Variable Sparsity Kernel Learning

This paper(1) presents novel algorithms and applications for a particular class of mixed-norm regularization based Multiple Kernel Learning (MKL) formulations. The formulations assume that the given kernels are grouped and employ l(1) norm regularization for promoting sparsity within RKHS norms of each group and l(s), s >= 2 norm regularization for promoting non-sparse combinations across groups. Various sparsity levels in combining the kernels can be achieved by varying the grouping of kernels-hence we name the formulations as Variable Sparsity Kernel Learning (VSKL) formulations. While previous attempts have a non-convex formulation, here we present a convex formulation which admits efficient Mirror-Descent (MD) based solving techniques. The proposed MD based algorithm optimizes over product of simplices and has a computational complexity of O (m(2)n(tot) log n(max)/epsilon(2)) where m is no. training data points, n(max), n(tot) are the maximum no. kernels in any group, total no. kernels respectively and epsilon is the error in approximating the objective. A detailed proof of convergence of the algorithm is also presented. Experimental results show that the VSKL formulations are well-suited for multi-modal learning tasks like object categorization. Results also show that the MD based algorithm outperforms state-of-the-art MKL solvers in terms of computational efficiency.

Long term monitering of vegetation in a tropical deciduous forest in Mudumalai,southern India

As part of an international network of large plots to study tropical vegetation dynamics on a long-term basis, a 50-hectare permanent plot was set up during 1988-89 in the deciduous forests of Mudumalai, southern India. Within this plot 25,929 living woody plants (71 species) above 1 cm DBH (diameter at breast height) were identified, measured, tagged and mapped. Species abundances corresponded to the characteristic log-normal distribution. The four most abundant species (Kydia calycina, Lagerstroemia microcarpa, Terminalia crenulata and Helicteres isora) constituted nearly 56% of total stems, while seven species were represented by only one individual each in the plot. Variance/mean ratios of density showed most species to have clumped distributions. The population declined overall by 14% during the first two years, largely due to elephant and fire-mediated damage to Kydia calycina and Helicteres isora. In this article we discuss the need for large plots to study vegetation dynamics.

Hierarchies of circuit classes that are closed under complement

We examine three hierarchies of circuit classes and show they are closed under complementation. (1) The class of languages recognized by a family of polynomial size skew circuits with width O(w), are closed under complement. (2) The class of languages recognized by family of polynomial size circuits with width O(w) and polynomial tree-size, are closed under complement. (3) The class of languages recognized by a family of polynomial size, O(log(n)) depth, bounded AND fan-in with OR fan-in f (f⩾log(n)) circuits are closed under complement. These improve upon the results of (i) Immerman (1988) and Szelepcsenyi (1988), who show that 𝒩L𝒪𝒢 is closed under complementation, and (ii) Borodin et al. (1989), who show that L𝒪𝒢𝒞ℱL is closed under complement

Role of Li+ ions in corrosion behaviour of 8090 Al-Li alloy and aluminium in pH 12 aqueous solutions

The influence of Li+ ions on the corrosion behaviour of the Al-Li alloy 8090-T851 and of commercially pure aluminium in aqueous solutions at pH 12 was studied by weight loss and electrochemical polarisation methods. The inhibiting role of Li+ was concentration dependent, corrosion rate decreasing lineally with log[Li+] in the concentration range 10(-4)-10(-1) mol L(-1). A change from general to pitting corrosion was evident from scanning election microscopy studies. Polarisation studies revealed that Li+ primarily acts as an anodic inhibitor (passivator). Passive film formation and stability also become more feasible with increasing Li+ concentration. Fitting potential was dependent on the Cl- ion concentration in the solution. Both materials were affected similarly by the presence of Li+ ions, the corrosion rate of the alloy being slightly lower. This is attributed to the lithium in the alloy acting as a source of lithium for passive film formation. (C) 1995 The Institute of Materials.

Maintaining dynamic sequences under equality tests in polylogarithmic time

We present a randomized and a deterministic data structure for maintaining a dynamic family of sequences under equality tests of pairs of sequences and creations of new sequences by joining or splitting existing sequences. Both data structures support equality tests in O(1) time. The randomized version supports new sequence creations in O(log(2) n) expected time where n is the length of the sequence created. The deterministic solution supports sequence creations in O(log n (log m log* m + log n)) time for the mth operation.

