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.

Stability and relapse of maxillary anterior crowding treatment in Class I and Class II Division 1 malocclusions

Introduction: The maxillary anterior teeth are the most important to facial esthetics because they are the first to show on a smile. Therefore, stability of the maxillary anterior teeth alignment is an important issue. The objective of this study was to compare the stability of maxillary anterior tooth alignment in Class I and Class II Division 1 malocclusions. Methods: The sample comprised dental casts of 70 patients with Class I and Class II Division 1 malocclusions and a minimum of 3 mm of maxillary anterior crowding measured by an irregularity index. The patients were treated with extractions and evaluated at pretreatment and posttreatment and at least 5 years after treatment. The sample was divided into 3 groups: group 1, Class I malocclusion treated with 4 first premolar extractions comprising 30 subjects, with an initial age of 13.16 years and 8.59 mm of initial maxillary irregularity; group 2, Class II malocclusion treated with 4 first premolar extractions comprising 20 subjects, with an initial age of 12.95 years and 11.10 mm of maxillary irregularity; and group 3, Class II malocclusion treated with 2 first maxillary premolar extractions comprising 20 subjects, with an initial age of 13.09 years and 9.68 mm of maxillary irregularity. Results: The decrease in the maxillary irregularity index was significantly greater in group 2 than in group 1 during treatment. The stability of maxillary anterior alignment was 88.12% over the long term; 77% of the linear displacement of the anatomic contact points tended to return to their original positions. Conclusions: Stability of maxillary anterior alignment between the 3 groups was similar. The stability of maxillary anterior alignment was high over the long term, but a high percentage of teeth tended to return to their original positions. (Am J Orthod Dentofacial Orthop 2011; 139: 768-74)

Techniques to determine ignition, flame stability and burnout of blended coals in p.f. power station boilers

The blending of coals has become popular to improve the performance of coals, to meet specifications of power plants and, to reduce the cost of coals, This article reviews the results and provides new information on ignition, flame stability, and carbon burnout studies of blended coals. The reviewed studies were conducted in laboratory-, pilot-, and full-scale facilities. The new information was taken in pilot-scale studies. The results generally show that blending a high-volatile coal with a low-volatile coal or anthracite can improve the ignition, flame stability and burnout of the blends. This paper discusses two general methods to predict the performance of blended coals: (1) experiment; and (2) indices. Laboratory- and pilot-scale tests, at least, provide a relative ranking of the combustion performance of coal/blends in power station boilers. Several indices, volatile matter content, heating value and a maceral index, can be used to predict the relative ranking of ignitability and flame stability of coals and blends. The maceral index, fuel ratio, and vitrinite reflectance can also be used to predict the absolute carbon burnout of coal and blends within limits. (C) 2000 Elsevier Science Ltd. All rights reserved.

Dynamical Stability and Predictability of Football Players: The Study of One Match

The game of football demands new computational approaches to measure individual and collective performance. Understanding the phenomena involved in the game may foster the identification of strengths and weaknesses, not only of each player, but also of the whole team. The development of assertive quantitative methodologies constitutes a key element in sports training. In football, the predictability and stability inherent in the motion of a given player may be seen as one of the most important concepts to fully characterise the variability of the whole team. This paper characterises the predictability and stability levels of players during an official football match. A Fractional Calculus (FC) approach to define a player’s trajectory. By applying FC, one can benefit from newly considered modeling perspectives, such as the fractional coefficient, to estimate a player’s predictability and stability. This paper also formulates the concept of attraction domain, related to the tactical region of each player, inspired by stability theory principles. To compare the variability inherent in the player’s process variables (e.g., distance covered) and to assess his predictability and stability, entropy measures are considered. Experimental results suggest that the most predictable player is the goalkeeper while, conversely, the most unpredictable players are the midfielders. We also conclude that, despite his predictability, the goalkeeper is the most unstable player, while lateral defenders are the most stable during the match.

Normal forms, stability and splitting of invariant manifolds I. Gevrey Hamiltonians

In this paper, we give a new construction of resonant normal forms with a small remainder for near-integrable Hamiltonians at a quasi-periodic frequency. The construction is based on the special case of a periodic frequency, a Diophantine result concerning the approximation of a vector by independent periodic vectors and a technique of composition of periodic averaging. It enables us to deal with non-analytic Hamiltonians, and in this first part we will focus on Gevrey Hamiltonians and derive normal forms with an exponentially small remainder. This extends a result which was known for analytic Hamiltonians, and only in the periodic case for Gevrey Hamiltonians. As applications, we obtain an exponentially large upper bound on the stability time for the evolution of the action variables and an exponentially small upper bound on the splitting of invariant manifolds for hyperbolic tori, generalizing corresponding results for analytic Hamiltonians.

