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.

Algebraic design techniques for reliable stabilization

In this paper we study two problems in feedback stabilization. The first is the simultaneous stabilization problem, which can be stated as follows. Given plantsG_{0}, G_{1},..., G_{l}, does there exist a single compensatorCthat stabilizes all of them? The second is that of stabilization by a stable compensator, or more generally, a "least unstable" compensator. Given a plantG, we would like to know whether or not there exists a stable compensatorCthat stabilizesG; if not, what is the smallest number of right half-place poles (counted according to their McMillan degree) that any stabilizing compensator must have? We show that the two problems are equivalent in the following sense. The problem of simultaneously stabilizingl + 1plants can be reduced to the problem of simultaneously stabilizinglplants using a stable compensator, which in turn can be stated as the following purely algebraic problem. Given2lmatricesA_{1}, ..., A_{l}, B_{1}, ..., B_{l}, whereA_{i}, B_{i}are right-coprime for alli, does there exist a matrixMsuch thatA_{i} + MB_{i}, is unimodular for alli?Conversely, the problem of simultaneously stabilizinglplants using a stable compensator can be formulated as one of simultaneously stabilizingl + 1plants. The problem of determining whether or not there exists anMsuch thatA + BMis unimodular, given a right-coprime pair (A, B), turns out to be a special case of a question concerning a matrix division algorithm in a proper Euclidean domain. We give an answer to this question, and we believe this result might be of some independent interest. We show that, given twon times mplantsG_{0} and G_{1}we can generically stabilize them simultaneously provided eithernormis greater than one. In contrast, simultaneous stabilizability, of two single-input-single-output plants, g0and g1, is not generic.

Large cryptic internal sequence repeats in protein structures from Homo sapiens

Amino acid sequences are known to constantly mutate and diverge unless there is a limiting condition that makes such a change deleterious. However, closer examination of the sequence and structure reveals that a few large, cryptic repeats are nevertheless sequentially conserved. This leads to the question of why only certain repeats are conserved at the sequence level. It would be interesting to find out if these sequences maintain their conservation at the three-dimensional structure level. They can play an active role in protein and nucleotide stability, thus not only ensring proper functioning but also potentiating malfunction and disease. Therefore, insights into any aspect of the repeats - be it structure, function or evolution - would prove to be of some importance. This study aims to address the relationship between protein sequence and its three-dimensional structure, by examining if large cryptic sequence repeats have the same structure.

Analysis of an internally mountable accelerometer balance system for use with non-isotropic models in shock tunnels

Knowledge of drag force is an important design parameter in aerodynamics. Measurement of aerodynamic forces at hypersonic speed is a challenge and usually ground test facilities like shock tunnels are used to carry out such tests. Accelerometer based force balances are commonly employed for measuring aerodynamic drag around bodies in hypersonic shock tunnels. In this study, we present an analysis of the effect of model material on the performance of an accelerometer balance used for measurement of drag in impulse facilities. From the experimental studies performed on models constructed out of Bakelite HYLEM and Aluminum, it is clear that the rigid body assumption does not hold good during the short testing duration available in shock tunnels. This is notwithstanding the fact that the rubber bush used for supporting the model allows unconstrained motion of the model during the short testing time available in the shock tunnel. The vibrations induced in the model on impact loading in the shock tunnel are damped out in metallic model, resulting in a smooth acceleration signal, while the signal become noisy and non-linear when we use non-isotropic materials like Bakelite HYLEM. This also implies that careful analysis and proper data reduction methodologies are necessary for measuring aerodynamic drag for non-metallic models in shock tunnels. The results from the drag measurements carried out using a 60 degrees half angle blunt cone is given in the present analysis.

A note on acyclic edge coloring of complete bipartite graphs

An acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic (2-colored) cycles. The acyclic chromatic index of a graph is the minimum number k such that there is an acyclic edge coloring using k colors and is denoted by a'(G). Let Delta = Delta(G) denote the maximum degree of a vertex in a graph G. A complete bipartite graph with n vertices on each side is denoted by K-n,K-n. Alon, McDiarmid and Reed observed that a'(K-p-1,K-p-1) = p for every prime p. In this paper we prove that a'(K-p,K-p) <= p + 2 = Delta + 2 when p is prime. Basavaraju, Chandran and Kummini proved that a'(K-n,K-n) >= n + 2 = Delta + 2 when n is odd, which combined with our result implies that a'(K-p,K-p) = p + 2 = Delta + 2 when p is an odd prime. Moreover we show that if we remove any edge from K-p,K-p, the resulting graph is acyclically Delta + 1 = p + 1-edge-colorable. (C) 2009 Elsevier B.V. All rights reserved.

