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.

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.

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.

VIP expression in vessels of the vaginal wall: relationship with estrogen status

Objective Vasoactive intestinal peptide (VIP) is a neuropeptide with elevated expression in regions that control urogenital functions. Estrogen appears to modulate VIP expression in various organs, but this effect has not been demonstrated in the vaginal wall. The aim of this study was to evaluate the influence of estrogen status on VIP expression in vessels of the vaginal wall. Methods Surgical specimens were removed from the vaginal walls of 18 premenopausal women and 12 postmenopausal women who were given surgery for genital prolapse grade I or II. Vaginal specimens were stained with estrogen receptor-alpha (ER-alpha) and VIP antibodies. Levels of follicle stimulating hormone (FSH), estradiol, prolactin, fasting glucose and serum thyroxine stimulating hormone were also measured. Estrogen status was assessed on the basis of FSH and ER-alpha scores. Results The vaginal walls of premenopausal women had significantly higher ER-alpha scores than those of menopausal women (premenopausal group, 3.6 +/- 2.2; menopausal group, 1.4 +/- 1.8; p = 0.01). Premenopausal women also had significantly higher levels of VIP in the vaginal wall than menopausal women (p = 0.02). Increasing age was associated with lower level of VIP staining (odds ratio 0.88; 95% confidence interval 0.78-0.99). Conclusion Levels of ER-alpha and VIP expression in the posterior vaginal wall were higher in premenopausal than in menopausal women, but VIP expression was not associated with estrogen status. Age was an independent predictor of VIP staining in vaginal wall biopsies.

Characterization of the procera Tomato Mutant Shows Novel Functions of the SlDELLA Protein in the Control of Flower Morphology, Cell Division and Expansion, and the Auxin-Signaling Pathway during Fruit-Set and Development

procera (pro) is a tall tomato (Solanum lycopersicum) mutant carrying a point mutation in the GRAS region of the gene encoding SlDELLA, a repressor in the gibberellin (GA) signaling pathway. Consistent with the SlDELLA loss of function, pro plants display a GA-constitutive response phenotype, mimicking wild-type plants treated with GA(3). The ovaries from both nonemasculated and emasculated pro flowers had very strong parthenocarpic capacity, associated with enhanced growth of preanthesis ovaries due to more and larger cells. pro parthenocarpy is facultative because seeded fruits were obtained by manual pollination. Most pro pistils had exserted stigmas, thus preventing self-pollination, similar to wild-type pistils treated with GA(3) or auxins. However, Style2.1, a gene responsible for long styles in noncultivated tomato, may not control the enhanced style elongation of pro pistils, because its expression was not higher in pro styles and did not increase upon GA(3) application. Interestingly, a high percentage of pro flowers had meristic alterations, with one additional petal, sepal, stamen, and carpel at each of the four whorls, respectively, thus unveiling a role of SlDELLA in flower organ development. Microarray analysis showed significant changes in the transcriptome of preanthesis pro ovaries compared with the wild type, indicating that the molecular mechanism underlying the parthenocarpic capacity of pro is complex and that it is mainly associated with changes in the expression of genes involved in GA and auxin pathways. Interestingly, it was found that GA activity modulates the expression of cell division and expansion genes and an auxin signaling gene (tomato AUXIN RESPONSE FACTOR7) during fruit-set.

An extension of the invariance principle for dwell-time switched nonlinear systems

In this paper, we propose an extension of the invariance principle for nonlinear switched systems under dwell-time switched solutions. This extension allows the derivative of an auxiliary function V, also called a Lyapunov-like function, along the solutions of the switched system to be positive on some sets. The results of this paper are useful to estimate attractors of nonlinear switched systems and corresponding basins of attraction. Uniform estimates of attractors and basin of attractions with respect to time-invariant uncertain parameters are also obtained. Results for a common Lyapunov-like function and multiple Lyapunov-like functions are given. Illustrative examples show the potential of the theoretical results in providing information on the asymptotic behavior of nonlinear dynamical switched systems. (C) 2012 Elsevier B.V. All rights reserved.