Normal forms, stability and splitting of invariant manifolds II. Finitely differentiable Hamiltonians

This paper is a sequel to ``Normal forms, stability and splitting of invariant manifolds I. Gevrey Hamiltonians", in which we gave a new construction of resonant normal forms with an exponentially small remainder for near-integrable Gevrey Hamiltonians at a quasi-periodic frequency, using a method of periodic approximations. In this second part we focus on finitely differentiable Hamiltonians, and we derive normal forms with a polynomially small remainder. As applications, we obtain a polynomially large upper bound on the stability time for the evolution of the action variables and a polynomially small upper bound on the splitting of invariant manifolds for hyperbolic tori.

Stability and robustness of blood variables in an antidoping context.

Introduction:  With the setting up of the newly Athlete's Biological Passport antidoping programme, novel guidelines have been introduced to guarantee results beyond reproach. We investigated in this context, the effect of storage time on the variables commonly measured for the haematological passport. We also wanted to assess for these variables, the within and between analyzer variations. Methods:  Blood samples were obtained from top level male professional cyclists (27 samples for the first part of the study and 102 for the second part) taking part to major stage races. After collection, they were transported under refrigerated conditions (2 °C < T < 12 °C), delivered to the antidoping laboratory, analysed and then stored at approximately 4 °C to conduct analysis at different time points up to 72 h after delivery. A mixed-model procedure was used to determine the stability of the different variables. Results:  As expected haemoglobin concentration was not affected by storage and showed stability for at least 72 h. Under the conditions of our investigation, the reticulocytes percentage showed a much better stability than previous published data (> 48 h) and the technical comparison of the haematology analyzer demonstrated excellent results. Conclusion:  In conclusion, our data clearly demonstrate that as long as the World Anti-Doping Agency's guidelines are followed rigorously, all blood results reach the quality level required in the antidoping context.

Stability and adaptability of runner peanut genotypes based on nonlinear regression and AMMI analysis

The objective of this work was to estimate the stability and adaptability of pod and seed yield in runner peanut genotypes based on the nonlinear regression and AMMI analysis. Yield data from 11 trials, distributed in six environments and three harvests, carried out in the Northeast region of Brazil during the rainy season were used. Significant effects of genotypes (G), environments (E), and GE interactions were detected in the analysis, indicating different behaviors among genotypes in favorable and unfavorable environmental conditions. The genotypes BRS Pérola Branca and LViPE‑06 are more stable and adapted to the semiarid environment, whereas LGoPE‑06 is a promising material for pod production, despite being highly dependent on favorable environments.

Lon protease negatively affects GacA protein stability and expression of the Gac/Rsm signal transduction pathway in Pseudomonas protegens.

In Pseudomonas protegens CHA0 and other fluorescent pseudomonads, the Gac/Rsm signal transduction pathway controls secondary metabolism and suppression of fungal root pathogens via the expression of regulatory small RNAs (sRNAs). Because of its high cost, this pathway needs to be protected from overexpression and to be turned off in response to environmental stress such as the lack of nutrients. However, little is known about its underlying molecular mechanisms. In this study, we demonstrated that Lon protease, a member of the ATP-dependent protease family, negatively regulated the Gac/Rsm cascade. In a lon mutant, the steady-state levels and the stability of the GacA protein were significantly elevated at the end of exponential growth. As a consequence, the expression of the sRNAs RsmY and RsmZ and that of dependent physiological functions such as antibiotic production were significantly enhanced. Biocontrol of Pythium ultimum on cucumber roots required fewer lon mutant cells than wild-type cells. In starved cells, the loss of Lon function prolonged the half-life of the GacA protein. Thus, Lon protease is an important negative regulator of the Gac/Rsm signal transduction pathway in P. protegens.

