Indexing and integrating multiple features for WWW images

In this paper, we present a novel indexing technique called Multi-scale Similarity Indexing (MSI) to index image's multi-features into a single one-dimensional structure. Both for text and visual feature spaces, the similarity between a point and a local partition's center in individual space is used as the indexing key, where similarity values in different features are distinguished by different scale. Then a single indexing tree can be built on these keys. Based on the property that relevant images have similar similarity values from the center of the same local partition in any feature space, certain number of irrelevant images can be fast pruned based on the triangle inequity on indexing keys. To remove the dimensionality curse existing in high dimensional structure, we propose a new technique called Local Bit Stream (LBS). LBS transforms image's text and visual feature representations into simple, uniform and effective bit stream (BS) representations based on local partition's center. Such BS representations are small in size and fast for comparison since only bit operation are involved. By comparing common bits existing in two BSs, most of irrelevant images can be immediately filtered. To effectively integrate multi-features, we also investigated the following evidence combination techniques-Certainty Factor, Dempster Shafer Theory, Compound Probability, and Linear Combination. Our extensive experiment showed that single one-dimensional index on multi-features improves multi-indices on multi-features greatly. Our LBS method outperforms sequential scan on high dimensional space by an order of magnitude. And Certainty Factor and Dempster Shafer Theory perform best in combining multiple similarities from corresponding multiple features.

T-Q relation and exact solution for the XYZ chain with general non-diagonal boundary terms

We propose that the Baxter's Q-operator for the quantum XYZ spin chain with open boundary conditions is given by the j -> infinity limit of the corresponding transfer matrix with spin-j (i.e., (2j + I)-dimensional) auxiliary space. The associated T-Q relation is derived from the fusion hierarchy of the model. We use this relation to determine the Bethe Ansatz solution of the eigenvalues of the fundamental transfer matrix. The solution yields the complete spectrum of the Hamiltonian. (c) 2006 Elsevier B.V. All rights reserved.

Indexing text and visual features for WWW images

In this paper, we present a novel indexing technique called Multi-scale Similarity Indexing (MSI) to index imagersquos multi-features into a single one-dimensional structure. Both for text and visual feature spaces, the similarity between a point and a local partitionrsquos center in individual space is used as the indexing key, where similarity values in different features are distinguished by different scale. Then a single indexing tree can be built on these keys. Based on the property that relevant images haves similar similarity values from the center of the same local partition in any feature space, certain number of irrelevant images can be fast pruned based on the triangle inequity on indexing keys. To remove the ldquodimensionality curserdquo existing in high dimensional structure, we propose a new technique called Local Bit Stream (LBS). LBS transforms imagersquos text and visual feature representations into simple, uniform and effective bit stream (BS) representations based on local partitionrsquos center. Such BS representations are small in size and fast for comparison since only bit operation are involved. By comparing common bits existing in two BSs, most of irrelevant images can be immediately filtered. Our extensive experiment showed that single one-dimensional index on multi-features improves multi-indices on multi-features greatly. Our LBS method outperforms sequential scan on high dimensional space by an order of magnitude.

The chemistry of ceramic glazes

The development of ideas and theories concerning the structure of glazes, as one of the glassy materials, are reviewed in the general introduction. The raw materials and the manufacturing process for glazes are described (Chapter One). A number of new vanadyl(IV) dipyridylamine and tripyrldylamine complexes have been prepared, various spectroscopic techniques are used in the investigation of the vanadyl ion in a weak ligand field, the situation of those found in a glaze environment (Chapter Three). In glaze recipes containing silica, potash feldspar, china clay, MO(M= Ca, Sr, Sa, Ti and Zn) and NiO, the ligand field theory is used in the elucidation of the effect of M (in MO) on the absorption spectra and coordination behaviour of Ni(II) in glazes. The magnetic and visible spectral results are reviewed in terms of Dietzel's idea of field strength of M and also in terms of Shteinberg's theory of glaze structure. X-ray diffraction is used for the identification of various species that formed after the firing process of glazes (Chapter Four). In Chapter Five, [] Mossbauer spectroscopy, supplemented by E.S.R., X-ray and visible spectral measurements are used in the investigation of iron in a glaze composition similar to that used in Chapter Four. The Mossbauer results are used in following the influence of; M in MO (M= Sr, Ca and Ba), oxides of titanium(IV) and vanadium(V ), and firing conditions on the chemistry of iron. Generally the iron(II) and iron(III) in the fired glazes are in octahedral sites although there are a range of similar, though not identical environments. A quite noticable influence of M (in MO) on the resonance line width is seen. In one case evidence is found for iron(IV) in an iron/vanadium glaze. E.S.R. of vanadium containing glazes indicate that vanadium is present as V02+ in a highly distorted tetragonal environment .

