A dual-slope analogue-to-digital converter for generating polynomials

A new digital polynomial generator using the principle of dual-slope analogue-to-digital conversion is proposed. Techniques for realizing a wide range of integer as well as fractional coefficients to obtain the desired polynomial have been discussed. The suitability of realizing the proposed polynomial generator in integrated circuit form is also indicated.

Probiotic Bacillus amyloliquefaciens Strain H57 Improves the Performance of Pregnant and Lactating Ewes Fed a Diet Based on Palm Kernel Meal

Probiotic supplements are single or mixed strain cultures of live microorganisms that benefit the host by improving the properties of the indigenous microflora (Seo et al 2010). In a pilot study at the University of Queensland, Norton et al (2008) found that Bacillus amyloliquefaciens Strain H57 (H57), primarily investigated as an inoculum to make high-quality hay, improved feed intake and nitrogen utilisation over several weeks in pregnant ewes. The purpose of the following study was to further challenge the potential of H57 -to show it survives the steam-pelleting process, and that it improves the performance of ewes fed pellets based on an agro-industrial by-product with a reputation for poor palatability, palm kernel meal (PKM), (McNeill 2013). Thirty-two first-parity White Dorper ewes (day 37 of pregnancy, mean liveweight = 47.3 kg, mean age = 15 months) were inducted into individual pens in the animal house at the University of Queensland, Gatton. They were adjusted onto PKM-based pellets (g/kg drymatter (DM): PKM, 408; sorghum, 430; chick pea hulls, 103; minerals and vitamins; Crude protein, 128; ME: 11.1MJ/kg DM) until day 89 of pregnancy and thereafter fed a predominately pelleted diet incorporating with or without H57 spores (10 9 colony forming units (cfu)/kg pellet, as fed), plus 100g/ewe/day oaten chaff, until day 7 of lactation. From day 7 to 20 of lactation the pelleted component of the diet was steadily reduced to be replaced by a 50:50 mix of lucerne: oaten chaff, fed ad libitum, plus 100g/ewe/day of ground sorghum grain with or without H57 (10 9 cfu/ewe/day). The period of adjustment in pregnancy (day 37-89) extended beyond expectations due to some evidence of mild ruminal acidosis after some initially high intakes that were followed by low intakes. During that time the diet was modified, in an attempt to improve palatability, by the addition of oaten chaff and the removal of an acidifying agent (NH4Cl) that was added initially to reduce the risk of urinary calculi. Eight ewes were removed due to inappetence, leaving 24 ewes to start the trial at day 90 of pregnancy. From day 90 of pregnancy until day 63 of lactation, liveweights of the ewes and their lambs were determined weekly and at parturition. Feed intakes of the ewes were determined weekly. Once lambing began, 1 ewe was removed as it gave birth to twin lambs (whereas the rest gave birth to a single lamb), 4 due to the loss of their lambs (2 to dystocia), and 1 due to copper toxicity. The PKM pellets were suspected to be the cause of the copper toxicity and so were removed in early lactation. Hence, the final statistical analysis using STATISTICA 8 (Repeated measures ANOVA for feed intake, One-way ANOVA for liveweight change and birth weight) was completed on 23 ewes for the pregnancy period (n = 11 fed H57; n = 12 control), and 18 ewes or lambs for the lactation period (n = 8 fed H57; n = 10 control). From day 90 of pregnancy until parturition the H57 supplemented ewes ate 17 more DM (g/day: 1041 vs 889, sed = 42.4, P = 0.04) and gained more liveweight (g/day: 193 vs 24.0, sed = 25.4, P = 0.0002), but produced lambs with a similar birthweight (kg: 4.18 vs 3.99, sed = 0.19, P = 0.54). Over the 63 days of lactation the H57 ewes ate similar amounts of DM but grew slower than the control ewes (g/day: 1.5 vs 97.0, sed = 21.7, P = 0.012). The lambs of the H57 ewes grew faster than those of the control ewes for the first 21 days of lactation (g/day: 356 vs 265, sed = 16.5, P = 0.006). These data support the findings of Norton et al (2008) and Kritas et al (2006) that certain Bacillus spp. supplements can improve the performance of pregnant and lactating ewes. In the current study we particularly highlighted the capacity of H57 to stimulate immature ewes to continue to grow maternal tissue through pregnancy, possibly through an enhanced appetite, which appeared then to stimulate a greater capacity to partition nutrients to their lambs through milk, at least for the first few weeks of lactation, a critical time for optimising lamb survival. To conclude, H57 can survive the steam pelleting process to improve feed intake and maternal liveweight gain in late pregnancy, and performance in early lactation, of first-parity ewes fed a diet based on PKM.

