Cell image classification using histograms, higher order statistics and adaboost

A cell classification algorithm that uses first, second and third order statistics of pixel intensity distributions over pre-defined regions is implemented and evaluated. A cell image is segmented into 6 regions extending from a boundary layer to an inner circle. First, second and third order statistical features are extracted from histograms of pixel intensities in these regions. Third order statistical features used are one-dimensional bispectral invariants. 108 features were considered as candidates for Adaboost based fusion. The best 10 stage fused classifier was selected for each class and a decision tree constructed for the 6-class problem. The classifier is robust, accurate and fast by design.

A finite volume method for solving the two-sided time-space fractional advection-dispersion equation

We present a finite volume method to solve the time-space two-sided fractional advection-dispersion equation on a one-dimensional domain. The spatial discretisation employs fractionally-shifted Grünwald formulas to discretise the Riemann-Liouville fractional derivatives at control volume faces in terms of function values at the nodes. We demonstrate how the finite volume formulation provides a natural, convenient and accurate means of discretising this equation in conservative form, compared to using a conventional finite difference approach. Results of numerical experiments are presented to demonstrate the effectiveness of the approach.

Eigenstrain boundary integral equations with local Eshelby matrix for stress analysis of ellipsoidal particles

Aiming at the large scale numerical simulation of particle reinforced materials, the concept of local Eshelby matrix has been introduced into the computational model of the eigenstrain boundary integral equation (BIE) to solve the problem of interactions among particles. The local Eshelby matrix can be considered as an extension of the concepts of Eshelby tensor and the equivalent inclusion in numerical form. Taking the subdomain boundary element method as the control, three-dimensional stress analyses are carried out for some ellipsoidal particles in full space with the proposed computational model. Through the numerical examples, it is verified not only the correctness and feasibility but also the high efficiency of the present model with the corresponding solution procedure, showing the potential of solving the problem of large scale numerical simulation of particle reinforced materials.

Random projections on manifolds of symmetric positive definite matrices for image classification

Recent advances suggest that encoding images through Symmetric Positive Definite (SPD) matrices and then interpreting such matrices as points on Riemannian manifolds can lead to increased classification performance. Taking into account manifold geometry is typically done via (1) embedding the manifolds in tangent spaces, or (2) embedding into Reproducing Kernel Hilbert Spaces (RKHS). While embedding into tangent spaces allows the use of existing Euclidean-based learning algorithms, manifold shape is only approximated which can cause loss of discriminatory information. The RKHS approach retains more of the manifold structure, but may require non-trivial effort to kernelise Euclidean-based learning algorithms. In contrast to the above approaches, in this paper we offer a novel solution that allows SPD matrices to be used with unmodified Euclidean-based learning algorithms, with the true manifold shape well-preserved. Specifically, we propose to project SPD matrices using a set of random projection hyperplanes over RKHS into a random projection space, which leads to representing each matrix as a vector of projection coefficients. Experiments on face recognition, person re-identification and texture classification show that the proposed approach outperforms several recent methods, such as Tensor Sparse Coding, Histogram Plus Epitome, Riemannian Locality Preserving Projection and Relational Divergence Classification.

Reduction of amplitude equations by the renormalization group approach

This article elucidates and analyzes the fundamental underlying structure of the renormalization group (RG) approach as it applies to the solution of any differential equation involving multiple scales. The amplitude equation derived through the elimination of secular terms arising from a naive perturbation expansion of the solution to these equations by the RG approach is reduced to an algebraic equation which is expressed in terms of the Thiele semi-invariants or cumulants of the eliminant sequence { Zi } i=1 . Its use is illustrated through the solution of both linear and nonlinear perturbation problems and certain results from the literature are recovered as special cases. The fundamental structure that emerges from the application of the RG approach is not the amplitude equation but the aforementioned algebraic equation. © 2008 The American Physical Society.

