Stability threshold approach for complex dynamical systems

Acknowledgments This paper was developed within the scope of the IRTG 1740/TRP 2011/50151-0, funded by the DFG/FAPESP, and supported by the Government of the Russian Federation (Agreement No. 14.Z50.31.0033 with the Institute of Applied Physics RAS). The first author thanks Dr Roman Ovsyannikov for valuable discussions regarding estimation of the mistake probability.

Symmetry, stability, and dynamics of multidomain and multicomponent protein systems

Symmetry is commonly observed in many biological systems. Here we discuss representative examples of the role of symmetry in structural molecular biology. Point group symmetries are observed in many protein oligomers whose three-dimensional atomic structures have been elucidated by x-ray crystallography. Approximate symmetry also occurs in multidomain proteins. Symmetry often confers stability on the molecular system and results in economical usage of basic components to build the macromolecular structure. Symmetry is also associated with cooperativity. Mild perturbation from perfect symmetry may be essential in some systems for dynamic functions.

Stability of Coulomb systems in a magnetic field.

I study N electrons and M protons in a magnetic field. It is shown that the total energy per particle is bounded below by a constant independent of M and N, provided the fine structure constant is small. Here, the total energy includes the energy of the magnetic field.

Quantitative stability of linear infinite inequality systems under block perturbations with applications to convex systems

The original motivation for this paper was to provide an efficient quantitative analysis of convex infinite (or semi-infinite) inequality systems whose decision variables run over general infinite-dimensional (resp. finite-dimensional) Banach spaces and that are indexed by an arbitrary fixed set J. Parameter perturbations on the right-hand side of the inequalities are required to be merely bounded, and thus the natural parameter space is l ∞(J). Our basic strategy consists of linearizing the parameterized convex system via splitting convex inequalities into linear ones by using the Fenchel–Legendre conjugate. This approach yields that arbitrary bounded right-hand side perturbations of the convex system turn on constant-by-blocks perturbations in the linearized system. Based on advanced variational analysis, we derive a precise formula for computing the exact Lipschitzian bound of the feasible solution map of block-perturbed linear systems, which involves only the system’s data, and then show that this exact bound agrees with the coderivative norm of the aforementioned mapping. In this way we extend to the convex setting the results of Cánovas et al. (SIAM J. Optim. 20, 1504–1526, 2009) developed for arbitrary perturbations with no block structure in the linear framework under the boundedness assumption on the system’s coefficients. The latter boundedness assumption is removed in this paper when the decision space is reflexive. The last section provides the aimed application to the convex case.

Short-time stability in linear time-varying systems.

"SFOSR 748."

Stability of multi-agent systems

This work attempts to shed light to the fundamental concepts behind the stability of Multi-Agent Systems. We view the system as a discrete time Markov chain with a potentially unknown transitional probability distribution. The system will be considered to be stable when its state has converged to an equilibrium distribution. Faced with the non-trivial task of establishing the convergence to such a distribution, we propose a hypothesis testing approach according to which we test whether the convergence of a particular system metric has occurred. We describe some artificial multi-agent ecosystems that were developed and we present results based on these systems which confirm that this approach qualitatively agrees with our intuition.

Viability, Optimality and Stability of Dynamical Systems and Estimation of Convergence of Numerical Schemes

AMS subject classification: 49N35,49N55,65Lxx.

Control of cascaded DC-DC converter-based hybrid battery energy storage systems - Part I:stability Issue

There is an emerging application which uses a mixture of batteries within an energy storage system. These hybrid battery solutions may contain different battery types. A DC-side cascaded boost converters along with a module based distributed power sharing strategy has been proposed to cope with variations in battery parameters such as, state-of-charge and/or capacity. This power sharing strategy distributes the total power among the different battery modules according to these battery parameters. Each module controller consists of an outer voltage loop with an inner current loop where the desired control reference for each control loop needs to be dynamically varied according to battery parameters to undertake this sharing. As a result, the designed control bandwidth or stability margin of each module control loop may vary in a wide range which can cause a stability problem within the cascaded converter. This paper reports such a unique issue and thoroughly investigates the stability of the modular converter under the distributed sharing scheme. The paper shows that a cascaded PI control loop approach cannot guarantee the system stability throughout the operating conditions. A detailed analysis of the stability issue and the limitations of the conventional approach are highlighted. Finally in-depth experimental results are presented to prove the stability issue using a modular hybrid battery energy storage system prototype under various operating conditions.

