Learning and forgetting-based worker selection for tasks of varying complexity

This paper presents an approach for selecting workers for tasks of varying complexity based on individual learning and forgetting characteristics in order to improve system productivity. The performance of a learning and forgetting-based selection (LFBS) policy is examined using simulation and compared to a baseline policy representing criteria used in practice. The effects of factors including worker redundancy and task-tenure on productivity are also examined in the environment of continuously staffed independent tasks. Results demonstrate that the LFBs policy significantly improves productivity relative to common practice and suggests that lower levels of redundancy and shorter task-tenures tend to mitigate some of the negative effects of forgetting.     

Conditional quantiles with varying Gaussians

In this paper we study conditional quantile regression by learning algorithms generated from Tikhonov regularization schemes associated with pinball loss and varying Gaussian kernels. Our main goal is to provide convergence rates for the algorithm and illustrate differences between the conditional quantile regression and the least square regression. Applying varying Gaussian kernels improves the approximation ability of the algorithm. Bounds for the sample error are achieved by using a projection operator, a variance-expectation bound derived from a condition on conditional distributions and a tight bound for the covering numbers involving the Gaussian kernels.     

Rational approximation with varying weights I

We investigate two problems concerning uniform approximation by weighted rationals {w ⁿr_n～ _∞ ⁿ⁼¹ }, wherer _n=p_n Namely, forw(x):=e ^x we prove that uniform convergence to 1 ofw ⁿr_n is not possible on any interval [0,a] witha>2π. Forw(x):=x ^?, ?>1, we show that uniform convergence to 1 ofw ⁿr_n is not possible on any interval [b, 1] withb<tan ⁴(π(??1)/4?). (The latter result can be interpreted as a rational analogue of results concerning “incomplete polynomials.”) More generally, for α≥0, β≥0, α+β>0, we investigate forw(x)=e ^x andw(x)=x ^?, the possibility of approximation byw ⁿ p_n/q_n～ _∞ ⁿ⁼¹ , where depp _n≤αn, degq _n≤βn. The analysis utilizes potential theoretic methods. These are essentially sharp results though this will not be established in this paper.     

The product of two dependent random variables with regularly varying or rapidly varying tails

Let X and Y be two nonnegative and dependent random variables following a generalized Farlie-Gumbel-Morgenstern distribution. In this short note, we study the impact of a dependence structure of X and Y on the tail behavior of XY. We quantify the impact as the limit, as x→∞, of the quotient of Pr(XY>x) and Pr(X^∗Y^∗>x), where X^∗ and Y^∗ are independent random variables identically distributed as X and Y, respectively. We obtain an explicit expression for this limit when X is regularly varying or rapidly varying tailed.     

A queuing system with time varying rates

We obtain the queue length distribution of a multiple-server queuing system with time varying arrival and service rates when these rates are high.     

Moving estimates test with time varying bandwidth

In this paper, we consider the problem of testing for parameter changes in time series models based on a moving estimates (ME) test. It is widely accepted that detecting some changes, for instance, those caused by temporary parameter shifts by the existing cusum test is difficult. A MV test with a fixed bandwidth has been developed to circumvent the defect, but the test still does not perform well under certain conditions. Motivated by this, we propose a MV test with a time varying bandwidth to outperform the original test. In order to illustrate our findings, we have provided simulation results.     

Locally periodic thin domains with varying period

We analyze the behavior of the solutions of the Laplace equation with Neumann boundary conditions in a thin domain with a highly oscillatory behavior. The oscillations are locally periodic in the sense that both the amplitude and the period of the oscillations may not be constant and actually they vary in space. We obtain the asymptotic homogenized limit and provide some correctors. To accomplish this goal, we extend the unfolding operator method to the locally periodic case. The main ideas of this extension may be applied to other cases like perforated domains or reticulated structures, which are locally periodic with not necessarily a constant period.     

Support vector quantile regression with varying coefficients

Quantile regression has received a great deal of attention as an important tool for modeling statistical quantities of interest other than the conditional mean. Varying coefficient models are widely used to explore dynamic patterns among popular models available to avoid the curse of dimensionality. We propose a support vector quantile regression model with varying coefficients and its two estimation methods. One uses the quadratic programming, and the other uses the iteratively reweighted least squares procedure. The proposed method can be applied easily and effectively to estimating the nonlinear regression quantiles depending on the high-dimensional vector of smoothing variables. We also present the model selection method that employs generalized cross validation and generalized approximate cross validation techniques for choosing the hyperparameters, which affect the performance of the proposed model. Numerical studies are conducted to illustrate the performance of the proposed model.     