Processing map for the hot working of near-alpha titanium alloy 685

Using a dynamic materials model, processing and instability maps have been developed for near-alpha titanium alloy 685 in the temperature range 775-1025 degrees C and strain-rate range of 0.001-10 s(-1) to optimise its hot workability. The alloy's beta-transus temperature lies at about 1020 degrees C. The material undergoes superplasticity with a peak efficiency of 80% at 975 degrees C and 0.001 s(-1), which are the optimum parameters for alpha-beta working. The occurrence of superplasticity is attributed to two-phase microduplex structure, higher strain-rate sensitivity, low flow stress and sigmoidal variation between log flow stress and log strain rate. The material also exhibits how localisation due to adiabatic shear-band formation up to its beta-transus temperature with strain rates greater than 0.02 s(-1) and thus cracking along these regions. (C) 1997 Published by Elsevier Science S.A.

Velocity distribution function for a dilute granular material in shear flow

The velocity distribution function for the steady shear flow of disks (in two dimensions) and spheres (in three dimensions) in a channel is determined in the limit where the frequency of particle-wall collisions is large compared to particle-particle collisions. An asymptotic analysis is used in the small parameter epsilon, which is naL in two dimensions and na(2)L in three dimensions, where; n is the number density of particles (per unit area in two dimensions and per unit volume in three dimensions), L is the separation of the walls of the channel and a is the particle diameter. The particle-wall collisions are inelastic, and are described by simple relations which involve coefficients of restitution e(t) and e(n) in the tangential and normal directions, and both elastic and inelastic binary collisions between particles are considered. In the absence of binary collisions between particles, it is found that the particle velocities converge to two constant values (u(x), u(y)) = (+/-V, O) after repeated collisions with the wall, where u(x) and u(y) are the velocities tangential and normal to the wall, V = (1 - e(t))V-w/(1 + e(t)), and V-w and -V-w, are the tangential velocities of the walls of the channel. The effect of binary collisions is included using a self-consistent calculation, and the distribution function is determined using the condition that the net collisional flux of particles at any point in velocity space is zero at steady state. Certain approximations are made regarding the velocities of particles undergoing binary collisions :in order to obtain analytical results for the distribution function, and these approximations are justified analytically by showing that the error incurred decreases proportional to epsilon(1/2) in the limit epsilon --> 0. A numerical calculation of the mean square of the difference between the exact flux and the approximate flux confirms that the error decreases proportional to epsilon(1/2) in the limit epsilon --> 0. The moments of the velocity distribution function are evaluated, and it is found that [u(x)(2)] --> V-2, [u(y)(2)] similar to V-2 epsilon and -[u(x)u(y)] similar to V-2 epsilon log(epsilon(-1)) in the limit epsilon --> 0. It is found that the distribution function and the scaling laws for the velocity moments are similar for both two- and three-dimensional systems.

Secondary compression factor

When the variation of secondary compression, with log(10) t is non-linear, the quantification of secondary settlement through the coefficient of secondary compression, C-alpha epsilon, becomes difficult which frequently leads to an underestimate of the settlement, Log(10) delta - log(10) t representation of such true-compression data has the distinct advantage of exhibiting linear secondary compression behaviour over an appreciably larger time span. The slope of the secondary compression portion of the log(10) e - log(10) t curve expressed as Delta(log e)/(log t) and called the 'secondary compression factor', m, proves to be a better alternative to C-alpha epsilon and the prediction of secondary settlement is improved.

Efficient algorithms for learning kernels from multiple similarity matrices with general convex loss functions

In this paper we consider the problem of learning an n × n kernel matrix from m(1) similarity matrices under general convex loss. Past research have extensively studied the m = 1 case and have derived several algorithms which require sophisticated techniques like ACCP, SOCP, etc. The existing algorithms do not apply if one uses arbitrary losses and often can not handle m > 1 case. We present several provably convergent iterative algorithms, where each iteration requires either an SVM or a Multiple Kernel Learning (MKL) solver for m > 1 case. One of the major contributions of the paper is to extend the well knownMirror Descent(MD) framework to handle Cartesian product of psd matrices. This novel extension leads to an algorithm, called EMKL, which solves the problem in O(m2 log n 2) iterations; in each iteration one solves an MKL involving m kernels and m eigen-decomposition of n × n matrices. By suitably defining a restriction on the objective function, a faster version of EMKL is proposed, called REKL,which avoids the eigen-decomposition. An alternative to both EMKL and REKL is also suggested which requires only an SVMsolver. Experimental results on real world protein data set involving several similarity matrices illustrate the efficacy of the proposed algorithms.

