The non-linear response of a gyrostabilized platform: Effects of correction torque time delay and of random inputs

First, the non-linear response of a gyrostabilized platform to a small constant input torque is analyzed in respect to the effect of the time delay (inherent or deliberately introduced) in the correction torque supplied by the servomotor, which itself may be non-linear to a certain extent. The equation of motion of the platform system is a third order nonlinear non-homogeneous differential equation. An approximate analytical method of solution of this equation is utilized. The value of the delay at which the platform response becomes unstable has been calculated by using this approximate analytical method. The procedure is illustrated by means of a numerical example. Second, the non-linear response of the platform to a random input has been obtained. The effects of several types of non-linearity on reducing the level of the mean square response have been investigated, by applying the technique of equivalent linearization and solving the resulting integral equations by using laguerre or Gaussian integration techniques. The mean square responses to white noise and band limited white noise, for various values of the non-linear parameter and for different types of non-linearity function, have been obtained. For positive values of the non-linear parameter the levels of the non-linear mean square responses to both white noise and band-limited white noise are low as compared to the linear mean square response. For negative values of the non-linear parameter the level of the non-linear mean square response at first increases slowly with increasing values of the non-linear parameter and then suddenly jumps to a high level, at a certain value of the non-linearity parameter.

Synthesis, biological studies of linear and branched arabinofuranoside-containing glycolipids and their interaction with surfactant protein A

Oligoarabinofuranoside-containing glycolipids relevant to mycobacterial cell wall components were synthesized in order to understand the functional roles of such glycolipids. A series of linear tetra-, hexa-, octa-and a branched heptasaccharide oligoarabinofuranosides, with 1 -> 2 and 1 -> 5 a-linkages between the furanoside residues, were synthesized by chemical methods from readily available monomer building blocks. Upon the synthesis of glycolipids, constituted with a double alkyl chain-substituted sn-glycerol core and oligosaccharide fragments, biological studies were performed to identify the effect of synthetic glycolipids on the biofilm formation and sliding motilities of Mycobacterium smegmatis. Synthetic glycolipids and arabinofuranosides displayed an inhibitory effect on the growth profile, but mostly on the biofilm formation and maturation. Similarly, synthetic compounds also influenced the sliding motility of the bacteria. Further, biophysical studies were undertaken, so as to identify the interactions of the glycolipids with a pulmonary surfactant protein, namely surfactant protein A (SP-A), with the aid of the surface plasmon resonance technique. Specificities of each glycolipid interacting with SP-A were thus evaluated. From this study, glycolipids were found to exhibit higher apparent association constants than the corresponding oligosaccharide portion alone, without the double alkyl group-substituted glycerol core.

Maximum Margin Classifiers with Specified False Positive and False Negative Error Rates

This paper addresses the problem of maximum margin classification given the moments of class conditional densities and the false positive and false negative error rates. Using Chebyshev inequalities, the problem can be posed as a second order cone programming problem. The dual of the formulation leads to a geometric optimization problem, that of computing the distance between two ellipsoids, which is solved by an iterative algorithm. The formulation is extended to non-linear classifiers using kernel methods. The resultant classifiers are applied to the case of classification of unbalanced datasets with asymmetric costs for misclassification. Experimental results on benchmark datasets show the efficacy of the proposed method.

A Fast Linear Separability Test by Projection of Positive Points on Subspaces

A geometric and non parametric procedure for testing if two finite set of points are linearly separable is proposed. The Linear Separability Test is equivalent to a test that determines if a strictly positive point h > 0 exists in the range of a matrix A (related to the points in the two finite sets). The algorithm proposed in the paper iteratively checks if a strictly positive point exists in a subspace by projecting a strictly positive vector with equal co-ordinates (p), on the subspace. At the end of each iteration, the subspace is reduced to a lower dimensional subspace. The test is completed within r ≤ min(n, d + 1) steps, for both linearly separable and non separable problems (r is the rank of A, n is the number of points and d is the dimension of the space containing the points). The worst case time complexity of the algorithm is O(nr3) and space complexity of the algorithm is O(nd). A small review of some of the prominent algorithms and their time complexities is included. The worst case computational complexity of our algorithm is lower than the worst case computational complexity of Simplex, Perceptron, Support Vector Machine and Convex Hull Algorithms, if d

