Determination of optimal trajectory under design constraints for a satellite launch vehicle

An optimal pitch steering programme of a solid-fuel satellite launch vehicle to maximize either (1) the injection velocity at a given altitude, or (2) the size of circular orbit, for a given payload is presented. The two-dimensional model includes the rotation of atmosphere with the Earth, the vehicle's lift and drag, variation of thrust with time and altitude, inverse-square gravitational field, and the specified initial vertical take-off. The inequality constraints on the aerodynamic load, control force, and turning rates are also imposed. Using the properties of the central force motion the terminal constraint conditions at coast apogee are transferred to the penultimate stage burnout. Such a transformation converts a time-free problem into a time-fixed one, reduces the number of terminal constraints, improves accuracy, besides demanding less computer memory and time. The adjoint equations are developed in a compact matrix form. The problem is solved on an IBM 360/44 computer using a steepest ascent algorithm. An illustrative analysis of a typical launch vehicle establishes the speed of convergence, and accuracy and applicability of the algorithm.

A lower bound to the survival probability and an approximate first passage time distribution for Markovian and non-Markovian dynamics in phase space

We derive a very general expression of the survival probability and the first passage time distribution for a particle executing Brownian motion in full phase space with an absorbing boundary condition at a point in the position space, which is valid irrespective of the statistical nature of the dynamics. The expression, together with the Jensen's inequality, naturally leads to a lower bound to the actual survival probability and an approximate first passage time distribution. These are expressed in terms of the position-position, velocity-velocity, and position-velocity variances. Knowledge of these variances enables one to compute a lower bound to the survival probability and consequently the first passage distribution function. As examples, we compute these for a Gaussian Markovian process and, in the case of non-Markovian process, with an exponentially decaying friction kernel and also with a power law friction kernel. Our analysis shows that the survival probability decays exponentially at the long time irrespective of the nature of the dynamics with an exponent equal to the transition state rate constant.

Selection of intrusion detection system threshold bounds for effective sensor fusion

The motivation behind the fusion of Intrusion Detection Systems was the realization that with the increasing traffic and increasing complexity of attacks, none of the present day stand-alone Intrusion Detection Systems can meet the high demand for a very high detection rate and an extremely low false positive rate. Multi-sensor fusion can be used to meet these requirements by a refinement of the combined response of different Intrusion Detection Systems. In this paper, we show the design technique of sensor fusion to best utilize the useful response from multiple sensors by an appropriate adjustment of the fusion threshold. The threshold is generally chosen according to the past experiences or by an expert system. In this paper, we show that the choice of the threshold bounds according to the Chebyshev inequality principle performs better. This approach also helps to solve the problem of scalability and has the advantage of failsafe capability. This paper theoretically models the fusion of Intrusion Detection Systems for the purpose of proving the improvement in performance, supplemented with the empirical evaluation. The combination of complementary sensors is shown to detect more attacks than the individual components. Since the individual sensors chosen detect sufficiently different attacks, their result can be merged for improved performance. The combination is done in different ways like (i) taking all the alarms from each system and avoiding duplications, (ii) taking alarms from each system by fixing threshold bounds, and (iii) rule-based fusion with a priori knowledge of the individual sensor performance. A number of evaluation metrics are used, and the results indicate that there is an overall enhancement in the performance of the combined detector using sensor fusion incorporating the threshold bounds and significantly better performance using simple rule-based fusion.

Stability of systems with power-law non-linearities

It is shown that a sufficient condition for the asymptotic stability-in-the-large of an autonomous system containing a linear part with transfer function G(jω) and a non-linearity belonging to a class of power-law non-linearities with slope restriction [0, K] in cascade in a negative feedback loop is ReZ(jω)[G(jω) + 1 K] ≥ 0 for all ω where the multiplier is given by, Z(jω) = 1 + αjω + Y(jω) - Y(-jω) with a real, y(t) = 0 for t < 0 and ∫ 0 ∞ |y(t)|dt < 1 2c2, c2 being a constant associated with the class of non-linearity. Any allowable multiplier can be converted to the above form and this form leads to lesser restrictions on the parameters in many cases. Criteria for the case of odd monotonic non-linearities and of linear gains are obtained as limiting cases of the criterion developed. A striking feature of the present result is that in the linear case it reduces to the necessary and sufficient conditions corresponding to the Nyquist criterion. An inequality of the type |R(T) - R(- T)| ≤ 2c2R(0) where R(T) is the input-output cross-correlation function of the non-linearity, is used in deriving the results.

