Multiple contour extraction from graylevel images using an artificial neural network

For active contour modeling (ACM), we propose a novel self-organizing map (SOM)-based approach, called the batch-SOM (BSOM), that attempts to integrate the advantages of SOM- and snake-based ACMs in order to extract the desired contours from images. We employ feature points, in the form of ail edge-map (as obtained from a standard edge-detection operation), to guide the contour (as in the case of SOM-based ACMs) along with the gradient and intensity variations in a local region to ensure that the contour does not "leak" into the object boundary in case of faulty feature points (weak or broken edges). In contrast with the snake-based ACMs, however, we do not use an explicit energy functional (based on gradient or intensity) for controlling the contour movement. We extend the BSOM to handle extraction of contours of multiple objects, by splitting a single contour into as many subcontours as the objects in the image. The BSOM and its extended version are tested on synthetic binary and gray-level images with both single and multiple objects. We also demonstrate the efficacy of the BSOM on images of objects having both convex and nonconvex boundaries. The results demonstrate the superiority of the BSOM over others. Finally, we analyze the limitations of the BSOM.

Partially conserved axial-vector current inS-matrix theory

Mandelstam�s argument that PCAC follows from assigning Lorentz quantum numberM=1 to the massless pion is examined in the context of multiparticle dual resonance model. We construct a factorisable dual model for pions which is formulated operatorially on the harmonic oscillator Fock space along the lines of Neveu-Schwarz model. The model has bothm ? andm ? as arbitrary parameters unconstrained by the duality requirement. Adler self-consistency condition is satisfied if and only if the conditionm?2?m?2=1/2 is imposed, in which case the model reduces to the chiral dual pion model of Neveu and Thorn, and Schwarz. The Lorentz quantum number of the pion in the dual model is shown to beM=0.

Holographic Superfluids and Solitons

Superfluidity is perhaps one of the most remarkable observed macroscopic quantum effect. Superfluidity appears when a macroscopic number of particles occupies a single quantum state. Using modern experimental techniques one dark solitons) and vortices. There is a large literature on theoretical work studying the properties of such solitons using semiclassical methods. This thesis describes an alternative method for the study of superfluid solitons. The method used here is a holographic duality between a class of quantum field theories and gravitational theories. The classical limit of the gravitational system maps into a strong coupling limit of the quantum field theory. We use a holographic model of superfluidity to study solitons in these systems. One particularly appealing feature of this technique is that it allows us to take into account finite temperature effects in a large range of temperatures.

Aspiration-based utility functions in a planning model for timber flow management.

The study presents a theory of utility models based on aspiration levels, as well as the application of this theory to the planning of timber flow economics. The first part of the study comprises a derivation of the utility-theoretic basis for the application of aspiration levels. Two basic models are dealt with: the additive and the multiplicative. Applied here solely for partial utility functions, aspiration and reservation levels are interpreted as defining piecewisely linear functions. The standpoint of the choices of the decision-maker is emphasized by the use of indifference curves. The second part of the study introduces a model for the management of timber flows. The model is based on the assumption that the decision-maker is willing to specify a shape of income flow which is different from that of the capital-theoretic optimum. The utility model comprises four aspiration-based compound utility functions. The theory and the flow model are tested numerically by computations covering three forest holdings. The results show that the additive model is sensitive even to slight changes in relative importances and aspiration levels. This applies particularly to nearly linear production possibility boundaries of monetary variables. The multiplicative model, on the other hand, is stable because it generates strictly convex indifference curves. Due to a higher marginal rate of substitution, the multiplicative model implies a stronger dependence on forest management than the additive function. For income trajectory optimization, a method utilizing an income trajectory index is more efficient than one based on the use of aspiration levels per management period. Smooth trajectories can be attained by squaring the deviations of the feasible trajectories from the desired one.

On some results of A. E. Livingston and coefficient problems for concave univalent functions

We consider functions that map the open unit disc conformally onto the complement of a bounded convex set. We call these functions concave univalent functions. In 1994, Livingston presented a characterization for these functions. In this paper, we observe that there is a minor flaw with this characterization. We obtain certain sharp estimates and the exact set of variability involving Laurent and Taylor coefficients for concave functions. We also present the exact set of variability of the linear combination of certain successive Taylor coefficients of concave functions.

