On the solvability of implicit differential inclusions

In the paper, the set-valued covering mappings are studied. The statements on solvability, solution estimates, and well-posedness of inclusions with conditionally covering mappings are proved. The results obtained are applied to the investigation of differential inclusions unsolved for the unknown function. The statements on solvability, solution estimates, and well-posedness of these inclusions are derived.

Singular Perturbation for the Discounted Continuous Control of Piecewise Deterministic Markov Processes

This paper deals with the expected discounted continuous control of piecewise deterministic Markov processes (PDMP`s) using a singular perturbation approach for dealing with rapidly oscillating parameters. The state space of the PDMP is written as the product of a finite set and a subset of the Euclidean space a""e (n) . The discrete part of the state, called the regime, characterizes the mode of operation of the physical system under consideration, and is supposed to have a fast (associated to a small parameter epsilon > 0) and a slow behavior. By using a similar approach as developed in Yin and Zhang (Continuous-Time Markov Chains and Applications: A Singular Perturbation Approach, Applications of Mathematics, vol. 37, Springer, New York, 1998, Chaps. 1 and 3) the idea in this paper is to reduce the number of regimes by considering an averaged model in which the regimes within the same class are aggregated through the quasi-stationary distribution so that the different states in this class are replaced by a single one. The main goal is to show that the value function of the control problem for the system driven by the perturbed Markov chain converges to the value function of this limit control problem as epsilon goes to zero. This convergence is obtained by, roughly speaking, showing that the infimum and supremum limits of the value functions satisfy two optimality inequalities as epsilon goes to zero. This enables us to show the result by invoking a uniqueness argument, without needing any kind of Lipschitz continuity condition.

LIPSCHITZ CLASSIFICATION OF FUNCTIONS ON A HOLDER TRIANGLE

The problem of semialgebraic Lipschitz classification of quasihomogeneous polynomials on a Holder triangle is studied. For this problem, the ""moduli"" are described completely in certain combinatorial terms.

Sensitivity to measurement perturbation of single-atom dynamics in cavity QED

We consider continuous observation of the nonlinear dynamics of single atom trapped in an optical cavity by a standing wave with intensity modulation. The motion of the atom changes the phase of the field which is then monitored by homodyne detection of the output field. We show that the conditional Hilbert space dynamics of this system, subject to measurement-induced perturbations, depends strongly on whether the corresponding classical dynamics is regular or chaotic. If the classical dynamics is chaotic, the distribution of conditional Hilbert space vectors corresponding to different observation records tends to be orthogonal. This is a characteristic feature of hypersensitivity to perturbation for quantum chaotic systems.

Differential perturbation of neuronal and glial glutamate transport systems in retinal ischaemia

Glutamate is the major excitatory neurotransmitter in the retina and is removed from the extracellular space by an energy-dependent process involving neuronal and glial cell transporters. The radial glial Muller cells express the glutamate transporter, GLAST, and preferentially accumulate glutamate. However, during an ischaemic episode, extracellular glutamate concentrations may rise to excitotoxic levels. Is this catastrophic rise in extracellular glutamate due to a failure of GLAST? Using immunocytochemistry, we monitored the transport of the glutamate transporter substrate, D-aspartate, in the retina under normal and ischaemic conditions. Two models of compromised retinal perfusion were compared: (1) Anaesthetised rats had their carotid arteries occluded for 7 days to produce a chronic reduction in retinal blood flow. Retinal function was assessed by electroretinography. D-aspartate was injected into the eye for 45 min, Following euthanasia, the retina was processed for D-aspartate. GLAST and glutamate immunocytochemistry. Although reduced retinal perfusion suppresses the electroretinogram b-wave, neither retinal histology, GLAST expression, nor the ability of Muller cells to uptake D-aspartate is affected. As this insult does not appear to cause excitotoxic neuronal damage, these data suggest that GLAST function and glutamate clearance are maintained during periods of reduced retinal perfusion. (2) Occlusion of the central retinal artery for 60 min abolishes retinal perfusion, inducing histological damage and electroretinogram suppression. Although GLAST expression appears to be normal. its ability to transport D-aspartate into Muller cells is greatly reduced. Interestingly, D-aspartate is transported into neuronal cells, i.e. photoreceptors, bipolar and ganglion cells. This suggests that while GLAST is vitally important for the clearance of excess extracellular glutamate, its capability to sustain inward transport is particularly susceptible to an acute ischaemic attack. Manipulation of GLAST function could alleviate the degeneration and blindness that result from ischaemic retinal disease. (C) 2001 Elsevier Science Ltd, All rights reserved.

