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.

CHARACTERIZATION OF EXPONENTIAL DIVERGENCE OF THE KALMAN FILTER FOR TIME-VARYING SYSTEMS

This paper studies semistability of the recursive Kalman filter in the context of linear time-varying (LTV), possibly nondetectable systems with incorrect noise information. Semistability is a key property, as it ensures that the actual estimation error does not diverge exponentially. We explore structural properties of the filter to obtain a necessary and sufficient condition for the filter to be semistable. The condition does not involve limiting gains nor the solution of Riccati equations, as they can be difficult to obtain numerically and may not exist. We also compare semistability with the notions of stability and stability w.r.t. the initial error covariance, and we show that semistability in a sense makes no distinction between persistent and nonpersistent incorrect noise models, as opposed to stability. In the linear time invariant scenario we obtain algebraic, easy to test conditions for semistability and stability, which complement results available in the context of detectable systems. Illustrative examples are included.

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.

Instability of the time dependent Horava-Witten model

We consider scalar perturbations in the time dependent Horava-Witten model in order to probe its stability. We show that during the nonsingular epoque the model evolves without instabilities until it encounters the curvature singularity where a big crunch is supposed to occur. We compute the frequencies of the scalar field oscillation during the stable period and show how the oscillations can be used to prove the presence of such a singularity.

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.

Time Constraints in the School Environment: What Does a Sleepy Student Tell Us?

In this article, we discuss school schedules and their implications in the context of chronobiological contemporary knowledge, arguing for the need to reconsider time planning in the school setting. We present anecdotal observations regarding chronobiological challenges imposed by the school system throughout different ages and discuss the effects of these schedules in terms of sleepiness and its deleterious consequences on learning, memory, and attention. Different settings (including urban vs. rural habitats) influence timing, which also depends on self-selected sleep schedules. Finally, we criticize the traditional view of a necessary strict stability of sleep-wake habits.

Influence of gelation time on the morphological and physico-chemical properties of the sol-gel entrapped lipase

Different gelation times (4, 18, 24 and 48 h) were used for the preparation of silica sol-gel supports and encapsulated Candida rugosa lipase using tetraethoxysilane (TEOS) as precursor. The hydrophobic matrices and immobilized lipases produced were characterized with regard to pore volume and size by nitrogen adsorption (BJH method), weight loss upon heating (TGA), differential scanning calorimetry (DSC), scanning electron microscopy (SEM), chemical composition (FTIR) and percentage of hydrolysis (POH%) of olive oil. These structural parameters were found to change with the gelation time, but no direct relation was found between the percentage of oil hydrolysis (POH%) and the gelation time. The best combination of high thermal stability and high POH% (99.5%) occurred for encapsulated lipase produced with 24 h gelation time. (C) 2007 Elsevier B.V. All rights reserved.

Rapid solidification and phase stability evaluation of Ti-Si-B alloys

Ti-rich Ti-Si-B alloys can be considered for structural applications at high temperatures (max. 700 degrees C), however, phase equilibria data is reported only for T = 1250 degrees C. Thus, in this work the phase stability of this system has been evaluated at 700 degrees C. In order to attain equilibrium conditions in shorter time, rapid solidified samples have been prepared and carefully characterized. The microstructural characterization of the produced materials were based on X-ray diffraction (XRD), scanning electron microscopy (SEM-BSE), high resolution transmission electron microscopy (HRTEM), High Temperature X-ray diffraction with Synchrotron radiation (XRDSR) and Differential Scanning Calorimetry (DSC). Amorphous and amorphous with embedded nanocrystals have been observed after rapid solidification from specific alloy compositions. The values of the crystallization temperature (Tx) of the alloys were in the 509-647 degrees C temperature range. After Differential Scanning Calorimetry and High Temperature X-ray Diffraction with Synchrotron radiation, the alloys showed crystalline and basically formed by two or three of the following phases: alpha Ti, Ti(6)Si(2)B; Ti(5)Si(3); Ti(3)Si and TiB. It has been shown the stability of the Ti(3)Si and Ti(6)Si(2)B phases at 700 degrees C and the proposition of an isothermal section at this temperature. (C) 2011 Elsevier B.V. All rights reserved.

Synthesis of PID controllers for a class of time delay systems

In this paper we use the Hermite-Biehler theorem to establish results on the design of proportional plus integral plus derivative (PID) controllers for a class of time delay systems. Using the property of interlacing at high frequencies of the class of systems considered and linear programming we obtain the set of all stabilizing PID controllers. As far as we know, previous results on the synthesis of PID controllers rely on the solution of transcendental equations. This paper also extends previous results on the synthesis of proportional controllers for a class of delay systems Of retarded type to a larger class of delay systems. (C) 2009 Elsevier Ltd. All rights reserved.

AnSBBR Applied to a Personal Care Industry Wastewater Treatment: Effects of Fill Time, Volume Treated Per Cycle, and Organic Load

A study was performed regarding the effect of the relation between fill time, volume treated per cycle, and influent concentration at different applied organic loadings on the stability and efficiency of an anaerobic sequencing batch reactor containing immobilized biomass on polyurethane foam with recirculation of the liquid phase (AnSBBR) applied to the treatment of wastewater from a personal care industry. Total cycle length of the reactor was 8 h (480 min). Fill times were 10 min in the batch operation, 4 h in the fed-batch operation, and a 10-min batch followed by a 4-h fed batch in the mixed operation. Settling time was not necessary since the biomass was immobilized and decant time was 10 min. Volume of liquid medium in the reactor was 2.5 L, whereas volume treated per cycle ranged from 0.88 to 2.5 L in accordance with fill time. Influent concentration varied from 300 to 1,425 mg COD/L, resulting in an applied volumetric organic load of 0.9 and 1.5 g COD/L.d. Recirculation flow rate was 20 L/h, and the reactor was maintained at 30 A degrees C. Values of organic matter removal efficiency of filtered effluent samples were below 71% in the batch operations and above 74% in the operations of fed batch followed by batch. Feeding wastewater during part of the operational cycle was beneficial to the system, as it resulted in indirect control over the conversion of substrate into intermediates that would negatively interfere with the biochemical reactions regarding the degradation of organic matter. As a result, the average substrate consumption increased, leading to higher organic removal efficiencies in the fed-batch operations.

Effect of Fill Time on the Performance of Pilot-scale ASBR and AnSBBR Applied to Sanitary Wastewater Treatment

Many lab-scale studies have been carried out regarding the effect of feed strategy on the performance of anaerobic sequencing batch reactors (ASBR); however, more detailed pilot-scale studies should be performed to assess the real applicability of this type of operation. Therefore, the objective of this work was to assess the effect of feed strategy or fill time in a 1-m(3) mechanically stirred pilot-scale sequencing batch reactor, treating 0.65 m(3) sanitary wastewater in 8-h cycles at ambient temperature. Two reactor configurations were used: one containing granular biomass (denominated ASBR) and the other immobilized biomass on polyurethane foam as inert support (denominated anaerobic sequencing batch biofilm reactor (AnSBBR)). The reactors were operated under five distinct feed strategies, namely: typical batch and fed-batch for 25%, 50%, 75%, and 100% of the cycle length. Stirring frequency in the ASBR was 40 rpm with two flat-blade turbine impellers and 80 rpm in the AnSBBR with two helix impellers. The results showed that both the ASBR and AnSBBR when operated under typical batch, fed-batch for 50% and 75% of the cycle length, presented improved organic matter removal efficiencies, without significant differences in performance, thus showing important operational flexibility. In addition, the reactors presented operation stability under all conditions.