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.

Effects of acute physical exercise on executive functions: a comparison between aerobic and strength exercise

The aim of this study was to compare the effects of acute aerobic and strength exercises on selected executive functions. A counterbalanced, crossover, randomized trial was performed. Forty-two healthy women were randomly submitted to three different conditions: (1) aerobic exercise, (2) strength exercise, and (3) control condition. Before and after each condition, executive functions were measured by the Stroop Test and the Trail Making Test. Following the aerobic and strength sessions, the time to complete the Stroop "non-color word" and "color word" condition was lower when compared with that of the control session. The performance in the Trail Making Test was unchanged. In conclusion, both acute aerobic and strength exercises improve the executive functions. Nevertheless, this positive effect seems to be task and executive function dependent.

A possible new mechanism for the control of miRNA expression in neurons

The control of gene expression by miRNAs has been widely investigated in different species and cell types. Following a probabilistic rather than a deterministic regimen, the action of these short nucleotide sequences on specific genes depends on intracellular concentration,which in turn reflects the balance between biosynthesis and degradation. Recent studies have described the involvement of XRN2, an exoribonuclease, in miRNA degradation and PAPD4, an atypical poly(A) polymerase, in miRNA stability. Herein, we examined the expression of XRN2 and PAPD4 in developing and adult rat hippocampi. Combining bioinformatics and real-time PCR,we demonstrated that XRN2 and PAPD4 expression is regulated by the uncorrelated action of transcription factors, resulting in distinct gene expression profiles during development. Analyses of nuclei position and nestin labeling revealed that both proteins progressively accumulated during neuronal differentiation, and that they are weakly expressed in immature neurons and absent in glial and endothelial cells. Despite the differences in subcellular localization, both genes were concurrently identified within identical neuronal subpopulations, including specific inhibitory interneurons. Thus, we cope with a singular circumstance in biology: an almost complete intersected expression of functional-opposed genes, reinforcing that their antagonistically driven actions on miRNAs “make sense” if simultaneously present at the same cells. Considering that the transcriptome in the nervous system is finely tuned to physiological processes, it was remarkable that miRNA stability-related genes were oncurrently identified in neurons that play essential roles in cognitive functions such as memory and learning. In summary, this study reveals a possible new mechanism for the control of miRNA expression.

A control and automation system for wave basins

This paper presents the new active absorption wave basin, named Hydrodynamic Calibrator (HC), constructed at the University of São Paulo (USP), in the Laboratory facilities of the Numerical Offshore Tank (TPN). The square (14 m 14 m) tank is able to generate and absorb waves from 0.5 Hz to 2.0 Hz, by means of 148 active hinged flap wave makers. An independent mechanical system drives each flap by means of a 1HP servo-motor and a ball-screw based transmission system. A customized ultrasonic wave probe is installed in each flap, and is responsible for measuring wave elevation in the flap. A complex automation architecture was implemented, with three Programmable Logic Computers (PLCs), and a low-level software is responsible for all the interlocks and maintenance functions of the tank. Furthermore, all the control algorithms for the generation and absorption are implemented using higher level software (MATLAB /Simulink block diagrams). These algorithms calculate the motions of the wave makers both to generate and absorb the required wave field by taking into account the layout of the flaps and the limits of wave generation. The experimental transfer function that relates the flap amplitude to the wave elevation amplitude is used for the calculation of the motion of each flap. This paper describes the main features of the tank, followed by a detailed presentation of the whole automation system. It includes the measuring devices, signal conditioning, PLC and network architecture, real-time and synchronizing software and motor control loop. Finally, a validation of the whole automation system is presented, by means of the experimental analysis of the transfer function of the waves generated and the calculation of all the delays introduced by the automation system.