Stability and ergodicity of piecewise deterministic Markov processes

The main goal of this paper is to establish some equivalence results on stability, recurrence, and ergodicity between a piecewise deterministic Markov process ( PDMP) {X( t)} and an embedded discrete-time Markov chain {Theta(n)} generated by a Markov kernel G that can be explicitly characterized in terms of the three local characteristics of the PDMP, leading to tractable criterion results. First we establish some important results characterizing {Theta(n)} as a sampling of the PDMP {X( t)} and deriving a connection between the probability of the first return time to a set for the discrete-time Markov chains generated by G and the resolvent kernel R of the PDMP. From these results we obtain equivalence results regarding irreducibility, existence of sigma-finite invariant measures, and ( positive) recurrence and ( positive) Harris recurrence between {X( t)} and {Theta(n)}, generalizing the results of [ F. Dufour and O. L. V. Costa, SIAM J. Control Optim., 37 ( 1999), pp. 1483-1502] in several directions. Sufficient conditions in terms of a modified Foster-Lyapunov criterion are also presented to ensure positive Harris recurrence and ergodicity of the PDMP. We illustrate the use of these conditions by showing the ergodicity of a capacity expansion model.

AVERAGE CONTINUOUS CONTROL OF PIECEWISE DETERMINISTIC MARKOV PROCESSES

This paper deals with the long run average continuous control problem of piecewise deterministic Markov processes (PDMPs) taking values in a general Borel space and with compact action space depending on the state variable. The control variable acts on the jump rate and transition measure of the PDMP, and the running and boundary costs are assumed to be positive but not necessarily bounded. Our first main result is to obtain an optimality equation for the long run average cost in terms of a discrete-time optimality equation related to the embedded Markov chain given by the postjump location of the PDMP. Our second main result guarantees the existence of a feedback measurable selector for the discrete-time optimality equation by establishing a connection between this equation and an integro-differential equation. Our final main result is to obtain some sufficient conditions for the existence of a solution for a discrete-time optimality inequality and an ordinary optimal feedback control for the long run average cost using the so-called vanishing discount approach. Two examples are presented illustrating the possible applications of the results developed in the paper.

Ecdysteroid-Dependent Expression of the Tweedle and Peroxidase Genes during Adult Cuticle Formation in the Honey Bee, Apis mellifera

Cuticle renewal is a complex biological process that depends on the cross talk between hormone levels and gene expression. This study characterized the expression of two genes encoding cuticle proteins sharing the four conserved amino acid blocks of the Tweedle family, AmelTwdl1 and AmelTwdl2, and a gene encoding a cuticle peroxidase containing the Animal haem peroxidase domain, Ampxd, in the honey bee. Gene sequencing and annotation validated the formerly predicted tweedle genes, and revealed a novel gene, Ampxd, in the honey bee genome. Expression of these genes was studied in the context of the ecdysteroid-coordinated pupal-to-adult molt, and in different tissues. Higher transcript levels were detected in the integument after the ecdysteroid peak that induces apolysis, coinciding with the synthesis and deposition of the adult exoskeleton and its early differentiation. The effect of this hormone was confirmed in vivo by tying a ligature between the thorax and abdomen of early pupae to prevent the abdominal integument from coming in contact with ecdysteroids released from the prothoracic gland. This procedure impaired the natural increase in transcript levels in the abdominal integument. Both tweedle genes were expressed at higher levels in the empty gut than in the thoracic integument and trachea of pharate adults. In contrast, Ampxd transcripts were found in higher levels in the thoracic integument and trachea than in the gut. Together, the data strongly suggest that these three genes play roles in ecdysteroid-dependent exoskeleton construction and differentiation and also point to a possible role for the two tweedle genes in the formation of the cuticle (peritrophic membrane) that internally lines the gut.