L2-Stability Of A Class Of Nonlinear-Systems

Sufficient conditions are given for the L2-stability of a class of feedback systems consisting of a linear operator G and a nonlinear gain function, either odd monotone or restricted by a power-law, in cascade, in a negative feedback loop. The criterion takes the form of a frequency-domain inequality, Re[1 + Z(jω)] G(jω) δ > 0 ω ε (−∞, +∞), where Z(jω) is given by, Z(jω) = β[Y1(jω) + Y2(jω)] + (1 − β)[Y3(jω) − Y3(−jω)], with 0 β 1 and the functions y1(·), y2(·) and y3(·) satisfying the time-domain inequalities, ∝−∞+∞¦y1(t) + y2(t)¦ dt 1 − ε, y1(·) = 0, t < 0, y2(·) = 0, t > 0 and ε > 0, and , c2 being a constant depending on the order of the power-law restricting the nonlinear function. The criterion is derived using Zames' passive operator theory and is shown to be more general than the existing criteria

Some nonstandard error analysis of discontinuous Galerkin methods for elliptic problems

An a priori error analysis of discontinuous Galerkin methods for a general elliptic problem is derived under a mild elliptic regularity assumption on the solution. This is accomplished by using some techniques from a posteriori error analysis. The model problem is assumed to satisfy a GAyenrding type inequality. Optimal order L (2) norm a priori error estimates are derived for an adjoint consistent interior penalty method.

The evolution of genomic imprinting

We explore three possible pathways for the evolution of genomic imprinting. (1) Imprinting may be advantageous in itself when imprinted and unimprinted alleles of a locus confer different phenotypes. If a segment of DNA is imprinted in the gametes of one sex but not in those of the other, it might lead to effects correlated with sexual dimorphism. More fundamentally, in certain organisms, sex determination might have evolved because of imprinting. When imprinting leads to chromosome elimination or inactivation and occurs in some embryos but not in others, two classes of embryos, differing in the number of functional gene copies, would result. A model for sex determination based on inequality in the actual or effective copy-number of particular noncoding, regulatory sequences of DNA has been proposed (Chandra, Proc. natn. Acad. Sci. U.S.A. 82. 1165–1169 and 6947–6949, 1985). Maternal control of offspring sex is another possible consequence of imprinting; this would indicate a potential role for imprinting in sex ratio evolution. (2) Genes responsible for imprinting may have pleiotropic effects and they may have been selected for reasons other than their imprinting ability. Lack of evidence precludes further consideration of this possibility. (3) Imprinting could have co-evolved with other traits. For instance, gamete-specific imprinting could lead to a lowered fitness of androgenetic or gynogenetic diploids relative to the fitness of ‘normal’ diploids. This in turn would reinforce the evolution of anisogamy. The reversibility of imprinting raises the possibility of occasional incomplete or improper erasure. If the site of imprinting is the egg – as appears to be the case with the human X (Chandra and Brown, Nature 253. 165–168, 1975) – either improper imprinting or improper erasure could lead to unusual patterns of inheritance (as in the fragile-X syndrome) or fitness effects skipping generations.

Stochastic Approximation Algorithms for Constrained Optimization via Simulation

We develop four algorithms for simulation-based optimization under multiple inequality constraints. Both the cost and the constraint functions are considered to be long-run averages of certain state-dependent single-stage functions. We pose the problem in the simulation optimization framework by using the Lagrange multiplier method. Two of our algorithms estimate only the gradient of the Lagrangian, while the other two estimate both the gradient and the Hessian of it. In the process, we also develop various new estimators for the gradient and Hessian. All our algorithms use two simulations each. Two of these algorithms are based on the smoothed functional (SF) technique, while the other two are based on the simultaneous perturbation stochastic approximation (SPSA) method. We prove the convergence of our algorithms and show numerical experiments on a setting involving an open Jackson network. The Newton-based SF algorithm is seen to show the best overall performance.

An actor-critic algorithm with function approximation for discounted cost constrained Markov decision processes

We develop in this article the first actor-critic reinforcement learning algorithm with function approximation for a problem of control under multiple inequality constraints. We consider the infinite horizon discounted cost framework in which both the objective and the constraint functions are suitable expected policy-dependent discounted sums of certain sample path functions. We apply the Lagrange multiplier method to handle the inequality constraints. Our algorithm makes use of multi-timescale stochastic approximation and incorporates a temporal difference (TD) critic and an actor that makes a gradient search in the space of policy parameters using efficient simultaneous perturbation stochastic approximation (SPSA) gradient estimates. We prove the asymptotic almost sure convergence of our algorithm to a locally optimal policy. (C) 2010 Elsevier B.V. All rights reserved.

