A global convergence criterion for discrete-time multivariable adaptive systems

The paper deals with the basic problem of adjusting a matrix gain in a discrete-time linear multivariable system. The object is to obtain a global convergence criterion, i.e. conditions under which a specified error signal asymptotically approaches zero and other signals in the system remain bounded for arbitrary initial conditions and for any bounded input to the system. It is shown that for a class of up-dating algorithms for the adjustable gain matrix, global convergence is crucially dependent on a transfer matrix G(z) which has a simple block diagram interpretation. When w(z)G(z) is strictly discrete positive real for a scalar w(z) such that w-1(z) is strictly proper with poles and zeros within the unit circle, an augmented error scheme is suggested and is proved to result in global convergence. The solution avoids feeding back a quadratic term as recommended in other schemes for single-input single-output systems.

On Convergence of Differential Evolution Over a Class of Continuous Functions With Unique Global Optimum

Differential evolution (DE) is arguably one of the most powerful stochastic real-parameter optimization algorithms of current interest. Since its inception in the mid 1990s, DE has been finding many successful applications in real-world optimization problems from diverse domains of science and engineering. This paper takes a first significant step toward the convergence analysis of a canonical DE (DE/rand/1/bin) algorithm. It first deduces a time-recursive relationship for the probability density function (PDF) of the trial solutions, taking into consideration the DE-type mutation, crossover, and selection mechanisms. Then, by applying the concepts of Lyapunov stability theorems, it shows that as time approaches infinity, the PDF of the trial solutions concentrates narrowly around the global optimum of the objective function, assuming the shape of a Dirac delta distribution. Asymptotic convergence behavior of the population PDF is established by constructing a Lyapunov functional based on the PDF and showing that it monotonically decreases with time. The analysis is applicable to a class of continuous and real-valued objective functions that possesses a unique global optimum (but may have multiple local optima). Theoretical results have been substantiated with relevant computer simulations.

Convergence of Power Control in a Random Channel Environment

In this paper, we study the Foschini Miljanic algorithm, which was originally proposed in a static channel environment. We investigate the algorithm in a random channel environment, study its convergence properties and apply the Gerschgorin theorem to derive sufficient conditions for the convergence of the algorithm. We apply the Foschini and Miljanic algorithm to cellular networks and derive sufficient conditions for the convergence of the algorithm in distribution and validate the results with simulations. In cellular networks, the conditions which ensure convergence in distribution can be easily verified.

Learning the global maximum with parameterized learning automata

A feedforward network composed of units of teams of parameterized learning automata is considered as a model of a reinforcement teaming system. The internal state vector of each learning automaton is updated using an algorithm consisting of a gradient following term and a random perturbation term. It is shown that the algorithm weakly converges to a solution of the Langevin equation implying that the algorithm globally maximizes an appropriate function. The algorithm is decentralized, and the units do not have any information exchange during updating. Simulation results on common payoff games and pattern recognition problems show that reasonable rates of convergence can be obtained.

A Global Constraint On Relative Rotation To Avoid Lumped Compliant Mechanisms In Topology Optimization

Some of the well known formulations for topology optimization of compliant mechanisms could lead to lumped compliant mechanisms. In lumped compliance, most of the elastic deformation in a mechanism occurs at few points, while rest of the mechanism remains more or less rigid. Such points are referred to as point-flexures. It has been noted in literature that high relative rotation is associated with point-flexures. In literature we also find a formulation of local constraint on relative rotations to avoid lumped compliance. However it is well known that a global constraint is easier to handle than a local constraint, by a numerical optimization algorithm. The current work presents a way of putting global constraint on relative rotations. This constraint is also simpler to implement since it uses linearized rotation at the center of finite-elements, to compute relative rotations. I show the results obtained by using this constraint oil the following benchmark problems - displacement inverter and gripper.

An E-Convergence Method For The Evaluation Of Critical Parameters

A simple cconversence technique is applied to obtain accurate estimates of critical temperatures and critical it\ponmts of a few two- and threpdiniensional king models. When applied to the virial series for hard spheres and hard discs, this method predicts a divergence of the equation-of-state at the density of closest packing.

