelo de risco controlado por resseguro e desigualdades para a probabilidade de ruína

In the work reported here we present theoretical and numerical results about a Risk Model with Interest Rate and Proportional Reinsurance based on the article Inequalities for the ruin probability in a controlled discrete-time risk process by Ros ario Romera and Maikol Diasparra (see [5]). Recursive and integral equations as well as upper bounds for the Ruin Probability are given considering three di erent approaches, namely, classical Lundberg inequality, Inductive approach and Martingale approach. Density estimation techniques (non-parametrics) are used to derive upper bounds for the Ruin Probability and the algorithms used in the simulation are presented

Explorando a execução de técnicas estendidas no oboé encontradas em quatro peças contemporâneas

This dissertation presents an investigation of the evolutionary process of extended oboe techniques, through literary analysis and practical research. The objective of this work is to provide assistance to oboists interested in learning these techniques. Additionally, this work encourages the student, through the process of experimentation, to explore the questions that may arise around the aesthetics of sound, the concept of gesture as an additional visual and aural element in music, and the collaboration and “real-time” creation processes. Discussed within the work, are the relationship between the instrument (the oboe) and extended techniques, and two possible definitions of extended techniques, provided by Luk Vaes (2009) and Gardner Read (1993). Also explored are the how and why some composers have utilized extended techniques in their compositions, including brief discussions relating to extended techniques in real-time composition (improvisation), extended techniques and technological resources, theatrical gesture as an extended technique, and suggestions of how musicians might approach theatrical gestures in performance. Four works were visited: “I Know This Room So Well” – Lisa Bielawa (2007-9); “Four Pieces for Oboe and Piano” – Ernst Krenek (1966); “In Freundschaft” – Karlheinz Stockhausen (1978); “Atem” – Mauricio Kagel (1969-70); and an exploration of the difficulties and solutions associated with each extended technique found within these pieces, was carried out. The following founding works on extended oboe techniques were used, as a basis for research: books - Heinz Holliger’s Pro Musica Nova (1972); Gardner Read’s Compendium of Modern Instrumental Techniques (1993); Peter Veale & Claus-Steffen Mahnkopf’s The Techniques of Oboe Playing (1994); and Libby Van Cleve’s Oboe Unbound: Contemporary Techniques (2004); and articles - Nora Post’s “Monophonic sound resources for the oboe: Part I – Timbre” (1984), “Part II- Pitch and other techniques” (1984), and “Multiphonics for the oboe” (1982).

Um controlador dual subótimo com fator de peso variável no tempo

This work concerns a refinement of a suboptimal dual controller for discrete time systems with stochastic parameters. The dual property means that the control signal is chosen so that estimation of the model parameters and regulation of the output signals are optimally balanced. The control signal is computed in such a way so as to minimize the variance of output around a reference value one step further, with the addition of terms in the loss function. The idea is add simple terms depending on the covariance matrix of the parameter estimates two steps ahead. An algorithm is used for the adaptive adjustment of the adjustable parameter lambda, for each step of the way. The actual performance of the proposed controller is evaluated through a Monte Carlo simulations method.