GINZBURG-LANDAU LIKE THEORY OF HIGH TEMPERATURE SUPERCONDUCTIVITY IN THE CUPRATES: EMERGENT d-WAVE ORDER

High temperature superconductivity in the cuprates remains one of the most widely investigated, constantly surprising and poorly understood phenomena in physics. Here, we describe briefly a new phenomenological theory inspired by the celebrated description of superconductivity due to Ginzburg and Landau and believed to describe its essence. This posits a free energy functional for the superconductor in terms of a complex order parameter characterizing it. We propose that there is, for superconducting cuprates, a similar functional of the complex, in plane, nearest neighbor spin singlet bond (or Cooper) pair amplitude psi(ij). Further, we suggest that a crucial part of it is a (short range) positive interaction between nearest neighbor bond pairs, of strength J'. Such an interaction leads to nonzero long wavelength phase stiffness or superconductive long range order, with the observed d-wave symmetry, below a temperature T-c similar to zJ' where z is the number of nearest neighbors; d-wave superconductivity is thus an emergent, collective consequence. Using the functional, we calculate a large range of properties, e. g., the pseudogap transition temperature T* as a function of hole doping x, the transition curve T-c(x), the superfluid stiffness rho(s)(x, T), the specific heat (without and with a magnetic field) due to the fluctuating pair degrees of freedom and the zero temperature vortex structure. We find remarkable agreement with experiment. We also calculate the self-energy of electrons hopping on the square cuprate lattice and coupled to electrons of nearly opposite momenta via inevitable long wavelength Cooper pair fluctuations formed of these electrons. The ensuing results for electron spectral density are successfully compared with recent experimental results for angle resolved photo emission spectroscopy (ARPES), and comprehensively explain strange features such as temperature dependent Fermi arcs above T-c and the ``bending'' of the superconducting gap below T-c.

A QUADRATIC C degrees INTERIOR PENALTY METHOD FOR LINEAR FOURTH ORDER BOUNDARY VALUE PROBLEMS WITH BOUNDARY CONDITIONS OF THE CAHN-HILLIARD TYPE

We develop a quadratic C degrees interior penalty method for linear fourth order boundary value problems with essential and natural boundary conditions of the Cahn-Hilliard type. Both a priori and a posteriori error estimates are derived. The performance of the method is illustrated by numerical experiments.

Phase synchronization in brain networks derived from correlation between probabilities of recurrences in functional MRI data

It is increasingly being recognized that resting state brain connectivity derived from functional magnetic resonance imaging (fMRI) data is an important marker of brain function both in healthy and clinical populations. Though linear correlation has been extensively used to characterize brain connectivity, it is limited to detecting first order dependencies. In this study, we propose a framework where in phase synchronization (PS) between brain regions is characterized using a new metric ``correlation between probabilities of recurrence'' (CPR) and subsequent graph-theoretic analysis of the ensuing networks. We applied this method to resting state fMRI data obtained from human subjects with and without administration of propofol anesthetic. Our results showed decreased PS during anesthesia and a biologically more plausible community structure using CPR rather than linear correlation. We conclude that CPR provides an attractive nonparametric method for modeling interactions in brain networks as compared to standard correlation for obtaining physiologically meaningful insights about brain function.

Functional analysis of ultra high information rates conveyed by rat vibrissal primary afferents

Sensory receptors determine the type and the quantity of information available for perception. Here, we quantified and characterized the information transferred by primary afferents in the rat whisker system using neural system identification. Quantification of ``how much'' information is conveyed by primary afferents, using the direct method (DM), a classical information theoretic tool, revealed that primary afferents transfer huge amounts of information (up to 529 bits/s). Information theoretic analysis of instantaneous spike-triggered kinematic stimulus features was used to gain functional insight on ``what'' is coded by primary afferents. Amongst the kinematic variables tested-position, velocity, and acceleration-primary afferent spikes encoded velocity best. The other two variables contributed to information transfer, but only if combined with velocity. We further revealed three additional characteristics that play a role in information transfer by primary afferents. Firstly, primary afferent spikes show preference for well separated multiple stimuli (i.e., well separated sets of combinations of the three instantaneous kinematic variables). Secondly, neurons are sensitive to short strips of the stimulus trajectory (up to 10 ms pre-spike time), and thirdly, they show spike patterns (precise doublet and triplet spiking). In order to deal with these complexities, we used a flexible probabilistic neuron model fitting mixtures of Gaussians to the spike triggered stimulus distributions, which quantitatively captured the contribution of the mentioned features and allowed us to achieve a full functional analysis of the total information rate indicated by the DM. We found that instantaneous position, velocity, and acceleration explained about 50% of the total information rate. Adding a 10 ms pre-spike interval of stimulus trajectory achieved 80-90%. The final 10-20% were found to be due to non-linear coding by spike bursts.