Proposed role of w chromosome inactivation and the absence of dosage compensation in avian sex determination

Three features of avian sex chromosomes - female heterogamety (ZZ male, ZW female), the apparently inactive state of the W chromosome, and dose-dependent expression of Z-linked genes - are examined in regard to their possible relation to sex determination. It is proposed that the W chromosome is facultatively heterochromatic and that the Z and W chromosomes carry one or more homologous sex-determination genes. The absence of dosage compensation in ZZ embryos, and W inactivation in ZW embryos, would then bring about a 2n(ZZ)-n(ZW) inequality in the effective copy number of such genes. The absence of dosage compensation of Z-linked genes in ZZ embryos is viewed as a means by which two copies of Z-W homologous sex determination genes are kept active to meet the requirements of testis determination. W inactivation may promote ovarian development by reducing the effective copy number of these genes from 2n to n. If there is a W-specific gene for femaleness, spread of heterochromatization to this gene in cells forming the right gonadal primordium may explain the latter's normally undifferentiated state; reversal of heterochromatization may similarly explain the development of the right gonad into a testis following left ovariectomy.

On Walkup's class K (d) and a minimal triangulation of (S-3 (sic) S-1)(#3)

For d >= 2, Walkup's class K (d) consists of the d-dimensional simplicial complexes all whose vertex-links are stacked (d - 1)-spheres. Kalai showed that for d >= 4, all connected members of K (d) are obtained from stacked d-spheres by finitely many elementary handle additions. According to a result of Walkup, the face vector of any triangulated 4-manifold X with Euler characteristic chi satisfies f(1) >= 5f(0) - 15/2 chi, with equality only for X is an element of K(4). Kuhnel observed that this implies f(0)(f(0) - 11) >= -15 chi, with equality only for 2-neighborly members of K(4). Kuhnel also asked if there is a triangulated 4-manifold with f(0) = 15, chi = -4 (attaining equality in his lower bound). In this paper, guided by Kalai's theorem, we show that indeed there is such a triangulation. It triangulates the connected sum of three copies of the twisted sphere product S-3 (sic) S-1. Because of Kuhnel's inequality, the given triangulation of this manifold is a vertex-minimal triangulation. By a recent result of Effenberger, the triangulation constructed here is tight. Apart from the neighborly 2-manifolds and the infinite family of (2d + 3)-vertex sphere products Sd-1 X S-1 (twisted for d odd), only fourteen tight triangulated manifolds were known so far. The present construction yields a new member of this sporadic family. We also present a self-contained proof of Kalai's result. (C) 2011 Elsevier B.V. All rights reserved.

Solving linear programming problems exactly

A linear programming problem in an inequality form having a bounded solution is solved error-free using an algorithm that sorts the inequalities, removes the redundant ones, and uses the p-adic arithmetic. (C) Elsevier Science Inc., 1997

Robust Formulations for Handling Uncertainty in Kernel Matrices

We study the problem of uncertainty in the entries of the Kernel matrix, arising in SVM formulation. Using Chance Constraint Programming and a novel large deviation inequality we derive a formulation which is robust to such noise. The resulting formulation applies when the noise is Gaussian, or has finite support. The formulation in general is non-convex, but in several cases of interest it reduces to a convex program. The problem of uncertainty in kernel matrix is motivated from the real world problem of classifying proteins when the structures are provided with some uncertainty. The formulation derived here naturally incorporates such uncertainty in a principled manner leading to significant improvements over the state of the art. 1.

Precoder Designs for MIMO Broadcast Channels with Imperfect CSI

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Flux Partitioning of Species Approach in Binary Interdiffusion Process

Validation of the flux partitioning of species model has been illustrated. Various combinations of inequality expression for the fluxes of species A and B in two successively grown hypothetical intermetallic phases in the interdiffusion zone have been considered within the constraints of this concept. Furthermore, ratio of intrinsic diffusivities of the species A and B in those two phases has been correlated in four different cases. Moreover, complete and or partial validation or invalidation of this model with respect to both the species, has been proven theoretically and also discussed with the Co-Si system as an example.