Department of Mathematics

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Strict collapsibility and model collapsibility are two important concepts associated with the dimension reduction of a multidimensional contingency table, without losing the relevant information. In this paper, we obtain some necessary and sufficient conditions for the strict collapsibility of the full model, with respect to an interaction factor or a set of interaction factors, based on the interaction parameters of the conditional/layer log-linear models. For hierarchical log-linear models, we present also necessary and sufficient conditions for the full model to be model collapsible, based on the conditional interaction parameters. We discuss both the cases where one variable or a set of variables is conditioned. The connections between the strict collapsibility and the model collapsibility are also pointed out. Our results are illustrated through suitable examples, including a real life application. © 2009 Elsevier B.V. All rights reserved.

World University root node

Journal of Statistical Planning and Inference

Collapsibility of contingency tables based on conditional models

In this paper, a new robust watermarking scheme is proposed using fractional Fourier transform (FrFT) and singular value decomposition. The core idea of the proposed scheme is to decompose an image using FrFT followed by the non-overlapping block segmentation. A new key matrix is then formed by taking maximum singular values of all non-overlapping blocks. For embedding this key matrix is used and is done by modifying singular values with the singular values of the watermark. The experimental results show better visual imperceptibility and resiliency of the proposed scheme against intentional or un-intentional variety of attacks. © 2010 Springer-Verlag Berlin Heidelberg.

Communications in Computer and Information Science

A new SVD based watermarking framework in fractional Fourier domain

This chapter discusses an ab initio frequency domain model of circular microresonators, built on the physical notions that commonly enter the description of the resonator functioning in terms of interaction between fields in the circular cavity with the modes supported by the straight bus waveguides. Quantitative evaluation of this abstract model requires propagation constants associated with the cavity/bend segments, and scattering matrices, that represent the wave interaction in the coupler regions. These quantities are obtained by an analytical (2-D) or numerical (3-D) treatment of bent waveguides, along with spatial coupled mode theory (CMT) for the couplers. The required CMT formulation is described in detail. Also, quasi-analytical approximations for fast and accurate computation of the resonator spectra are discussed. The formalism discussed in this chapter provides valuable insight into the functioning of the resonators, and it is suitable for practical device design. © 2010, Springer-Verlag US.

Springer Series in Optical Sciences

Circular Integrated Optical Microresonators: Analytical Methods and Computational Aspects

Disparity estimation from stereo imagery has gained substantial interest of research community from its commencement with the recent trend being the use of multiresolution methods. Existing multiresolution based methods are relatively independent and do not, in general, relate to a continuous progress in the research. As a result, the relative advantages and disadvantages of a particular multiresolution method in disparity estimation are hard to understand. Present work is an effort to put different multiresolution methods together to highlight their expediency and suitability along with the comparison to get a better understanding. Three different frameworks are used having different strengths and limitations followed by the comparison in the terms of time complexity, quality of matching and effect of different levels of decomposition. Qualitative and quantitative results have been provided for four types of standard multiresolution methods. © Springer-Verlag Berlin Heidelberg 2010.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Performance evaluation of multiresolution methods in disparity estimation

Due to unique feature of high electric field confinement in low refractive index slots, microresonators based on cavities with a slot were investigated for novel sensing and nonlinear applications. The resonance properties of such slot resonators are significantly affected by the position of the slot inside the cavity. In this work we investigate this dependence numerically. Consistent handling of discontinuous fields and efficient resolution of sub-wavelength slot pose a numerical challenge in simulation of slot microresonators. We address these difficulties by modelling the slot resonators using coupled mode theory. Using this model, effects of the slot position on the resonances of the slot microresonators are analyzed. © 2010 IEEE.

2010 12th International Conference on Transparent Optical Networks, ICTON 2010

Effect of the slot position on the response of slot microresonators: Numerical investigation

Let (X,d) be a compact metric space and (K(X),dH) be the space of all non-empty compact subsets of X equipped with the Hausdorff metric dH. The dynamical system (X,f) induces another dynamical system (K(X),f{topbar}). We study the relations between the various forms of sensitivity of the systems (X,f) and (K(X),f{topbar}). We prove that all forms of sensitivity of (K(X),f{topbar}) partly imply the same for (X,f), and the converse holds in some cases. © 2010 Elsevier B.V.

Fulltext

Topology and its Applications

Inducing sensitivity on hyperspaces

In this paper we wish to relate the dynamics of the base map to the dynamics of the induced map. In the process, we obtain conditions on the endowed hyperspace topology under which the chaotic behaviour of the map on the base space is inherited by the induced map on the hyperspace. Several of the known results come up as corollaries to our results. We also discuss some metric related dynamical properties on the hyperspace that cannot be deduced for the base dynamics. © Universidad Politécnica de Valencia.

Applied General Topology

Topological dynamics on hyperspaces

In this paper, a robust watermarking technique based on fractional cosine transform and singular value decomposition is presented to improve the protection of the images. A meaningful gray scale image is used as watermark instead of randomly generated Gaussian noise type watermark. First, host image is transformed by the means of fractional cosine transform. Now, the positions of all frequency coefficients are changed with respect to some rule and this rule is secret and only known to the owner/creator. Then inverse fractional cosine transform is performed to get the reference image. Watermark logo is embedded in the reference image by modifying its singular values. For embedding, the singular values of the reference image are found and then modify it by adding the singular values of the watermark image. A reliable watermark extraction algorithm is developed for extracting watermark from possibly attacked image. The experimental results show better visual imperceptibility and resiliency of the proposed scheme against intentional or un-intentional variety of attacks. © 2010 Copyright SPIE - The International Society for Optical Engineering.

Proceedings of SPIE - The International Society for Optical Engineering

SVD-based robust watermarking using fractional cosine transform

The Fourier transform is undoubtedly one of the most valuable and frequently used tools in signal processing and analysis but it has some limitations. In this paper, we rectify these limitations by proposing a newer version of Fourier transform, namely, Distributed Multiresolution Discrete Fourier Transform (D-MR-DFT) and its application in digital watermarking. The core idea of the proposed watermarking scheme is to decompose an image into four frequency sub-bands using D-MR-DFT and then singular values of every sub-band are modified with the singular values of the watermark. The experimental results show better visual imperceptibility and resiliency of the proposed scheme against intentional or unintentional variety of attacks. © 2010 World Scientific Publishing Company.

International Journal of Wavelets, Multiresolution and Information Processing

Distributed Multiresolution Discrete Fourier Transform and its application to watermarking

Effects of perturbations of the whispering gallery modes (WGMs) in cylindrical microcavity resonators by embedded nano size particles are studied by the finite difference time domain modeling. Apart from the foreseeable effects of spectral shift and broadening of WGM resonances, we also observed a key feature of splitting of the WGM peaks. This splitting occurs as a result of formation of symmetric and antisymmetric standing waves inside the cavity. It is demonstrated that magnitude of the splitting reaches several angstroms for 5 μm cavities with index 1.59 supporting moderately high quality (Q≈10 5) WGMs. We show that this effect allows developing biomolecular sensors based on measuring this splitting in porous cavities or in cavities with liquid cores. ©2009 IEEE.