Reducibility behavior of polynomials with varying coefficients

LetK be a number field, and leth∈K[Y] be a polynomial of degreen. Fix an integer 0≤i≤n and compare the set ν of those integersa ofK such thath(Y)−aY ⁱhas a root inK with the set of those integersa, such thath(Y)−aY ⁱis reducible overK. Ifi is coprime ton, then we classify the rare cases where ν is not cofinite in . The main tools are a theorem of Siegel about integral points on algebraic curves and the theory of finite groups.     

Optimum stratification in sampling with varying probabilities

Summary The paper considers the problem of optimum stratification on an auxiliary variablex when the units from the different strate are selected with probability proportional to the value of the auxiliary variable. Under a super-population set-up assuming the form, of the regression of the estimation variabley on the auxiliary variablex as also the form of the variance functionV(y/x), minimal equations giving optimum strata boundaries have been obtained for the Neyman allocation method. As the minimal equations cannot be solved easily, methods to find approximate solutions have been given. A numerical illustration has also been given to study the effect of optimum stratification.     

Oscillatory reaction-diffusion equations with temporally varying parameters

Periodic wave trains are the generic one-dimensional solution form for reaction-diffusion equations with a limit cycle in the kinetics. Such systems are widely used as models for oscillatory phenomena in chemistry, ecology, and cell biology. In this paper, we study the way in which periodic wave solutions of such systems are modified by periodic forcing of kinetic parameters. Such forcing will occur in many ecological applications due to seasonal variations. We study temporal forcing in detail for systems of two reaction diffusion equations close to a supercritical Hopf bifurcation in the kinetics, with equal diffusion coefficients. In this case, the kinetics can be approximated by the Hopf normal form, giving reaction-diffusion equations of λ-ω type. Numerical simulations show that a temporal variation in the kinetic parameters causes the wave train amplitude to oscillate in time, whereas in the absence of any temporal forcing, this wave train amplitude is constant. Exploiting the mathematical simplicity of the λ-ω form, we derive analytically an approximation to the amplitude of the wave train oscillations with small forcing. We show that the amplitude of these oscillations depends crucially on the period of forcing.     

Bayesian nonparametric regression with varying residual density

We consider the problem of robust Bayesian inference on the mean regression function allowing the residual density to change flexibly with predictors. The proposed class of models is based on a Gaussian process (GP) prior for the mean regression function and mixtures of Gaussians for the collection of residual densities indexed by predictors. Initially considering the homoscedastic case, we propose priors for the residual density based on probit stick-breaking mixtures. We provide sufficient conditions to ensure strong posterior consistency in estimating the regression function, generalizing existing theory focused on parametric residual distributions. The homoscedastic priors are generalized to allow residual densities to change nonparametrically with predictors through incorporating GP in the stick-breaking components. This leads to a robust Bayesian regression procedure that automatically down-weights outliers and influential observations in a locally adaptive manner. The methods are illustrated using simulated and real data applications.     

Brownian motion with drift on spaces with varying dimension

Many properties of Brownian motion on spaces with varying dimension (BMVD in abbreviation) have been explored in Chen and Lou (2018). In this paper, we study Brownian motion with drift on spaces with varying dimension (BMVD with drift in abbreviation). Such a process can be conveniently defined by a regular Dirichlet form that is not necessarily symmetric. Through the method of Duhamel’s principle, it is established in this paper that the transition density of BMVD with drift has the same type of two-sided Gaussian bounds as that for BMVD (without drift). As a corollary, we derive Green function estimate for BMVD with drift.     

Necessary and sufficient conditions for parameter insensitive disturbance-rejection problems with dynamic output feedback

Email: otsuka{at}j.dendai.ac.jp Received on November 11, 2005; Accepted on December 16, 2006 In this paper, necessary and sufficient conditions for the parameterinsensitive disturbance-rejection problem with dynamic outputfeedback which was studied in Otsuka (1999) to be solvable aregiven for the structured uncertain linear systems. Further,necessary and sufficient conditions for the solvability of theproblems with static output feedback and state feedback arealso studied as special cases. The obtained results containsome extensions of the previous results to the structured uncertainlinear systems.     

