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.

The inducing NO-vasodilation by chemical reduction of coordinated nitrite ion in cis-[Ru(NO(2))L(bpy)(2)](+) complex

The synthesis of [Ru(NO(2)) L(bpy)(2)](+) (bpy = 2,2'-bipyridine and L = pyridine (py) and pyrazine (pz)) can be accomplished by addition of [Ru(NO) L(bpy) 2](PF(6))(3) to aqueous solutions of physiological pH. The electrochemical processes of [Ru(NO2) L(bpy) 2]+ in aqueous solution were studied by cyclic voltammetry and differential pulse voltammetry. The anodic scan shows a peak around 1.00 V vs. Ag/AgCl attributed to the oxidation process centered on the metal ion. However, in the cathodic scan a second peak around-0.60 V vs. Ag/AgCl was observed and attributed to the reduction process centered on the nitrite ligand. The controlled reduction potential electrolysis at-0.80 V vs. Ag/AgCl shows NO release characteristics as judged by NO measurement with a NO-sensor. This assumption was confirmed by ESI/MS(+) and spectroelectrochemical experiment where cis-[Ru(bpy)(2)L(H(2)O)](2+) was obtained as a product of the reduction of cis-[Ru(II)(NO(2)) L(bpy)(2)](+). The vasorelaxation observed in denuded aortic rings pre-contracted with 0.1 mu mol L(-1) phenylephrine responded with relaxation in the presence of cis-[RuII(NO2) L(bpy) 2]+. The potential of rat aorta cells to metabolize cis-[RuII(NO(2)) L(bpy)(2)](+) was also followed by confocal analysis. The obtained results suggest that NO release happens by reduction of cis-[RuII(NO(2)) L(bpy)(2)](+) inside the cell. The maximum vasorelaxation was achieved with 1 x 10(-5) mol L(-1) of cis-[RuII(NO(2)) L(bpy)(2)](+) complex.

Photolysis of ferric ions in the presence of sulfate or chloride ions: implications for the photo-Fenton process

The photo-Fenton process (Fe(2+)/Fe(3+), H(2)O(2), UV light) is one of the most efficient and advanced oxidation processes for the mineralization of the organic pollutants of industrial effluents and wastewater. The overall rate of the photo-Fenton process is controlled by the rate of the photolytic step that converts Fe(3+) back to Fe(2+). In this paper, the effect of sulfate or chloride ions on the net yield of Fe(2+) during the photolysis of Fe(3+) has been investigated in aqueous solution at pH 3.0 and 1.0 in the absence of hydrogen peroxide. A kinetic model based on the principal reactions that occur in the system fits the data for formation of Fe(2+) satisfactorily. Both experimental data and model prediction show that the availability of Fe(2+) produced by photolysis of Fe(3+) is inhibited much more in the presence of sulfate ion than in the presence of chloride ion as a function of the irradiation time at pH 3.0.

The Borg Scale as an Important Tool of Self-Monitoring and Self-Regulation of Exercise Prescription in Heart Failure Patients During Hydrotherapy - A Randomized Blinded Controlled Trial

Background: The Borg Scale may be a useful tool for heart failure patients to self-monitor and self-regulate exercise on land or in water (hydrotherapy) by maintaining the heart rate (HR) between the anaerobic threshold and respiratory compensation point. Methods and Results: Patients performed a cardiopulmonary exercise test to determine their anaerobic threshold/respiratory compensation points. The percentage of the mean HR during the exercise session in relation to the anaerobic threshold HR (%EHR-AT), in relation to the respiratory compensation point (%EHR-RCP), in relation to the peak HR by the exercise test (%EHR-Peak) and in relation to the maximum predicted HR (%EHR-Predicted) was calculated. Next, patients were randomized into the land or water exercise group. One blinded investigator instructed the patients in each group to exercise at a level between ""relatively easy and slightly tiring"". The mean HR throughout the 30-min exercise session was recorded. The %EHR-AT and %EHR-Predicted did not differ between the land and water exercisegroups, but they differed in the %EHR-RCP (95 +/- 7 to 86 +/- 7. P<0.001) and in the %EHR-Peak (85 +/- 8 to 78 +/- 9, P=0.007). Conclusions: Exercise guided by the Borg scale maintains the patient's HR between the anaerobic threshold and respiratory compensation point (ie, in the exercise training zone). (Circ J 2009; 73: 1871-1876)

A Randomized, Double-Blind, Placebo-Controlled Phase II Study of Vandetanib Plus Docetaxel/Prednisolone in Patients with Hormone-Refractory Prostate Cancer

