Continuity of Lyapunov functions and of energy level for generalized gradient semigroup

The global attractor of a gradient-like semigroup has a Morse decomposition. Associated to this Morse decomposition there is a Lyapunov function (differentiable along solutions)-defined on the whole phase space- which proves relevant information on the structure of the attractor. In this paper we prove the continuity of these Lyapunov functions under perturbation. On the other hand, the attractor of a gradient-like semigroup also has an energy level decomposition which is again a Morse decomposition but with a total order between any two components. We claim that, from a dynamical point of view, this is the optimal decomposition of a global attractor; that is, if we start from the finest Morse decomposition, the energy level decomposition is the coarsest Morse decomposition that still produces a Lyapunov function which gives the same information about the structure of the attractor. We also establish sufficient conditions which ensure the stability of this kind of decomposition under perturbation. In particular, if connections between different isolated invariant sets inside the attractor remain under perturbation, we show the continuity of the energy level Morse decomposition. The class of Morse-Smale systems illustrates our results.

Average control of Markov decision processes with Feller transition probabilities and general action spaces

This paper studies the average control problem of discrete-time Markov Decision Processes (MDPs for short) with general state space, Feller transition probabilities, and possibly non-compact control constraint sets A(x). Two hypotheses are considered: either the cost function c is strictly unbounded or the multifunctions A(r)(x) = {a is an element of A(x) : c(x, a) <= r} are upper-semicontinuous and compact-valued for each real r. For these two cases we provide new results for the existence of a solution to the average-cost optimality equality and inequality using the vanishing discount approach. We also study the convergence of the policy iteration approach under these conditions. It should be pointed out that we do not make any assumptions regarding the convergence and the continuity of the limit function generated by the sequence of relative difference of the alpha-discounted value functions and the Poisson equations as often encountered in the literature. (C) 2012 Elsevier Inc. All rights reserved.

A generalized finite element method with global-local enrichment functions for confined plasticity problems

The main feature of partition of unity methods such as the generalized or extended finite element method is their ability of utilizing a priori knowledge about the solution of a problem in the form of enrichment functions. However, analytical derivation of enrichment functions with good approximation properties is mostly limited to two-dimensional linear problems. This paper presents a procedure to numerically generate proper enrichment functions for three-dimensional problems with confined plasticity where plastic evolution is gradual. This procedure involves the solution of boundary value problems around local regions exhibiting nonlinear behavior and the enrichment of the global solution space with the local solutions through the partition of unity method framework. This approach can produce accurate nonlinear solutions with a reduced computational cost compared to standard finite element methods since computationally intensive nonlinear iterations can be performed on coarse global meshes after the creation of enrichment functions properly describing localized nonlinear behavior. Several three-dimensional nonlinear problems based on the rate-independent J (2) plasticity theory with isotropic hardening are solved using the proposed procedure to demonstrate its robustness, accuracy and computational efficiency.

LONG TIME CORRELATIONS OF NONLINEAR LUTTINGER LIQUIDS

An overview is given of the limitations of Luttinger liquid theory in describing the real time equilibrium dynamics of critical one-dimensional systems with nonlinear dispersion relation. After exposing the singularities of perturbation theory in band curvature effects that break the Lorentz invariance of the Tomonaga-Luttinger model, the origin of high frequency oscillations in the long time behaviour of correlation functions is discussed. The notion that correlations decay exponentially at finite temperature is challenged by the effects of diffusion in the density-density correlation due to umklapp scattering in lattice models.

On S-asymptotically omega-periodic functions and applications

Let (X, parallel to . parallel to) be a Banach space and omega is an element of R. A bounded function u is an element of C([0, infinity); X) is called S-asymptotically omega-periodic if lim(t ->infinity)[u(t + omega) - u(t)] = 0. In this paper, we establish conditions under which an S-asymptotically omega-periodic function is asymptotically omega-periodic and we discuss the existence of S-asymptotically omega-periodic and asymptotically omega-periodic solutions for an abstract integral equation. Some applications to partial differential equations and partial integro-differential equations are considered. (C) 2011 Elsevier Ltd. All rights reserved.

Characterization of Stability Region for General Autonomous Nonlinear Dynamical Systems

The existing characterization of stability regions was developed under the assumption that limit sets on the stability boundary are exclusively composed of hyperbolic equilibrium points and closed orbits. The characterizations derived in this technical note are a generalization of existing results in the theory of stability regions. A characterization of the stability boundary of general autonomous nonlinear dynamical systems is developed under the assumption that limit sets on the stability boundary are composed of a countable number of disjoint and indecomposable components, which can be equilibrium points, closed orbits, quasi-periodic solutions and even chaotic invariant sets.

TYPE-ZERO SADDLE-NODE BIFURCATIONS AND STABILITY REGION ESTIMATION OF NONLINEAR AUTONOMOUS DYNAMICAL SYSTEMS

A complete characterization of the stability boundary of a class of nonlinear dynamical systems that admit energy functions is developed in this paper. This characterization generalizes the existing results by allowing the type-zero saddle-node nonhyperbolic equilibrium points on the stability boundary. Conceptual algorithms to obtain optimal estimates of the stability region (basin of attraction) in the form of level sets of a given family of energy functions are derived. The behavior of the stability region and the corresponding estimates are investigated for parameter variation in the neighborhood of a type-zero saddle-node bifurcation value.