Application of ultraspherical polynomials to forced oscillations of a third-order non-linear system

In this paper the method of ultraspherical polynomial approximation is applied to study the steady-state response in forced oscillations of a third-order non-linear system. The non-linear function is expanded in ultraspherical polynomials and the expansion is restricted to the linear term. The equation for the response curve is obtained by using the linearized equation and the results are presented graphically. The agreement between the approximate solution and the analog computer solution is satisfactory. The problem of stability is not dealt with in this paper.

Ultraspherical polynomials approach to the study of third-order non-linear systems

In this study, the Krylov-Bogoliubov-Mitropolskii-Popov asymptotic method is used to determine the transient response of third-order non-linear systems. Instead of averaging the non-linear functions over a cycle, they are expanded in ultraspherical polynomials and the constant term is retained. The resulting equations are solved to obtain the approximate solution. A numerical example is considered and the approximate solution is compared with the digital solution. The results show that there is good agreement between the two values.

R1STM: One-class support tensor machine with randomised kernel

Identifying unusual or anomalous patterns in an underlying dataset is an important but challenging task in many applications. The focus of the unsupervised anomaly detection literature has mostly been on vectorised data. However, many applications are more naturally described using higher-order tensor representations. Approaches that vectorise tensorial data can destroy the structural information encoded in the high-dimensional space, and lead to the problem of the curse of dimensionality. In this paper we present the first unsupervised tensorial anomaly detection method, along with a randomised version of our method. Our anomaly detection method, the One-class Support Tensor Machine (1STM), is a generalisation of conventional one-class Support Vector Machines to higher-order spaces. 1STM preserves the multiway structure of tensor data, while achieving significant improvement in accuracy and efficiency over conventional vectorised methods. We then leverage the theory of nonlinear random projections to propose the Randomised 1STM (R1STM). Our empirical analysis on several real and synthetic datasets shows that our R1STM algorithm delivers comparable or better accuracy to a state-of-the-art deep learning method and traditional kernelised approaches for anomaly detection, while being approximately 100 times faster in training and testing.

On the growth of the Bergman kernel near an infinite-type point

We study diagonal estimates for the Bergman kernels of certain model domains in C-2 near boundary points that are of infinite type. To do so, we need a mild structural condition on the defining functions of interest that facilitates optimal upper and lower bounds. This is a mild condition; unlike earlier studies of this sort, we are able to make estimates for non-convex pseudoconvex domains as well. Thisn condition quantifies, in some sense, how flat a domain is at an infinite-type boundary point. In this scheme of quantification, the model domains considered below range-roughly speaking-from being mildly infinite-type'' to very flat at the infinite-type points.

Kernel-based spatial-color modeling for fast moving object tracking

Visual tracking has been a challenging problem in computer vision over the decades. The applications of Visual Tracking are far-reaching, ranging from surveillance and monitoring to smart rooms. Mean-shift (MS) tracker, which gained more attention recently, is known for tracking objects in a cluttered environment and its low computational complexity. The major problem encountered in histogram-based MS is its inability to track rapidly moving objects. In order to track fast moving objects, we propose a new robust mean-shift tracker that uses both spatial similarity measure and color histogram-based similarity measure. The inability of MS tracker to handle large displacements is circumvented by the spatial similarity-based tracking module, which lacks robustness to object's appearance change. The performance of the proposed tracker is better than the individual trackers for tracking fast-moving objects with better accuracy.

