Multiple UAV Coalitions for a Search and Prosecute Mission

Unmanned aerial vehicles (UAVs) have the potential to carry resources in support of search and prosecute operations. Often to completely prosecute a target, UAVs may have to simultaneously attack the target with various resources with different capacities. However, the UAVs are capable of carrying only limited resources in small quantities, hence, a group of UAVs (coalition) needs to be assigned that satisfies the target resource requirement. The assigned coalition must be such that it minimizes the target prosecution delay and the size of the coalition. The problem of forming coalitions is computationally intensive due to the combinatorial nature of the problem, but for real-time applications computationally cheap solutions are required. In this paper, we propose decentralized sub-optimal (polynomial time) and decentralized optimal coalition formation algorithms that generate coalitions for a single target with low computational complexity. We compare the performance of the proposed algorithms to that of a global optimal solution for which we need to solve a centralized combinatorial optimization problem. This problem is computationally intensive because the solution has to (a) provide a coalition for each target, (b) design a sequence in which targets need to be prosecuted, and (c) take into account reduction of UAV resources with usage. To solve this problem we use the Particle Swarm Optimization (PSO) technique. Through simulations, we study the performance of the proposed algorithms in terms of mission performance, complexity of the algorithms and the time taken to form the coalition. The simulation results show that the solution provided by the proposed algorithms is close to the global optimal solution and requires far less computational resources.

On the performance of strain smoothing for quadratic and enriched finite element approximations (XFEM/GFEM/PUFEM)

By using the strain smoothing technique proposed by Chen et al. (Comput. Mech. 2000; 25: 137-156) for meshless methods in the context of the finite element method (FEM), Liu et al. (Comput. Mech. 2007; 39(6): 859-877) developed the Smoothed FEM (SFEM). Although the SFEM is not yet well understood mathematically, numerical experiments point to potentially useful features of this particularly simple modification of the FEM. To date, the SFEM has only been investigated for bilinear and Wachspress approximations and is limited to linear reproducing conditions. The goal of this paper is to extend the strain smoothing to higher order elements and to investigate numerically in which condition strain smoothing is beneficial to accuracy and convergence of enriched finite element approximations. We focus on three widely used enrichment schemes, namely: (a) weak discontinuities; (b) strong discontinuities; (c) near-tip linear elastic fracture mechanics functions. The main conclusion is that strain smoothing in enriched approximation is only beneficial when the enrichment functions are polynomial (cases (a) and (b)), but that non-polynomial enrichment of type (c) lead to inferior methods compared to the standard enriched FEM (e.g. XFEM). Copyright (C) 2011 John Wiley & Sons, Ltd.

Nonlinear static and dynamic damped response of a composite rectangular plate resting on a two-parameter elastic foundation

Nonlinear static and dynamic response analyses of a clamped. rectangular composite plate resting on a two-parameter elastic foundation have been studied using von Karman's relations. Incorporating the material damping, the governing coupled, nonlinear partial differential equations are obtained for the plate under step pressure pulse load excitation. These equations have been solved by a one-term solution and by applying Galerkin's technique to the deflection equation. This yields an ordinary nonlinear differential equation in time. The nonlinear static solution is obtained by neglecting the time-dependent variables. Thc nonlinear dynamic damped response is obtained by applying the ultraspherical polynomial approximation (UPA) technique. The influences of foundation modulus, shear modulus, orthotropy, etc. upon the nonlinear static and dynamic responses have been presented.

Hierarchies of circuit classes that are closed under complement

We examine three hierarchies of circuit classes and show they are closed under complementation. (1) The class of languages recognized by a family of polynomial size skew circuits with width O(w), are closed under complement. (2) The class of languages recognized by family of polynomial size circuits with width O(w) and polynomial tree-size, are closed under complement. (3) The class of languages recognized by a family of polynomial size, O(log(n)) depth, bounded AND fan-in with OR fan-in f (f⩾log(n)) circuits are closed under complement. These improve upon the results of (i) Immerman (1988) and Szelepcsenyi (1988), who show that 𝒩L𝒪𝒢 is closed under complementation, and (ii) Borodin et al. (1989), who show that L𝒪𝒢𝒞ℱL is closed under complement

