We study a mathematical model of biological neuronal
networks composed by any finite number N≥ 2 of non-necessarily
identical cells. The model is a deterministic dynamical system governed by
finite-dimensional impulsive differential equations. The statical structure of
the network is described by a directed and weighted graph whose nodes are certain
subsets of neurons, and whose edges are the groups of synaptical connections among
those subsets. First, we prove that among all the possible networks such as their
respective graphs are mutually isomorphic, there exists a dynamical optimum.
This optimal network exhibits the richest dynamics: namely, it is capable to
show the most diverse set of responses (i.e. orbits in the future) under external stimulus or signals. Second, we prove that
all the neurons of a dynamically optimal neuronal network necessarily satisfy
Dale’s Principle, i.e. each neuron
must be either excitatory or inhibitory, but not mixed. So, Dale’s Principle is
a mathematical necessary consequence of a theoretic optimization process of the
dynamics of the network. Finally, we prove that Dale’s Principle is not
sufficient for the dynamical optimization of the network.

Abstract:
We prove that topologically generic orbits of C^{0} , transitive and non-uniquely ergodic dynamical systems, exhibit an extremely oscillating asymptotical statistics. Precisely, the minimum weak* compact set of invariant probabilities that describes the asymptotical statistics of each orbit of a residual set contains all the ergodic probabilities. If besides f is ergodic with respect to the Lebesgue measure, then also Lebesgue-almost all the orbits exhibit that kind of extremely oscillating statistics.

Abstract:
In this article it is shown analytically that the charge spectrum generated by ionizing particles in Resistive Plate Chambers under Townsend avalanche conditions, that is, for sufficiently small avalanches not affected by space-charge and considering single-electron ionization clusters follows closely the statistical gamma distribution. This distribution describes well comparable simulation data taken from the literature, but seems to describe as well experimental data measured beyond these assumptions, rising some interpretation issues.

Abstract:
In this study the signal propagation in multistrip Resistive Plate Chambers is formulated exactly in the framework of the multiconductor transmission line theory in the frequency domain, allowing losses to be incorporated. For the case of weak coupling and low losses a first-order expansion yields simple, fully analytical, expressions that include reflections. In this approximation the modal spectrum can be calculated analytically as well, allowing to estimate easily the strength of the modal dispersion phenomenon.

Abstract:
In this paper we construct a global, continuous flow of solutions to the Camassa-Holm equation on the space H^1(R). In a previous paper [2], A. Bressan and the author constructed spatially periodic solutions, whereas in this paper the solutions are defined in all the real line. We introduce a distance functional, defined in terms of an optimal transportation problem, which allows us to study the continuous dependance w.r.t. the inital data with a certain decay at infinity.

Abstract:
this article accepts the general proposition that love and passion are essential elements of the school education practice. however, contrary to the contemporary trends that argue that the loving facet of education dismisses truth and the objective knowledge and takes place as a linguistic experience, i advocate that the primordial eros of school education is not effective without objective knowledge and its appropriation. to develop this idea, i borrow some of plato's considerations on love in his classical text symposium in order to rethink them based on the reflections about passion in marx's economical and philosophical manuscripts.

Abstract:
this paper focuses on two questions: what is the place of post-structuralism and neopragmatism in the production of knowledge on curriculum studies? what are their ethical, political and philosophical consequences for the educational field in general? when dealing with these issues, the text brings into question some beliefs about these two theoretical trends, such as: they contribute to oppose the positivist tradition; they strengthen the notion of democratic coexistence by defending plurality and difference; finally, they enrich the production of academic knowledge in education and the creation of innovative practices for experiencing the curriculum.

Abstract:
in a contribution to the analysis of the new sceptical wave that has been pervading educational research, i investigate how lenin and lukács refuted, in ontological and gnosiological terms, the scepticism at their time. in the beginning of the 20th century, lenin elucidated the supposed empiric-critic neutrality. later on, during the 20th century, lukács, in his turn, analyzed neo-positivism as the highest point of this perspective. nowadays, we live in a similar crypto-positivist atmosphere. while positivist tradition has nominally banished ontology, the current trends maintain it, in an attempt to deny the possibility of saying anything about the world; thus, they establish a new way of exiling ontology. with this, an underlying kind of ontology is strengthened, as connected to an immediate practice, ready to fit the interests of the ones who keep capital under control. to avoid ratifying this theoretical retraction, the educational field faces the challenge of opposing today's scepticism.