Vandetanib (ZACTIMA(TM)) is a once-daily oral anticancer drug that selectively inhibits vascular endothelial growth factor receptor, epidermal growth factor receptor, and rearranged during transfection signaling. This randomized (1: 1), double-blind study evaluated vandetanib (100mg/day) or placebo in combination with docetaxel (D; 75mg/m(2) every 3 weeks) and prednisolone (P; 2 x 5 mg/day) in 86 patients with metastatic hormone-refractory prostate cancer (mHRPC). The primary assessment was prostate-specific antigen (PSA) response (confirmed reduction of >= 50% from baseline) and a greater number of patients showed a PSA response with placebo + DP (67%) versus vandetanib + DP (40%); hazard ratio = 2.23 (one-sided 80% confidence limit = 2.90; one-sided p = 0.99). More patients experienced progression events (disease progression or death from any cause) with vandetanib + DP (65%) versus placebo + DP (60%); hazard ratio = 1.13 (one-sided 80% confidence limit = 1.44; one-sided p = 0.67). The overall incidence of adverse events was similar in both groups, although more patients experienced adverse events, leading to permanent discontinuation with vandetanib + DP (28%) versus placebo + DP (12%). However, the safety and tolerability profile for vandetanib was similar to that previously reported; adverse events that occurred more frequently in the vandetanib + DP arm were hypertension (14% vs. 2%), erythematous rash (14% vs. 2%), and exfoliative rash (12% vs. 2%). In this study of patients with mHRPC, vandetanib + DP did not demonstrate any efficacy benefit, compared with placebo + DP.

Effects of Low-Level Laser Therapy on Pain and Scar Formation After Inguinal Herniation Surgery: A Randomized Controlled Single-Blind Study

Objective: The aim of this study was to investigate the efficacy of an infrared GaAlAs laser operating with a wavelength of 830 nm in the postsurgical scarring process after inguinal-hernia surgery. Background: Low-level laser therapy (LLLT) has been shown to be beneficial in the tissue-repair process, as previously demonstrated in tissue culture and animal experiments. However, there is lack of studies on the effects of LLLT on postsurgical scarring of incisions in humans using an infrared 830-nm GaAlAs laser. Method: Twenty-eight patients who underwent surgery for inguinal hernias were randomly divided into an experimental group (G1) and a control group (G2). G1 received LLLT, with the first application performed 24 h after surgery and then on days 3, 5, and 7. The incisions were irradiated with an 830-nm diode laser operating with a continuous power output of 40 mW, a spot-size aperture of 0.08 cm(2) for 26 s, energy per point of 1.04 J, and an energy density of 13 J/cm(2). Ten points per scar were irradiated. Six months after surgery, both groups were reevaluated using the Vancouver Scar Scale (VSS), the Visual Analog Scale, and measurement of the scar thickness. Results: G1 showed significantly better results in the VSS totals (2.14 +/- 1.51) compared with G2 (4.85 +/- 1.87); in the thickness measurements (0.11 cm) compared with G2 (0.19 cm); and in the malleability (0.14) compared with G2 (1.07). The pain score was also around 50% higher in G2. Conclusion: Infra-red LLLT (830 nm) applied after inguinal-hernia surgery was effective in preventing the formation of keloids. In addition, LLLT resulted in better scar appearance and quality 6 mo postsurgery.

rst Transcriptional Activity Influences kirre mRNA Concentration in the Drosophila Pupal Retina during the Final Steps of Ommatidial Patterning

Background: Drosophila retinal architecture is laid down between 24-48 hours after puparium formation, when some of the still uncommitted interommatidial cells (IOCs) are recruited to become secondary and tertiary pigment cells while the remaining ones undergo apoptosis. This choice between survival and death requires the product of the roughest (rst) gene, an immunoglobulin superfamily transmembrane glycoprotein involved in a wide range of developmental processes. Both temporal misexpression of Rst and truncation of the protein intracytoplasmic domain, lead to severe defects in which IOCs either remain mostly undifferentiated and die late and erratically or, instead, differentiate into extra pigment cells. Intriguingly, mutants not expressing wild type protein often have normal or very mild rough eyes. Methodology/Principal Findings: By using quantitative real time PCR to examine rst transcriptional dynamics in the pupal retina, both in wild type and mutant alleles we showed that tightly regulated temporal changes in rst transcriptional rate underlie its proper function during the final steps of eye patterning. Furthermore we demonstrated that the unexpected wild type eye phenotype of mutants with low or no rst expression correlates with an upregulation in the mRNA levels of the rst paralogue kin-of-irre (kirre), which seems able to substitute for rst function in this process, similarly to their role in myoblast fusion. This compensatory upregulation of kirre mRNA levels could be directly induced in wild type pupa upon RNAi-mediated silencing of rst, indicating that expression of both genes is also coordinately regulated in physiological conditions. Conclusions/Significance: These findings suggest a general mechanism by which rst and kirre expression could be fine tuned to optimize their redundant roles during development and provide a clearer picture of how the specification of survival and apoptotic fates by differential cell adhesion during the final steps of retinal morphogenesis in insects are controlled at the transcriptional level.