Generalized azimuthal shear deformations in compressible isotropic elastic materials

In this article we study the azimuthal shear deformations in a compressible Isotropic elastic material. This class of deformations involves an azimuthal displacement as a function of the radial and axial coordinates. The equilibrium equations are formulated in terms of the Cauchy-Green strain tensors, which form an overdetermined system of partial differential equations for which solutions do not exist in general. By means of a Legendre transformation, necessary and sufficient conditions for the material to support this deformation are obtained explicitly, in the sense that every solution to the azimuthal equilibrium equation will satisfy the remaining two equations. Additionally, we show how these conditions are sufficient to support all currently known deformations that locally reduce to simple shear. These conditions are then expressed both in terms of the invariants of the Cauchy-Green strain and stretch tensors. Several classes of strain energy functions for which this deformation can be supported are studied. For certain boundary conditions, exact solutions to the equilibrium equations are obtained. © 2005 Society for Industrial and Applied Mathematics.

The eight variable homogeneous degree three bent functions

We determine the affine equivalence classes of the eight variable degree three homogeneous bent functions using a new algorithm. Our algorithm applies to general bent functions and can systematically determine the automorphism groups. We provide a partial verification of the enumeration of eight variable degree three homogeneous bent functions obtained by Meng et al. We determine the affine equivalence classes of these functions.

A strain-based failure criterion for pillar stability analysis

Strain-based failure criteria have several advantages over stress-based failure criteria: they can account for elastic and inelastic strains, they utilise direct, observables effects instead of inferred effects (strain gauges vs. stress estimates), and model complete stress-strain curves including pre-peak, non-linear elasticity and post-peak strain weakening. In this study, a strain-based failure criterion derived from thermodynamic first principles utilising the concepts of continuum damage mechanics is presented. Furthermore, implementation of this failure criterion into a finite-element simulation is demonstrated and applied to the stability of underground mining coal pillars. In numerical studies, pillar strength is usually expressed in terms of critical stresses or stress-based failure criteria where scaling with pillar width and height is common. Previous publications have employed the finite-element method for pillar stability analysis using stress-based failure criterion such as Mohr-Coulomb and Hoek-Brown or stress-based scalar damage models. A novel constitutive material model, which takes into consideration anisotropy as well as elastic strain and damage as state variables has been developed and is presented in this paper. The damage threshold and its evolution are strain-controlled, and coupling of the state variables is achieved through the damage-induced degradation of the elasticity tensor. This material model is implemented into the finite-element software ABAQUS and can be applied to 3D problems. Initial results show that this new material model is capable of describing the non-linear behaviour of geomaterials commonly observed before peak strength is reached as well as post-peak strain softening. Furthermore, it is demonstrated that the model can account for directional dependency of failure behaviour (i.e. anisotropy) and has the potential to be expanded to environmental controls like temperature or moisture.

Finite volume methods for simulating anomalous transport

In this thesis a new approach for solving a certain class of anomalous diffusion equations was developed. The theory and algorithms arising from this work will pave the way for more efficient and more accurate solutions of these equations, with applications to science, health and industry. The method of finite volumes was applied to discretise the spatial derivatives, and this was shown to outperform existing methods in several key respects. The stability and convergence of the new method were rigorously established.

Dual compressible hybrid quantum secret sharing schemes based on extended unitary operations

A crucial issue with hybrid quantum secret sharing schemes is the amount of data that is allocated to the participants. The smaller the amount of allocated data, the better the performance of a scheme. Moreover, quantum data is very hard and expensive to deal with, therefore, it is desirable to use as little quantum data as possible. To achieve this goal, we first construct extended unitary operations by the tensor product of n, n ≥ 2, basic unitary operations, and then by using those extended operations, we design two quantum secret sharing schemes. The resulting dual compressible hybrid quantum secret sharing schemes, in which classical data play a complementary role to quantum data, range from threshold to access structure. Compared with the existing hybrid quantum secret sharing schemes, our proposed schemes not only reduce the number of quantum participants, but also the number of particles and the size of classical shares. To be exact, the number of particles that are used to carry quantum data is reduced to 1 while the size of classical secret shares also is also reduced to l−2 m−1 based on ((m+1, n′)) threshold and to l−2 r2 (where r2 is the number of maximal unqualified sets) based on adversary structure. Consequently, our proposed schemes can greatly reduce the cost and difficulty of generating and storing EPR pairs and lower the risk of transmitting encoded particles.