ADC Static Nonlinearity Estimation Using Linearity Property of Sinewave

Prohibitive test time, nonuniformity of excitation, and signal nonlinearity are major concerns associated with employing dc, sine, and triangular/ramp signals, respectively, while determining static nonlinearity of analog-to-digital converters (ADCs) with high resolution (i.e., ten or more bits). Attempts to overcome these issues have been examined with some degree of success. This paper describes a novel method of estimating the ``true'' static nonlinearity of an ADC using a low-frequency sine signal (for example, less than 10 Hz) by employing the histogram-based approach. It is based on the well-known fact that the variation of a sine signal is ``reasonably linear'' when the angle is small, for example, in the range of +/- 5 degrees to +/- 7 degrees. In the proposed method, the ADC under test has to be ``fed'' with this ``linear'' portion of the sinewave. The presence of any harmonics and offset in input excitation makes this linear part of the sine signal marginally different compared with that of an ideal ramp signal of equal amplitude. However, since it is a sinusoid, this difference can be accurately determined and later compensated from the measured ADC output. Thus, the corrected ADC output will correspond to the true ADC static nonlinearity. The implementation of the proposed method is discussed along with experimental results for two 8-b ADCs and one 10-b ADC which are then compared with the static characteristics estimated by the conventional DC method.

Fast computation of Legendre and Zernike moments

This paper presents recursive algorithms for fast computation of Legendre and Zernike moments of a grey-level image intensity distribution. For a binary image, a contour integration method is developed for the evaluation of Legendre moments using only the boundary information. A method for recursive calculation of Zernike polynomial coefficients is also given. A square-to-circular image transformation scheme is introduced to minimize the computation involved in Zernike moment functions. The recursive formulae can also be used in inverse moment transforms to reconstruct the original image from moments. The mathematical framework of the algorithms is given in detail, and illustrated with binary and grey-level images.

Photochemical intramolecular gamma-hydrogen abstraction in a ketone and an alkene and the role of tunneling of hydrogen

Intramolecular gamma-hydrogen abstraction reactions were examined in pentane-2-one and 2-methyl-1-pentene in their lowest triplet states using the AM1 semi-empirical molecular orbital method with the complete geometry optimization in the unrestricted Hartree-Fock frame. The results reveal that the oxygen atom of the carbonyl group and the end carbon atom of the olefinic bond acquire high free valence and spin density indices in their respective lowest triplet states, leading to abstraction of hydrogen from the gamma-position relative to the carbonyl and olefinic bonds. The theoretical energy profiles fit with a polynomial and the probability of tunneling of hydrogen was estimated by the WKB (Wentzel, Kramer and Brillouin) method. The results, after thermal averaging of the rate constants, reveal that tunneling of hydrogen is significant at room temperature.

Vibration and buckling of hybrid laminated curved panels

Vibration and buckling of curved plates, made of hybrid laminated composite materials, are studied using first-order shear deformation theory and Reissner's shallow shell theory. For an initial study, only simply-supported boundary conditions are considered. The natural frequencies and critical buckling loads are calculated using the energy method (Lagrangian approach) by assuming a combination of sine and cosine functions in the form of double Fourier series. The effects of curvature, aspect ratio, stacking sequence and ply-orientation are studied. The non-dimensional frequencies and critical buckling load of a hybrid laminate lie in between the values for laminates made of all plies of higher strength and lower strength fibres. Curvature enhances natural frequencies and it is more predominant for a thin panel than a thick one.

Uniform algebras generated by holomorphic and close-to-harmonic functions

The initial motivation for this paper is to discuss a more concrete approach to an approximation theorem of Axler and Shields, which says that the uniform algebra on the closed unit disc (D) over bar generated by z and h, where h is a nowhere-holomorphic harmonic function on D that is continuous up to partial derivative D, equals C((D) over bar). The abstract tools used by Axler and Shields make harmonicity of h an essential condition for their result. We use the concepts of plurisubharmonicity and polynomial convexity to show that, in fact, the same conclusion is reached if h is replaced by h + R, where R is a non-harmonic perturbation whose Laplacian is ``small'' in a certain sense.