Discrete time second order sliding mode observer for uncertain linear multi-output system

This paper presents a second order sliding mode observer (SOSMO) design for discrete time uncertain linear multi-output system. The design procedure is effective for both matched and unmatched bounded uncertainties and/or disturbances. A second order sliding function and corresponding sliding manifold for discrete time system are defined similar to the lines of continuous time counterpart. A boundary layer concept is employed to avoid switching across the defined sliding manifold and the sliding trajectory is confined to a boundary layer once it converges to it. The condition for existence of convergent quasi-sliding mode (QSM) is derived. The observer estimation errors satisfying given stability conditions converge to an ultimate finite bound (within the specified boundary layer) with thickness O(T-2) where T is the sampling period. A relation between sliding mode gain and boundary layer is established for the existence of second order discrete sliding motion. The design strategy is very simple to apply and is demonstrated for three examples with different class of disturbances (matched and unmatched) to show the effectiveness of the design. Simulation results to show the robustness with respect to the measurement noise are given for SOSMO and the performance is compared with pseudo-linear Kalman filter (PLKF). (C) 2013 Published by Elsevier Ltd. on behalf of The Franklin Institute

Constrained Linear Spectral Unmixing Technique for Regional Land Cover Mapping Using MODIS Data

Over the last few decades, there has been a significant land cover (LC) change across the globe due to the increasing demand of the burgeoning population and urban sprawl. In order to take account of the change, there is a need for accurate and up-to-date LC maps. Mapping and monitoring of LC in India is being carried out at national level using multi-temporal IRS AWiFS data. Multispectral data such as IKONOS, Landsat-TM/ETM+, IRS-ICID LISS-III/IV, AWiFS and SPOT-5, etc. have adequate spatial resolution (similar to 1m to 56m) for LC mapping to generate 1:50,000 maps. However, for developing countries and those with large geographical extent, seasonal LC mapping is prohibitive with data from commercial sensors of limited spatial coverage. Superspectral data from the MODIS sensor are freely available, have better temporal (8 day composites) and spectral information. MODIS pixels typically contain a mixture of various LC types (due to coarse spatial resolution of 250, 500 and 1000 in), especially in more fragmented landscapes. In this context, linear spectral unmixing would be useful for mapping patchy land covers, such as those that characterise much of the Indian subcontinent. This work evaluates the existing unmixing technique for LC mapping using MODIS data, using end-members that are extracted through Pixel Purity Index (PPI), Scatter plot and N-dimensional visualisation. The abundance maps were generated for agriculture, built up, forest, plantations, waste land/others and water bodies. The assessment of the results using ground truth and a LISS-III classified map shows 86% overall accuracy, suggesting the potential for broad-scale applicability of the technique with superspectral data for natural resource planning and inventory applications. Index Terms-Remote sensing, digital

Conformation-activity correlations for chemotactic tripeptide analogs incorporating dialkyl residues with linear and cyclic alkyl sidechains at position 2

Five stereochemically constrained analogs of the chemotactic tripeptide incorporating 1-aminocycloalkane-1-carboxylic acid (Ac(n)c) and alpha,alpha-dialkylglycines (Deg, diethylglycine; Dpg, n,n-dipropylglycine and Dbg, n,n-dibutylglycine) at position 2 have been synthesized. NMR studies of peptides For-Met-Xxx-Phe-OMe (Xxx = Ac(7)c, I; Ac(8)c, II; Deg, III; Dpg, IV and Dbg, V; For, formyl) establish that peptides with cycloalkyl residues, I and II, adopt folded beta-turn conformations in CDCl3 and (CD3)(2)SO. In contrast, analogs with linear alkyl sidechains, III-V, favour fully extended (C-5) conformations in solution. Peptides I-V exhibit high activity in inducing beta-glucosaminidase release from rabbit neutrophils, with ED(50) values ranging from 1.4-8.0 x 10(-11)M. In human neutrophils the Dxg peptides III-V have ED(50) values ranging from 2.3 x 10(-8) to 5.9 x 10(-10) M, with the activity order being V > IV > III. While peptides I-IV are less active than the parent. For-Met-Leu-Phe-OH, in stimulating histamine release from human basophils, the Dbg peptide V is appreciably more potent, suggesting its potential utility as a probe for formyl peptide receptors.

