Towards dimension expanders over finite fields

In this paper we study the problem of explicitly constructing a dimension expander raised by [3]: Let \mathbbFⁿ \mathbb{F}^n be the n dimensional linear space over the field \mathbbF\mathbb{F}. Find a small (ideally constant) set of linear transformations from \mathbbFⁿ \mathbb{F}^n to itself {A _i } _i∈I such that for every linear subspace V ⊂ \mathbbFⁿ \mathbb{F}^n of dimension dim(V)<n/2 we have

Resource allocation in dynamic PERT networks with finite capacity

This article models the resource allocation problem in dynamic PERT networks with finite capacity of concurrent projects (COnstant Number of Projects In Process (CONPIP)), where activity durations are independent random variables with exponential distributions, and the new projects are generated according to a Poisson process. The system is represented as a queuing network with finite concurrent projects, where each activity of a project is performed at a devoted service station with one server located in a node of the network. For modeling dynamic PERT networks with CONPIP, we first convert the network of queues into a stochastic network. Then, by constructing a proper finite-state continuous-time Markov model, a system of differential equations is created to solve and find the completion time distribution for any particular project. Finally, we propose a multi-objective model with three conflict objectives to optimally control the resources allocated to the servers, and apply the goal attainment method to solve a discrete-time approximation of the original multi-objective problem.     

Channel Coordination with Cooperative Advertising Considering Effect of Advertising on Willingness to Pay

In this paper, cooperative advertising in a manufacturer–retailer supply chain is studied. Advertising can enhance willingness to pay (WTP) of customers. This trade-off between the benefits of increasing WTP of customers and the advertising expenditure is a key to understanding the retailers optimal advertising decision. On the other hand, it is interesting to understand in which condition supporting the retailer for his advertising expenditure is beneficial for the manufacturer. In this study, in order to capture pricing and advertising strategies of the channel member, three non-cooperative games including Nash, Stackelberg retailer and Stackelberg manufacturer game-theoretic models are established. In spite of the related studies which restrict price in order to prevent negative demand, the proposed model allows channel members to increase their prices by enhancing WTP of customers. In this study, contrary to similar additive form demand functions applied in the co-op ad literature which limits their studies for cases that profit function is concave with respect to variables, optimal prices and advertising strategies are obtained for all the solution space. Surprisingly for the very high values of the advertising effect coefficient, a finite optimal advertising expenditure is achieved.     

Primal and dual predicted decrease approximation methods

We introduce the notion of predicted decrease approximation (PDA) for constrained convex optimization, a flexible framework which includes as special cases known algorithms such as generalized conditional gradient, proximal gradient, greedy coordinate descent for separable constraints and working set methods for linear equality constraints with bounds. The new scheme allows the development of a unified convergence analysis for these methods. We further consider a partially strongly convex nonsmooth model and show that dual application of PDA-based methods yields new sublinear convergence rate estimates in terms of both primal and dual objectives. As an example of an application, we provide an explicit working set selection rule for SMO-type methods for training the support vector machine with an improved primal convergence analysis.     

Faraday rotation in a two-dimensional photonic crystal with a magneto-optic defect

We study the magneto-optic (MO) Faraday rotation in a two-dimensional square-lattice photonic crystal with a central MO defect layer in the optical wavelength range. We show that when a TM plane wave is incident upon a photonic crystal, an enhancement of Faraday rotation takes place in a region where a resonance peak appears in the photonic bandgap. In this region the mode conversion is high.     

Adaptive fuzzy sliding-mode control for multi-input multi-output chaotic systems

This paper describes an adaptive fuzzy sliding-mode control algorithm for controlling unknown or uncertain, multi-input multi-output (MIMO), possibly chaotic, dynamical systems. The control approach encompasses a fuzzy system and a robust controller. The fuzzy system is designed to mimic an ideal sliding-mode controller, and the robust controller compensates the difference between the fuzzy controller and the ideal one. The parameters of the fuzzy system, as well as the uncertainty bound of the robust controller, are tuned adaptively. The adaptive laws are derived in the Lyapunov sense to guarantee the asymptotic stability and tracking of the controlled system. The effectiveness of the proposed method is shown by applying it to some well-known chaotic systems.     

