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.

Chemical characterization and oxidative stability of the oils from three morphotypes of Mauritia flexuosa L.f, from the Peruvian Amazon

Three morphotypes of aguaje Mauritia flexuosa were tested, classified by the color of their mesocarpium: ""color"", ""shambo"" and ""amarillo"", collected from different areas near the city of Iquitos, Peru. Also, physical-chemical analyses of the mesocarpium were performed, such as the characterization of fatty acids by gas chromatography, determination of beta- carotene y alpha tocopherol by high efficiency liquid chromatography system in normal and reverse phase and the determination of oxidation induction time in the Rancimat apparatus. Proximate, mineral and fatty acid analyses were done on the seeds. The aguaje mesocarpium is rich in oleic oil (""amarillo"": 75.63% +/- 0.31), (beta-carotene (""amarillo"": 342.42ug/g 0.71) and alpha- tocopherol (""color"": 685.81mg/L +/- 1.04), plus the morphotype ""color"" has a superior oxidation induction time compared to other morphotypes with 6.91 +/- 0.01. The aguaje seed contains significant amounts of (06 (linoleic oil) in ""shambo"" with 36.04 +/- 0.09%. The results indicate that these oils, regardless their classification, contain important chemical compounds that give them a special nutritive value.

Modification of composition of a nanoemulsion with different cholesteryl ester molecular species: Effects on stability, peroxidation, and cell uptake

Purpose: Use of lipid nanoemulsions as carriers of drugs for therapeutic or diagnostic purposes has been increasingly studied. Here, it was tested whether modifications of core particle constitution could affect the characteristics and biologic properties of lipid nanoemulsions. Methods: Three nanoemulsions were prepared using cholesteryl oleate, cholesteryl stearate, or cholesteryl linoleate as main core constituents. Particle size, stability, pH, peroxidation of the nanoemulsions, and cell survival and uptake by different cell lines were evaluated. Results: It was shown that cholesteryl stearate nanoemulsions had the greatest particle size and all three nanoemulsions were stable during the 237-day observation period. The pH of the three nanoemulsion preparations tended to decrease over time, but the decrease in pH of cholesteryl stearate was smaller than that of cholesteryl oleate and cholesteryl linoleate. Lipoperoxidation was greater in cholesteryl linoleate than in cholesteryl oleate and cholesteryl stearate. After four hours' incubation of human umbilical vein endothelial cells (HUVEC) with nanoemulsions, peroxidation was minimal in the presence of cholesteryl oleate and more pronounced with cholesteryl linoleate and cholesteryl stearate. In contrast, macrophage incubates showed the highest peroxidation rates with cholesteryl oleate. Cholesteryl linoleate induced the highest cell peroxidation rates, except in macrophages. Uptake of cholesteryl oleate nanoemulsion by HUVEC and fibroblasts was greater than that of cholesteryl linoleate and cholesteryl stearate. Uptake of the three nanoemulsions by monocytes was equal. Uptake of cholesteryl oleate and cholesteryl linoleate by macrophages was negligible, but macrophage uptake of cholesteryl stearate was higher. In H292 tumor cells, cholesteryl oleate showed the highest uptakes. HUVEC showed higher survival rates when incubated with cholesteryl stearate and smaller survival with cholesteryl linoleate. H292 survival was greater with cholesteryl stearate. Conclusion: Although all three nanoemulsion types were stable for a long period, considerable differences were observed in size, oxidation status, and cell survival and nanoemulsion uptake in all tested cell lines. Those differences may be helpful in protocol planning and interpretation of data from experiments with lipid nanoemulsions.

Adipose Tissue-Derived Stem Cells from Humans and Mice Differ in Proliferative Capacity and Genome Stability in Long-Term Cultures

Adipose tissue-derived stem cells (ASCs) are among the more attractive adult stem cell options for potential therapeutic applications. Here, we studied and compared the basic biological characteristics of ASCs isolated from humans (hASCs) and mice (mASCs) and maintained in identical culture conditions, which must be examined prior to considering further potential clinical applications. hASCs and mASCs were compared for immunophenotype, differentiation potential, cell growth characteristics, senescence, nuclear morphology, and DNA content. Although both strains of ASCs displayed a similar immunophenotype, the percentage of CD73(+) cells was markedly lower and CD31(+) was higher in mASC than in hASC cultures. The mean population doubling time was 98.08 +/- 6.15 h for hASCs and 52.58 +/- 3.74 h for mASCs. The frequency of nuclear aberrations was noticeably lower in hASCs than in mASCs regardless of the passage number. Moreover, as the cells went through several in vitro passages, mASCs showed changes in DNA content and cell cycle kinetics (frequency of hypodiploid, G0/G1, G2/M, and hyperdiploid cells), whereas all of these parameters remained constant in hASCs. Collectively, these results suggest that mASCs display higher proliferative capacity and are more unstable than hASCs in long-term cultures. These results underscore the need to consider specificities among model systems that may influence outcomes when designing potential human applications.

PARTIAL STABILITY FOR A CLASS OF NONLINEAR SYSTEMS

This paper studies a nonlinear, discrete-time matrix system arising in the stability analysis of Kalman filters. These systems present an internal coupling between the state components that gives rise to complex dynamic behavior. The problem of partial stability, which requires that a specific component of the state of the system converge exponentially, is studied and solved. The convergent state component is strongly linked with the behavior of Kalman filters, since it can be used to provide bounds for the error covariance matrix under uncertainties in the noise measurements. We exploit the special features of the system-mainly the connections with linear systems-to obtain an algebraic test for partial stability. Finally, motivated by applications in which polynomial divergence of the estimates is acceptable, we study and solve a partial semistability problem.