Safety envelope for security

We present an approach for detecting sensor spoofing attacks on a cyber-physical system. Our approach consists of two steps. In the first step, we construct a safety envelope of the system. Under nominal conditions (that is, when there are no attacks), the system always stays inside its safety envelope. In the second step, we build an attack detector: a monitor that executes synchronously with the system and raises an alarm whenever the system state falls outside the safety envelope. We synthesize safety envelopes using a modified machine learning procedure applied on data collected from the system when it is not under attack. We present experimental results that show effectiveness of our approach, and also validate the several novel features that we introduced in our learning procedure.

Turbulence and Mixing in the Environment: Multi-Device Study in a Sub-tropical Estuary

In an estuary, mixing and dispersion result from a combination of large-scale advection and smallscale turbulence, which are complex to estimate. The predictions of scalar transport and mixing are often inferred and rarely accurate, due to inadequate understanding of the contributions of these difference scales to estuarine recirculation. A multi-device field study was conducted in a small sub-tropical estuary under neap tide conditions with near-zero fresh water discharge for about 48 hours. During the study, acoustic Doppler velocimeters (ADV) were sampled at high frequency (50 Hz), while an acoustic Doppler current profiler (ADCP) and global positioning system (GPS) tracked drifters were used to obtain some lower frequency spatial distribution of the flow parameters within the estuary. The velocity measurements were complemented with some continuous measurement of water depth, conductivity, temperature and some other physiochemical parameters. Thorough quality control was carried out by implementation of relevant error removal filters on the individual data set to intercept spurious data. A triple decomposition (TD) technique was introduced to access the contributions of tides, resonance and ‘true’ turbulence in the flow field. The time series of mean flow measurements for both the ADCP and drifter were consistent with those of the mean ADV data when sampled within a similar spatial domain. The tidal scale fluctuation of velocity and water level were used to examine the response of the estuary to tidal inertial current. The channel exhibited a mixed type wave with a typical phase-lag between 0.035π– 0.116π. A striking feature of the ADV velocity data was the slow fluctuations, which exhibited large amplitudes of up to 50% of the tidal amplitude, particularly in slack waters. Such slow fluctuations were simultaneously observed in a number of physiochemical properties of the channel. The ensuing turbulence field showed some degree of anisotropy. For all ADV units, the horizontal turbulence ratio ranged between 0.4 and 0.9, and decreased towards the bed, while the vertical turbulence ratio was on average unity at z = 0.32 m and approximately 0.5 for the upper ADV (z = 0.55 m). The result of the statistical analysis suggested that the ebb phase turbulence field was dominated by eddies that evolved from ejection type process, while that of the flood phase contained mixed eddies with significant amount related to sweep type process. Over 65% of the skewness values fell within the range expected of a finite Gaussian distribution and the bulk of the excess kurtosis values (over 70%) fell within the range of -0.5 and +2. The TD technique described herein allowed the characterisation of a broader temporal scale of fluctuations of the high frequency data sampled within the durations of a few tidal cycles. The study provides characterisation of the ranges of fluctuation required for an accurate modelling of shallow water dispersion and mixing in a sub-tropical estuary.