Crystal structure, thermal expansion and electrical conductivity of Nd0.7Sr0.3Fe1-xCoxO3 (0 <= x <= 0.8)

The crystal structure, thermal expansion and electrical conductivity of the solid solution Nd0.7Sr0.3Fe1-xCoxO3 for 0 less than or equal to x less than or equal to 0.8 were investigated. All compositions had the GdFeO3-type orthorhombic perovskite structure. The lattice parameters were determined at room temperature by X-ray powder diffraction (XRPD). The pseudo-cubic lattice constant decreased continuously with x. The average linear thermal expansion coefficient (TEC) in the temperature range from 573 to 973 K was found to increase with x. The thermal expansion curves for all values of x displayed rapid increase in slope at high temperatures. The electrical conductivity increased with x for the entire temperature range of measurement. The calculated activation energy values indicate that electrical conduction takes place primarily by the small polaron hopping mechanism. The charge compensation for the divalent ion on the A-site is provided by the formation of Fe4+ ions on the B-site (in preference to Co4+ ions) and vacancies on the oxygen sublattice for low values of x. The large increase in the conductivity with x in the range from 0.6 to 0.8 is attributed to the substitution of Fe4+ ions by Co4+ ions. The Fe site has a lower small polaron site energy than Co and hence behaves like a carrier trap, thereby drastically reducing the conductivity. The non-linear behaviour in the dependence of log sigmaT with reciprocal temperature can be attributed to the generation of additional charge carriers with increasing temperature by the charge disproportionation of Co3+ ions. (C) 2002 Elsevier Science B.V. All rights reserved.

The restriction mapping problem revisited

In computational molecular biology, the aim of restriction mapping is to locate the restriction sites of a given enzyme on a DNA molecule. Double digest and partial digest are two well-studied techniques for restriction mapping. While double digest is NP-complete, there is no known polynomial-time algorithm for partial digest. Another disadvantage of the above techniques is that there can be multiple solutions for reconstruction. In this paper, we study a simple technique called labeled partial digest for restriction mapping. We give a fast polynomial time (O(n(2) log n) worst-case) algorithm for finding all the n sites of a DNA molecule using this technique. An important advantage of the algorithm is the unique reconstruction of the DNA molecule from the digest. The technique is also robust in handling errors in fragment lengths which arises in the laboratory. We give a robust O(n(4)) worst-case algorithm that can provably tolerate an absolute error of O(Delta/n) (where Delta is the minimum inter-site distance), while giving a unique reconstruction. We test our theoretical results by simulating the performance of the algorithm on a real DNA molecule. Motivated by the similarity to the labeled partial digest problem, we address a related problem of interest-the de novo peptide sequencing problem (ACM-SIAM Symposium on Discrete Algorithms (SODA), 2000, pp. 389-398), which arises in the reconstruction of the peptide sequence of a protein molecule. We give a simple and efficient algorithm for the problem without using dynamic programming. The algorithm runs in time O(k log k), where k is the number of ions and is an improvement over the algorithm in Chen et al. (C) 2002 Elsevier Science (USA). All rights reserved.

A lower bound for the hitting set size for combinatorial rectangles and an application

We prove a lower bound of Omega(1/epsilon (m + log(d - a)) where a = [log(m) (1/4epsilon)] for the hitting set size for combinatorial rectangles of volume at least epsilon in [m](d) space, for epsilon is an element of [m(-(d-2)), 2/9] and d > 2. (C) 2002 Elsevier Science B.V. All rights reserved.

