Matrix Designs and Methods for Secure and Efficient Compressed Sensing

The idea of balancing the resources spent in the acquisition and encoding of natural signals strictly to their intrinsic information content has interested nearly a decade of research under the name of compressed sensing. In this doctoral dissertation we develop some extensions and improvements upon this technique's foundations, by modifying the random sensing matrices on which the signals of interest are projected to achieve different objectives. Firstly, we propose two methods for the adaptation of sensing matrix ensembles to the second-order moments of natural signals. These techniques leverage the maximisation of different proxies for the quantity of information acquired by compressed sensing, and are efficiently applied in the encoding of electrocardiographic tracks with minimum-complexity digital hardware. Secondly, we focus on the possibility of using compressed sensing as a method to provide a partial, yet cryptanalysis-resistant form of encryption; in this context, we show how a random matrix generation strategy with a controlled amount of perturbations can be used to distinguish between multiple user classes with different quality of access to the encrypted information content. Finally, we explore the application of compressed sensing in the design of a multispectral imager, by implementing an optical scheme that entails a coded aperture array and Fabry-Pérot spectral filters. The signal recoveries obtained by processing real-world measurements show promising results, that leave room for an improvement of the sensing matrix calibration problem in the devised imager.

Gene array of primary human osteoblasts exposed to enamel matrix derivative in combination with a natural bone mineral

OBJECTIVES The application of an enamel matrix derivative (EMD) for regenerative periodontal surgery has been shown to promote formation of new cementum, periodontal ligament, and alveolar bone. In intrabony defects with a complicated anatomy, the combination of EMD with various bone grafting materials has resulted in additional clinical improvements, but the initial cellular response of osteoblasts coming in contact with these particles have not yet been fully elucidated. The objective of the present study was to evaluate the in vitro effects of EMD combined with a natural bone mineral (NBM) on a wide variety of genes, cytokines, and transcription factors and extracellular matrix proteins on primary human osteoblasts. MATERIAL AND METHODS Primary human osteoblasts were seeded on NBM particles pre-coated with versus without EMD and analyzed for gene differences using a human osteogenesis gene super-array (Applied Biosystems). Osteoblast-related genes include those transcribed during bone mineralization, ossification, bone metabolism, cell growth and differentiation, as well as gene products representing extracellular matrix molecules, transcription factors, and cell adhesion molecules. RESULTS EMD promoted gene expression of various osteoblast differentiation markers including a number of collagen types and isoforms, SMAD intracellular proteins, osteopontin, cadherin, alkaline phosphatase, and bone sialoprotein. EMD also upregulated a variety of growth factors including bone morphogenetic proteins, vascular endothelial growth factors, insulin-like growth factor, transforming growth factor, and their associated receptor proteins. CONCLUSION The results from the present study demonstrate that EMD is capable of activating a wide variety of genes, growth factors, and cytokines when pre-coated onto NBM particles. CLINICAL RELEVANCE The described in vitro effects of EMD on human primary osteoblasts provide further biologic support for the clinical application of a combination of EMD with NBM particles in periodontal and oral regenerative surgery.

Full S matrix calculation via a single real-symmetric Lanczos recursion: The Lanczos artificial boundary inhomogeneity method

We present an efficient and robust method for the calculation of all S matrix elements (elastic, inelastic, and reactive) over an arbitrary energy range from a single real-symmetric Lanczos recursion. Our new method transforms the fundamental equations associated with Light's artificial boundary inhomogeneity approach [J. Chem. Phys. 102, 3262 (1995)] from the primary representation (original grid or basis representation of the Hamiltonian or its function) into a single tridiagonal Lanczos representation, thereby affording an iterative version of the original algorithm with greatly superior scaling properties. The method has important advantages over existing iterative quantum dynamical scattering methods: (a) the numerically intensive matrix propagation proceeds with real symmetric algebra, which is inherently more stable than its complex symmetric counterpart; (b) no complex absorbing potential or real damping operator is required, saving much of the exterior grid space which is commonly needed to support these operators and also removing the associated parameter dependence. Test calculations are presented for the collinear H+H-2 reaction, revealing excellent performance characteristics. (C) 2004 American Institute of Physics.