Genetic and environmental influences on neuroimaging phenotypes: A meta-analytical perspective on twin imaging studies

Because brain structure and function are affected in neurological and psychiatric disorders, it is important to disentangle the sources of variation in these phenotypes. Over the past 15 years, twin studies have found evidence for both genetic and environmental influences on neuroimaging phenotypes, but considerable variation across studies makes it difficult to draw clear conclusions about the relative magnitude of these influences. Here we performed the first meta-analysis of structural MRI data from 48 studies on >1,250 twin pairs, and diffusion tensor imaging data from 10 studies on 444 twin pairs. The proportion of total variance accounted for by genes (A), shared environment (C), and unshared environment (E), was calculated by averaging A, C, and E estimates across studies from independent twin cohorts and weighting by sample size. The results indicated that additive genetic estimates were significantly different from zero for all metaanalyzed phenotypes, with the exception of fractional anisotropy (FA) of the callosal splenium, and cortical thickness (CT) of the uncus, left parahippocampal gyrus, and insula. For many phenotypes there was also a significant influence of C. We now have good estimates of heritability for many regional and lobar CT measures, in addition to the global volumes. Confidence intervals are wide and number of individuals small for many of the other phenotypes. In conclusion, while our meta-analysis shows that imaging measures are strongly influenced by genes, and that novel phenotypes such as CT measures, FA measures, and brain activation measures look especially promising, replication across independent samples and demographic groups is necessary.

Relationship of a variant in the NTRK1 gene to white matter microstructure in young adults

The NTRK1 gene (also known as TRKA) encodes a high-affinity receptor for NGF, a neurotrophin involved in nervous system development and myelination. NTRK1 has been implicated in neurological function via links between the T allele at rs6336 (NTRK1-T) and schizophrenia risk. A variant in the neurotrophin gene, BDNF, was previously associated with white matter integrity in young adults, highlighting the importantce of neurotrophins to white matter development. We hypothesized that NTRK1-T would relate to lower fractional anisotropy in healthy adults. We scanned 391 healthy adult human twins and their siblings (mean age: 23.6 ± 2.2 years; 31 NTRK1-T carriers, 360 non-carriers) using 105-gradient diffusion tensor imaging at 4 tesla. We evaluated in brain white matter how NTRK1-T and NTRK1 rs4661063 allele A (rs4661063-A, which is in moderate linkage disequilibrium with rs6336) related to voxelwise fractional anisotropy-acommondiffusion tensor imaging measure of white matter microstructure. We used mixed-model regression to control for family relatedness, age, and sex. The sample was split in half to test reproducibility of results. The false discovery rate method corrected for voxelwise multiple comparisons. NTRK1-T and rs4661063-A correlated with lower white matter fractional anisotropy, independent of age and sex (multiple-comparisons corrected: false discovery rate critical p=0.038 forNTRK1-Tand0.013 for rs4661063-A). In each half-sample, theNTRK1-T effectwasreplicated in the cingulum, corpus callosum, superior and inferior longitudinal fasciculi, inferior fronto-occipital fasciculus, superior corona radiata, and uncinate fasciculus. Our results suggest that NTRK1-T is important for developing white matter microstructure.

Common Alzheimer's disease risk variant within the CLU gene affects white matter microstructure in young adults

There is a strong genetic risk for late-onset Alzheimer's disease (AD), but so far few gene variants have been identified that reliably contribute to that risk. A newly confirmed genetic risk allele C of the clusterin (CLU) gene variant rs11136000 is carried by ~88% of Caucasians. The C allele confers a 1.16 greater odds of developing late-onset AD than the T allele. AD patients have reductions in regional white matter integrity. We evaluated whether the CLU risk variant was similarly associated with lower white matter integrity in healthy young humans. Evidence of early brain differences would offer a target for intervention decades before symptom onset. We scanned 398 healthy young adults (mean age, 23.6 ± 2.2 years) with diffusion tensor imaging, a variation of magnetic resonance imaging sensitive to white matter integrity in the living brain. We assessed genetic associations using mixed-model regression at each point in the brain to map the profile of these associations with white matter integrity. Each C allele copy of the CLUvariant was associated with lower fractional anisotropy-a widely accepted measure of white matter integrity-in multiple brain regions, including several known to degenerate in AD. These regions included the splenium of the corpus callosum, the fornix, cingulum, and superior and inferior longitudinal fasciculi in both brain hemispheres. Young healthy carriers of the CLU gene risk variant showed a distinct profile of lower white matter integrity that may increase vulnerability to developing AD later in life.