Novel hardwired distributive tactile sensing system for medical applications

This thesis described the research carried out on the development of a novel hardwired tactile sensing system tailored for the application of a next generation of surgical robotic and clinical devices, namely a steerable endoscope with tactile feedback, and a surface plate for patient posture and balance. Two case studies are examined. The first is a one-dimensional sensor for the steerable endoscope retrieving shape and ‘touch’ information. The second is a two-dimensional surface which interprets the three-dimensional motion of a contacting moving load. This research can be used to retrieve information from a distributive tactile sensing surface of a different configuration, and can interpret dynamic and static disturbances. This novel approach to sensing has the potential to discriminate contact and palpation in minimal invasive surgery (MIS) tools, and posture and balance in patients. The hardwired technology uses an embedded system based on Field Programmable Gate Arrays (FPGA) as the platform to perform the sensory signal processing part in real time. High speed robust operation is an advantage from this system leading to versatile application involving dynamic real time interpretation as described in this research. In this research the sensory signal processing uses neural networks to derive information from input pattern from the contacting surface. Three neural network architectures namely single, multiple and cascaded were introduced in an attempt to find the optimum solution for discrimination of the contacting outputs. These architectures were modelled and implemented into the FPGA. With the recent introduction of modern digital design flows and synthesis tools that essentially take a high-level sensory processing behaviour specification for a design, fast prototyping of the neural network function can be achieved easily. This thesis outlines the challenge of the implementations and verifications of the performances.

Random input problem for the nonlinear Schrödinger equation

We consider the random input problem for a nonlinear system modeled by the integrable one-dimensional self-focusing nonlinear Schrödinger equation (NLSE). We concentrate on the properties obtained from the direct scattering problem associated with the NLSE. We discuss some general issues regarding soliton creation from random input. We also study the averaged spectral density of random quasilinear waves generated in the NLSE channel for two models of the disordered input field profile. The first model is symmetric complex Gaussian white noise and the second one is a real dichotomous (telegraph) process. For the former model, the closed-form expression for the averaged spectral density is obtained, while for the dichotomous real input we present the small noise perturbative expansion for the same quantity. In the case of the dichotomous input, we also obtain the distribution of minimal pulse width required for a soliton generation. The obtained results can be applied to a multitude of problems including random nonlinear Fraunhoffer diffraction, transmission properties of randomly apodized long period Fiber Bragg gratings, and the propagation of incoherent pulses in optical fibers.

Random walks in local dynamics of network losses

We suggest a model for data losses in a single node (memory buffer) of a packet-switched network (like the Internet) which reduces to one-dimensional discrete random walks with unusual boundary conditions. By construction, the model has critical behavior with a sharp transition from exponentially small to finite losses with increasing data arrival rate. We show that for a finite-capacity buffer at the critical point the loss rate exhibits strong fluctuations and non-Markovian power-law correlations in time, in spite of the Markovian character of the data arrival process.

Caputo Derivatives in Viscoelasticity: A Non-Linear Finite-Deformation Theory for Tissue

Mathematics Subject Classification: 26A33, 74B20, 74D10, 74L15

On a Class of Fractional Type Integral Equations in Variable Exponent Spaces

2000 Mathematics Subject Classification: 45A05, 45B05, 45E05,45P05, 46E30

Time-varying airy pulses

Pulses in the form of the Airy function as solutions to an equation similar to the Schrodinger equation but with opposite roles of the time and space variables are derived. The pulses are generated by an Airy time varying field at a source point and propagate in vacuum preserving their shape and magnitude. The pulse motion is decelerating according to a quadratic law. Its velocity changes from infinity at the source point to zero in infinity. These one dimensional results are extended to the 3D+time case for a similar Airy-Bessel pulse with the same behaviour, the non-diffractive preservation and the deceleration. This pulse is excited by the field at a plane aperture perpendicular to the direction of the pulse propagation. © 2011 IEEE.

Decelerating Airy pulses

It is shown that an electromagnetic wave equation in time domain is reduced in paraxial approximation to an equation similar to the Schrodinger equation but in which the time and space variables play opposite roles. This equation has solutions in form of time-varying pulses with the Airy function as an envelope. The pulses are generated by a source point with an Airy time varying field and propagate in vacuum preserving their shape and magnitude. The motion is according to a quadratic law with the velocity changing from infinity at the source point to zero in infinity. These one-dimensional results are extended to the 3D+time case when a similar Airy-Bessel pulse is excited by the field at a plane aperture. The same behaviour of the pulses, the non-diffractive preservation and their deceleration, is found. © 2011 IEEE.