Embedded fibre Bragg grating array sensors in aluminium alloy matrix by ultrasonic consolidation

Fibre Bragg Grating (FBG) array sensors have been successfully embedded in aluminium alloy matrix by ultrasonic consolidation (UC) technique. The temperature and loading responses of the embedded FBG arrays have been systematically characterised. The embedded grating sensors exhibit an average temperature sensitivity of ~36pm/°C, which is three times higher than that of normal FBGs, and a loading responsivity of ~0.1nm/kg within the dynamic range from 0kg to 3kg. This initial experiment clearly demonstrates that FBG array sensors can be embedded in metal matrix together with other passive and active fibres to fabricate smart materials to monitor the operation and health of engineering structures.

Embedded fibre Bragg grating array sensors in aluminium alloy matrix by ultrasonic consolidation

Fibre Bragg Grating (FBG) array sensors have been successfully embedded in aluminium alloy matrix by ultrasonic consolidation (UC) technique. The temperature and loading responses of the embedded FBG arrays have been systematically characterised. The embedded grating sensors exhibit an average temperature sensitivity of ~36pm/°C, which is three times higher than that of normal FBGs, and a loading responsivity of ~0.1nm/kg within the dynamic range from 0kg to 3kg. This initial experiment clearly demonstrates that FBG array sensors can be embedded in metal matrix together with other passive and active fibres to fabricate smart materials to monitor the operation and health of engineering structures.

Secure Wireless Key Establishment Using Retrodirective Array

In this paper a new method of establishing secret keys for wireless communications is proposed. A retrodirective array (RDA) that is configured to receive and re-transmit at different frequencies is utilized as a relay node. Specifically the analogue RDA is able to respond in ‘real-time’, reducing the required number of time slots for key establishment to two, compared with at least three in previous relay key generation schemes. More importantly, in the proposed architecture equivalent reciprocal wireless channels between legitimate keying nodes can be randomly updated within one channel coherence time period, leading to greatly increased key generation rates (KGRs) in slow fading environment. The secrecy performance of this RDA assisted key generation system is evaluated and it is shown that it outperforms previous relay key generation systems.

INFERENCE FOR EIGENVALUES AND EIGENVECTORS OF GAUSSIAN SYMMETRIC MATRICES

This article presents maximum likelihood estimators (MLEs) and log-likelihood ratio (LLR) tests for the eigenvalues and eigenvectors of Gaussian random symmetric matrices of arbitrary dimension, where the observations are independent repeated samples from one or two populations. These inference problems are relevant in the analysis of diffusion tensor imaging data and polarized cosmic background radiation data, where the observations are, respectively, 3 x 3 and 2 x 2 symmetric positive definite matrices. The parameter sets involved in the inference problems for eigenvalues and eigenvectors are subsets of Euclidean space that are either affine subspaces, embedded submanifolds that are invariant under orthogonal transformations or polyhedral convex cones. We show that for a class of sets that includes the ones considered in this paper, the MLEs of the mean parameter do not depend on the covariance parameters if and only if the covariance structure is orthogonally invariant. Closed-form expressions for the MLEs and the associated LLRs are derived for this covariance structure.

Phase-only optical encryption based on the zeroth-order phase-contrast technique

A phase-only encryption/decryption scheme with the readout based on the zeroth-order phase-contrast technique (ZOPCT), without the use of a phase-changing plate on the Fourier plane of an optical system based on the 4f optical correlator, is proposed. The encryption of a gray-level image is achieved by multiplying the phase distribution obtained directly from the gray-level image by a random phase distribution. The robustness of the encoding is assured by the nonlinearity intrinsic to the proposed phase-contrast method and the random phase distribution used in the encryption process. The experimental system has been implemented with liquid-crystal spatial modulators to generate phase-encrypted masks and a decrypting key. The advantage of this method is the easy scheme to recover the gray-level information from the decrypted phase-only mask applying the ZOPCT. An analysis of this decryption method was performed against brute force attacks. (C) 2009 Society of Photo-Optical Instrumentation Engineers. [DOI: 10.1117/1.3223629]

Matrix Method for Acoustic Levitation Simulation

A matrix method is presented for simulating acoustic levitators. A typical acoustic levitator consists of an ultrasonic transducer and a reflector. The matrix method is used to determine the potential for acoustic radiation force that acts on a small sphere in the standing wave field produced by the levitator. The method is based on the Rayleigh integral and it takes into account the multiple reflections that occur between the transducer and the reflector. The potential for acoustic radiation force obtained by the matrix method is validated by comparing the matrix method results with those obtained by the finite element method when using an axisymmetric model of a single-axis acoustic levitator. After validation, the method is applied in the simulation of a noncontact manipulation system consisting of two 37.9-kHz Langevin-type transducers and a plane reflector. The manipulation system allows control of the horizontal position of a small levitated sphere from -6 mm to 6 mm, which is done by changing the phase difference between the two transducers. The horizontal position of the sphere predicted by the matrix method agrees with the horizontal positions measured experimentally with a charge-coupled device camera. The main advantage of the matrix method is that it allows simulation of non-symmetric acoustic levitators without requiring much computational effort.