Basin stability approach for quantifying responses of multistable systems with parameters mismatch

Acknowledgement This work is funded by the National Science Center Poland based on the decision number DEC-2015/16/T/ST8/00516. PB is supported by the Foundation for Polish Science (FNP).

Chitosan Nanoparticles Loaded The Herbicide Paraquat: The Influence Of The Aquatic Humic Substances On The Colloidal Stability And Toxicity.

Polymeric nanoparticles have been developed for several applications, among them as carrier system of pesticides. However, few studies have investigated the fate of these materials in the environment in relation to colloidal stability and toxicity. In nature, humic substances are the main agents responsible for complexation with metals and organic compounds, as well as responsible for the dynamics of these nanoparticles in aquatic and terrestrial environments. In this context, the evaluation of the influence of aquatic humic substances (AHS) on the colloidal stability and toxicity of polymeric nanoparticles of chitosan/tripolyphosphate with or without paraquat was performed. In this study, the nanoparticles were prepared by the ionic gelation method and characterized by size distribution measurements (DLS and NTA), zeta potential, infrared and fluorescence spectroscopy. Allium cepa genotoxicity studies and ecotoxicity assays with the alga Pseudokirchneriella subcapitata were used to investigate the effect of aquatic humic substances (AHS) on the toxicity of this delivery system. No changes were observed in the physical-chemical stability of the nanoparticles due to the presence of AHS using DLS and NTA techniques. However some evidence of interaction between the nanoparticles and AHS was observed by infrared and fluorescence spectroscopies. The ecotoxicity and genotoxicity assays showed that humic substances can decrease the toxic effects of nanoparticles containing paraquat. These results are interesting because they are important for understanding the interaction of these nanostructured carrier systems with species present in aquatic ecosystems such as humic substances, and in this way, opening new perspectives for studies on the dynamics of these carrier systems in the ecosystem.

Prediction of good glass formers in the Al-Ni-La and Al-Ni-Gd systems using topological instability and electronegativity

A new criterion has been recently proposed combining the topological instability (lambda criterion) and the average electronegativity difference (Delta e) among the elements of an alloy to predict and select new glass-forming compositions. In the present work, this criterion (lambda.Delta e) is applied to the Al-Ni-La and Al-Ni-Gd ternary systems and its predictability is validated using literature data for both systems and additionally, using own experimental data for the Al-La-Ni system. The compositions with a high lambda.Delta e value found in each ternary system exhibit a very good correlation with the glass-forming ability of different alloys as indicated by their supercooled liquid regions (Delta T(x)) and their critical casting thicknesses. In the case of the Al-La-Ni system, the alloy with the largest lambda.Delta e value, La(56)Al(26.5)Ni(17.5), exhibits the highest glass-forming ability verified for this system. Therefore, the combined lambda.Delta e criterion is a simple and efficient tool to select new glass-forming compositions in Al-Ni-RE systems. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3563099]

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.

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.

POLLING SYSTEMS WITH PARAMETER REGENERATION, THE GENERAL CASE

We consider a polling model with multiple stations, each with Poisson arrivals and a queue of infinite capacity. The service regime is exhaustive and there is Jacksonian feedback of served customers. What is new here is that when the server comes to a station it chooses the service rate and the feedback parameters at random; these remain valid during the whole stay of the server at that station. We give criteria for recurrence, transience and existence of the sth moment of the return time to the empty state for this model. This paper generalizes the model, when only two stations accept arriving jobs, which was considered in [Ann. Appl. Probab. 17 (2007) 1447-1473]. Our results are stated in terms of Lyapunov exponents for random matrices. From the recurrence criteria it can be seen that the polling model with parameter regeneration can exhibit the unusual phenomenon of null recurrence over a thick region of parameter space.