Characterizing and recognizing weak visibility polygons

A polygon is said to be a weak visibility polygon if every point of the polygon is visible from some point of an internal segment. In this paper we derive properties of shortest paths in weak visibility polygons and present a characterization of weak visibility polygons in terms of shortest paths between vertices. These properties lead to the following efficient algorithms: (i) an O(E) time algorithm for determining whether a simple polygon P is a weak visibility polygon and for computing a visibility chord if it exist, where E is the size of the visibility graph of P and (ii) an O(n2) time algorithm for computing the maximum hidden vertex set in an n-sided polygon weakly visible from a convex edge.

Controlled Diffusions with Constraints, II

We consider the ergodic control for a controlled nondegenerate diffusion when m other (m finite) ergodic costs are required to satisfy prescribed bounds. Under a condition on the cost functions that penalizes instability, the existence of an optimal stable Markov control is established by convex analytic arguments.

On extremal solutions to stochastic control problems, II

The set of attainable laws of the joint state-control process of a controlled diffusion is analyzed from a convex analytic viewpoint. Various equivalence relations depending on one-dimensional marginals thereof are defined on this set and the corresponding equivalence classes are studied.

Hydrodynamics of R-charged D1-branes

We study the hydrodynamic properties of strongly coupled SU(N) Yang-Mills theory of the D1-brane at finite temperature and at a non-zero density of R-charge in the framework of gauge/gravity duality. The gravity dual description involves a charged black hole solution of an Einstein-Maxwell-dilaton system in 3 dimensions which is obtained by a consistent truncation of the spinning D1-brane in 10 dimensions. We evaluate thermal and electrical conductivity as well as the bulk viscosity as a function of the chemical potential conjugate to the R-charges of the D1-brane. We show that the ratio of bulk viscosity to entropy density is independent of the chemical potential and is equal to 1/4 pi. The thermal conductivity and bulk viscosity obey a relationship similar to the Wiedemann-Franz law. We show that at the boundary of thermodynamic stability, the charge diffusion mode becomes unstable and the transport coefficients exhibit critical behaviour. Our method for evaluating the transport coefficients relies on expressing the second order differential equations in terms of a first order equation which dictates the radial evolution of the transport coefficient. The radial evolution equations can be solved exactly for the transport coefficients of our interest. We observe that transport coefficients of the D1-brane theory are related to that of the M2-brane by an overall proportionality constant which sets the dimensions.

Chance constrained uncertain classification via robust optimization

This paper studies the problem of constructing robust classifiers when the training is plagued with uncertainty. The problem is posed as a Chance-Constrained Program (CCP) which ensures that the uncertain data points are classified correctly with high probability. Unfortunately such a CCP turns out to be intractable. The key novelty is in employing Bernstein bounding schemes to relax the CCP as a convex second order cone program whose solution is guaranteed to satisfy the probabilistic constraint. Prior to this work, only the Chebyshev based relaxations were exploited in learning algorithms. Bernstein bounds employ richer partial information and hence can be far less conservative than Chebyshev bounds. Due to this efficient modeling of uncertainty, the resulting classifiers achieve higher classification margins and hence better generalization. Methodologies for classifying uncertain test data points and error measures for evaluating classifiers robust to uncertain data are discussed. Experimental results on synthetic and real-world datasets show that the proposed classifiers are better equipped to handle data uncertainty and outperform state-of-the-art in many cases.

Robust Semi-Blind Estimation for Beamforming Based MIMO Wireless Communication

In this paper, we present robust semi-blind (SB) algorithms for the estimation of beamforming vectors for multiple-input multiple-output wireless communication. The transmitted symbol block is assumed to comprise of a known sequence of training (pilot) symbols followed by information bearing blind (unknown) data symbols. Analytical expressions are derived for the robust SB estimators of the MIMO receive and transmit beamforming vectors. These robust SB estimators employ a preliminary estimate obtained from the pilot symbol sequence and leverage the second-order statistical information from the blind data symbols. We employ the theory of Lagrangian duality to derive the robust estimate of the receive beamforming vector by maximizing an inner product, while constraining the channel estimate to lie in a confidence sphere centered at the initial pilot estimate. Two different schemes are then proposed for computing the robust estimate of the MIMO transmit beamforming vector. Simulation results presented in the end illustrate the superior performance of the robust SB estimators.