Survival and Neuronal Differentiation of Mesenchymal Stem Cells Transplanted into the Rodent Brain Are Dependent upon Microenvironment

Introduction: The successful integration of stem cells in adult brain has become a central issue in modern neuroscience. In this study we sought to test the hypothesis that survival and neurodifferentiation of mesenchymal stem cells (MSCs) may be dependent upon microenvironmental conditions according to the site of implant in the brain. Methods: MSCs were isolated from adult rats and labeled with enhanced-green fluorescent protein (eGFP) lentivirus. A cell suspension was implanted stereotactically into the brain of 50 young rats, into one neurogenic area (hippocampus), and into another nonneurogenic area (striatum). Animals were sacrificed 6 or 12 weeks after surgery, and brains were stained for mature neuronal markers. Cells coexpressing NeuN (neuronal specific nuclear protein) and GFP (green fluorescent protein) were counted stereologically at both targets. Results: The isolated cell population was able to generate neurons positive for microtubule-associated protein 2 (MAP2), neuronal-specific nuclear protein (NeuN), and neurofilament 200 (NF200) in vitro. Electrophysiology confirmed expression of voltage-gated ionic channels. Once implanted into the hippocampus, cells survived for up to 12 weeks, migrated away from the graft, and gave rise to mature neurons able to synthesize neurotransmitters. By contrast, massive cell degeneration was seen in the striatum, with no significant migration. Induction of neuronal differentiation with increased cyclic adenosine monophosphate in the culture medium before implantation favored differentiation in vivo. Conclusions: Our data demonstrated that survival and differentiation of MSCs is strongly dependent upon a permissive microenvironment. Identification of the pro-neurogenic factors present in the hippocampus could subsequently allow for the integration of stem cells into nonpermissive areas of the central nervous system.

Expression and cellular localization of microRNA-29b and RAX, an activator of the RNA-dependent protein kinase (PKR), in the retina of streptozotocin-induced diabetic rats

Purpose: The apoptosis of retinal neurons plays a critical role in the pathogenesis of diabetic retinopathy (DR), but the molecular mechanisms underlying this phenomenon remain unclear. The purpose of this study was to investigate the cellular localization and the expression of microRNA-29b (miR-29b) and its potential target PKR associated protein X (RAX), an activator of the pro-apoptotic RNA-dependent protein kinase (PKR) signaling pathway, in the retina of normal and diabetic rats. Methods: Retinas were obtained from normal and diabetic rats within 35 days after streptozotocin (STZ) injection. In silico analysis indicated that RAX is a potential target of miR-29b. The cellular localization of miR-29b and RAX was assessed by in situ hybridization and immunofluorescence, respectively. The expression levels of miR-29b and RAX mRNA were evaluated by quantitative reverse transcription PCR (qRT-PCR), and the expression of RAX protein was evaluated by western blot. A luciferase reporter assay and inhibition of endogenous RAX were performed to confirm whether RAX is a direct target of miR-29b as predicted by the in silico analysis. Results: We found that miR-29b and RAX are localized in the retinal ganglion cells (RGCs) and the cells of the inner nuclear layer (INL) of the retinas from normal and diabetic rats. Thus, the expression of miR-29b and RAX, as assessed in the retina by quantitative RT-PCR, reflects their expression in the RGCs and the cells of the INL. We also revealed that RAX protein is upregulated (more than twofold) at 3, 6, 16, and 22 days and downregulated (70%) at 35 days, whereas miR-29b is upregulated (more than threefold) at 28 and 35 days after STZ injection. We did not confirm the computational prediction that RAX is a direct target of miR-29b. Conclusions: Our results suggest that RAX expression may be indirectly regulated by miR-29b, and the upregulation of this miRNA at the early stage of STZ-induced diabetes may have a protective effect against the apoptosis of RGCs and cells of the INL by the pro-apoptotic RNA-dependent protein kinase (PKR) signaling pathway.