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.

Hydrogen bond interactions between acetone and supercritical water

Hydrogen bond interactions between acetone and supercritical water are investigated using a combined and sequential Monte Carlo/quantum mechanics (S-MC/QM) approach. Simulation results show a dominant presence of con. gurations with one hydrogen bond for different supercritical states, indicating that this specific interaction plays an important role on the solvation properties of acetone in supercritical water. Using QM MP2/aug-cc-pVDZ the calculated average interaction energy reveals that the hydrogen-bonded acetone-water complex is energetically more stable under supercritical conditions than ambient conditions and its stability is little affected by variations of temperature and/or pressure. All average results reported here are statistically converged.

Stability, causality, and quasinormal modes of cosmic strings and cylinders

In this work we consider the evolution of a massive scalar field in cylindrically symmetric space-times. Quasinormal modes have been calculated for static and rotating cosmic cylinders. We found unstable modes in some cases. Rotating as well as static cosmic strings, i.e., without regular interior solutions, do not display quasinormal oscillation modes. We conclude that rotating cosmic cylinder space-times that present closed timelike curves are unstable against scalar perturbations.

Phase transitions and regions of stability in Reissner-Nordstrom holographic superconductors

The phase transition of Reissner-Nordstrom AdS(4) interacting with a massive charged scalar field has been further revisited. We found exactly one stable and one unstable quasinormal mode region for the scalar field. The two of them are separated by the first marginally stable solution.

Gravitational stability of simply rotating Myers-Perry black holes: Tensorial perturbations

We study the stability of D >= 7 asymptotically flat black holes rotating in a single two-plane against tensor-type gravitational perturbations. The extensive search of quasinormal modes for these black holes did not indicate any presence of growing modes, implying the stability of simply rotating Myers-Perry black holes against tensor-type perturbations.

Stability of higher dimensional Reissner-Nordstrom-anti-de Sitter black holes

We investigate stability of the D-dimensional Reissner-Nordstrom-anti-de Sitter metrics as solutions of the Einstein-Maxwell equations. We have shown that asymptotically anti-de Sitter (AdS) black holes are dynamically stable for all values of charge and anti-de Sitter radius in D=5,6...11 dimensional space-times. This does not contradict dynamical instability of RNAdS black holes found by Gubser in N=8 gauged supergravity, because the latter instability comes from the tachyon mode of the scalar field, coupled to the system. Asymptotically AdS black holes are known to be thermodynamically unstable for some region of parameters, yet, as we have shown here, they are stable against gravitational perturbations.

(In)stability of D-dimensional black holes in Gauss-Bonnet theory

We make an extensive study of evolution of gravitational perturbations of D-dimensional black holes in Gauss-Bonnet theory. There is an instability at higher multipoles l and large Gauss-Bonnet coupling alpha for D = 5, 6, which is stabilized at higher D. Although a small negative gap of the effective potential for the scalar type of gravitational perturbations exists for higher D and whatever alpha, it does not lead to any instability.

GLOBAL WELL-POSEDNESS AND NON-LINEAR STABILITY OF PERIODIC TRAVELING WAVES FOR A SCHRODINGER-BENJAMIN-ONO SYSTEM

The objective of this paper is two-fold: firstly, we develop a local and global (in time) well-posedness theory for a system describing the motion of two fluids with different densities under capillary-gravity waves in a deep water flow (namely, a Schrodinger-Benjamin-Ono system) for low-regularity initial data in both periodic and continuous cases; secondly, a family of new periodic traveling waves for the Schrodinger-Benjamin-Ono system is given: by fixing a minimal period we obtain, via the implicit function theorem, a smooth branch of periodic solutions bifurcating a Jacobian elliptic function called dnoidal, and, moreover, we prove that all these periodic traveling waves are nonlinearly stable by perturbations with the same wavelength.

POSITIVITY PROPERTIES OF THE FOURIER TRANSFORM AND THE STABILITY OF PERIODIC TRAVELLING-WAVE SOLUTIONS

In this paper we establish a method to obtain the stability of periodic travelling-wave solutions for equations of Korteweg-de Vries-type u(t) + u(p)u(x) - Mu(x) = 0, with M being a general pseudodifferential operator and where p >= 1 is an integer. Our approach uses the theory of totally positive operators, the Poisson summation theorem, and the theory of Jacobi elliptic functions. In particular we obtain the stability of a family of periodic travelling waves solutions for the Benjamin Ono equation. The present technique gives a new way to obtain the existence and stability of cnoidal and dnoidal waves solutions associated with the Korteweg-de Vries and modified Korteweg-de Vries equations, respectively. The theory has prospects for the study of periodic travelling-wave solutions of other partial differential equations.

Instantaneous characterization of vegetable oils via TAG and FFA profiles by easy ambient sonic-spray ionization mass spectrometry

A fast and reliable method is presented for the analysis of vegetable oils. Easy ambient sonic-spray ionization mass spectrometry (EASI-MS) is shown to efficiently desorb and ionize the main oil constituents from an inert surface under ambient conditions and to provide comprehensive triacylglyceride (TAG) and free fatty acid (FFA) profiles detected mainly as either [ TAG + Na](+) or [FFA - H](-) ions. EASI(+/-)-MS analysis is simple, easily implemented, requires just a tiny droplet of the oil and is performed without any pre-separation or chemical manipulation. It also causes no fragmentation of TAG ions hence diacylglyceride (DAG) and monoacylglyceride (MAG) profiles and contents can also be measured. The EASI(+/-)-MS profiles of TAG and FFA permit authentication and quality control and can be used, for instance, to access levels of adulteration, acidity, oxidation or hydrolysis of vegetable oils in general.