A new method for decision making in multi-objective optimization problems

Many engineering sectors are challenged by multi-objective optimization problems. Even if the idea behind these problems is simple and well established, the implementation of any procedure to solve them is not a trivial task. The use of evolutionary algorithms to find candidate solutions is widespread. Usually they supply a discrete picture of the non-dominated solutions, a Pareto set. Although it is very interesting to know the non-dominated solutions, an additional criterion is needed to select one solution to be deployed. To better support the design process, this paper presents a new method of solving non-linear multi-objective optimization problems by adding a control function that will guide the optimization process over the Pareto set that does not need to be found explicitly. The proposed methodology differs from the classical methods that combine the objective functions in a single scale, and is based on a unique run of non-linear single-objective optimizers.

A new approach for modeling and control of nonlinear systems via norm-bounded linear differential inclusions

A systematic approach to model nonlinear systems using norm-bounded linear differential inclusions (NLDIs) is proposed in this paper. The resulting NLDI model is suitable for the application of linear control design techniques and, therefore, it is possible to fulfill certain specifications for the underlying nonlinear system, within an operating region of interest in the state-space, using a linear controller designed for this NLDI model. Hence, a procedure to design a dynamic output feedback controller for the NLDI model is also proposed in this paper. One of the main contributions of the proposed modeling and control approach is the use of the mean-value theorem to represent the nonlinear system by a linear parameter-varying model, which is then mapped into a polytopic linear differential inclusion (PLDI) within the region of interest. To avoid the combinatorial problem that is inherent of polytopic models for medium- and large-sized systems, the PLDI is transformed into an NLDI, and the whole process is carried out ensuring that all trajectories of the underlying nonlinear system are also trajectories of the resulting NLDI within the operating region of interest. Furthermore, it is also possible to choose a particular structure for the NLDI parameters to reduce the conservatism in the representation of the nonlinear system by the NLDI model, and this feature is also one important contribution of this paper. Once the NLDI representation of the nonlinear system is obtained, the paper proposes the application of a linear control design method to this representation. The design is based on quadratic Lyapunov functions and formulated as search problem over a set of bilinear matrix inequalities (BMIs), which is solved using a two-step separation procedure that maps the BMIs into a set of corresponding linear matrix inequalities. Two numerical examples are given to demonstrate the effectiveness of the proposed approach.

Systemic Determinants of the Information Systems Outsourcing Decision: A Comparative Study of German and United States Firms

The practice of information systems (IS) outsourcing is widely established among organizations. Nonetheless, evidence suggests that organizations differ considerably in the extent to which they deploy IS outsourcing. This variation has motivated research into the determinants of the IS outsourcing decision. Most of this research is based on the assumption that a decision on the outsourcing of a particular IS function is made independently of other IS functions. This modular view ignores the systemic nature of the IS function, which posits that IS effectiveness depends on how the various IS functions work together effectively. This study proposes that systemic influences are important criteria in evaluating the outsourcing option. It further proposes that the recognition of systemic influences in outsourcing decisions is culturally sensitive. Specifically, we provide evidence that systemic effects are factored into the IS outsourcing decision differently in more individualist cultures than in collectivist ones. Our results of a survey of United States and German firms indicate that perceived in-house advantages in the systemic impact of an IS function are, indeed, a significant determinant of IS outsourcing in a moderately individualist country (i.e., Germany), whereas insignificant in a strongly individualist country (i.e., the United States). The country differences are even stronger with regard to perceived in-house advantages in the systemic view of IS professionals. In fact, the direction of this impact is reversed in the United States sample. Other IS outsourcing determinants that were included as controls, such as cost efficiency, did not show significant country differences.

Extended kalman filter for estimation of parameters in nonlinear state-space models of biochemical networks.

It is system dynamics that determines the function of cells, tissues and organisms. To develop mathematical models and estimate their parameters are an essential issue for studying dynamic behaviors of biological systems which include metabolic networks, genetic regulatory networks and signal transduction pathways, under perturbation of external stimuli. In general, biological dynamic systems are partially observed. Therefore, a natural way to model dynamic biological systems is to employ nonlinear state-space equations. Although statistical methods for parameter estimation of linear models in biological dynamic systems have been developed intensively in the recent years, the estimation of both states and parameters of nonlinear dynamic systems remains a challenging task. In this report, we apply extended Kalman Filter (EKF) to the estimation of both states and parameters of nonlinear state-space models. To evaluate the performance of the EKF for parameter estimation, we apply the EKF to a simulation dataset and two real datasets: JAK-STAT signal transduction pathway and Ras/Raf/MEK/ERK signaling transduction pathways datasets. The preliminary results show that EKF can accurately estimate the parameters and predict states in nonlinear state-space equations for modeling dynamic biochemical networks.