Popular mixed matchings

We study the problem of matching applicants to jobs under one-sided preferences; that is, each applicant ranks a non-empty subset of jobs under an order of preference, possibly involving ties. A matching M is said to be more popular than T if the applicants that prefer M to T outnumber those that prefer T to M. A matching is said to be popular if there is no matching more popular than it. Equivalently, a matching M is popular if phi(M, T) >= phi(T, M) for all matchings T, where phi(X, Y) is the number of applicants that prefer X to Y. Previously studied solution concepts based on the popularity criterion are either not guaranteed to exist for every instance (e.g., popular matchings) or are NP-hard to compute (e.g., least unpopular matchings). This paper addresses this issue by considering mixed matchings. A mixed matching is simply a probability distribution over matchings in the input graph. The function phi that compares two matchings generalizes in a natural manner to mixed matchings by taking expectation. A mixed matching P is popular if phi(P, Q) >= phi(Q, P) for all mixed matchings Q. We show that popular mixed matchings always exist and we design polynomial time algorithms for finding them. Then we study their efficiency and give tight bounds on the price of anarchy and price of stability of the popular matching problem. (C) 2010 Elsevier B.V. All rights reserved.

Singularity structure of third-order dynamical systems .2

The singularity structure of the solutions of a general third-order system, with polynomial right-hand sides of degree less than or equal to two, is studied about a movable singular point, An algorithm for transforming the given third-order system to a third-order Briot-Bouquet system is presented, The dominant behavior of a solution of the given system near a movable singularity is used to construct a transformation that changes the given system directly to a third-order Briot-Bouquet system. The results of Horn for the third-order Briot-Bouquet system are exploited to give the complete form of the series solutions of the given third-order system; convergence of these series in a deleted neighborhood of the singularity is ensured, This algorithm is used to study the singularity structure of the solutions of the Lorenz system, the Rikitake system, the three-wave interaction problem, the Rabinovich system, the Lotka-Volterra system, and the May-Leonard system for different sets of parameter values. The proposed approach goes far beyond the ARS algorithm.

Space vector pulsewidth modulation — A status review

The technique of space vector pulsewidth modulation (SVM) is reviewed. The basic principle of SVM is derived and is compared with sine-triangle PWM. Operation in the overmodulation range is explained. Extension of SVM to other inverter-motor combinations such as three level inverters and split phase motors are discussed.

The existence of homeomorphic subgraphs in chordal graphs

We establish conditions for the existence, in a chordal graph, of subgraphs homeomorphic to K-n (n greater than or equal to 3), K-m,K-n (m,n greater than or equal to 2), and wheels W-r (r greater than or equal to 3). Using these results, we develop a simple linear time algorithm for testing planarity of chordal graphs. We also show how these results lead to simple polynomial time algorithms for the Fixed Subgraph Homeomorphism problem on chordal graphs for some special classes of pattern graphs.

Distributed intrusion detection in the presence of correlated sensor readings: Signal-space and communication-complexity view-point

The problem of sensor-network-based distributed intrusion detection in the presence of clutter is considered. It is argued that sensing is best regarded as a local phenomenon in that only sensors in the immediate vicinity of an intruder are triggered. In such a setting, lack of knowledge of intruder location gives rise to correlated sensor readings. A signal-space view-point is introduced in which the noise-free sensor readings associated to intruder and clutter appear as surfaces f(s) and f(g) and the problem reduces to one of determining in distributed fashion, whether the current noisy sensor reading is best classified as intruder or clutter. Two approaches to distributed detection are pursued. In the first, a decision surface separating f(s) and f(g) is identified using Neyman-Pearson criteria. Thereafter, the individual sensor nodes interactively exchange bits to determine whether the sensor readings are on one side or the other of the decision surface. Bounds on the number of bits needed to be exchanged are derived, based on communication-complexity (CC) theory. A lower bound derived for the two-party average case CC of general functions is compared against the performance of a greedy algorithm. Extensions to the multi-party case is straightforward and is briefly discussed. The average case CC of the relevant greaterthan (CT) function is characterized within two bits. Under the second approach, each sensor node broadcasts a single bit arising from appropriate two-level quantization of its own sensor reading, keeping in mind the fusion rule to be subsequently applied at a local fusion center. The optimality of a threshold test as a quantization rule is proved under simplifying assumptions. Finally, results from a QualNet simulation of the algorithms are presented that include intruder tracking using a naive polynomial-regression algorithm. 2010 Elsevier B.V. All rights reserved.

The 2D Coulomb gas on a 1D lattice

The statistical mechanics of a two-dimensional Coulomb gas confined to one dimension is studied, wherein hard core particles move on a ring. Exact self-duality is shown for a version of the sine-Gordon model arising in this context, thereby locating the transition temperature exactly. We present asymptotically exact results for the correlations in the model and characterize the low- and high-temperature phases. Numerical simulations provide support to these renormalization group calculations. Connections with other interesting problems, such as the quantum Brownian motion of a panicle in a periodic potential and impurity problems, are pointed out.