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.

Clustering Based Large Margin Classification: A Scalable Approach using SOCP Formulation

This paper presents a novel Second Order Cone Programming (SOCP) formulation for large scale binary classification tasks. Assuming that the class conditional densities are mixture distributions, where each component of the mixture has a spherical covariance, the second order statistics of the components can be estimated efficiently using clustering algorithms like BIRCH. For each cluster, the second order moments are used to derive a second order cone constraint via a Chebyshev-Cantelli inequality. This constraint ensures that any data point in the cluster is classified correctly with a high probability. This leads to a large margin SOCP formulation whose size depends on the number of clusters rather than the number of training data points. Hence, the proposed formulation scales well for large datasets when compared to the state-of-the-art classifiers, Support Vector Machines (SVMs). Experiments on real world and synthetic datasets show that the proposed algorithm outperforms SVM solvers in terms of training time and achieves similar accuracies.

KCL, Ray Theories and Application to Sonic Boom

We first review a general formulation of ray theory and write down the conservation forms of the equations of a weakly nonlinear ray theory (WNLRT) and a shock ray theory (SRT) for a weak shock in a polytropic gas. Then we present a formulation of the problem of sonic boom by a maneuvering aerofoil as a one parameter family of Cauchy problems. The system of equations in conservation form is hyperbolic for a range of values of the parameter and has elliptic nature else where, showing that unlike the leading shock, the trailing shock is always smooth.

Calculation of the front part of the sonic boom signature for a Maneuvering aerofopil

The sonic boom at a large distance from its source consists of a leading shock, a trailing shock and a one parameter family of nonlinear wavefronts in between these shocks. A new ray theoretical method using a shock ray theory and a weakly nonlinear lay theory has been used to obtain the shock fronts and wavefronts respectively, for a maneuvering aerofoil in a homogeneous medium. This method introduces a one parameter family of Cauchy problems to calculate the shock and wave fronts emerging from the surface of the aerofoil. These problems are solved numerically to obtain the leading shock front and the nonlinear wavefronts emerging from the front portion of the aerofoil.

Minimization of Constraint Violation in Fuzzy Multiobjective Programming

Fuzzy multiobjective programming for a deterministic case involves maximizing the minimum goal satisfaction level among conflicting goals of different stakeholders using Max-min approach. Uncertainty due to randomness in a fuzzy multiobjective programming may be addressed by modifying the constraints using probabilistic inequality (e.g., Chebyshev’s inequality) or by addition of new constraints using statistical moments (e.g., skewness). Such modifications may result in the reduction of the optimal value of the system performance. In the present study, a methodology is developed to allow some violation in the newly added and modified constraints, and then minimizing the violation of those constraints with the objective of maximizing the minimum goal satisfaction level. Fuzzy goal programming is used to solve the multiobjective model. The proposed methodology is demonstrated with an application in the field of Waste Load Allocation (WLA) in a river system.

First-order structural transition in the magnetically ordered phase of Fe(1.13)Te

Specific heat, resistivity, magnetic susceptibility, linear thermal expansion (LTE), and high-resolution synchrotron x-ray powder diffraction investigations of single crystals Fe(1+y) Te (0.06 <= y <= 0.15) reveal a splitting of a single, first-order transition for y <= 0.11 into two transitions for y >= 0.13. Most strikingly, all measurements on identical samples Fe(1.13)Te consistently indicate that, upon cooling, the magnetic transition at T(N) precedes the first-order structural transition at a lower temperature T(s). The structural transition in turn coincides with a change in the character of the magnetic structure. The LTE measurements along the crystallographic c axis display a small distortion close to T(N) due to a lattice striction as a consequence of magnetic ordering, and a much larger change at T(s). The lattice symmetry changes, however, only below T(s) as indicated by powder x-ray diffraction. This behavior is in stark contrast to the sequence in which the phase transitions occur in Fe pnictides.

Detection of a periodic structure embedded in surface roughness, for various correlation functions

This paper deals with surface profilometry, where we try to detect a periodic structure, hidden in randomness using the matched filter method of analysing the intensity of light, scattered from the surface. From the direct problem of light scattering from a composite rough surface of the above type, we find that the detectability of the periodic structure can be hindered by the randomness, being dependent on the correlation function of the random part. In our earlier works, we had concentrated mainly on the Cauchy-type correlation function for the rough part. In the present work, we show that this technique can determine the periodic structure of different kinds of correlation functions of the roughness, including Cauchy, Gaussian etc. We study the detection by the matched filter method as the nature of the correlation function is varied.

Real-time monitoring of critical nodes with minimal number of Phasor Measurement Units

This paper presents a method for placement of Phasor Measurement Units, ensuring the monitoring of vulnerable buses which are obtained based on transient stability analysis of the overall system. Real-time monitoring of phase angles across different nodes, which indicates the proximity to instability, the very purpose will be well defined if the PMUs are placed at buses which are more vulnerable. The issue is to identify the key buses where the PMUs should be placed when the transient stability prediction is taken into account considering various disturbances. Integer Linear Programming technique with equality and inequality constraints is used to find out the optimal placement set with key buses identified from transient stability analysis. Results on IEEE-14 bus system are presented to illustrate the proposed approach.

An Online Actor-Critic Algorithm with Function Approximation for Constrained Markov Decision Processes

We develop an online actor-critic reinforcement learning algorithm with function approximation for a problem of control under inequality constraints. We consider the long-run average cost Markov decision process (MDP) framework in which both the objective and the constraint functions are suitable policy-dependent long-run averages of certain sample path functions. The Lagrange multiplier method is used to handle the inequality constraints. We prove the asymptotic almost sure convergence of our algorithm to a locally optimal solution. We also provide the results of numerical experiments on a problem of routing in a multi-stage queueing network with constraints on long-run average queue lengths. We observe that our algorithm exhibits good performance on this setting and converges to a feasible point.

