STABILITY ANALYSIS WITH APPLICATIONS OF A TWO-DIMENSIONAL DYNAMICAL SYSTEM ARISING FROM A STOCHASTIC MODEL FOR AN ASSET MARKET

We analyze the stability properties of equilibrium solutions and periodicity of orbits in a two-dimensional dynamical system whose orbits mimic the evolution of the price of an asset and the excess demand for that asset. The construction of the system is grounded upon a heterogeneous interacting agent model for a single risky asset market. An advantage of this construction procedure is that the resulting dynamical system becomes a macroscopic market model which mirrors the market quantities and qualities that would typically be taken into account solely at the microscopic level of modeling. The system`s parameters correspond to: (a) the proportion of speculators in a market; (b) the traders` speculative trend; (c) the degree of heterogeneity of idiosyncratic evaluations of the market agents with respect to the asset`s fundamental value; and (d) the strength of the feedback of the population excess demand on the asset price update increment. This correspondence allows us to employ our results in order to infer plausible causes for the emergence of price and demand fluctuations in a real asset market. The employment of dynamical systems for studying evolution of stochastic models of socio-economic phenomena is quite usual in the area of heterogeneous interacting agent models. However, in the vast majority of the cases present in the literature, these dynamical systems are one-dimensional. Our work is among the few in the area that construct and study analytically a two-dimensional dynamical system and apply it for explanation of socio-economic phenomena.

Stability of numerical schemes on staggered grids

This paper considers the stability of explicit, implicit and Crank-Nicolson schemes for the one-dimensional heat equation on a staggered grid. Furthemore, we consider the cases when both explicit and implicit approximations of the boundary conditions arc employed. Why we choose to do this is clearly motivated and arises front solving fluid flow equations with free surfaces when the Reynolds number can be very small. in at least parts of the spatial domain. A comprehensive stability analysis is supplied: a novel result is the precise stability restriction on the Crank-Nicolson method when the boundary conditions are approximated explicitly, that is, at t =n delta t rather than t = (n + 1)delta t. The two-dimensional Navier-Stokes equations were then solved by a marker and cell approach for two simple problems that had analytic solutions. It was found that the stability results provided in this paper were qualitatively very similar. thereby providing insight as to why a Crank-Nicolson approximation of the momentum equations is only conditionally, stable. Copyright (C) 2008 John Wiley & Sons, Ltd.

Reliability of orbital fits for resonant extrasolar planetary systems: the case of HD82943

We perform a statistical study of the process of orbital determination of the HD82943 extrasolar planetary system, using the current observational data set of N = 165 radial velocity (RV) measurements. Our aim is to analyse the dispersion of possible orbital fits leading to residuals compatible with the best solution, and to discuss the sensitivity of the results with respect to both the data set and the error distribution around the best fit. Although some orbital parameters (e.g. semimajor axis) appear well constrained, we show that the best fits for the HD82943 system are not robust, and at present it is not possible to estimate reliable solutions for these bodies. Finally, we discuss the possibility of a third planet, with a mass of 0.35M(Jup) and an orbital period of 900 d. Stability analysis and simulations of planetary migration indicate that such a hypothetical three-planet system could be locked in a double 2/1 mean-motion resonance, similar to the so-called Laplace resonance of the three inner Galilean satellites of Jupiter.

Extensive microsatellite diversity in the human malaria parasite Plasmodium vivax

The population structure of Plasmodium vivax remains elusive. The markers of choice for large-scale population genetic studies of eukaryotes, short tandem repeats known as microsatellites, have been recently reported to be less polymorphic in R vivax. Here we investigate the microsatellite diversity and geographic structure in P vivax, at both local and global levels, using 14 new markers consisting of tri- or tetranucleotide repeats. The local-level analysis, which involved 50 field isolates from Sri Lanka, revealed unexpectedly high diversity (average virtual heterozygosity [H-E], 0.807) and significant multilocus linkage disequilibrium in this region of low malaria endemicity. Multiple-clone infections occurred in 60% of isolates sampled in 2005. The global-level analysis of field isolates or monkey-adapted strains identified 150 unique haplotypes among 164 parasites from four continents. Individual P. vivax isolates could not be unambiguously assigned to geographic populations. For example, we found relatively low divergence among parasites from Central America, Africa, Southeast Asia and Oceania, but substantial differentiation between parasites from the same continent (South Asia and Southeast Asia) or even from the same country (Brazil). Parasite relapses, which may extend the duration of P. vivax carriage in humans, are suggested to facilitate the spread of strains across continents, breaking down any pre-existing geographic structure. (C) 2008 Elsevier B.V. All rights reserved.

Contributions to the theory of magnetorotational instability and waves in a rotating plasma

The one-fluid magnetohydrodynamic (MHD) theory of magnetorotational instability (MRI) in an ideal plasma is presented. The theory predicts the possibility of MRI for arbitrary 0, where 0 is the ratio of the plasma pressure to the magnetic field pressure. The kinetic theory of MRI in a collisionless plasma is developed. It is demonstrated that as in the ideal MHD, MRI can occur in such a plasma for arbitrary P. The mechanism of MRI is discussed; it is shown that the instability appears because of a perturbed parallel electric field. The electrodynamic description of MRI is formulated under the assumption that the dispersion relation is expressed in terms of the permittivity tensor; general properties of this tensor are analyzed. It is shown to be separated into the nonrotational and rotational parts. With this in mind, the first step for incorporation of MRI into the general theory of plasma instabilities is taken. The rotation effects on Alfven waves are considered.