Signal Characterization using Fractal Dimension

Fractal Dimensions (FD) are popular metrics for characterizing signals. They are used as complexity measuresin signal analysis applications in various fields. However, proper interpretation of such analyses has not been thoroughly addressed. In this paper, we study the effect of various signal properties on FD and interpret results in terms of classical signal processing concepts such as amplitude, frequency,number of harmonics, noise power and signal bandwidth. We have used Higuchi’s method for estimating FDs. This study helps in gaining a better understanding of the FD complexity measure for various signal parameters. Our results indicate that FD is a useful metric in estimating various signal properties. As an application of the FD measure in real world scenario, the FD is used as a feature in discriminating seizures from seizure free intervals in intracranial EEG data recordings and the FD feature has given good discrimination performance.

Reassessing the earthquake hazard in Kerala based on the historical and current seismicity

Given the lack of proper constraints in understanding earthquake mechanisms in the cratonic interiors and the general absence of good quality database, here we reassess the seismic hazard in the province of Kerala, a part of the aEuro cent stable continental interioraEuro cent, based on an improved historical and instrumental database. The temporal pattern of the current seismicity suggests that > 60% of the microtremors in Kerala occurs with a time lag after the peak rainfall, indicating that hydroseismicity may be a plausible model to explain the low-level seismicity in this region. Further, an increment in overall seismicity rate in the region in the recent years is explained as due to increased anthropogenic activities, which includes changes in hydrological pathways as a consequence of rapid landscape changes. Our analyses of the historical database eliminate a few events that are ascribed to this region; this exercise has also led to identification of a few events, not previously noted. The improved historical database essentially suggests that the central midland region is more prone to seismic activity compared to other parts of Kerala. This region appears to have generated larger number of significant earthquakes; the most prominent being the multiple events (doublets) of 1856 and 1953, whose magnitudes are comparable to that of the 2000/2001 (central Kerala) events. Occurrences of these historical events and the recent earthquakes, and the local geology indicative of pervasive faulting as shown by widely distributed pseudotachylite veins suggest that the NNW-SSE trending faults in central midland Kerala may host discrete potentially active sources that may be capable of generating light to moderate size earthquakes. The frequency of earthquakes in central Kerala evident from the historical database requires that the seismic codes stipulated for this region are made mandatory.

Acyclic Edge Coloring of Graphs with Maximum Degree 4

An acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The acyclic chromatic index of a graph is the minimum number k such that there is an acyclic edge coloring using k colors and is denoted by a'(G). It was conjectured by Alon, Sudakov, and Zaks that for any simple and finite graph G, a'(G) <= Delta+2, where Delta=Delta(G) denotes the maximum degree of G. We prove the conjecture for connected graphs with Delta(G)<= 4, with the additional restriction that m <= 2n-1, where n is the number of vertices and m is the number of edges in G. Note that for any graph G, m <= 2n, when Delta(G)<= 4. It follows that for any graph G if Delta(G)<= 4, then a'(G) <= 7.

On the kinetics of crystal growth from a supercooled melt

We present a theoretical analysis of the dynamics of crystal growth from a supercooled melt. A molecular theory of crystal growth that pays proper attention to the structure at the liquid-solid interface is discussed.