A phylogenetic study of Lepidapedoides Yamaguti, 1970 (Digenea) with a key and descriptions of two new species from western Australia

Two new species of the genus Lepidapedoides are described from the aulopodid teleost Aulopus purpurissatus from south-western Australia. Both are distinguished from other Lepidapedoides spp. by their pedunculate ventral sucker. Lepidapedoides pistoris n. sp. and L. elongatrium n. sp. are distinguished by the possession of a narrow, elongate form, a long ventral sucker to ovary distance: the vitellarium reaching only to the posterior level of the cirrus-sac, the cirrus-sac length and the deep genital atrium with the metraterm entering distally to its base in L. elongatrium. A key to species of the genus is given. A character matrix is included for the genus. Poorly resolved phylogenetic trees indicate two main lineages in the genus. The two new species described here are resolved as sister taxa. The new combination Lepidapedoides freitasi (Kohn gr Fernandes, 1970) is formed for Acanthocolpoides freitasi.

Expokit: A software package for computing matrix exponentials

Expokit provides a set of routines aimed at computing matrix exponentials. More precisely, it computes either a small matrix exponential in full, the action of a large sparse matrix exponential on an operand vector, or the solution of a system of linear ODEs with constant inhomogeneity. The backbone of the sparse routines consists of matrix-free Krylov subspace projection methods (Arnoldi and Lanczos processes), and that is why the toolkit is capable of coping with sparse matrices of large dimension. The software handles real and complex matrices and provides specific routines for symmetric and Hermitian matrices. The computation of matrix exponentials is a numerical issue of critical importance in the area of Markov chains and furthermore, the computed solution is subject to probabilistic constraints. In addition to addressing general matrix exponentials, a distinct attention is assigned to the computation of transient states of Markov chains.

A numerical study of large sparse matrix exponentials arising in Markov chains

Krylov subspace techniques have been shown to yield robust methods for the numerical computation of large sparse matrix exponentials and especially the transient solutions of Markov Chains. The attractiveness of these methods results from the fact that they allow us to compute the action of a matrix exponential operator on an operand vector without having to compute, explicitly, the matrix exponential in isolation. In this paper we compare a Krylov-based method with some of the current approaches used for computing transient solutions of Markov chains. After a brief synthesis of the features of the methods used, wide-ranging numerical comparisons are performed on a power challenge array supercomputer on three different models. (C) 1999 Elsevier Science B.V. All rights reserved.AMS Classification: 65F99; 65L05; 65U05.

Drinfeld twists and symmetric Bethe vectors of supersymmetric fermion models

We construct the Drinfeld twists ( factorizing F-matrices) of the gl(m-n)-invariant fermion model. Completely symmetric representation of the pseudo-particle creation operators of the model are obtained in the basis provided by the F-matrix ( the F-basis). We resolve the hierarchy of the nested Bethe vectors in the F-basis for the gl(m-n) supersymmetric model.

Expression of extracellular matrix proteins in adenomatoid odontogenic tumor

Altered expression of extracellular matrix (ECM) components has been reported in several pathologies; however, few ECM proteins have been evaluated in adenomatoid odontogenic tumor (AOT). The aim of this study was to analyze the expression and distribution of the ECM proteoglycans: biglycan and decorin; and glycoproteins: osteonectin, osteopontin, bone sialoprotein and osteocalcin in the AOT. Three-micrometer sections from paraffin-embedded specimens were evaluated employing a streptavidin-biotin immunohistochemical method with the antibodies against the proteins previously cited. Only the osteonectin was expressed in the epithelial cells. The eosinophilic amorphous material and the connective tissue showed expression of all components studied. The calcification foci expressed only osteopontin. In conclusion, the low expression of the components studied in neoplastic epithelial cells suggests that the epithelial cells act probably as stimulators of the expression by the stroma, which in turn can act as agonist or antagonist of the tumor growth. These results suggest that the components studied probably have a key role in the biological behavior of the AOT.