A Numerical Scheme for Three-Dimensional Front Propagation and Control of Jordan Mode

As an example of a front propagation, we study the propagation of a three-dimensional nonlinear wavefront into a polytropic gas in a uniform state and at rest. The successive positions and geometry of the wavefront are obtained by solving the conservation form of equations of a weakly nonlinear ray theory. The proposed set of equations forms a weakly hyperbolic system of seven conservation laws with an additional vector constraint, each of whose components is a divergence-free condition. This constraint is an involution for the system of conservation laws, and it is termed a geometric solenoidal constraint. The analysis of a Cauchy problem for the linearized system shows that when this constraint is satisfied initially, the solution does not exhibit any Jordan mode. For the numerical simulation of the conservation laws we employ a high resolution central scheme. The second order accuracy of the scheme is achieved by using MUSCL-type reconstructions and Runge-Kutta time discretizations. A constrained transport-type technique is used to enforce the geometric solenoidal constraint. The results of several numerical experiments are presented, which confirm the efficiency and robustness of the proposed numerical method and the control of the Jordan mode.

AN ITERATIVE ALGORITHM FOR PHASE RETRIEVAL WITH SPARSITY CONSTRAINTS: APPLICATION TO FREQUENCY DOMAIN OPTICAL COHERENCE TOMOGRAPHY

We address the problem of phase retrieval, which is frequently encountered in optical imaging. The measured quantity is the magnitude of the Fourier spectrum of a function (in optics, the function is also referred to as an object). The goal is to recover the object based on the magnitude measurements. In doing so, the standard assumptions are that the object is compactly supported and positive. In this paper, we consider objects that admit a sparse representation in some orthonormal basis. We develop a variant of the Fienup algorithm to incorporate the condition of sparsity and to successively estimate and refine the phase starting from the magnitude measurements. We show that the proposed iterative algorithm possesses Cauchy convergence properties. As far as the modality is concerned, we work with measurements obtained using a frequency-domain optical-coherence tomography experimental setup. The experimental results on real measured data show that the proposed technique exhibits good reconstruction performance even with fewer coefficients taken into account for reconstruction. It also suppresses the autocorrelation artifacts to a significant extent since it estimates the phase accurately.

A novel Q-learning algorithm with function approximation for constrained Markov decision processes

We present a novel multi-timescale Q-learning algorithm for average cost control in a Markov decision process subject to multiple inequality constraints. We formulate a relaxed version of this problem through the Lagrange multiplier method. Our algorithm is different from Q-learning in that it updates two parameters - a Q-value parameter and a policy parameter. The Q-value parameter is updated on a slower time scale as compared to the policy parameter. Whereas Q-learning with function approximation can diverge in some cases, our algorithm is seen to be convergent as a result of the aforementioned timescale separation. We show the results of experiments on a problem of constrained routing in a multistage queueing network. Our algorithm is seen to exhibit good performance and the various inequality constraints are seen to be satisfied upon convergence of the algorithm.

Robust formulations for clustering-based large-scale classification

Chebyshev-inequality-based convex relaxations of Chance-Constrained Programs (CCPs) are shown to be useful for learning classifiers on massive datasets. In particular, an algorithm that integrates efficient clustering procedures and CCP approaches for computing classifiers on large datasets is proposed. The key idea is to identify high density regions or clusters from individual class conditional densities and then use a CCP formulation to learn a classifier on the clusters. The CCP formulation ensures that most of the data points in a cluster are correctly classified by employing a Chebyshev-inequality-based convex relaxation. This relaxation is heavily dependent on the second-order statistics. However, this formulation and in general such relaxations that depend on the second-order moments are susceptible to moment estimation errors. One of the contributions of the paper is to propose several formulations that are robust to such errors. In particular a generic way of making such formulations robust to moment estimation errors is illustrated using two novel confidence sets. An important contribution is to show that when either of the confidence sets is employed, for the special case of a spherical normal distribution of clusters, the robust variant of the formulation can be posed as a second-order cone program. Empirical results show that the robust formulations achieve accuracies comparable to that with true moments, even when moment estimates are erroneous. Results also illustrate the benefits of employing the proposed methodology for robust classification of large-scale datasets.

Minimum uncertainty and entanglement

We address the question, does a system A being entangled with another system B, put any constraints on the Heisenberg uncertainty relation (or the Schrodinger-Robertson inequality)? We find that the equality of the uncertainty relation cannot be reached for any two noncommuting observables, for finite dimensional Hilbert spaces if the Schmidt rank of the entangled state is maximal. One consequence is that the lower bound of the uncertainty relation can never be attained for any two observables for qubits, if the state is entangled. For infinite-dimensional Hilbert space too, we show that there is a class of physically interesting entangled states for which no two noncommuting observables can attain the minimum uncertainty equality.

Nonquadratic penalization improves near-infrared diffuse optical tomography

A new approach that can easily incorporate any generic penalty function into the diffuse optical tomographic image reconstruction is introduced to show the utility of nonquadratic penalty functions. The penalty functions that were used include quadratic (l(2)), absolute (l(1)), Cauchy, and Geman-McClure. The regularization parameter in each of these cases was obtained automatically by using the generalized cross-validation method. The reconstruction results were systematically compared with each other via utilization of quantitative metrics, such as relative error and Pearson correlation. The reconstruction results indicate that, while the quadratic penalty may be able to provide better separation between two closely spaced targets, its contrast recovery capability is limited, and the sparseness promoting penalties, such as l(1), Cauchy, and Geman-McClure have better utility in reconstructing high-contrast and complex-shaped targets, with the Geman-McClure penalty being the most optimal one. (C) 2013 Optical Society of America