The transcriptional response to cadmium, organic hydroperoxide, singlet oxygen and UV-A mediated by the sigma(E)-ChrR system in Caulobacter crescentus

Caulobacter crescentus sigma(E) belongs to the ECF (extracytoplasmic function) subfamily of RNA polymerase sigma factors, whose members regulate gene expression in response to distinct environmental stresses. During physiological growth conditions, data indicate that sigma(E) is maintained in reduced levels due to the action of ChrR, a negative regulator of rpoE gene expression and function. However, once bacterial cells are exposed to cadmium, organic hydroperoxide, singlet oxygen or UV-A irradiation, transcription of rpoE is induced in a sigma(E)-dependent manner. Site-directed mutagenesis indicated that residue C188 in ChrR is critical for the cadmium response while residues H140 and H142 are required for the bacterial response to organic hydroperoxide, singlet oxygen and UV-A. Global transcriptional analysis showed that sigma(E) regulates genes involved in protecting cells against oxidative damages. A combination of transcriptional start site identification and promoter prediction revealed that some of these genes contain a putative sigma(E)-dependent motif in their upstream regions. Furthermore, deletion of rpoE and two sigma(E)-dependent genes (cfaS and hsp20) impairs Caulobacter survival when singlet oxygen is constantly generated in the cells.

Global attractor for a model of extensible beam with nonlinear damping and source terms

This paper is concerned with the existence of a global attractor for the nonlinear beam equation, with nonlinear damping and source terms, u(tt) + Delta(2)u -M (integral(Omega)vertical bar del u vertical bar(2)dx) Delta u + f(u) + g(u(t)) = h in Omega x R(+), where Omega is a bounded domain of R(N), M is a nonnegative real function and h is an element of L(2)(Omega). The nonlinearities f(u) and g(u(t)) are essentially vertical bar u vertical bar(rho) u - vertical bar u vertical bar(sigma) u and vertical bar u(t)vertical bar(r) u(t) respectively, with rho, sigma, r > 0 and sigma < rho. This kind of problem models vibrations of extensible beams and plates. (C) 2010 Elsevier Ltd. All rights reserved.

Global Gene Expression Analysis during Germination in the Chytridiomycete Blastocladiella emersonii

Blastocladiella emersonii is an aquatic fungus of the Chytridiomycete class. During germination, the zoospore, a motile nongrowing cell, goes through a cascade of morphological changes that culminates with its differentiation into the germling cell, capable of coenocytic vegetative growth. Transcriptome analyses of B. emersonii cells were carried out during germination induced under various environmental conditions. Microarray data analyzing 3,563 distinct B. emersonii genes revealed that 26% of them are differentially expressed during germination in nutrient medium at at least one of the time points investigated. Over 500 genes are upregulated during the time course of germination under those conditions, most being related to cell growth, including genes involved in protein biosynthesis, DNA transcription, energetic metabolism, carbohydrate and oligopeptide transport, and cell cycle control. On the other hand, several transcripts stored in the zoospores are downregulated during germination in nutrient medium, such as genes involved in signal transduction, amino acid transport, and chromosome organization. In addition, germination induced in the presence of nutrients was compared with that triggered either by adenine or potassium ions in inorganic salt solution. Several genes involved in cell growth, induced during germination in nutrient medium, do not show increased expression when B. emersonii zoospores germinate in inorganic solution, suggesting that nutrients exert a positive effect on gene transcription. The transcriptome data also revealed that most genes involved in cell signaling show the same expression pattern irrespective of the initial germination stimulus.

Global Gene Expression Analysis during Sporulation of the Aquatic Fungus Blastocladiella emersonii

The Blastocladiella emersonii life cycle presents a number of drastic biochemical and morphological changes, mainly during two cell differentiation stages: germination and sporulation. To investigate the transcriptional changes taking place during the sporulation phase, which culminates with the production of the zoospores, motile cells responsible for the dispersal of the fungus, microarray experiments were performed. Among the 3,773 distinct genes investigated, a total of 1,207 were classified as differentially expressed, relative to time zero of sporulation, at at least one of the time points analyzed. These results indicate that accurate transcriptional control takes place during sporulation, as well as indicating the necessity for distinct molecular functions throughout this differentiation process. The main functional categories overrepresented among upregulated genes were those involving the microtubule, the cytoskeleton, signal transduction involving Ca(2+), and chromosome organization. On the other hand, protein biosynthesis, central carbon metabolism, and protein degradation were the most represented functional categories among downregulated genes. Gene expression changes were also analyzed in cells sporulating in the presence of subinhibitory concentrations of glucose or tryptophan. Data obtained revealed overexpression of microtubule and cytoskeleton transcripts in the presence of glucose, probably causing the shape and motility problems observed in the zoospores produced under this condition. In contrast, the presence of tryptophan during sporulation led to upregulation of genes involved in oxidative stress, proteolysis, and protein folding. These results indicate that distinct physiological pathways are involved in the inhibition of sporulation due to these two classes of nutrient sources.

Ab Initio Analysis of Monomers and Dimers of Trialkylphosphine Oxides: Structural and Thermodynamic Stability

Structural and thermodynamic stabilities of monomers and dimers of trialkylphosphine oxides (TRPO) were Studied using quantum chemistry calculations. Density functional theory calculations were carried Out and the structures Of four TRPO have been determined: TMPO (methyl; R = CH(3)), TEPO (ethyl; R = CH(3)CH(2)), TBPO (n-butyl; R = CH(3)(CH(2))(3)), and TOPO (n-octyl; R = CH(3)(CH(2))(7)). TRPO homodimers were investigated considering two isomeric possibilities for each dimer. Relative binding energies and the enthalpic and entropic contributions to the Gibbs free energy were Calculated for all dimers. The formation of dimers from the individual monomeric TRPO species as a function of temperature was also analyzed. (C) 2008 Wiley Periodicals, Inc. Int J Quantum Chem 109: 250-258, 2009