Prolonged Survival of Allografts Induced by Mycobacterial Hsp70 Is Dependent on CD4+CD25+Regulatory T Cells

Background: Heat shock proteins (Hsps) are stress induced proteins with immunomodulatory properties. The Hsp70 of Mycobacterium tuberculosis (TBHsp70) has been shown to have an anti-inflammatory role on rodent autoimmune arthritis models, and the protective effects were demonstrated to be dependent on interleukin-10 (IL-10). We have previously observed that TBHsp70 inhibited maturation of dendritic cells (DCs) and induced IL-10 production by these cells, as well as in synovial fluid cells. Methodology/Principal Findings: We investigated if TBHsp70 could inhibit allograft rejection in two murine allograft systems, a transplanted allogeneic melanoma and a regular skin allograft. In both systems, treatment with TBHsp70 significantly inhibited rejection of the graft, and correlated with regulatory T cells (Tregs) recruitment. This effect was not tumor mediated because injection of TBHsp70 in tumor-free mice induced an increase of Tregs in the draining lymph nodes as well as inhibition of proliferation of lymph node T cells and an increase in IL-10 production. Finally, TBHsp70 inhibited skin allograft acute rejection, and depletion of Tregs using a monoclonal antibody completely abolished this effect. Conclusions/Significance: We present the first evidence for an immunosuppressive role for this protein in a graft rejection system, using an innovative approach - immersion of the graft tissue in TBHsp70 solution instead of protein injection. Also, this is the first study that demonstrates dependence on Treg cells for the immunosuppressive role of TBHsp70. This finding is relevant for the elucidation of the immunomodulatory mechanism of TBHsp70. We propose that this protein can be used not only for chronic inflammatory diseases, but is also useful for organ transplantation management.

Suppression subtractive hybridization analysis reveals expression of conserved and novel genes in male accessory glands of the ant Leptothorax gredleri

Background: During mating, insect males eject accessory gland proteins (Acps) into the female genital tract. These substances are known to affect female post-mating behavior and physiology. In addition, they may harm the female, e. g., in reducing its lifespan. This is interpreted as a consequence of sexual antagonistic co-evolution. Whereas sexual conflict abounds in non-social species, the peculiar life history of social insects (ants, bees, wasps) with lifelong pair-bonding and no re-mating aligns the reproductive interests of the sexes. Harming the female during mating would negatively affect male fitness and sexual antagonism is therefore not expected. Indeed, mating appears to increase female longevity in at least one ant species. Acps are presumed to play a role in this phenomenon, but the underlying mechanisms are unknown. In this study, we investigated genes, which are preferentially expressed in male accessory glands of the ant Leptothorax gredleri, to determine which proteins might be transferred in the seminal fluid. Results: By a suppression subtractive hybridization protocol we obtained 20 unique sequences (USs). Twelve had mutual best matches with genes predicted for Apis mellifera and Nasonia vitripennis. Functional information (Gene Ontology) was available only for seven of these, including intracellular signaling, energy-dependent transport and metabolic enzyme activities. The remaining eight USs did not match sequences from other species. Six genes were further analyzed by quantitative RT-PCR in three life cycle stages of male ants. A gene with carboxy-lyase activity and one of unpredicted function were significantly overexpressed in accessory glands of sexually mature males. Conclusions: Our study is the first one to investigate differential gene expression in ants in a context related to mating. Our findings indicate that male accessory glands of L. gredleri express a series of genes that are unique to this species, possibly representing novel genes, in addition to conserved ones for which functions can be predicted. Identifying differentially expressed genes might help to better understand molecular mechanisms involved in reproductive processes in eusocial Hymenoptera. While the novel genes could account for rapidly evolving ones driven by intra-sexual conflict between males, conserved genes imply that rather beneficial traits might get fixed by a process described as inter-sexual cooperation between males and females.