Strongly localized moving discrete dissipative breather-solitons in Kerr nonlinear media supported by intrinsic gain

We investigate the mobility of nonlinear localized modes in a generalized discrete Ginzburg-Landau-type model, describing a one-dimensional waveguide array in an active Kerr medium with intrinsic, saturable gain and damping. It is shown that exponentially localized, traveling discrete dissipative breather-solitons may exist as stable attractors supported only by intrinsic properties of the medium, i.e., in the absence of any external field or symmetry-breaking perturbations. Through an interplay by the gain and damping effects, the moving soliton may overcome the Peierls-Nabarro barrier, present in the corresponding conservative system, by self-induced time-periodic oscillations of its power (norm) and energy (Hamiltonian), yielding exponential decays to zero with different rates in the forward and backward directions. In certain parameter windows, bistability appears between fast modes with small oscillations and slower, large-oscillation modes. The velocities and the oscillation periods are typically related by lattice commensurability and exhibit period-doubling bifurcations to chaotically "walking" modes under parameter variations. If the model is augmented by intersite Kerr nonlinearity, thereby reducing the Peierls-Nabarro barrier of the conservative system, the existence regime for moving solitons increases considerably, and a richer scenario appears including Hopf bifurcations to incommensurately moving solutions and phase-locking intervals. Stable moving breathers also survive in the presence of weak disorder. © 2014 American Physical Society.

Learning from Geometry

Subspaces and manifolds are two powerful models for high dimensional signals. Subspaces model linear correlation and are a good fit to signals generated by physical systems, such as frontal images of human faces and multiple sources impinging at an antenna array. Manifolds model sources that are not linearly correlated, but where signals are determined by a small number of parameters. Examples are images of human faces under different poses or expressions, and handwritten digits with varying styles. However, there will always be some degree of model mismatch between the subspace or manifold model and the true statistics of the source. This dissertation exploits subspace and manifold models as prior information in various signal processing and machine learning tasks.

A near-low-rank Gaussian mixture model measures proximity to a union of linear or affine subspaces. This simple model can effectively capture the signal distribution when each class is near a subspace. This dissertation studies how the pairwise geometry between these subspaces affects classification performance. When model mismatch is vanishingly small, the probability of misclassification is determined by the product of the sines of the principal angles between subspaces. When the model mismatch is more significant, the probability of misclassification is determined by the sum of the squares of the sines of the principal angles. Reliability of classification is derived in terms of the distribution of signal energy across principal vectors. Larger principal angles lead to smaller classification error, motivating a linear transform that optimizes principal angles. This linear transformation, termed TRAIT, also preserves some specific features in each class, being complementary to a recently developed Low Rank Transform (LRT). Moreover, when the model mismatch is more significant, TRAIT shows superior performance compared to LRT.

The manifold model enforces a constraint on the freedom of data variation. Learning features that are robust to data variation is very important, especially when the size of the training set is small. A learning machine with large numbers of parameters, e.g., deep neural network, can well describe a very complicated data distribution. However, it is also more likely to be sensitive to small perturbations of the data, and to suffer from suffer from degraded performance when generalizing to unseen (test) data.

From the perspective of complexity of function classes, such a learning machine has a huge capacity (complexity), which tends to overfit. The manifold model provides us with a way of regularizing the learning machine, so as to reduce the generalization error, therefore mitigate overfiting. Two different overfiting-preventing approaches are proposed, one from the perspective of data variation, the other from capacity/complexity control. In the first approach, the learning machine is encouraged to make decisions that vary smoothly for data points in local neighborhoods on the manifold. In the second approach, a graph adjacency matrix is derived for the manifold, and the learned features are encouraged to be aligned with the principal components of this adjacency matrix. Experimental results on benchmark datasets are demonstrated, showing an obvious advantage of the proposed approaches when the training set is small.

Stochastic optimization makes it possible to track a slowly varying subspace underlying streaming data. By approximating local neighborhoods using affine subspaces, a slowly varying manifold can be efficiently tracked as well, even with corrupted and noisy data. The more the local neighborhoods, the better the approximation, but the higher the computational complexity. A multiscale approximation scheme is proposed, where the local approximating subspaces are organized in a tree structure. Splitting and merging of the tree nodes then allows efficient control of the number of neighbourhoods. Deviation (of each datum) from the learned model is estimated, yielding a series of statistics for anomaly detection. This framework extends the classical {\em changepoint detection} technique, which only works for one dimensional signals. Simulations and experiments highlight the robustness and efficacy of the proposed approach in detecting an abrupt change in an otherwise slowly varying low-dimensional manifold.

