Colored noise in spatially extended systems

We study the effects of time and space correlations of an external additive colored noise on the steady-state behavior of a time-dependent Ginzburg-Landau model. Simulations show the existence of nonequilibrium phase transitions controlled by both the correlation time and length of the noise. A Fokker-Planck equation and the steady probability density of the process are obtained by means of a theoretical approximation.

Exactly solvable phase oscillator models with syncrhonization dynamics

Populations of phase oscillators interacting globally through a general coupling function f(x) have been considered. We analyze the conditions required to ensure the existence of a Lyapunov functional giving close expressions for it in terms of a generating function. We have also proposed a family of exactly solvable models with singular couplings showing that it is possible to map the synchronization phenomenon into other physical problems. In particular, the stationary solutions of the least singular coupling considered, f(x) = sgn(x), have been found analytically in terms of elliptic functions. This last case is one of the few nontrivial models for synchronization dynamics which can be analytically solved.

Synchronization in a lattice model of pulse-coupled oscillators

We analyze the collective behavior of a lattice model of pulse-coupled oscillators. By means of computer simulations we find the relation between the intrinsic dynamics of each member of the population and their mutual interactions that ensures, in a general context, the existence of a fully synchronized regime. This condition turns out to be the same as that obtained for the globally coupled population. When the condition is not completely satisfied we find different spatial structures. This also gives some hints about self-organized criticality.

Periodic points of holomorphic maps via Lefschetz numbers

In this paper we study the set of periods of holomorphic maps on compact manifolds, using the periodic Lefschetz numbers introduced by Dold and Llibre, which can be computed from the homology class of the map. We show that these numbers contain information about the existence of periodic points of a given period; and, if we assume the map to be transversal, then they give us the exact number of such periodic orbits. We apply this result to the complex projective space of dimension n and to some special type of Hopf surfaces, partially characterizing their set of periods. In the first case we also show that any holomorphic map of CP(n) of degree greater than one has infinitely many distinct periodic orbits, hence generalizing a theorem of Fornaess and Sibony. We then characterize the set of periods of a holomorphic map on the Riemann sphere, hence giving an alternative proof of Baker's theorem.

Interiority of the optimal population growth rate with endogenous fertility

This paper analyzes the issue of the interiority of the optimal population growth rate in a two-period overlapping generations model with endogenous fertility. Using Cobb-Douglas utility and production functions, we show that the introduction of a cost of raising children allows for the possibility of the existence of an interior global maximum in the planner¿s problem, contrary to the exogenous fertility case

SIMSAFADIM-CLASTIC: A new approach to mathematical 3D forward simulation modelling for terrigenous and carbonate marine sedimentation

Most sedimentary modelling programs developed in recent years focus on either terrigenous or carbonate marine sedimentation. Nevertheless, only a few programs have attempted to consider mixed terrigenous-carbonate sedimentation, and most of these are two-dimensional, which is a major restriction since geological processes take place in 3D. This paper presents the basic concepts of a new 3D mathematical forward simulation model for clastic sediments, which was developed from SIMSAFADIM, a previous 3D carbonate sedimentation model. The new extended model, SIMSAFADIM-CLASTIC, simulates processes of autochthonous marine carbonate production and accumulation, together with clastic transport and sedimentation in three dimensions of both carbonate and terrigenous sediments. Other models and modelling strategies may also provide realistic and efficient tools for prediction of stratigraphic architecture and facies distribution of sedimentary deposits. However, SIMSAFADIM-CLASTIC becomes an innovative model that attempts to simulate different sediment types using a process-based approach, therefore being a useful tool for 3D prediction of stratigraphic architecture and facies distribution in sedimentary basins. This model is applied to the neogene Vallès-Penedès half-graben (western Mediterranean, NE Spain) to show the capacity of the program when applied to a realistic geologic situation involving interactions between terrigenous clastics and carbonate sediments.