Generalized Burgers equations and Euler-Painlev transcendents. I

Initial-value problems for the generalized Burgers equation (GBE) ut+u betaux+lambdaualpha =(delta/2)uxx are discussed for the single hump type of initial data both continuous and discontinuous. The numerical solution is carried to the self-similar ``intermediate asymptotic'' regime when the solution is given analytically by the self-similar form. The nonlinear (transformed) ordinary differential equations (ODE's) describing the self-similar form are generalizations of a class discussed by Euler and Painlevé and quoted by Kamke. These ODE's are new, and it is postulated that they characterize GBE's in the same manner as the Painlev equations categorize the Kortweg-de Vries (KdV) type. A connection problem for some related ODE's satisfying proper asymptotic conditions at x=±[infinity], is solved. The range of amplitude parameter is found for which the solution of the connection problem exists. The other solutions of the above GBE, which display several interesting features such as peaking, breaking, and a long shelf on the left for negative values of the damping coefficient lambda, are also discussed. The results are compared with those holding for the modified KdV equation with damping. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Tuning of PID controllers for water networks—different approaches

Better operational control of water networks can help reduce leakage, maintain pressure, and control flow. Proportional integral derivative (PID) controllers, with proper fine-tuning, can help water utility operators achieve targets faster without creating undue transients. The authors compared three tuning methods, in different test situations, involving flow and level control to different reservoirs. Although target values were reached with all three tuning methods, the methods’ performances varied significantly. The lowest performer among the three was the method most widely used in the industry—standard tuning by the Ziegler-Nichols method. Achieving better results was offline tuning by genetic algorithms. Achieving the best control, though, was a fuzzy logic–based online tuning approach—the FZPID controller. The FZPID controller had fewer overshoots and took significantly less time to tune the gains for each problem. This new tuning approach for PID controllers can be applied to a variety of problems and can increase the performance of water networks of any size and structure

On the axiomatic approach to the maximum entropy principle of inference

Recent axiomatic derivations of the maximum entropy principle from consistency conditions are critically examined. We show that proper application of consistency conditions alone allows a wider class of functionals, essentially of the form ∝ dx p(x)[p(x)/g(x)] s , for some real numbers, to be used for inductive inference and the commonly used form − ∝ dx p(x)ln[p(x)/g(x)] is only a particular case. The role of the prior densityg(x) is clarified. It is possible to regard it as a geometric factor, describing the coordinate system used and it does not represent information of the same kind as obtained by measurements on the system in the form of expectation values.

A Newton-Euler formulation for the inverse dynamics of the Stewart platform manipulator

This paper presents an inverse dynamic formulation by the Newton–Euler approach for the Stewart platform manipulator of the most general architecture and models all the dynamic and gravity effects as well as the viscous friction at the joints. It is shown that a proper elimination procedure results in a remarkably economical and fast algorithm for the solution of actuator forces, which makes the method quite suitable for on-line control purposes. In addition, the parallelism inherent in the manipulator and in the modelling makes the algorithm quite efficient in a parallel computing environment, where it can be made as fast as the corresponding formulation for the 6-dof serial manipulator. The formulation has been implemented in a program and has been used for a few trajectories planned for a test manipulator. Results of simulation presented in the paper reveal the nature of the variation of actuator forces in the Stewart platform and justify the dynamic modelling for control.

Probing into the role of conserved N-glycosylation sites in the Tyrosinase glycoprotein family

N-linked glycosylation has a profound effect on the proper folding, oligomerization and stability of glycoproteins. These glycans impart many properties to proteins that may be important for their proper functioning, besides having a tendency to exert a chaperone-like effect on them. Certain glycosylation sites in a protein however, are more important than other sites for their function and stability. It has been observed that some N-glycosylation sites are conserved over families of glycoproteins over evolution, one such being the tyrosinase related protein family. The role of these conserved N-glycosylation sites in their trafficking, sorting, stability and activity has been examined here. By scrutinizing the different glycosylation sites on this family of glycoproteins it was inferred that different sites in the same family of polypeptides can perform distinct functions and conserved sites across the paralogues may perform diverse functions.

On the Purity of Atmospheric Glow-Discharge Plasma

Purity of the glow-discharge plasma at atmospheric pressure for surface modification applications is always debatable, since it works at ambient atmosphere. We have demonstrated on the use of optical emission spectroscopy to test the purity of this kind of plasma. The effect of gas flow pattern, nature of gas, and its flow rate on the plasma chemistry was studied. The importance of proper system design in maintaining a uniform flow of heavy and inert gases as carrier gas in atmospheric glow-discharge plasma was confirmed. The surface of a plasma-treated PET sample was analyzed using X-ray photoelectron spectroscopy to verify the studies on plasma purity done using emission spectrum.