Bone Marrow Concentrate and Bovine Bone Mineral for Sinus Floor Augmentation: A Controlled, Randomized, Single-Blinded Clinical and Histological Trial-Per-Protocol Analysis

Purpose: The purpose of this work was to evaluate the potential of substituting autogenous bone (AB) by bone marrow aspirate concentrate (BMAC). Both AB and BMAC were tested in combination with a bovine bone mineral (BBM) for their ability of new bone formation (NBF) in a multicentric, randomized, controlled, clinical and histological noninferiority trial. Materials and Methods: Forty-five severely atrophied maxillary sinus from 26 patients were evaluated in a partial cross-over design. As test arm, 34 sinus of 25 patients were augmented with BBM and BMAC containing mesenchymal stem cells. Eleven control sinus from 11 patients were augmented with a mixture of 70% BBM and 30% AB. Biopsies were obtained after a 3-4-month healing period at time of implant placement and histomorphometrically analyzed for NBF. Results: NBF was 14.3%+/- 1.8% for the control and nonsignificantly lower (12.6%+/- 1.7%) for the test (90% confidence interval: -4.6 to 1.2). Values for BBM (31.3%+/- 2.7%) were significantly higher for the test compared with control (19.3%+/- 2.5%) (p < 0.0001). Nonmineralized tissue was lower by 3.3% in the test compared with control (57.6%; p = 0.137). Conclusions: NBF after 3-4 months is equivalent in sinus, augmented with BMAC and BBM or a mixture of AB and BBM. This technique could be an alternative for using autografts to stimulate bone formation.

Recurrence quantification analysis of turbulent fluctuations in the plasma edge of Tokamak Chauffage Alfveacuten Breacutesilien tokamak

Recurrences are close returns of a given state in a time series, and can be used to identify different dynamical regimes and other related phenomena, being particularly suited for analyzing experimental data. In this work, we use recurrence quantification analysis to investigate dynamical patterns in scalar data series obtained from measurements of floating potential and ion saturation current at the plasma edge of the Tokamak Chauffage Alfveacuten Breacutesilien [R. M. O. Galva approximate to o , Plasma Phys. Controlled Fusion 43, 1181 (2001)]. We consider plasma discharges with and without the application of radial electric bias, and also with two different regimes of current ramp. Our results indicate that biasing improves confinement through destroying highly recurrent regions within the plasma column that enhance particle and heat transport.

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.

Reduction of chaotic particle transport driven by drift waves in sheared flows

Investigations of chaotic particle transport by drift waves propagating in the edge plasma of tokamaks with poloidal zonal flow are described. For large aspect ratio tokamaks, the influence of radial electric field profiles on convective cells and transport barriers, created by the nonlinear interaction between the poloidal flow and resonant waves, is investigated. For equilibria with edge shear flow, particle transport is seen to be reduced when the electric field shear is reversed. The transport reduction is attributed to the robust invariant tori that occur in nontwist Hamiltonian systems. This mechanism is proposed as an explanation for the transport reduction in Tokamak Chauffage Alfven Bresilien [R. M. O. Galvao , Plasma Phys. Controlled Fusion 43, 1181 (2001)] for discharges with a biased electrode at the plasma edge.

Cavity-Controlled Collective Scattering at the Recoil Limit

We study collective scattering with Bose-Einstein condensates interacting with a high-finesse ring cavity. The condensate scatters the light of a transverse pump beam superradiantly into modes which, in contrast to previous experiments, are not determined by the geometrical shape of the condensate, but specified by a resonant cavity mode. Moreover, since the recoil-shifted frequency of the scattered light depends on the initial momentum of the scattered fraction of the condensate, we show that it is possible to employ the good resolution of the cavity as a filter selecting particular quantized momentum states.

Shared information in stationary states of stochastic processes

We present four estimators of the shared information (or interdepency) in ground states given that the coefficients appearing in the wave function are all real non-negative numbers and therefore can be interpreted as probabilities of configurations. Such ground states of Hermitian and non-Hermitian Hamiltonians can be given, for example, by superpositions of valence bond states which can describe equilibrium but also stationary states of stochastic models. We consider in detail the last case, the system being a classical not a quantum one. Using analytical and numerical methods we compare the values of the estimators in the directed polymer and the raise and peel models which have massive, conformal invariant and nonconformal invariant massless phases. We show that like in the case of the quantum problem, the estimators verify the area law with logarithmic corrections when phase transitions take place.

Analytical results on Muller's ratchet effect in growing populations

Fontanari introduced [Phys. Rev. Lett. 91, 218101 (2003)] a model for studying Muller's ratchet phenomenon in growing asexual populations. They studied two situations, either including a death probability for each newborn or not, but were able to find analytical (recursive) expressions only in the no-decay case. In this Brief Report a branching process formalism is used to find recurrence equations that generalize the analytical results of the original paper besides confirming the interesting effects their simulations revealed.