The qWR star HD 45166 - II. Fundamental stellar parameters and evidence of a latitude-dependent wind

Context. The enigmatic object HD 45166 is a qWR star in a binary system with an orbital period of 1.596 day, and presents a rich emission-line spectrum in addition to absorption lines from the companion star (B7 V). As the system inclination is very small (i = 0.77 degrees +/- 0.09 degrees), HD 45166 is an ideal laboratory for wind-structure studies. Aims. The goal of the present paper is to determine the fundamental stellar and wind parameters of the qWR star. Methods. A radiative transfer model for the wind and photosphere of the qWR star was calculated using the non-LTE code CMFGEN. The wind asymmetry was also analyzed using a recently-developed version of CMFGEN to compute the emerging spectrum in two-dimensional geometry. The temporal-variance spectrum (TVS) was calculated to study the line-profile variations. Results. Abundances and stellar and wind parameters of the qWR star were obtained. The qWR star has an effective temperature of T(eff) = 50 000 +/- 2000 K, a luminosity of log(L/L(circle dot)) = 3.75 +/- 0.08, and a corresponding photospheric radius of R(phot) = 1.00 R(circle dot). The star is helium-rich (N(H)/N(He) = 2.0), while the CNO abundances are anomalous when compared either to solar values, to planetary nebulae, or to WR stars. The mass-loss rate is. M = 2.2 x 10(-7) M(circle dot) yr(-1), and the wind terminal velocity is v(infinity) = 425 km s(-1). The comparison between the observed line profiles and models computed under different latitude-dependent wind densities strongly suggests the presence of an oblate wind density enhancement, with a density contrast of at least 8: 1 from equator to pole. If a high velocity polar wind is present (similar to 1200 km s(-1)), the minimum density contrast is reduced to 4:1. Conclusions. The wind parameters determined are unusual when compared to O-type stars or to typical WR stars. While for WR stars v(infinity)/v(esc) > 1.5, in the case of HD 45166 it is much smaller (v(infinity)/v(esc) = 0.32). In addition, the efficiency of momentum transfer is eta = 0.74, which is at least 4 times smaller than in a typical WR. We find evidence for the presence of a wind compression zone, since the equatorial wind density is significantly higher than the polar wind. The TVS supports the presence of such a latitude-dependent wind and a variable absorption/scattering gas near the equator.

Cosmic distance duality relation and the shape of galaxy clusters

Context. Observations in the cosmological domain are heavily dependent on the validity of the cosmic distance-duality (DD) relation, eta = D(L)(z)(1+ z)(2)/D(A)(z) = 1, an exact result required by the Etherington reciprocity theorem where D(L)(z) and D(A)(z) are, respectively, the luminosity and angular diameter distances. In the limit of very small redshifts D(A)(z) = D(L)(z) and this ratio is trivially satisfied. Measurements of Sunyaev-Zeldovich effect (SZE) and X-rays combined with the DD relation have been used to determine D(A)(z) from galaxy clusters. This combination offers the possibility of testing the validity of the DD relation, as well as determining which physical processes occur in galaxy clusters via their shapes. Aims. We use WMAP (7 years) results by fixing the conventional Lambda CDM model to verify the consistence between the validity of DD relation and different assumptions about galaxy cluster geometries usually adopted in the literature. Methods. We assume that. is a function of the redshift parametrized by two different relations: eta(z) = 1+eta(0)z, and eta(z) = 1+eta(0)z/(1+z), where eta(0) is a constant parameter quantifying the possible departure from the strict validity of the DD relation. In order to determine the probability density function (PDF) of eta(0), we consider the angular diameter distances from galaxy clusters recently studied by two different groups by assuming elliptical (isothermal) and spherical (non-isothermal) beta models. The strict validity of the DD relation will occur only if the maximum value of eta(0) PDF is centered on eta(0) = 0. Results. It was found that the elliptical beta model is in good agreement with the data, showing no violation of the DD relation (PDF peaked close to eta(0) = 0 at 1 sigma), while the spherical (non-isothermal) one is only marginally compatible at 3 sigma. Conclusions. The present results derived by combining the SZE and X-ray surface brightness data from galaxy clusters with the latest WMAP results (7-years) favors the elliptical geometry for galaxy clusters. It is remarkable that a local property like the geometry of galaxy clusters might be constrained by a global argument provided by the cosmic DD relation.