On rotating circular disks with varying material properties

Taking Young’s modulus, thermal expansion coefficient and density to be the functions of the radial coordinate, a closed form solution of rotating circular disks made of functionally graded materials subjected to a constant angular velocity and a uniform temperature change is proposed in this paper. Excellent agreement with the solution from Mathematica 5.0 indicates the correctness of the proposed closed form solution. Distributions of the radial displacement and stresses in the disks are determined with the proposed approach and how material properties, temperature change, geometric size and different material coefficients affect deformations and stresses is investigated.     

Multivariate Markov-switching ARMA processes with regularly varying noise

The tail behaviour of stationary R^d-valued Markov-switching ARMA (MS-ARMA) processes driven by a regularly varying noise is analysed. It is shown that under appropriate summability conditions the MS-ARMA process is again regularly varying as a sequence. Moreover, it is established that these summability conditions are satisfied if the sum of the norms of the autoregressive parameters is less than one for all possible values of the parameter chain, which leads to feasible sufficient conditions.Our results complement in particular those of Saporta [Tail of the stationary solution of the stochastic equation Y_n+1=a_nY_n+b_n with Markovian coefficients, Stochastic Process. Appl. 115 (2005) 1954-1978.] where regularly varying tails of one-dimensional MS-AR(1) processes coming from consecutive large values of the parameter chain were studied.     

An extremal problem for edge domination insensitive graphs

A connected graph is edge domination insensitive if the domination number is unchanged when any single edge is removed. The minimum number of edges required by such a graph is determined. Similar results are given when the graph must remain connected upon any edge's removal and when the dominating set must remain fixed.     

Learning from imprecise and fuzzy observations: Data disambiguation through generalized loss minimization

Methods for analyzing or learning from “fuzzy data” have attracted increasing attention in recent years. In many cases, however, existing methods (for precise, non-fuzzy data) are extended to the fuzzy case in an ad-hoc manner, and without carefully considering the interpretation of a fuzzy set when being used for modeling data. Distinguishing between an ontic and an epistemic interpretation of fuzzy set-valued data, and focusing on the latter, we argue that a “fuzzification” of learning algorithms based on an application of the generic extension principle is not appropriate. In fact, the extension principle fails to properly exploit the inductive bias underlying statistical and machine learning methods, although this bias, at least in principle, offers a means for “disambiguating” the fuzzy data. Alternatively, we therefore propose a method which is based on the generalization of loss functions in empirical risk minimization, and which performs model identification and data disambiguation simultaneously. Elaborating on the fuzzification of specific types of losses, we establish connections to well-known loss functions in regression and classification. We compare our approach with related methods and illustrate its use in logistic regression for binary classification.     

Multirate finite step methods with varying step sizes

Many partial differential equations consist of slow and fast scales. Often, the right hand side of semidiscretized PDEs can be split additively in corresponding fast and slow parts. Many methods utilise the additive splitting of these equations, like generalized additive Runge-Kutta (GARK) methods or multirate infinitesimal step methods. The latter one treat the slow part with macro step sizes, whereas the fast part is integrated a ODE solver. The corresponding order conditions assume the exact solution of the auxiliary ODE, i.e. assume an infinite number of small steps. We extend the MIS approach by fixing the number of steps, which leads to the multirate finite steps (MFS) method. The order conditions are derived, such that the order is independent in the number of small steps in each stage. Finally, we confirm the theoretical results by numerical experiments. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On rotating circular disks with varying material properties

Taking Young’s modulus, thermal expansion coefficient and density to be the functions of the radial coordinate, a closed form solution of rotating circular disks made of functionally graded materials subjected to a constant angular velocity and a uniform temperature change is proposed in this paper. Excellent agreement with the solution from Mathematica 5.0 indicates the correctness of the proposed closed form solution. Distributions of the radial displacement and stresses in the disks are determined with the proposed approach and how material properties, temperature change, geometric size and different material coefficients affect deformations and stresses is investigated.