High order iterative methods for decomposition‐coordination problems

Many real‐life optimization problems are of the multiobjective type and highdimensional. Possibilities for solving large scale optimization problems on a computer network or multiprocessor computer using a multi‐level approach are studied. The paper treats numerical methods in which procedural and rounding errors are unavoidable, for example, those arising in mathematical modelling and simulation. For the solution of involving decomposition‐coordination problems some rapidly convergent interative methods are developed based on the classical cubically convergent method of tangent hyperbolas (Chebyshev‐Halley method) and the method of tangent parabolas (Euler‐Chebyshev method). A family of iterative methods having the convergence order equal to four is also considered. Convergence properties and computational aspects of the methods under consideration are examined. The problems of their global implementation and polyalgorithmic strategy are discussed as well. Daugialaipsniai iteraciniai metodai skaidymo ir jungimo problemoms spręsti Santrauka Daugelis realių optimizavimo uždavinių yra daugiatiksliai ir daugiadimensiai. Straipsnyje nagrinėjamos sudėtingų optimizacijos uûdavinių sprendimų galimybės daugialaipsniu metodu, naudojant kompiuterinį tinklą arba daugiaprocesorinį kompiuterį. Apžvelgiami tokie įprastininiai skaitiniai metodai, kaip matematinis modeliavimas, kuriame neiövegiama paklaidų apvalinimo. Skaidymo ir jungimo problemoms spręsti, remiantis tangentinės hiperbolės (Čebyševo ir Halėjaus) ir tangentinės parabolės (Oilerio ir Čebyševo) metodais, sukurti keli greitos konvergencijos interaciniai metodai. Taip pat aptariama ketvirtojo laipsnio konvergencijos metodų šeima. Nagrinėjamos sukurtųjų metodų konvergavimo savybės ir skaičiavimo jais aspektai. Svarstomos pasiūlytųjų metodų ir polialgoritminės strategijos visuotinio taikymo galimybės. First Published Online: 21 Oct 2010 Reikšminiai žodžiai: Banacho erdvė, daugiatikslė optimizacija, hierachinis sprendimų priėmimas, skaidymo ir jungimo schemos, tangentinės hiperbolės ir tangentinės parabolės metodai, globalinė konvergencija

On the Solution of Nonlinear Optimization Problems of High Dimension

A lot of real-life problems lead frequently to the solution of a complicated (large scale, multicriteria, unstable, nonsmooth etc.) nonlinear optimization problem. In order to cope with large scale problems and to develop many optimum plans a hiearchical approach to problem solving may be useful. The idea of hierarchical decision making is to reduce the overall complex problem into smaller and simpler approximate problems (subproblems) which may thereupon treated independently. One way to break a problem into smaller subproblems is the use of decomposition-coordination schemes. For finding proper values for coordination parameters in convex programming some rapidly convergent iterative methods are developed, their convergence properties and computational aspects are examined. Problems of their global implementation and polyalgorithmic approach are discussed as well

A class of rapidly convergent interative Methods for Problems in mathematical Modelling

Methods with the convergence order p 2 (Newton`s, tangent hyperbolas, tangent parabolas etc.) and their approximate variants are studied. Conditions are presented under which the approximate variants preserve their convergence rate intrinsic to these methods and some computational aspects (possibilities to organize parallel computation, globalization of a method, the solution of the linear equations versus the matrix inversion at every iteration etc.) are discussed. Polyalgorithmic computational schemes (hybrid methods) combining the best features of various methods are developed and possibilities of their application to numerical solution of two-point boundary-value problem in ordinary differential equations and decomposition-coordination problem in convex programming are analyzed

La culture sur le lieu de travail en Estonie et en France

L’objectif principal de ce mémoire est de voir si les résultats des recherches de Hofstede dans les années 1970 sont toujours d’actualité. Dans ce mémoire, nous allons comparer les cultures française et estonienne sur le lieu de travail à partir des quatre dimensions culturelles de Hofstede. L'auteur a choisi ces deux pays car il serait intéressant d'analyser deux pays totalement différents géographiquement et culturellement.https://www.ester.ee/record=b5456088*es

Some iterative regularized methods for highly nonlinear least squares problems

This report treats numerical methods for highly nonlinear least squares problems for which procedural and rounding errors are unavoidable, e.g. those arising in the development of various nonlinear system identification techniques based on input‐output representation of the model such as training of artificial neural networks. Let F be a Frechet‐differentiable operator acting between Hilbert spaces H1 and H2 and such that the range of its first derivative is not necessarily closed. For solving the equation F(x) = 0 or minimizing the functional f(x) = ½ ‖F(x)‖2 , x H 1, two‐parameter iterative regularization methods based on the Gauss‐Newton method under certain condition on a test function and the required solution are developed, their computational aspects are discussed and a local convergence theorem is proved. First published online: 14 Oct 201

