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.

Optimal time following fluorescein instillation to evaluate rigid gas permeable contact lens fit

PURPOSE: To examine the optimum time at which fluorescein patterns of gas permeable lenses (GPs) should be evaluated. METHODS: Aligned, 0.2mm steep and 0.2mm flat GPs were fitted to 17 patients (aged 20.6±1.1 years, 10 male). Fluorescein was applied to their upper temporal bulbar conjunctiva with a moistened fluorescein strip. Digital slit lamp images (CSO, Italy) at 10× magnification of the fluorescein pattern viewed with blue light through a yellow filter were captured every 15s. Fluorescein intensity in central, mid peripheral and edge regions of the superior, inferior, temporal and nasal quadrants of the lens were graded subjectively using a +2 to -2 scale and using ImageJ software on the simultaneously captured images. RESULTS: Subjectively graded and objectively image analysed fluorescein intensity changed with time (p<0.001), lens region (centre, mid-periphery and edge: p<0.05) and there was interaction between lens region with lens fit (p<0.001). For edge band width, there was a significant effect of time (F=118.503, p<0.001) and lens fit (F=5.1249, p=0.012). The expected alignment, flat and steep fitting patterns could be seen from approximately after 30 to 180s subjectively and 15 to 105s in captured images. CONCLUSION: Although the stability of fluorescein intensity can start to decline in as little as 45s post fluorescein instillation, the diagnostic pattern of alignment, steep or flat fit is seen in each meridian by subjective observation from about 30s to 3min indicating this is the most appropriate time window to evaluate GP lenses in clinical practice.

Strong-weak Stackelberg Problems in Finite Dimensional Spaces

We are concerned with two-level optimization problems called strongweak Stackelberg problems, generalizing the class of Stackelberg problems in the strong and weak sense. In order to handle the fact that the considered two-level optimization problems may fail to have a solution under mild assumptions, we consider a regularization involving ε-approximate optimal solutions in the lower level problems. We prove the existence of optimal solutions for such regularized problems and present some approximation results when the parameter ǫ goes to zero. Finally, as an example, we consider an optimization problem associated to a best bound given in [2] for a system of nondifferentiable convex inequalities.

Optimization of Discrete-Time, Stochastic Systems

* This research was supported by a grant from the Greek Ministry of Industry and Technology.

Travelling waves in a complex Ginzburg-Landau equation with time-delay feedback

One of the simplest ways to create nonlinear oscillations is the Hopf bifurcation. The spatiotemporal dynamics observed in an extended medium with diffusion (e.g., a chemical reaction) undergoing this bifurcation is governed by the complex Ginzburg-Landau equation, one of the best-studied generic models for pattern formation, where besides uniform oscillations, spiral waves, coherent structures and turbulence are found. The presence of time delay terms in this equation changes the pattern formation scenario, and different kind of travelling waves have been reported. In particular, we study the complex Ginzburg-Landau equation that contains local and global time-delay feedback terms. We focus our attention on plane wave solutions in this model. The first novel result is the derivation of the plane wave solution in the presence of time-delay feedback with global and local contributions. The second and more important result of this study consists of a linear stability analysis of plane waves in that model. Evaluation of the eigenvalue equation does not show stabilisation of plane waves for the parameters studied. We discuss these results and compare to results of other models.

Recent Results on Stability Analysis of an Optimal Assembly Line Balance

Two assembly line balancing problems are addressed. The first problem (called SALBP-1) is to minimize number of linearly ordered stations for processing n partially ordered operations V = {1, 2, ..., n} within the fixed cycle time c. The second problem (called SALBP-2) is to minimize cycle time for processing partially ordered operations V on the fixed set of m linearly ordered stations. The processing time ti of each operation i ∈V is known before solving problems SALBP-1 and SALBP-2. However, during the life cycle of the assembly line the values ti are definitely fixed only for the subset of automated operations V\V . Another subset V ⊆ V includes manual operations, for which it is impossible to fix exact processing times during the whole life cycle of the assembly line. If j ∈V , then operation times tj can differ for different cycles of the production process. For the optimal line balance b of the assembly line with operation times t1, t2, ..., tn, we investigate stability of its optimality with respect to possible variations of the processing times tj of the manual operations j ∈ V .