Career decision making, stability and actualization of career intentions : the case of entrepreneurial intentions

Career counselors are often concerned with stability and likelihood of implementation of clients' career intentions. It is often assumed that the status in career decision making (CDM) is one likely indicator; yet, empirical support for this assumption is sparse. The present study focused on entrepreneurial career intentions (EI) and showed that German university students (N = 1,221), with high EI can be found in very different empirically derived CDM statuses that range from preconcern to mature decidedness. Longitudinal analyses (n = 561) showed that career choice foreclosure (high decidedness/low exploration) related to more EI stability and that mature decidedness (high decidedness/high exploration) amplified effects of EI on opportunity identification, a form of EI actualization. The results imply that CDM statuses are useful to estimate stability and actualization of career intentions.

Stability and consistency of coping in adolescence: A longitudinal study

This study analyzed stability and consistency of coping among adolescents. The objectives were twofold: a) to analyze temporal stability and cross-situational consistency of coping responses after a 17- month interval, taking into account gender, age and type of stressor. b) To analyze the relative weight of contextual versus dispositional factors in predicting future coping. A cohort of 341 adolescents (51% girls and 49% boys aged between 12 and 16) were assessed twice by means of the Coping Responses Inventory - Youth. The results indicated that the coping responses were quite stable over time at the group level, but with important within-subject differences. Girls showed slightly more stability than boys. Among the girls, Avoidance coping showed as much stability as consistency and Approach coping showed more stability than consistency. Among the boys, Avoidance coping showed more stability than consistency, and Approach coping showed both low stability and low consistency. Among the boys, the coping used at Time 1 barely predicted that used at Time 2; in contrast, among the girls, the type of coping used in the past, especially Avoidance coping, predicted the coping that would be used in the future.

First principles analysis of the stability and diffusion of oxygen vacancies in meetal oxides

Oxygen vacancies in metal oxides are known to determine their chemistry and physics. The properties of neutral oxygen vacancies in metal oxides of increasing complexity (MgO, CaO, alpha-Al2O3, and ZnO) have been studied using density functional theory. Vacancy formation energies, vacancy-vacancy interaction, and the barriers for vacancy migration are determined and rationalized in terms of the ionicity, the Madelung potential, and lattice relaxation. It is found that the Madelung potential controls the oxygen vacancy properties of highly ionic oxides whereas a more complex picture arises for covalent ZnO.

Stability and properties of cellulose-sodium hydroxide solution systems

Since cellulose is a linear macromolecule it can be used as a material for regenerated cellulose fiber products e.g. in textile fibers or film manufacturing. Cellulose is not thermoformable, thus the manufacturing of these regenerated fibers is mainly possible through dissolution processes preceding the regeneration process. However, the dissolution of cellulose in common solvents is hindered due to inter- and intra-molecular hydrogen bonds in the cellulose chains, and relatively high crystallinity. Interestingly at subzero temperatures relatively dilute sodium hydroxide solutions can be used to dissolve cellulose to a certain extent. The objective of this work was to investigate the possible factors that govern the solubility of cellulose in aqueous NaOH and the solution stability. Cellulose-NaOH solutions have the tendency to form a gel over time and at elevated temperature, which creates challenges for further processing. The main target of this work was to achieve high solubility of cellulose in aqueous NaOH without excessively compromising the solution stability. In the literature survey an overview of the cellulose dissolution is given and possible factors contributing to the solubility and solution properties of cellulose in aqueous NaOH are reviewed. Furthermore, the concept of solution rheology is discussed. In the experimental part the focus was on the characterization of the used materials and properties of the prepared solutions mainly concentrating on cellulose solubility and solution stability.

Effect of ambient conditions on dimensional stability and stiffness of commercial paperboard and paperboard trays

The objective of this study was to develop laboratory test methods for characterizing the effects of changed moisture content on paperboard trays produced by press-forming process. Influence of moisture on the properties of unconverted paperboard such as bending stiffness, bursting strength, and curling was studied. Paperboard and tray samples were tested after storing in different relative humidity conditions (35, 50, 65, 80 and 95% RH). The effect of PE and PET extrusion coatings on these properties was also studied. It was found that increase in moisture content of paperboard decreases bending and bursting strength, dimensional stability and stiffness of paperboard trays. Such physical and mechanical properties as bending stiffness and curling of paperboard seem to define the stiffness of ready-made trays and their dimensional stability. Paperboards and trays with extruded PE and PET one sided coatings demonstrated higher strength properties but at the same time had lower dimensional stability comparing to uncoated paperboards. Samples with smaller polymer coat weight had better dimensional stability than respective samples with higher coat weight. It was also found that preconditioning of paperboard in lower humidity environment before press-forming could improve dimensional stability and stiffness of ready-made tray.