Numerical study of the effect of turbulence on rate of reactions in the MILD combustion regime

In this paper, the importance of fluctuations in flow field parameters is studied under MILD combustion conditions. In this way, a turbulent non-premixed CH₄+H₂ jet flame issuing into a hot and deficient co-flow air is modeled using the RANS Axisymmetric equations. The modeling is carried out using the EDC model to describe the turbulence-chemistry interaction. The DRM-22 reduced mechanism and the GRI2.11 full mechanism are used to represent the chemical reactions of H₂/methane jet flame. Results illustrate that although the fluctuations in temperature field are small and the reaction zone volume are large in the MILD regime, the fluctuations in temperature and species concentrations are still effective on the flow field. Also, inappropriate dealing with the turbulence effect on chemistry leads to errors in prediction of temperature up to 15% in the present flame. By decreasing of O₂ concentration of hot co-flow air, the effect of fluctuations in flow field parameters on flame characteristics are still significant and its effect on species reaction rates does not decrease. On the other hand, although decreasing of jet inlet Reynolds number at constant inlet turbulence intensity addresses to smaller fluctuations in flow filed, it does not lead to lower the effect of turbulence on species distribution and temperature field under MILD combustion conditions.     

Intelligent reversible watermarking technique in medical images using GA and PSO

The advances in recording, editing, and broadcasting multimedia contents in digital form motivate to protect these digital contents from illegal use, such as duplication, manipulation, and redistribution. However, watermarking algorithms are designed to satisfy requirements of applications, as different applications have different concerns. We intend to design a watermarking algorithm for applications which require high embedding capacity and imperceptibility, to maintain the integrity of the host signal as well as embedded information. Reversible watermarking is a promising technique which satisfies our requirements. In this paper, we concentrate on improving the watermark capacity and reducing the perceptual degradation of an image. We investigated the Luo's [1] additive interpolation-error expansion algorithm and enhanced it by incorporating with two intelligent techniques: genetic algorithm (GA), and particle swarm optimization (PSO). Genetic algorithm is applied to exploit the correlation of image pixel values to obtain better estimation of neighboring pixel values, which results in optimal balance between information storage capacity and imperceptibility. Particle swarm optimization (intelligent technique) is also applied for the same purpose. Experimental results show that PSO and GA nearly give the same results, but GA outperforms the PSO. Experimental results also reveal that the proposed strategy outperforms the state of art works in terms of perceptual quality and watermarking payload.     

Spatially Homogeneous Rotating Solution in f(R) Gravity and Its Energy Contents

In this paper, the metric approach of f(R) theory of gravity is used to investigate the exact vacuum solutions of spatially homogeneous rotating spacetimes. For this purpose, R is replaced by f(R) in the standard Einstein-Hilbert action and the set of modified Einstein field equations reduce to a single equation. We adopt the assumption of constant Ricci scalar which maybe zero or non-zero. Moreover, the energy density of the non-trivial solution has been evaluated by using the generalized Landau-Lifshitz energy-momentum complex in the perspective of f(R) gravity for some appropriate f(R) model, which turns out to be a constant quantity.     

Robust Mean-Squared Error Estimation of Multiple Signals in Linear Systems Affected by Model and Noise Uncertainties

This paper is a continuation of the work in [11] and [2] on the problem of estimating by a linear estimator, N unobservable input vectors, undergoing the same linear transformation, from noise-corrupted observable output vectors. Whereas in the aforementioned papers, only the matrix representing the linear transformation was assumed uncertain, here we are concerned with the case in which the second order statistics of the noise vectors (i.e., their covariance matrices) are also subjected to uncertainty. We seek a robust mean-squared error estimator immuned against both sources of uncertainty. We show that the optimal robust mean-squared error estimator has a special form represented by an elementary block circulant matrix, and moreover when the uncertainty sets are ellipsoidal-like, the problem of finding the optimal estimator matrix can be reduced to solving an explicit semidefinite programming problem, whose size is independent of N. The research was partially supported by BSF grant #2002038