Tight-Binding Approximations in 1D and 2D Coupled-Cavity Photonic Crystal Structures

Light confinement and controlling an optical field has numerous applications in the field of telecommunications for optical signals processing. When the wavelength of the electromagnetic field is on the order of the period of a photonic microstructure, the field undergoes reflection, refraction, and coherent scattering. This produces photonic bandgaps, forbidden frequency regions or spectral stop bands where light cannot exist. Dielectric perturbations that break the perfect periodicity of these structures produce what is analogous to an impurity state in the bandgap of a semiconductor. The defect modes that exist at discrete frequencies within the photonic bandgap are spatially localized about the cavity-defects in the photonic crystal. In this thesis the properties of two tight-binding approximations (TBAs) are investigated in one-dimensional and two-dimensional coupled-cavity photonic crystal structures We require an efficient and simple approach that ensures the continuity of the electromagnetic field across dielectric interfaces in complex structures. In this thesis we develop \textrm{E} -- and \textrm{D} --TBAs to calculate the modes in finite 1D and 2D two-defect coupled-cavity photonic crystal structures. In the \textrm{E} -- and \textrm{D} --TBAs we expand the coupled-cavity \overrightarrow{E} --modes in terms of the individual \overrightarrow{E} -- and \overrightarrow{D} --modes, respectively. We investigate the dependence of the defect modes, their frequencies and quality factors on the relative placement of the defects in the photonic crystal structures. We then elucidate the differences between the two TBA formulations, and describe the conditions under which these formulations may be more robust when encountering a dielectric perturbation. Our 1D analysis showed that the 1D modes were sensitive to the structure geometry. The antisymmetric \textrm{D} mode amplitudes show that the \textrm{D} --TBA did not capture the correct (tangential \overrightarrow{E} --field) boundary conditions. However, the \textrm{D} --TBA did not yield significantly poorer results compared to the \textrm{E} --TBA. Our 2D analysis reveals that the \textrm{E} -- and \textrm{D} --TBAs produced nearly identical mode profiles for every structure. Plots of the relative difference between the \textrm{E} and \textrm{D} mode amplitudes show that the \textrm{D} --TBA did capture the correct (normal \overrightarrow{E} --field) boundary conditions. We found that the 2D TBA CC mode calculations were 125-150 times faster than an FDTD calculation for the same two-defect PCS. Notwithstanding this efficiency, the appropriateness of either TBA was found to depend on the geometry of the structure and the mode(s), i.e. whether or not the mode has a large normal or tangential component.

Représentations et fusion des algèbres de Temperley-Lieb originale et diluée

Les algèbres de Temperley-Lieb originales, aussi dites régulières, apparaissent dans de nombreux modèles statistiques sur réseau en deux dimensions: les modèles d'Ising, de Potts, des dimères, celui de Fortuin-Kasteleyn, etc. L'espace d'Hilbert de l'hamiltonien quantique correspondant à chacun de ces modèles est un module pour cette algèbre et la théorie de ses représentations peut être utilisée afin de faciliter la décomposition de l'espace en blocs; la diagonalisation de l'hamiltonien s'en trouve alors grandement simplifiée. L'algèbre de Temperley-Lieb diluée joue un rôle similaire pour des modèles statistiques dilués, par exemple un modèle sur réseau où certains sites peuvent être vides; ses représentations peuvent alors être utilisées pour simplifier l'analyse du modèle comme pour le cas original. Or ceci requiert une connaissance des modules de cette algèbre et de leur structure; un premier article donne une liste complète des modules projectifs indécomposables de l'algèbre diluée et un second les utilise afin de construire une liste complète de tous les modules indécomposables des algèbres originale et diluée. La structure des modules est décrite en termes de facteurs de composition et par leurs groupes d'homomorphismes. Le produit de fusion sur l'algèbre de Temperley-Lieb originale permet de «multiplier» ensemble deux modules sur cette algèbre pour en obtenir un autre. Il a été montré que ce produit pouvait servir dans la diagonalisation d'hamiltoniens et, selon certaines conjectures, il pourrait également être utilisé pour étudier le comportement de modèles sur réseaux dans la limite continue. Un troisième article construit une généralisation du produit de fusion pour les algèbres diluées, puis présente une méthode pour le calculer. Le produit de fusion est alors calculé pour les classes de modules indécomposables les plus communes pour les deux familles, originale et diluée, ce qui vient ajouter à la liste incomplète des produits de fusion déjà calculés par d'autres chercheurs pour la famille originale. Finalement, il s'avère que les algèbres de Temperley-Lieb peuvent être associées à une catégorie monoïdale tressée, dont la structure est compatible avec le produit de fusion décrit ci-dessus. Le quatrième article calcule explicitement ce tressage, d'abord sur la catégorie des algèbres, puis sur la catégorie des modules sur ces algèbres. Il montre également comment ce tressage permet d'obtenir des solutions aux équations de Yang-Baxter, qui peuvent alors être utilisées afin de construire des modèles intégrables sur réseaux.