On global summer monsoonal drought mechanics

It is shown that within the framework of a linear five-level quasi-geostrophic steady state global model the middle latitude systems can always have significant influence on the Asian summer monsoonal system through the lower tropospheric monsoonal westerly window region around 80°E. It is hypothesized that quasistationarity of the middle latitude longwave systems results in stronger teleconnections through this window and the consequent monsoon breaks when the phase is right.

Small local variations in B-form DNA lead to a large variety of global geometries which can accommodate most DNA-binding protein motifs

An important question of biological relevance is the polymorphism of the double-helical DNA structure in its free form, and the changes that it undergoes upon protein-binding. We have analysed a database of free DNA crystal structures to assess the inherent variability of the free DNA structure and have compared it with a database of protein-bound DNA crystal structures to ascertain the protein-induced variations.

Molecular convergence of hexosamine biosynthetic pathway and ER stress leading to insulin resistance in L6 skeletal muscle cells

Augmentation of hexosamine biosynthetic pathway (HBP) and endoplasmic reticulum (ER) stress were independently related to be the underlying causes of insulin resistance. We hypothesized that there might be a molecular convergence of activated HBP and ER stress pathways leading to insulin resistance. Augmentation of HBP in L6 skeletal muscle cells either by pharmacological (glucosamine) or physiological (high-glucose) means, resulted in increased protein expression of ER chaperones (viz., Grp78, Calreticulin, and Calnexin), UDP-GlcNAc levels and impaired insulin-stimulated glucose uptake. Cells silenced for O-glycosyl transferase (OGT) showed improved insulin-stimulated glucose uptake (P < 0.05) but without any effect on ER chaperone upregulation. While cells treated with either glucosamine or high-glucose exhibited increased JNK activity, silencing of OGT resulted in inhibition of JNK and normalization of glucose uptake. Our study for the first time, demonstrates a molecular convergence of O-glycosylation processes and ER stress signals at the cross-road of insulin resistance in skeletal muscle.

An End-Use Oriented Global Energy Strategy

Abstract is not available.

Vibration-rotation pattern in acetylene. II. Introduction of Coriolis coupling in the global model and analysis of emission spectra of hot acetylene around 3 mu m

A high temperature source has been developed and coupled to a high resolution Fourier transform spectrometer to record emission spectra of acetylene around 3 mu m up to 1455 K under Doppler limited resolution (0.015 cm(-1)). The nu(3)-ground state (GS) and nu(2)+nu(4)+nu(5)(Sigma(+)(u) and Delta(u))-GS bands and 76 related hot bands, counting e and f parities separately, are assigned using semiautomatic methods based on a global model to reproduce all related vibration-rotation states. Significantly higher J-values than previously reported are observed for 40 known substates while 37 new e or f vibrational substates, up to about 6000 cm(-1), are identified and characterized by vibration-rotation parameters. The 3 811 new or improved data resulting from the analysis are merged into the database presented by Robert et al. [Mol. Phys. 106, 2581 (2008)], now including 15 562 lines accessing vibrational states up to 8600 cm(-1). A global model, updated as compared to the one in the previous paper, allows all lines in the database to be simultaneously fitted, successfully. The updates are discussed taking into account, in particular, the systematic inclusion of Coriolis interaction.

A robust initialization scheme for faster convergence of the dichotomous search algorithm for single frequency estimation

The estimation of the frequency of a sinusoidal signal is a well researched problem. In this work we propose an initialization scheme to the popular dichotomous search of the periodogram peak algorithm(DSPA) that is used to estimate the frequency of a sinusoid in white gaussian noise. Our initialization is computationally low cost and gives the same performance as the DSPA, while reducing the number of iterations needed for the fine search stage. We show that our algorithm remains stable as we reduce the number of iterations in the fine search stage. We also compare the performance of our modification to a previous modification of the DSPA and show that we enhance the performance of the algorithm with our initialization technique.

A Proof of Convergence of the B-RED and P-RED Algorithms for Random Early Detection

In [8], we recently presented two computationally efficient algorithms named B-RED and P-RED for random early detection. In this letter, we present the mathematical proof of convergence of these algorithms under general conditions to local minima.