A novel computer test to assess driving-relevant cognitive functions - a pilot study

BACKGROUND: The assessment of driving-relevant cognitive functions in older drivers is a difficult challenge as there is no clear-cut dividing line between normal cognition and impaired cognition and not all cognitive functions are equally important for driving. METHODS: To support decision makers, the Bern Cognitive Screening Test (BCST) for older drivers was designed. It is a computer-assisted test battery assessing visuo-spatial attention, executive functions, eye-hand coordination, distance judgment, and speed regulation. Here we compare the performance in BCST with the performance in paper and pencil cognitive screening tests and the performance in the driving simulator testing of 41 safe drivers (without crash history) and 14 unsafe drivers (with crash history). RESULTS: Safe drivers performed better than unsafe drivers in BCST (Mann-Whitney U test: U = 125.5; p = 0.001) and in the driving simulator (Student's t-test: t(44) = -2.64, p = 0.006). No clear group differences were found in paper and pencil screening tests (p > 0.05; ns). BCST was best at identifying older unsafe drivers (sensitivity 86%; specificity 61%) and was also better tolerated than the driving simulator test with fewer dropouts. CONCLUSIONS: BCST is more accurate than paper and pencil screening tests, and better tolerated than driving simulator testing when assessing driving-relevant cognition in older drivers.

An fMRI-Study on context-specificity of inhibitory functions in alcohol-dependency: Preliminary results

Introduction: Alcohol-dependency is a common disease with many negative consequences in the daily life. A typical symptom of alcoholic-patients is the persistent and uncontrollable desire to consume alcohol. Inspite of different treatments, alcohol-dependency has a relapse rate of about 85%. This high rate is facilitated by a dysfunction of cognitive control-processes. In order to understand this disease sustaining factor, the present study investigated the neurophysiological correlates of inhibition of alcoholic-patients in a neutral as well as an alcohol-related context. Methods: A total of 18 participants, (9 alcohol-dependent-patients (age range: 27-62 years), 9 healthy controls (age range: 29-60 years)) have been measured with functional magnetic resonance imaging while they participated in an alcohol-specific Go/NoGo-Task. Neurophysiological correlates of inhibition in an alcohol-related as well as a neutral context were compared in both groups. Results: When comparing correct stop-trials in alcohol-related to neutral context, only alcohol-dependent patients showed significant hyperactivation in frontal regions (superior and medial gyrus frontalis, anterior gyrus cinguli, gyrus paracentralis and the gyrus praecentralis). No significant differences were found in any of the behavioral analyses. Discussion: These preliminary results thus indicate that successful inhibition in a drug-related context demands additional resources in patients. Especially the hyperactivation of the anterior gyrus cinguli might be important because of its involvement in decision-processes. In the absent of deficits in behavioral data, this suggests that alcohol-dependent patients need more neuronal activity to achieve the same performance-level like healthy controls.

Soil and land information: How to support decision-making?

Soils are fundamental to ensuring water, energy and food security. Within the context of sus- tainable food production, it is important to share knowledge on existing and emerging tech- nologies that support land and soil monitoring. Technologies, such as remote sensing, mobile soil testing, and digital soil mapping, have the potential to identify degraded and non- /little-responsive soils, and may also provide a basis for programmes targeting the protection and rehabilitation of soils. In the absence of such information, crop production assessments are often not based on the spatio-temporal variability in soil characteristics. In addition, uncertain- ties in soil information systems are notable and build up when predictions are used for monitor- ing soil properties or biophysical modelling. Consequently, interpretations of model-based results have to be done cautiously. As such they provide a scientific, but not always manage- able, basis for farmers and/or policymakers. In general, the key incentives for stakeholders to aim for sustainable management of soils and more resilient food systems are complex at farm as well as higher levels. The same is true of drivers of soil degradation. The decision- making process aimed at sustainable soil management, be that at farm or higher level, also in- volves other goals and objectives valued by stakeholders, e.g. land governance, improved envi- ronmental quality, climate change adaptation and mitigation etc. In this dialogue session we will share ideas on recent developments in the discourse on soils, their functions and the role of soil and land information in enhancing food system resilience.

SOMS: SurrOgate MultiStart algorithm for use with nonlinear programming for global optimization

SOMS is a general surrogate-based multistart algorithm, which is used in combination with any local optimizer to find global optima for computationally expensive functions with multiple local minima. SOMS differs from previous multistart methods in that a surrogate approximation is used by the multistart algorithm to help reduce the number of function evaluations necessary to identify the most promising points from which to start each nonlinear programming local search. SOMS’s numerical results are compared with four well-known methods, namely, Multi-Level Single Linkage (MLSL), MATLAB’s MultiStart, MATLAB’s GlobalSearch, and GLOBAL. In addition, we propose a class of wavy test functions that mimic the wavy nature of objective functions arising in many black-box simulations. Extensive comparisons of algorithms on the wavy testfunctions and on earlier standard global-optimization test functions are done for a total of 19 different test problems. The numerical results indicate that SOMS performs favorably in comparison to alternative methods and does especially well on wavy functions when the number of function evaluations allowed is limited.