Real dimension of the Lie algebra of S-skew-Hermitian matrices

Let $M_n(\mathbb{C})$ be the set of $n\times n$ matrices over the complex numbers. Let $S \in M_n(\mathbb{C})$. A matrix $A\in M_n(\mathbb{C})$ is said to be $S$-skew-Hermitian if $SA^*=-AS$ where $A^*$ is the conjugate transpose of $A$. The set $\mathfrak{u}_S$ of all $S$-skew-Hermitian matrices is a Lie algebra. In this paper, we give a real dimension formula for $\mathfrak{u}_S$ using the Jordan block decomposition of the cosquare $S(S^*)^{-1}$ of $S$ when $S$ is nonsingular.

Applying Benford’s Law to Monitor Death Registration Data: A Management Tool for the COVID-19 Pandemic

In Spain, the COVID-19 pandemic has impacted the various regions of the country differently. The availability of reliable and up-to-date information has proved to be fundamental for the management of this health crisis. However, especially during the first wave of the pandemic (February–August 2020), the disparity in the recording criteria and in the timing of providing these figures to the central government created controversy and confusion regarding the real dimension of the pandemic. It is therefore necessary to have objective and homogeneous criteria at the national level to guide health managers in the correct recording and evaluation of the magnitude of the pandemic. Within this context, we propose using Benford’s Law as an auditing tool to monitor the reliability of the number of daily COVID-related deaths to identify possible deviations from the expected trend.

Normative Background: The Dis-abled Subject in International Human Rights Law

This chapter considers how the legal subject has been construed in the field of international human rights law. It argues that the notion of human rights has come to give priority to the able-bodied individual. It then suggests that the CRPD has given this notion a more real dimension through its consideration for distinct forms of embodiment. The chapter goes on to argue that disability can help broaden the range of human variety considered in the concept of human rights. It subsequently analyses Fineman’s vulnerability theory and how it actually fits with the concept of disability, as well as its usefulness in providing a broader approach to dealing with disability. It finally introduces the idea of the dis-abled subject, which allows both the universality of human rights to be strengthened and the Convention’s significance for the whole field of international human rights law to be revealed.

The Existence of Human Rights

Human rights are first, universal, second, fundamental, third, abstract, and fourth, moral rights that, fifth, take priority over all other norms. For the question of the existence of human rights, the fourth defining element, the moral character of human rights, is of special significance. The purely moral character distinguishes human rights from constitutional rights. Constitutional rights are positive law at the level of the constitution. This, however, is not to say that no connection exists between human rights and constitutional rights. On the contrary, constitutional rights have to be defined as rights that have been recorded in a constitution with the intention of transforming human rights into positive law. In this respect, constitutional rights have, along with their real dimension, an ideal dimension, that is, they have a dual nature. This implies that the problem of the existence of human rights is essential for constitutional rights, too. Now, human rights exist if they are justifiable. Eight justifications of human rights are considered: the religious, the biological, the intuitive, the consensual, the instrumental, the cultural, the explicative, and the existential. The result of this analysis is an explicative-existential justification, which, while not a perfect justification, is a good justification.

Introduction

This volume comprises three parts. The issue of Part I is the nature of law. The main thesis is that law has a dual nature. It comprises a real as well as an ideal dimension. The real dimension is defined by authoritative issuance and social efficacy, the ideal dimension by the claim to correctness, which includes a claim to justice. This connection of the real and the ideal dimension implies non-positivism. In Part II the connection between constitutional rights, human rights, and proportionality is taken up. The construction of constitutional rights as principles is to be found at the centre. The principles construction implies the necessity of proportionality analysis and, with this, the necessity of balancing. Balancing is defended against numerous critics as a form of rational legal argumentation. Part III concerns the relation between argumentation, correctness, and law.

Legal Argumentation as Rational Discourse

The discourse model of legal argumentation is presented in this chapter as a reaction to the weaknesses or deficiencies of alternative models. The most important alternative models are the model of deduction, the model of decision, the hermeneutic model, and the model of coherence. The discourse model connects the institutional or real dimension of legal argumentation with its non-institutional or ideal dimension. The result is the special case thesis. It combines institutional arguments, based on the authority of positive law, with substantive arguments, based on practical reason. This connection of the real dimension of legal argumentation with its ideal dimension is a central element of the institutionalization of practical reason.

Law's Ideal Dimension

Law in general, including constitutional rights and legal argumentation, has a dual nature. This is the underlying thesis of this collection of twenty-one chapters devoted to legal philosophy and constitutional law. Law connects a real dimension, defined by authoritative issuance and social efficacy, with an ideal dimension, defined by the claim to correctness, which essentially includes a claim to justice. The chapters of the first part of the book establish on this basis a non-positivistic concept of law. In the second part, the concept of constitutional rights is connected with proportionality analysis, explicated by principles theory and understood as a necessary condition of the rationality of the application of constitutional rights. In the third part, it is shown that rationality is possible in law because rational legal argumentation is possible. Here the basis is discourse theory. The final result is a system that brings the formal idea of legal certainty together with the substantive idea of justice.

Regimes and mechanisms of transient amplification in abstract and biological networks

We use upper triangular matrices as abstract representations of neuronal networks and directly manipulate their eigenspectra and non-normality to explore different regimes of transient amplification. Counter-intuitively, manipulating the imaginary distribution can lead to highly amplifying regimes. This is noteworthy, because biological networks are constrained by Dale's law and the non-existence of neuronal self-loops, limiting the range of manipulations in the real dimension. Within these constraints we can further manipulate transient amplification by controlling global inhibition.

Analysis of the number of deaths in Brazil between 2003 and 2020 and possible inferences about the COVID-19 pandemic and history of other diseases

ABSTRACTThis work explores data on the number of deaths in Brazil since the beginning of the historical series of IBGE, 2003, together with data for the period 2015-2020 of the Transparency Portal. The graphs for total deaths, deaths from violence and deaths in hospitals are discussed. The relationship between them leads to conclusions about the real dimension of the effect of COVID-19 in Brazilian society during the year 2020 and its relative importance to other diseases that had a lesser impact. Hypotheses are also made about the number of deaths in future years.

La revolución de la información

Cuando hablamos de productos y servicios de información generalmente estamos pensando en aquellos servicios que la Unidad de Información tradicional ofrece a sus clientes. La información en los tiempos de la globalización está empujando a los bibliotecólogos a ser más imaginativos, a entrar más activamente dentro del mundo de sus organizaciones, acercarse a mirar el ombligo de las mismas a fin de entender cual es su verdadera misión dentro de ellas. Su presencia en el seno de las organizaciones debe hacerse sentir con propuestas que beneficien a sus miembros, más allá de la mera información. Tal vez su participación en una decisión de negocios para el sector académico o empresarial aún no se ha visto en su real dimensión. Para ilustrar estas ideas hemos considerado tomar como referencia el mundo de Internet cuyo desarrollo está exigiendo cambios de actitud en empresarios, investigadores, académicos y bibliotecólogos.