On differentiability and analyticity of positive definite functions

We derive a set of differential inequalities for positive definite functions based on previous results derived for positive definite kernels by purely algebraic methods. Our main results show that the global behavior of a smooth positive definite function is, to a large extent, determined solely by the sequence of even-order derivatives at the origin: if a single one of these vanishes then the function is constant; if they are all non-zero and satisfy a natural growth condition, the function is real-analytic and consequently extends holomorphically to a maximal horizontal strip of the complex plane.

Children's metalinguistic activity in the construction of linguistic existence

In this paper we examine the construction of first entities in narratives produced by children of 5, 7, 10 years and adults1 . The study demonstrates that when children reformulate they try to construct entities detached from the situation of enunciation, which means that they construct a detached or a translated plane and they construct linguistic existence of entities. Entities must first be introduced into the enunciative space and then comments will be made in subsequent utterances. Constructing existence supposes extraction. This consists of “singling out an occurrence, that is, isolating and drawing its spatiotemporal boundaries” (Culioli, 1990, p. 182) . Once the occurrence of the notion is constructed (which means it has become a separate occurrence with situational properties), children can predicate about it. However, there are children who do not construct the linguistic existence of entities. I hypothesize that the mode of task presentation influences the success of constructing linguistic existence. Sharing the investigator’s knowledge about the stimulus images, children do not ascribe an existential status to the occurrence of the notional domain.

Quantitative description of the self-assembly of patchy particles into chains and rings

We numerically study a simple fluid composed of particles having a hard-core repulsion complemented by two patchy attractive sites on the particle poles. An appropriate choice of the patch angular width allows for the formation of ring structures which, at low temperatures and low densities, compete with the growth of linear aggregates. The simplicity of the model makes it possible to compare simulation results and theoretical predictions based on the Wertheim perturbation theory, specialized to the case in which ring formation is allowed. Such a comparison offers a unique framework for establishing the quality of the analytic predictions. We find that the Wertheim theory describes remarkably well the simulation results.

Activation of effector immune cells promotes tumor stochastic extinction: A homotopy analysis approach

In this article we provide homotopy solutions of a cancer nonlinear model describing the dynamics of tumor cells in interaction with healthy and effector immune cells. We apply a semi-analytic technique for solving strongly nonlinear systems – the Step Homotopy Analysis Method (SHAM). This algorithm, based on a modification of the standard homotopy analysis method (HAM), allows to obtain a one-parameter family of explicit series solutions. By using the homotopy solutions, we first investigate the dynamical effect of the activation of the effector immune cells in the deterministic dynamics, showing that an increased activation makes the system to enter into chaotic dynamics via a period-doubling bifurcation scenario. Then, by adding demographic stochasticity into the homotopy solutions, we show, as a difference from the deterministic dynamics, that an increased activation of the immune cells facilitates cancer clearance involving tumor cells extinction and healthy cells persistence. Our results highlight the importance of therapies activating the effector immune cells at early stages of cancer progression.

Explicit series solution for a glucose-induced electrical activity model of pancreatic beta-cells

In this work, we present the explicit series solution of a specific mathematical model from the literature, the Deng bursting model, that mimics the glucose-induced electrical activity of pancreatic beta-cells (Deng, 1993). To serve to this purpose, we use a technique developed to find analytic approximate solutions for strongly nonlinear problems. This analytical algorithm involves an auxiliary parameter which provides us with an efficient way to ensure the rapid and accurate convergence to the exact solution of the bursting model. By using the homotopy solution, we investigate the dynamical effect of a biologically meaningful bifurcation parameter rho, which increases with the glucose concentration. Our analytical results are found to be in excellent agreement with the numerical ones. This work provides an illustration of how our understanding of biophysically motivated models can be directly enhanced by the application of a newly analytic method.

On the analytical solutions of the Hindmarsh-Rose neuronal model

In this article we analytically solve the Hindmarsh-Rose model (Proc R Soc Lond B221:87-102, 1984) by means of a technique developed for strongly nonlinear problems-the step homotopy analysis method. This analytical algorithm, based on a modification of the standard homotopy analysis method, allows us to obtain a one-parameter family of explicit series solutions for the studied neuronal model. The Hindmarsh-Rose system represents a paradigmatic example of models developed to qualitatively reproduce the electrical activity of cell membranes. By using the homotopy solutions, we investigate the dynamical effect of two chosen biologically meaningful bifurcation parameters: the injected current I and the parameter r, representing the ratio of time scales between spiking (fast dynamics) and resting (slow dynamics). The auxiliary parameter involved in the analytical method provides us with an elegant way to ensure convergent series solutions of the neuronal model. Our analytical results are found to be in excellent agreement with the numerical simulations.

Derek Jarman’s allegories of spectacle: inter-artistic embodiment

ABSTRACT - Derek Jarman was a multifaceted artist whose intermedial versatility reinforces a strong authorial discourse. He constructs an immersive allegorical world of hybrid art where different layers of cinematic, theatrical and painterly materials come together to convey a lyrical form and express a powerful ideological message. In Caravaggio (1986) and Edward II (1991), Jarman approaches two european historical figures from two different but concomitant perspectives. In Caravaggio, through the use of tableaux of abstract meaning and by focusing on the detailing of the models’ poses, Jarman re-enacts the allegorical spirit of Caravaggio’s paintings through entirely cinematic resources. Edward II was a king, and as a statesman he possessed a certain dose of showmanship. In this film Jarman reconstructs the theatrical basis of Christopher Marlowe’s Elizabethan play bringing it up to date in a successfully abstract approach to the musical stage. In this article, I intend to conjoin the practice of allegory in film with certain notions of existential phenomenology as advocated by Vivian Sobchack and Laura U. Marks, in order to address the relationship between the corporeality of the film and the lived bodies of the spectators. In this context, the allegory is a means to convey intradiegetically the sense-ability at play in the cinematic experience, reinforcing the textural and sensual nature of both film and viewer, which, in turn, is also materially enhanced in the film proper, touching the spectator in a supplementary fashion. The two corporealities favour an inter-artistic immersion achieved through coenaesthesia.