Stochastic delay equations with non-negativity constraints driven by fractional Brownian motion

In this note we prove an existence and uniqueness result for the solution of multidimensional stochastic delay differential equations with normal reflection. The equations are driven by a fractional Brownian motion with Hurst parameter H > 1/2. The stochastic integral with respect to the fractional Brownian motion is a pathwise Riemann¿Stieltjes integral.

Stochastic differential equations with random coefficients

In this paper we establish the existence and uniqueness of a solution for different types of stochastic differential equation with random initial conditions and random coefficients. The stochastic integral is interpreted as a generalized Stratonovich integral, and the techniques used to derive these results are mainly based on the path properties of the Brownian motion, and the definition of the Stratonovich integral.

Stochastic delay differential equations driven by fractional Brownian motion with Hurst parameter H 1/2

We consider the Cauchy problem for a stochastic delay differential equation driven by a fractional Brownian motion with Hurst parameter H>¿. We prove an existence and uniqueness result for this problem, when the coefficients are sufficiently regular. Furthermore, if the diffusion coefficient is bounded away from zero and the coefficients are smooth functions with bounded derivatives of all orders, we prove that the law of the solution admits a smooth density with respect to Lebesgue measure on R.

Reciprocal Translocations in Cattle: frequency estimation

Chromosomal anomalies, like Robertsonian and reciprocal translocations represent a big problem in cattle breeding as their presence induces, in the carrier subjects, a well documented fertility reduction. In cattle reciprocal translocations (RCPs, a chromosome abnormality caused by an exchange of material between nonhomologous chromosomes) are considered rare as to date only 19 reciprocal translocations have been described. In cattle it is common knowledge that the Robertsonian translocations represent the most common cytogenetic anomalies, and this is probably due to the existence of the endemic 1;29 Robertsonian translocation. However, these considerations are based on data obtained using techniques that are unable to identify all reciprocal translocations and thus their frequency is clearly underestimated. The purpose of this work is to provide a first realistic estimate of the impact of RCPs in the cattle population studied, trying to eliminate the factors which have caused an underestimation of their frequency so far. We performed this work using a mathematical as well as a simulation approach and, as biological data, we considered the cytogenetic results obtained in the last 15 years. The results obtained show that only 16% of reciprocal translocations can be detected using simple Giemsa techniques and consequently they could be present in no less than 0,14% of cattle subjects, a frequency five times higher than that shown by de novo Robertsonian translocations. This data is useful to open a debate about the need to introduce a more efficient method to identify RCP in cattle.

Potential Accessibility of Web-based mathematical information resources

This paper presents a research concerning the conversion of non-accessible web pages containing mathematical formulae into accessible versions through an OCR (Optical Character Recognition) tool. The objective of this research is twofold. First, to establish criteria for evaluating the potential accessibility of mathematical web sites, i.e. the feasibility of converting non-accessible (non-MathML) math sites into accessible ones (Math-ML). Second, to propose a data model and a mechanism to publish evaluation results, making them available to the educational community who may use them as a quality measurement for selecting learning material.Results show that the conversion using OCR tools is not viable for math web pages mainly due to two reasons: many of these pages are designed to be interactive, making difficult, if not almost impossible, a correct conversion; formula (either images or text) have been written without taking into account standards of math writing, as a consequence OCR tools do not properly recognize math symbols and expressions. In spite of these results, we think the proposed methodology to create and publish evaluation reports may be rather useful in other accessibility assessment scenarios.

The existence of FGFR1-5-HT1A receptor heterocomplexes in midbrain 5-HT neurons of the rat: relevance for neuroplasticity