Dopamine protects neurons against glutamate-induced excitotoxicity

Glutamate excitotoxicity is responsible for neuronal death in acute neurological disorders including stroke, trauma and neurodegenerative disease. Loss of calcium homeostasis is a key mediator of glutamate-induced cell death. The neurotransmitter dopamine (DA) is known to modulate calcium signalling, and here we show that it can do so in response to physiological concentrations of glutamate. Furthermore, DA is able to protect neurons from glutamate-induced cell death at pathological concentrations of glutamate. We demonstrate that DA has a novel role in preventing delayed calcium deregulation in cortical, hippocampal and midbrain neurons. The effect of DA in abolishing glutamate excitotoxicity can be induced by DA receptor agonists, and is abolished by DA receptor antagonists. Our data indicate that the modulation of glutamate excitotoxicity by DA is receptor-mediated. We postulate that DA has a major physiological function as a safety catch to restrict the glutamate-induced calcium signal, and thereby prevent glutamate-induced cell death in the brain

Some rapidly convergent methods for nonlinear fredholm integral equation

Many problems in modelling can be reduced to the solution of a nonlinear equation F(x) = 0, where F is a Frechet‐differentiable (as many times as necessary) mapping between Banach spaces X and Y. For solving this equation we consider high order iteration methods of the type xk +1 =xk ‐ Q(xk, Ai k ), i ∈ I, I = {1,…, r}, r ≥ 1, k = 0, 1, …, where Q(x, Ai k ) is an operator from X into itself and Ai k, i ∈ I, are some approximations to the inverse operator(s) occurring in the associated exact method. In particular, this set of methods contains methods with successive approximation of the inverse operator(s) and those based on the use of iterative methods to obtain a cheap solution of limited accuracy for corresponding linear equation(s) at each iteration step. A convergence theorem is proved and computational aspects of the methods under consideration are examined. The solution of nonlinear Fredholm integral equation by means of methods with convergence order p ≥ 2 are considered and possibilities of organizing parallel computation in iteration process are also briefly discussed. Daug modeliavimo problemu galima suformuluoti netiesines lygties F(x) = 0 pavidalu. Čia F yra Banacho erdves X atvaizdavimas i Banacho erdve Y, turintis visas reikalingas Freshe išvestines. Lygčiai F(x) = 0 spresti taikomas aukštosios eiles iteracinis procesas tokio tipo xk + 1 =xk ‐ Q(xk, Ai k ), i ∈ {1,…, r}, k = 0, 1, …, Čia Q(x, Ai k ) yra tam tikras operatorius X → X, Ai k , yra atvirkštinio atvaizdavimo aproksimacijos. Irodyta konvergavimo teorema ir išnagrineti metodu taikymo skaičiavimo aspektai. Aptariamos skaičiavimu lygiagretinimo galimybes, taikant si ulomus metodus netiesinei Fredholmo integralinei lygčiai. First Published Online: 14 Oct 201

Dopamine Induced Neurodegeneration in a PINK1 Model of Parkinson's Disease

Parkinson's disease is a common neurodegenerative disease characterised by progressive loss of dopaminergic neurons, leading to dopamine depletion in the striatum. Mutations in the PINK1 gene cause an autosomal recessive form of Parkinson's disease. Loss of PINK1 function causes mitochondrial dysfunction, increased reactive oxygen species production and calcium dysregulation, which increases susceptibility to neuronal death in Parkinson's disease. The basis of neuronal vulnerability to dopamine in Parkinson's disease is not well understood

Assessment of ROS Production in the Mitochondria of Live Cells

Production of reactive oxygen species (ROS) in the mitochondria plays multiple roles in physiology, and excessive production of ROS leads to the development of various pathologies. ROS in the mitochondria are generated by various enzymes, mainly in the electron transporvt chain, and it is important to identify not only the trigger but also the source of free radical production. It is important to measure mitochondrial ROS in live, intact cells, because activation of ROS production could be initiated by changes in extramitochondrial processes which could be overseen when using isolated mitochondria. Here we describe the approaches, which allow to measure production of ROS in the matrix of mitochondria in live cells. We also demonstrate how to measure kinetic changes in lipid peroxidation in mitochondria of live cells. These methods could be used for understanding the mechanisms of pathology in a variety of disease models and also for testing neuro- or cardioprotective chemicals