Spatiotemporal optical bullets in two-dimensional fiber arrays and their stability

Long-lived light bullets fully localized in both space and time can be generated in novel photonic media such as multicore optical fiber or waveguide arrays. In this paper we present detailed theoretical analysis on the existence and stability of the discrete-continuous light bullets using a very generic model that occurs in a number of applications.

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

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

Real-time intensity domain characterization of fibre lasers using spatio-temporal dynamics

Fibre lasers are light sources that are synonymous with stability. They can give rise to highly coherent continuous-wave radiation, or a stable train of mode locked pulses with well-defined characteristics. However, they can also exhibit an exceedingly diverse range of nonlinear operational regimes spanning a multi-dimensional parameter space. The complex nature of the dynamics poses significant challenges in the theoretical and experimental studies of such systems. Here, we demonstrate how the real-time experimental methodology of spatio-temporal dynamics can be used to unambiguously identify and discern between such highly complex lasing regimes. This two-dimensional representation of laser intensity allows the identification and tracking of individual features embedded in the radiation as they make round-trip circulations inside the cavity. The salient features of this methodology are highlighted by its application to the case of Raman fibre lasers and a partially mode locked ring fibre laser operating in the normal dispersion regime.

Noise-induced standing waves in oscillatory systems with time-delayed feedback

In oscillatory reaction-diffusion systems, time-delay feedback can lead to the instability of uniform oscillations with respect to formation of standing waves. Here, we investigate how the presence of additive, Gaussian white noise can induce the appearance of standing waves. Combining analytical solutions of the model with spatio-temporal simulations, we find that noise can promote standing waves in regimes where the deterministic uniform oscillatory modes are stabilized. As the deterministic phase boundary is approached, the spatio-temporal correlations become stronger, such that even small noise can induce standing waves in this parameter regime. With larger noise strengths, standing waves could be induced at finite distances from the (deterministic) phase boundary. The overall dynamics is defined through the interplay of noisy forcing with the inherent reaction-diffusion dynamics.

Identification of a time-dependent bio-heat blood perfusion coefficient

In the paper the identification of the time-dependent blood perfusion coefficient is formulated as an inverse problem. The bio-heat conduction problem is transformed into the classical heat conduction problem. Then the transformed inverse problem is solved using the method of fundamental solutions together with the Tikhonov regularization. Some numerical results are presented in order to demonstrate the accuracy and the stability of the proposed meshless numerical algorithm.

Protocol optimization for the mild detemplation of mesoporous silica nanoparticles resulting in enhanced texture and colloidal stability

Porosity development of mesostructured colloidal silica nanoparticles is related to the removal of the organic templates and co-templates which is often carried out by calcination at high temperatures, 500-600 °C. In this study a mild detemplation method based on the oxidative Fenton chemistry has been investigated. The Fenton reaction involves the generation of OH radicals following a redox Fe3+/Fe2+ cycle that is used as catalyst and H2O2 as oxidant source. Improved material properties are anticipated since the Fenton chemistry comprises milder conditions than calcination. However, the general application of this methodology is not straightforward due to limitations in the hydrothermal stability of the particular system under study. The objective of this work is three-fold: 1) reducing the residual Fe in the resulting solid as this can be detrimental for the application of the material, 2) shortening the reaction time by optimizing the reaction temperature to minimize possible particle agglomeration, and finally 3) investigating the structural and textural properties of the resulting material in comparison to the calcined counterparts. It appears that the Fenton detemplation can be optimized by shortening the reaction time significantly at low Fe concentration. The milder conditions of detemplation give rise to enhanced properties in terms of surface area, pore volume, structural preservation, low Fe residue and high degree of surface hydroxylation; the colloidal particles are stable during storage. A relative particle size increase, expressed as 0.11%·h-1, has been determined.

