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.

A investigação criminal e a vedação ao anonimato no sistema jurídico brasileiro

The thesis, prepared with basis on deductive reasoning (through the utilization of general concepts of the fundamental rights theory) and on inductive logic (by means of the consideration of particular situations in which the theme has been approached) deals with the criminal investigation and the prohibition of anonymity in the Brazilian law system. The state criminal investigation activity presents not only a substantial constitutional basis, due to the objective dimension of fundamental rights (which imposes an obligation to protect these essential values), but also a formal constitutional basis, arising from the administrative principles of rule of law, morality and efficiency, referred to in article 37 of the Constitution. The criminal investigation, however, is not an unlimited pursuit, being restrained by the duty to consider fundamental rights that oppose to its realization. One of the limits of the state investigation activity, in the Brazilian law system, is the prohibition of anonymity, referred to in article 5°, IV, of the Constitution. This prohibition is a direct constitutional restriction to the freedom of expression that aims to ensure the credibility of the diffusion of ideas and prevent the abusive exercise of this fundamental right, which could harm both persons and the state, with no possibility of punishment to the offending party. Generally, based on this prohibition, it is affirmed that a criminal investigation cannot begin and progress founded on anonymous communication of crimes. Informations about crimes to the investigative authorities require the correct identification of the stakeholders. Therefore, it is sustained that the prohibition of anonymity also comprehends the prohibition of utilization of pseudonyms and heteronyms. The main purpose of this essay is to recognize the limits and possibilities in starting and conducting criminal investigations based on communication of crimes made by unidentified persons, behind the veil of anonymity or hidden by pseudonyms or heteronyms. Although the prohibition of article 5°, IV, of the Constitution is not submitted to direct or indirect constitutional restrictions, this impediment can be object of mitigation in certain cases, in attention to the constitutional values that support state investigation. The pertinence analysis of the restrictions to the constitutional anonymity prohibition must consider the proportionality, integrated by the partial elements of adequacy, necessity and strict sense proportionality. The criminal investigation is a means to achieve a purpose, the protection of fundamental rights, because the disclosure of facts, through the investigatory activity, gives rise to the accomplishment of measures in order to prevent or punish the violations eventually verified. So, the start and the development of the state criminal investigation activity, based on a crime communication carried out by an unidentified person, will depend on the demonstration that the setting up and continuity of an investigation procedure, in each case, are an adequate, necessary and (in a strict sense) proportional means to the protection of fundamental rights

A responsabilização criminal no estado democrático de direito: o equilíbrio entre a efetividade e os limites da pretensão punitiva da sociedade

This paper analyzes the relationship between fundamental rights and the exercise of the claim punitive society in a democratic state. It starts with the premise that there are fundamental rights that limit and determine the validity of all forms of manifestation of the claim punitive society (legislating, investigative, adjudicative or ministerial) and there are others that require the state the right exercise, fast and effective of these activities. Travels to history in order to see that the first meaning of these rights was built between the seventeenth and eighteenth centuries, after all a history of abuses committed by state agents in the exercise of criminal justice, and positively valued in the declarations of human rights and proclaimed in the constitutions after the American and French Revolutions, while the second meaning has been assigned between the nineteenth and twentieth centuries, when, because of the serious social problems generated largely by absenteeism state, it was noted that in addition to subjective rights the individual against the state, fundamental rights are also objective values, which trigger an order directed the state to protect them against the action of the offending individuals themselves (duty to protect), the mission of which the State seeks to discharge, among other means, through the issue of legal rules typifying the behavior detrimental to such rights, subject to penalties, and the concrete actions of public institutions created by the Constitution to operate penal law. Under this double bias, it is argued that the rule violates the Constitution in the exercise of the claim punitive society as much as by excess malfere fundamental rights that limit, as when it allows facts wrong by offending fundamental rights, remain unpunished either by inaction or by insufficient measures taken abstractly or concretely provided