The ascending midbrain 5-HT neurons to the forebrain may be dysregulated in depression and have a reduced trophic support. With in situ proximity ligation assay (PLA) and supported by coimmunoprecipitation and colocation of the FGFR1 and 5-HT1A immunoreactivities in the midbrain raphe cells, evidence for the existence of FGFR1-5-HT1A receptor heterocomplexes in the dorsal and median raphe nuclei of the Sprague Dawley rat as well as in the rat medullary raphe RN33B cells has been obtained. Especially after combined FGF-2 and 8-OH-DPAT treatment, a marked and significant increase in PLA clusters was found in the RN33B cells. Similar results were reached with the FRET technique in HEK293T cells, where TM-V of the 5HT1A receptor was found to be part of the receptor interface. The combined treatment with FGF-2 and the 5-HT1A agonist also synergistically increased FGFR1 and ERK1/2 phosphorylation in the raphe midline area of the midbrain and the RN33B cells as well as their differentiation, as seen from development of the increased number and length of extensions per cell and their increased 5-HT immunoreactivity. These signaling and differentiation events were dependent on the receptor interface since they were blocked by incubation with TM-V but not by TM-II. Together, the results indicate that the 5-HT1A autoreceptors by being part of a FGFR1-5-HT1A receptor heterocomplex in the midbrain raphe 5-HT nerve cells appear to have a trophic role in the central 5-HT neuron systems in addition to playing a key role in reducing the firing of these neurons

On the existence and function of galanin receptor heteromers in the central nervous system

Galanin receptor (GalR) subtypes 1-3 linked to central galanin neurons may form heteromers with each other and other types of G protein-coupled receptors in the central nervous system (CNS). These heteromers may be one molecular mechanism for galanin peptides and their N-terminal fragments (gal 1-15) to modulate the function of different types of glia-neuronal networks in the CNS, especially the emotional and the cardiovascular networks. GalR-5-HT1A heteromers likely exist with antagonistic GalR-5-HT1A receptor-receptor interactions in the ascending midbrain raphe 5-HT neuron systems and their target regions. They represent a novel target for antidepressant drugs. Evidence is given for the existence of GalR1-5-HT1A heteromers in cellular models with trans-inhibition of the protomer signaling. A GalR1-GalR2 heteromer is proposed to be a galanin N-terminal fragment preferring receptor (1-15) in the CNS. Furthermore, a GalR1-GalR2-5-HT1A heterotrimer is postulated to explain why only galanin (1-15) but not galanin (1-29) can antagonistically modulate the 5-HT1A receptors in the dorsal hippocampus rich in gal fragment binding sites. The results underline a putative role of different types of GalR-5-HT1A heteroreceptor complexes in depression. GalR antagonists may also have therapeutic actions in depression by blocking the antagonistic GalR-NPYY1 receptor interactions in putative GalR-NPYY1 receptor heteromers in the CNS resulting in increases in NPYY1 transmission and antidepressant effects. In contrast the galanin fragment receptor (a postulated GalR1-GalR2 heteromer) appears to be linked to the NPYY2 receptor enhancing the affinity of the NPYY2 binding sites in a putative GalR1-GalR2-NPYY2 heterotrimer. Finally, putative GalR-α2-adrenoreceptor heteromers with antagonistic receptor-receptor interactions may be a widespread mechanism in the CNS for integration of galanin and noradrenaline signals also of likely relevance for depression

SEM evidence for existence of an apical disc on the scolex of Clestobothrium crassiceps (Rudolphi, 1819): comparative results of various fixation techniques

The scolex of the bothriocephalidean cestode Clestobothrium crassiceps was studied by means of scanning electron microscopy (SEM). The comparative results of various fixation procedures and techniques are presented. The scolex of C. crassiceps is oval to globular and exhibits two deep bothria which appear in the form of two lobes separated by a longitudinal groove. At the apex of the scolex, resembling a beret, an apical disc is present (oval, flattened and with a sinuous edge). Our results are compared with those previously reported in other species of Clestobothrium. This study represents the first report which highlights the presence of an apical disc in the scolex of C. crassiceps. It describes the effects of different procedures applied to our material during preparation and a comparative analysis results obtained using these various methods.

Anticipating linear stochastic differential equations driven by a Lévy process

In this paper we study the existence of a unique solution for linear stochastic differential equations driven by a Lévy process, where the initial condition and the coefficients are random and not necessarily adapted to the underlying filtration. Towards this end, we extend the method based on Girsanov transformations on Wiener space and developped by Buckdahn [7] to the canonical Lévy space, which is introduced in [25].