On the stability of conventional and nano-structured carbon-based catalysts in the oxidative dehydrogenation of ethylbenzene under industrially relevant conditions

Relevant carbon-based materials, home-made carbon-silica hybrids, commercial activated carbon, and nanostructured multi-walled carbon nanotubes (MWCNT) were tested in the oxidative dehydrogenation of ethylbenzene (EB). Special attention was given to the reaction conditions, using a relatively concentrated EB feed (10 vol.% EB), and limited excess of O2 (O 2:EB = 0.6) in order to work at full oxygen conversion and consequently avoid O2 in the downstream processing and recycle streams. The temperature was varied between 425 and 475 °C, that is about 150-200 °C lower than that of the commercial steam dehydrogenation process. The stability was evaluated from runs of 60 h time on stream. Under the applied reactions conditions, all the carbon-based materials are apparently stable in the first 15 h time on stream. The effect of the gasification/burning was significantly visible only after this period where most of them fully decomposes. The carbon of the hybrids decomposes completely rendering the silica matrix and the activated carbon bed is fully consumed. Nano structured MWCNT is the most stable; the structure resists the demanding reaction conditions showing an EB conversion of ∼30% (but deactivating) with a steady selectivity of ∼80%. The catalyst stability under the ODH reaction conditions is predicted from the combustion apparent activation energies. © 2014 Elsevier Ltd. All rights reserved.

A Harrod modell strukturális stabilitása (Structural stability of the Harrod model)

In this study it is shown that the nontrivial hyperbolic fixed point of a nonlinear dynamical system, which is formulated by means of the adaptive expectations, corresponds to the unstable equilibrium of Harrod. We prove that this nonlinear dynamical (in the sense of Harrod) model is structurally stable under suitable economic conditions. In the case of structural stability, small changes of the functions (C1-perturbations of the vector field) describing the expected and the true time variation of the capital coefficients do not influence the qualitative properties of the endogenous variables, that is, although the trajectories may slightly change, their structure is the same as that of the unperturbed one, and therefore these models are suitable for long-time predictions. In this situation the critique of Lucas or Engel is not valid. There is no topological conjugacy between the perturbed and unperturbed models; the change of the growth rate between two levels may require different times for the perturbed and unperturbed models.

The thermodynamics and statistical mechanics of protein folding

The physics of self-organization and complexity is manifested on a variety of biological scales, from large ecosystems to the molecular level. Protein molecules exhibit characteristics of complex systems in terms of their structure, dynamics, and function. Proteins have the extraordinary ability to fold to a specific functional three-dimensional shape, starting from a random coil, in a biologically relevant time. How they accomplish this is one of the secrets of life. In this work, theoretical research into understanding this remarkable behavior is discussed. Thermodynamic and statistical mechanical tools are used in order to investigate the protein folding dynamics and stability. Theoretical analyses of the results from computer simulation of the dynamics of a four-helix bundle show that the excluded volume entropic effects are very important in protein dynamics and crucial for protein stability. The dramatic effects of changing the size of sidechains imply that a strategic placement of amino acid residues with a particular size may be an important consideration in protein engineering. Another investigation deals with modeling protein structural transitions as a phase transition. Using finite size scaling theory, the nature of unfolding transition of a four-helix bundle protein was investigated and critical exponents for the transition were calculated for various hydrophobic strengths in the core. It is found that the order of the transition changes from first to higher order as the strength of the hydrophobic interaction in the core region is significantly increased. Finally, a detailed kinetic and thermodynamic analysis was carried out in a model two-helix bundle. The connection between the structural free-energy landscape and folding kinetics was quantified. I show how simple protein engineering, by changing the hydropathy of a small number of amino acids, can enhance protein folding by significantly changing the free energy landscape so that kinetic traps are removed. The results have general applicability in protein engineering as well as understanding the underlying physical mechanisms of protein folding. ^