Finite Element Solution Of Surface-Tension Driven Flows In Laser Surface-Melting

Lasers are very efficient in heating localized regions and hence they find a wide application in surface treatment processes. The surface of a material can be selectively modified to give superior wear and corrosion resistance. In laser surface-melting and welding problems, the high temperature gradient prevailing in the free surface induces a surface-tension gradient which is the dominant driving force for convection (known as thermo-capillary or Marangoni convection). It has been reported that the surface-tension driven convection plays a dominant role in determining the melt pool shape. In most of the earlier works on laser-melting and related problems, the finite difference method (FDM) has been used to solve the Navier Stokes equations [1]. Since the Reynolds number is quite high in these cases, upwinding has been used. Though upwinding gives physically realistic solutions even on a coarse grid, the results are inaccurate. McLay and Carey have solved the thermo-capillary flow in welding problems by an implicit finite element method [2]. They used the conventional Galerkin finite element method (FEM) which requires that the pressure be interpolated by one order lower than velocity (mixed interpolation). This restricts the choice of elements to certain higher order elements which need numerical integration for evaluation of element matrices. The implicit algorithm yields a system of nonlinear, unsymmetric equations which are not positive definite. Computations would be possible only with large mainframe computers.Sluzalec [3] has modeled the pulsed laser-melting problem by an explicit method (FEM). He has used the six-node triangular element with mixed interpolation. Since he has considered the buoyancy induced flow only, the velocity values are small. In the present work, an equal order explicit FEM is used to compute the thermo-capillary flow in the laser surface-melting problem. As this method permits equal order interpolation, there is no restriction in the choice of elements. Even linear elements such as the three-node triangular elements can be used. As the governing equations are solved in a sequential manner, the computer memory requirement is less. The finite element formulation is discussed in this paper along with typical numerical results.

Fatigue Laws Via Functional Equations

In routine industrial design, fatigue life estimation is largely based on S-N curves and ad hoc cycle counting algorithms used with Miner's rule for predicting life under complex loading. However, there are well known deficiencies of the conventional approach. Of the many cumulative damage rules that have been proposed, Manson's Double Linear Damage Rule (DLDR) has been the most successful. Here we follow up, through comparisons with experimental data from many sources, on a new approach to empirical fatigue life estimation (A Constructive Empirical Theory for Metal Fatigue Under Block Cyclic Loading', Proceedings of the Royal Society A, in press). The basic modeling approach is first described: it depends on enforcing mathematical consistency between predictions of simple empirical models that include indeterminate functional forms, and published fatigue data from handbooks. This consistency is enforced through setting up and (with luck) solving a functional equation with three independent variables and six unknown functions. The model, after eliminating or identifying various parameters, retains three fitted parameters; for the experimental data available, one of these may be set to zero. On comparison against data from several different sources, with two fitted parameters, we find that our model works about as well as the DLDR and much better than Miner's rule. We finally discuss some ways in which the model might be used, beyond the scope of the DLDR.

Approximate solution of u'=-A2u using a relation between exp(-tA2) and exp(itA)

Let A be a positive definite operator in a Hilbert space and consider the initial value problem for u(t) = -A(2)u. Using a representation of the semigroup exp(-A(2)t) in terms of the group exp(iAt) we express u in terms of the solution of the standard heat equation w(t) = W-yy, with initial values v solving the initial value problem for v(y) = iAv. This representation is used to construct a method for approximating u in terms of approximations of v. In the case that A is a 2(nd) order elliptic operator the method is combined with finite elements in the spatial variable and then reduces the solution of the 4(th) order equation for u to that of the 2(nd) order equation for v, followed by the solution of the heat equation in one space variable.

Comparative kinomics of human and chimpanzee reveal unique kinship and functional diversity generated by new domain combinations

Background: Phosphorylation by protein kinases is a common event in many cellular processes. Further, many kinases perform specialized roles and are regulated by non-kinase domains tethered to kinase domain. Perturbation in the regulation of kinases leads to malignancy. We have identified and analysed putative protein kinases encoded in the genome of chimpanzee which is a close evolutionary relative of human. Result: The shared core biology between chimpanzee and human is characterized by many orthologous protein kinases which are involved in conserved pathways. Domain architectures specific to chimp/human kinases have been observed. Chimp kinases with unique domain architectures are characterized by deletion of one or more non-kinase domains in the human kinases. Interestingly, counterparts of some of the multi-domain human kinases in chimp are characterized by identical domain architectures but with kinase-like non-kinase domain. Remarkably, out of 587 chimpanzee kinases no human orthologue with greater than 95% sequence identity could be identified for 160 kinases. Variations in chimpanzee kinases compared to human kinases are brought about also by differences in functions of domains tethered to the catalytic kinase domain. For example, the heterodimer forming PB1 domain related to the fold of ubiquitin/Ras-binding domain is seen uniquely tethered to PKC-like chimpanzee kinase. Conclusion: Though the chimpanzee and human are evolutionary very close, there are chimpanzee kinases with no close counterpart in the human suggesting differences in their functions. This analysis provides a direction for experimental analysis of human and chimpanzee protein kinases in order to enhance our understanding on their specific biological roles.