THE BERGMAN KERNEL FUNCTION

In this note, we point out that a large family of n x n matrix valued kernel functions defined on the unit disc D subset of C, which were constructed recently in [9], behave like the familiar Bergman kernel function on ID in several different ways. We show that a number of questions involving the multiplication operator on the corresponding Hilbert space of holomorphic functions on D can be answered using this likeness.

A fast dual algorithm for kernel logistic regression

This paper gives a new iterative algorithm for kernel logistic regression. It is based on the solution of a dual problem using ideas similar to those of the Sequential Minimal Optimization algorithm for Support Vector Machines. Asymptotic convergence of the algorithm is proved. Computational experiments show that the algorithm is robust and fast. The algorithmic ideas can also be used to give a fast dual algorithm for solving the optimization problem arising in the inner loop of Gaussian Process classifiers.

Observation of a power-law memory kernel for fluctuations within a single protein molecule

The fluctuation of the distance between a fluorescein-tyrosine pair within a single protein complex was directly monitored in real time by photoinduced electron transfer and found to be a stationary, time-reversible, and non-Markovian Gaussian process. Within the generalized Langevin equation formalism, we experimentally determine the memory kernel K(t), which is proportional to the autocorrelation function of the random fluctuating force. K(t) is a power-law decay, t(-0.51 +/- 0.07) in a broad range of time scales (10(-3)-10 s). Such a long-time memory effect could have implications for protein functions.

Application of ultraspherical polynomials to non-linear autonomous systems

This paper deals with the approximate solutions of non-linear autonomous systems by the application of ultraspherical polynomials. From the differential equations for amplitude and phase, set up by the method of variation of parameters, the approximate solutions are obtained by a generalized averaging technique based on the ultraspherical polynomial expansions. The method is illustrated with examples and the results are compared with the digital and analog computer solutions. There is a close agreement between the analytical and exact results.

The heat kernel on AdS(3) and its applications

We derive the heat kernel for arbitrary tensor fields on S-3 and (Euclidean) AdS(3) using a group theoretic approach. We use these results to also obtain the heat kernel on certain quotients of these spaces. In particular, we give a simple, explicit expression for the one loop determinant for a field of arbitrary spin s in thermal AdS(3). We apply this to the calculation of the one loop partition function of N = 1 supergravity on AdS(3). We find that the answer factorizes into left- and right-moving super Virasoro characters built on the SL(2, C) invariant vacuum, as argued by Maloney and Witten on general grounds.

Solution concepts in continuous-kernel multicriteria games

This paper considers nonzero-sum multicriteria games with continuous kernels. Solution concepts based on the notions of Pareto optimality, equilibrium, and security are extended to these games. Separate necessary and sufficient conditions and existence results are presented for equilibrium, Pareto-optimal response, and Pareto-optimal security strategies of the players.

The Reproducing Kernel DMS-FEM: 3D Shape Functions and Applications to Linear Solid Mechanics

We propose a family of 3D versions of a smooth finite element method (Sunilkumar and Roy 2010), wherein the globally smooth shape functions are derivable through the condition of polynomial reproduction with the tetrahedral B-splines (DMS-splines) or tensor-product forms of triangular B-splines and ID NURBS bases acting as the kernel functions. While the domain decomposition is accomplished through tetrahedral or triangular prism elements, an additional requirement here is an appropriate generation of knotclouds around the element vertices or corners. The possibility of sensitive dependence of numerical solutions to the placements of knotclouds is largely arrested by enforcing the condition of polynomial reproduction whilst deriving the shape functions. Nevertheless, given the higher complexity in forming the knotclouds for tetrahedral elements especially when higher demand is placed on the order of continuity of the shape functions across inter-element boundaries, we presently emphasize an exploration of the triangular prism based formulation in the context of several benchmark problems of interest in linear solid mechanics. In the absence of a more rigorous study on the convergence analyses, the numerical exercise, reported herein, helps establish the method as one of remarkable accuracy and robust performance against numerical ill-conditioning (such as locking of different kinds) vis-a-vis the conventional FEM.

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.