Surface-ray tracing on hybrid surfaces of revolution for UTD mutual coupling analysis

An angle invariance property based on Hertz's principle of particle dynamics is employed to facilitate the surface-ray tracing on nondevelopable hybrid quadric surfaces of revolution (h-QUASOR's). This property, when used in conjunction with a Geodesic Constant Method, yields analytical expressions for all the ray-parameters required in the UTD formulation. Differential geometrical considerations require that some of the ray-parameters (defined heuristically in the UTD for the canonical convex surfaces) be modified before the UTD can be applied to such hybrid surfaces. Mutual coupling results for finite-dimensional slots have been presented as an example on a satellite launch vehicle modeled by general paraboloid of revolution and right circular cylinder.

A characteristic based numerical method with tracking for nonlinear wave equations

Many physical problems can be modeled by scalar, first-order, nonlinear, hyperbolic, partial differential equations (PDEs). The solutions to these PDEs often contain shock and rarefaction waves, where the solution becomes discontinuous or has a discontinuous derivative. One can encounter difficulties using traditional finite difference methods to solve these equations. In this paper, we introduce a numerical method for solving first-order scalar wave equations. The method involves solving ordinary differential equations (ODEs) to advance the solution along the characteristics and to propagate the characteristics in time. Shocks are created when characteristics cross, and the shocks are then propagated by applying analytical jump conditions. New characteristics are inserted in spreading rarefaction fans. New characteristics are also inserted when values on adjacent characteristics lie on opposite sides of an inflection point of a nonconvex flux function, Solutions along characteristics are propagated using a standard fourth-order Runge-Kutta ODE solver. Shocks waves are kept perfectly sharp. In addition, shock locations and velocities are determined without analyzing smeared profiles or taking numerical derivatives. In order to test the numerical method, we study analytically a particular class of nonlinear hyperbolic PDEs, deriving closed form solutions for certain special initial data. We also find bounded, smooth, self-similar solutions using group theoretic methods. The numerical method is validated against these analytical results. In addition, we compare the errors in our method with those using the Lax-Wendroff method for both convex and nonconvex flux functions. Finally, we apply the method to solve a PDE with a convex flux function describing the development of a thin liquid film on a horizontally rotating disk and a PDE with a nonconvex flux function, arising in a problem concerning flow in an underground reservoir.

Construction of solid model from measured point data

This paper describes an algorithm for constructing the solid model (boundary representation) from pout data measured from the faces of the object. The poznt data is assumed to be clustered for each face. This algorithm does not require any compuiier model of the part to exist and does not require any topological infarmation about the part to be input by the user. The property that a convex solid can be constructed uniquely from geometric input alone is utilized in the current work. Any object can be represented a5 a combznatzon of convex solids. The proposed algorithm attempts to construct convex polyhedra from the given input. The polyhedra so obtained are then checked against the input data for containment and those polyhedra, that satisfy this check, are combined (using boolean union operation) to realise the solid model. Results of implementation are presented.

Local polynomial convexity of the union of two totally-real surfaces at their intersection

We consider the following question: Let S (1) and S (2) be two smooth, totally-real surfaces in C-2 that contain the origin. If the union of their tangent planes is locally polynomially convex at the origin, then is S-1 boolean OR S-2 locally polynomially convex at the origin? If T (0) S (1) a (c) T (0) S (2) = {0}, then it is a folk result that the answer is yes. We discuss an obstruction to the presumed proof, and provide a different approach. When dim(R)(T0S1 boolean AND T0S2) = 1, we present a geometric condition under which no consistent answer to the above question exists. We then discuss conditions under which we can expect local polynomial convexity.