Low-Level Laser Irradiation (InGaAlP-660 nm) Increases Fibroblast Cell Proliferation and Reduces Cell Death in a Dose-Dependent Manner

Background and Objective: Impaired cell metabolism and increased cell death in fibroblast cells are physiological features of chronic tendinopathy. Although several studies have shown that low-level laser therapy (LLLT) at certain parameters has a biostimulatory effect on fibroblast cells, it remains uncertain if LLLT effects depend on the physiological state. Study Design/Material and Methods: High-metabolic immortal cell culture and primary human keloid fibroblast cell culture were used in this study. Trypan blue exclusion and the 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide (MTT) test were used to determine cell viability and proliferation. Propidium iodide stain was used for cell-cycle analysis by flow cytometry. Laser irradiation was performed daily on three consecutive days with a GaAlAs 660-nm laser (mean output: 50 mW, spot size 2 mm(2), power density = 2.5 W/cm(2)) and a typical LLLT dose and a high LLLT dose (irradiation times: 60 or 420 s; fluences: 150 or 1050 J/cm(2); energy delivered: 3 or 21 J). Results: Primary fibroblast cell culture from human keloids irradiated with 3 J showed significant proliferation by the trypan blue exclusion test (p < 0.05), whereas the 3T3 cell culture showed no difference using this method. Propidium iodide staining flow cytometry data showed a significant decrease in the percentage of cells being in proliferative phases of the cell cycle (S/g(2)/M) when irradiated with 21 J in both cell types (hypodiploid cells increased). Conclusions: Our data support the hypothesis that the physiological state of the cells affects the LLLT results, and that high-metabolic rate and short-cell-cycle 3T3 cells are not responsive to LLLT. In conclusion, LLLT with a dose of 3 J reduced cell death significantly, but did not stimulate cell cycle. A LLLT dose of 21 J had negative effects on the cells, as it increased cell death and inhibited cell proliferation.

Crystallite size-dependent phases in nanocrystalline ZrO(2)-Sc(2)O(3)

ZrO(2)-10, 12 and 14 mol% Sc(2)O(3) nanopowders were prepared by using a nitrate-lysine gel-combustion synthesis. These materials were studied by synchrotron X-ray powder diffraction (SXPD) and Raman spectroscopy after calcination at different temperatures from 650 to 1200 degrees C, which led to samples with different average crystallite sizes, up to about 100 nm. The results from SXPD and Raman analyses indicate that, depending on Sc(2)O(3) content, the metastable t ''-form of the tetragonal phase or the cubic phase are fully retained at room temperature in nanocrystalline powders, provided an average crystallite sizes lower than similar to 30 nm. By contrast, powders with larger average crystallite sizes exhibit the stable rhombohedral, beta and gamma, phases and do not retain or very partially retain the metastable t '' and cubic ones.

Polar organic marker compounds in atmospheric aerosols during the LBA-SMOCC 2002 biomass burning experiment in Rondonia, Brazil: sources and source processes, time series, diel variations and size distributions