The influence of a concurrent cognitive task on the compensatory stepping response to a perturbation in balance-impaired and healthy elders

This study investigated the influence of a concurrent cognitive task on the compensatory stepping response in balance-impaired elders and the attentional demand of the stepping response. Kinetic, kinematic and neuromuscular measures of a forward recovery step were investigated in 15 young adults, 15 healthy elders and 13 balance-impaired elders in a single task (postural recovery only) and dual task (postural recovery and vocal reaction time task) situation. Results revealed that reaction times were longer in all subjects when performed concurrently with a compensatory step, they were longer for a step than an in-place response and longer for balance-impaired older adults compared with young adults. An interesting finding was that the latter group difference may be related to prioritization between the two tasks rather than attentional demand, as the older adults completed the step before the reaction time, whereas the young adults could perform both concurrently. Few differences in step characteristics were found between tasks, with the most notable being a delayed latency and reduced magnitude of the early automatic postural response in healthy and balance-impaired elders with a concurrent task. (C) 2002 Elsevier Science B.V. All rights reserved.

A Perturbation and Observation Routine Used To Control A Power Converter

This paper presents a programable perturbation and observation control implementation for a wind generation system and its power electronic converter. The objective of the method in this particular application is to adjust the power delivered to charge a battery to its maximum and allowable value, function of the real values of several parameters and their continuous variation, the most important the wind velocity and the turbine efficiency. Also, to improve the power throughput and to use the turbine and generator marginal zones of operation, an unusual power converter is used, allowing a wide range for the input voltage values. The implemented control is continuously measuring the actual power and looks for a new and powerful operation point. © 2014 IEEE.

A perturbation and observation routine used to control a power converter

This paper presents a programable perturbation and observation control implementation for a wind generation system and its power electronic converter. The objective of the method in this particular application is to adjust the power delivered to charge a battery to its maximum and allowable value, function of the real values of several parameters and their continuous variation, the most important the wind velocity and the turbine efficiency. Also, to improve the power throughput and to use the turbine and generator marginal zones of operation, an unusual power converter is used, allowing a wide range for the input voltage values. The implemented control is continuously measuring the actual power and looks for a new and powerful operation point. © 2014 IEEE.

Tauroursodeoxycholic acid prevents Bax-induced membrane perturbation and cytochrome C release in isolated mitochondria

Biochemistry, 2003, 42 (10), pp 3070–3080 DOI: 10.1021/bi026979d

TP perturbation of TN matrices and totally positive directions

Here, we define and consider (linear) TP-directions and TP-paths for a totally nonnegative matrix, in an effort to more deeply understand perturbation of a TN matrix to a TP matrix. We give circumstances in which a TP-direction exists and an example to show that they do not always exist. A strategy to give (nonlinear) TP-paths is given (and applied to this example). A long term goal is to understand the sparsest TP-perturbation for application to completion problems.

Machine learning with Lipschitz classifiers

Magdeburg, Univ., Fak. für Elektrotechnik und Informationstechnik, Diss., 2010

Clarke critical values of subanalytic Lipschitz continuous functions

We prove that any subanalytic locally Lipschitz function has the Sard property. Such functions are typically nonsmooth and their lack of regularity necessitates the choice of some generalized notion of gradient and of critical point. In our framework these notions are defined in terms of the Clarke and of the convex-stable subdifferentials. The main result of this note asserts that for any subanalytic locally Lipschitz function the set of its Clarke critical values is locally finite. The proof relies on Pawlucki's extension of the Puiseuxlemma. In the last section we give an example of a continuous subanalytic function which is not constant on a segment of "broadly critical" points, that is, points for which we can find arbitrarily short convex combinations of gradients at nearby points.

The third order Melnikov function of a quadratic center under quadratic perturbation

We study quadratic perturbations of the integrable system (1+x)dH; where H =(x²+y²)=2: We prove that the first three Melnikov functions associated to the perturbed system give rise at most to three limit cycles.

Lipschitz harmonic capacity and Bilipschitz images of cantor sets

For bilipschitz images of Cantor sets in Rd we estimate the Lipschitz harmonic capacity and show this capacity is invariant under bilipschitz homeomorphisms.

Stability of periodic solutions obtained via the averaging method for nonsmooth Lipschitz system

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