Circular local likelihood

We introduce a class of local likelihood circular density estimators, which includes the kernel density estimator as a special case. The idea lies in optimizing a spatially weighted version of the log-likelihood function, where the logarithm of the density is locally approximated by a periodic polynomial. The use of von Mises density functions as weights reduces the computational burden. Also, we propose closed-form estimators which could form the basis of counterparts in the multidimensional Euclidean setting. Simulation results and a real data case study are used to evaluate the performance and illustrate the results

A note on nonparametric estimation of circular conditional densities

The conditional density offers the most informative summary of the relationship between explanatory and response variables. We need to estimate it in place of the simple conditional mean when its shape is not well-behaved. A motivation for estimating conditional densities, specific to the circular setting, lies in the fact that a natural alternative of it, like quantile regression, could be considered problematic because circular quantiles are not rotationally equivariant. We treat conditional density estimation as a local polynomial fitting problem as proposed by \cite{Fan et al.:1996} in the euclidean setting, and discuss a class of estimators in the cases when the conditioning variable is either circular or linear. Asymptotic properties for some members of the proposed class are derived. The effectiveness of the methods for finite sample sizes is illustrated by simulation experiments and an example using real data

Nonparametric estimating equations for circular probability density functions and their derivatives

We propose estimating equations whose unknown parameters are the values taken by a circular density and its derivatives at a point. Specifically, we solve equations which relate local versions of population trigonometric moments with their sample counterparts. Major advantages of our approach are: higher order bias without asymptotic variance inflation, closed form for the estimators, and absence of numerical tasks. We also investigate situations where the observed data are dependent. Theoretical results along with simulation experiments are provided

Kernel density classification and boosting: an L2 sub analysis

Kernel density estimation is a commonly used approach to classification. However, most of the theoretical results for kernel methods apply to estimation per se and not necessarily to classification. In this paper we show that when estimating the difference between two densities, the optimal smoothing parameters are increasing functions of the sample size of the complementary group, and we provide a small simluation study which examines the relative performance of kernel density methods when the final goal is classification. A relative newcomer to the classification portfolio is “boosting”, and this paper proposes an algorithm for boosting kernel density classifiers. We note that boosting is closely linked to a previously proposed method of bias reduction in kernel density estimation and indicate how it will enjoy similar properties for classification. We show that boosting kernel classifiers reduces the bias whilst only slightly increasing the variance, with an overall reduction in error. Numerical examples and simulations are used to illustrate the findings, and we also suggest further areas of research

Apoptotic epitope-specific CD8+ T cells and interferon signaling intersect in chronic hepatitis C virus infection

CD8(+) T cells specific to caspase-cleaved antigens derived from apoptotic T cells represent a principal player in chronic immune activation (CIA). Here, we found that both apoptotic epitope (AE)-specific and hepatitis C virus (HCV)-specific CD8(+) T cells were mostly confined within the effector memory (EM) or terminally differentiated EM CD45RA(+) cell subsets expressing a dysfunctional T-helper-1-like signature program in chronic (c)HCV infection. However, AE-specific CD8(+) T cells produced tumor necrosis factor (TNF)-α and interleukin-2 at the intrahepatic level significantly more than HCV-specific CD8(+) T cells, despite both populations acquiring high levels of programmed death-1 receptor expression. Contextually, only AE-specific CD8(+) T cells correlated with both interferon-stimulated gene levels in T cells and hepatic fibrosis score. Taken together, these data suggest that AE-specific CD8(+) T cells can sustain CIA by their capacity to produce TNF-α and be resistant to inhibitory signals more than HCV-specific CD8(+) T cells in cHCV infection

Configurational Entropy and its Crisis in Metastable States: Ideal Glass Transition in a Dimer Model as a Paragidm of a Molecular Glass

We discuss the need for discretization to evaluate the configurational entropy in a general model. We also discuss the prescription using restricted partition function formalism to study the stationary limit of metastable states. We introduce a lattice model of dimers as a paradigm of molecular fluid and study metastability in it to investigate the root cause of glassy behavior. We demonstrate the existence of the entropy crisis in metastable states, from which it follows that the entropy crisis is the root cause underlying the ideal glass transition in systems with particles of all sizes. The orientational interactions in the model control the nature of the liquid-liquid transition observed in recent years in molecular glasses.Comment: 36 pages, 9 figure

Magnetoelectrochemistry and asymmetric electrochemical reactions

Magnetoelectrochemistry is a branch of electrochemistry where magnetic fields play a vital role in the oxidation and reduction process of the molecules. When it comes to spin-dependent electrochemistry (SDE), becomes a new paradigm. This work presents electrochemical response during the “chiral imprinting” on working electrodes and the effects of potentiostatic and galvanostatic methods. We explore the use of the SDE concept, which is implemented for chiral-ferromagnetic (CFM) hybrid working electrodes, and we compare various electrochemical parameters affecting the quality of deposition. We electrochemically co-deposited nickel (Ni) with a chiral compound (tartaric acid) in its enantiopure forms (L and D), which allows us to obtain a chiral co-deposited nickel-tartaric acid (Ni-LTA or Ni-DTA) working electrode

Adaptive Density Estimation on the Circle by Nearly-Tight Frames

This work is concerned with the study of asymptotic properties of nonparametric density estimates in the framework of circular data. The estimation procedure here applied is based on wavelet thresholding methods: the wavelets used are the so-called Mexican needlets, which describe a nearly-tight frame on the circle. We study the asymptotic behaviour of the $L^{2}$-risk function for these estimates, in particular its adaptivity, proving that its rate of convergence is nearly optimal.Comment: 30 pages, 3 figure