Measurements of polar organic marker compounds were performed on aerosols that were collected at a pasture site in the Amazon basin (Rondonia, Brazil) using a high-volume dichotomous sampler (HVDS) and a Micro-Orifice Uniform Deposit Impactor (MOUDI) within the framework of the 2002 LBA-SMOCC (Large-Scale Biosphere Atmosphere Experiment in Amazonia - Smoke Aerosols, Clouds, Rainfall, and Climate: Aerosols From Biomass Burning Perturb Global and Regional Climate) campaign. The campaign spanned the late dry season (biomass burning), a transition period, and the onset of the wet season (clean conditions). In the present study a more detailed discussion is presented compared to previous reports on the behavior of selected polar marker compounds, including levoglucosan, malic acid, isoprene secondary organic aerosol (SOA) tracers and tracers for fungal spores. The tracer data are discussed taking into account new insights that recently became available into their stability and/or aerosol formation processes. During all three periods, levoglucosan was the most dominant identified organic species in the PM(2.5) size fraction of the HVDS samples. In the dry period levoglucosan reached concentrations of up to 7.5 mu g m(-3) and exhibited diel variations with a nighttime prevalence. It was closely associated with the PM mass in the size-segregated samples and was mainly present in the fine mode, except during the wet period where it peaked in the coarse mode. Isoprene SOA tracers showed an average concentration of 250 ng m(-3) during the dry period versus 157 ng m(-3) during the transition period and 52 ng m(-3) during the wet period. Malic acid and the 2-methyltetrols exhibited a different size distribution pattern, which is consistent with different aerosol formation processes (i.e., gas-to-particle partitioning in the case of malic acid and heterogeneous formation from gas-phase precursors in the case of the 2-methyltetrols). The 2-methyltetrols were mainly associated with the fine mode during all periods, while malic acid was prevalent in the fine mode only during the dry and transition periods, and dominant in the coarse mode during the wet period. The sum of the fungal spore tracers arabitol, mannitol, and erythritol in the PM(2.5) fraction of the HVDS samples during the dry, transition, and wet periods was, on average, 54 ng m(-3), 34 ng m(-3), and 27 ng m(-3), respectively, and revealed minor day/night variation. The mass size distributions of arabitol and mannitol during all periods showed similar patterns and an association with the coarse mode, consistent with their primary origin. The results show that even under the heavy smoke conditions of the dry period a natural background with contributions from bioaerosols and isoprene SOA can be revealed. The enhancement in isoprene SOA in the dry season is mainly attributed to an increased acidity of the aerosols, increased NO(x) concentrations and a decreased wet deposition.

Determination of the parity of the neutral pion via its four-electron decay

We present a new determination of the parity of the neutral pion via the double Dalitz decay pi(0) -> e(+)e(-)e(+)e(-). Our sample, which consists of 30511 candidate decays, was collected from K(L) -> pi(0)pi(0)pi(0) decays in flight at the KTeV-E799 experiment at Fermi National Accelerator Laboratory. We confirm the negative pi(0) parity and place a limit on scalar contributions to the pi(0) -> e(+)e(-)e(+)e(-) decay amplitude of less than 3.3% assuming CPT conservation. The pi(0)gamma(*)gamma(*) form factor is well described by a momentum-dependent model with a slope parameter fit to the final state phase-space distribution. Additionally, we have measured the branching ratio of this mode to be B(pi(0) -> e(+)e(-)e(+)e(-)) = (3.26 +/- 0.18) x 10(-5).

Particle-species dependent modification of jet-induced correlations in Au plus Au collisions at root s(NN)=200 GeV

Measurements in Au + Au collisions at root s(NN) = 200 GeV of jet correlations for a trigger hadron at intermediate transverse momentum (p(T,trig)) with associated mesons or baryons at lower p(T,assoc) indicate strong modification of the away-side jet. The ratio of jet-associated baryons to mesons increases with centrality and p(T,assoc). For the most central collisions, the ratio is similar to that for inclusive measurements. This trend is incompatible with in-vacuum fragmentation but could be due to jetlike contributions from correlated soft partons, which recombine upon hadronization.

Position-dependent noncommutativity in quantum mechanics

The model of the position-dependent noncommutativity in quantum mechanics is proposed. We start with given commutation relations between the operators of coordinates [(x) over cap (i), (x) over cap (j)] = omega(ij) ((x) over cap), and construct the complete algebra of commutation relations, including the operators of momenta. The constructed algebra is a deformation of a standard Heisenberg algebra and obeys the Jacobi identity. The key point of our construction is a proposed first-order Lagrangian, which after quantization reproduces the desired commutation relations. Also we study the possibility to localize the noncommutativity.