The ‘bursting’ phenomenon in a turbulent boundary layer

Using a hot wire in a turbulent boundary layer in air, an experimental study has been made of the frequent periods of activity (to be called ‘bursts’) noticed in a turbulent signal that has been passed through a narrow band-pass filter. Although definitive identification of bursts presents difficulties, it is found that a reasonable characteristic value for the mean interval between such bursts is consistent, at the same Reynolds number, with the mean burst periods measured by Kline et al. (1967), using hydrogen-bubble techniques in water. However, data over the wider Reynolds number range covered here show that, even in the wall or inner layer, the mean burst period scales with outer rather than inner variables; and that the intervals are distributed according to the log normal law. It is suggested that these ‘bursts’ are to be identified with the ‘spottiness’ of Landau & Kolmogorov, and the high-frequency intermittency observed by Batchelor & Townsend. It is also concluded that the dynamics of the energy balance in a turbulent boundary layer can be understood only on the basis of a coupling between the inner and outer layers.

Axisymmetric turbulent boundary layer along a circular cylinder at constant pressure

A constant-pressure axisymmetric turbulent boundary layer along a circular cylinder of radius a is studied at large values of the frictional Reynolds number a+ (based upon a) with the boundary-layer thickness δ of order a. Using the equations of mean motion and the method of matched asymptotic expansions, it is shown that the flow can be described by the same two limit processes (inner and outer) as are used in two-dimensional flow. The condition that the two expansions match requires the existence, at the lowest order, of a log region in the usual two-dimensional co-ordinates (u+, y+). Examination of available experimental data shows that substantial log regions do in fact exist but that the intercept is possibly not a universal constant. Similarly, the solution in the outer layer leads to a defect law of the same form as in two-dimensional flow; experiment shows that the intercept in the defect law depends on δ/a. It is concluded that, except in those extreme situations where a+ is small (in which case the boundary layer may not anyway be in a fully developed turbulent state), the simplest analysis of axisymmetric flow will be to use the two-dimensional laws with parameters that now depend on a+ or δ/a as appropriate.

Defining the ‘modified Griffin plot’ in vortex-induced vibration: revealing the effect of Reynolds number using controlled damping

In the present work, we study the transverse vortex-induced vibrations of an elastically mounted rigid cylinder in a fluid flow. We employ a technique to accurately control the structural damping, enabling the system to take on both negative and positive damping. This permits a systematic study of the effects of system mass and damping on the peak vibration response. Previous experiments over the last 30 years indicate a large scatter in peak-amplitude data ($A^*$) versus the product of mass–damping ($\alpha$), in the so-called ‘Griffin plot’. A principal result in the present work is the discovery that the data collapse very well if one takes into account the effect of Reynolds number ($\mbox{\textit{Re}}$), as an extra parameter in a modified Griffin plot. Peak amplitudes corresponding to zero damping ($A^*_{{\alpha}{=}0}$), for a compilation of experiments over a wide range of $\mbox{\textit{Re}}\,{=}\,500-33000$, are very well represented by the functional form $A^*_{\alpha{=}0} \,{=}\, f(\mbox{\textit{Re}}) \,{=}\, \log(0.41\,\mbox{\textit{Re}}^{0.36}$). For a given $\mbox{\textit{Re}}$, the amplitude $A^*$ appears to be proportional to a function of mass–damping, $A^*\propto g(\alpha)$, which is a similar function over all $\mbox{\textit{Re}}$. A good best-fit for a wide range of mass–damping and Reynolds number is thus given by the following simple expression, where $A^*\,{=}\, g(\alpha)\,f(\mbox{\textit{Re}})$: \[ A^* \,{=}\,(1 - 1.12\,\alpha + 0.30\,\alpha^2)\,\log (0.41\,\mbox{\textit{Re}}^{0.36}). \] In essence, by using a renormalized parameter, which we define as the ‘modified amplitude’, $A^*_M\,{=}\,A^*/A^*_{\alpha{=}0}$, the previously scattered data collapse very well onto a single curve, $g(\alpha)$, on what we refer to as the ‘modified Griffin plot’. There has also been much debate over the last three decades concerning the validity of using the product of mass and damping (such as $\alpha$) in these problems. Our results indicate that the combined mass–damping parameter ($\alpha$) does indeed collapse peak-amplitude data well, at a given $\mbox{\textit{Re}}$, independent of the precise mass and damping values, for mass ratios down to $m^*\,{=}\,1$.