Central limit theorem for asymmetric kernel functionals

Asymmetric kernels are quite useful for the estimation of density functions with bounded support. Gamma kernels are designed to handle density functions whose supports are bounded from one end only, whereas beta kernels are particularly convenient for the estimation of density functions with compact support. These asymmetric kernels are nonnegative and free of boundary bias. Moreover, their shape varies according to the location of the data point, thus also changing the amount of smoothing. This paper applies the central limit theorem for degenerate U-statistics to compute the limiting distribution of a class of asymmetric kernel functionals.

Estimates for the Poisson kernel and Hardy spaces on compact manifolds

We study Hardy spaces on the boundary of a smooth open subset or R-n and prove that they can be defined either through the intrinsic maximal function or through Poisson integrals, yielding identical spaces. This extends to any smooth open subset of R-n results already known for the unit ball. As an application, a characterization of the weak boundary values of functions that belong to holomorphic Hardy spaces is given, which implies an F. and M. Riesz type theorem. (C) 2004 Elsevier B.V. All rights reserved.

Conjectures and theorems in the theory of entire functions

Motivated by the recent solution of Karlin's conjecture, properties of functions in the Laguerre-Polya class are investigated. The main result of this paper establishes new moment inequalities fur a class of entire functions represented by Fourier transforms. The paper concludes with several conjectures and open problems involving the Laguerre-Polya class and the Riemann xi -function.

Kernel polynomials from L-orthogonal polynomials

A positive measure ψ defined on [a,b] such that its moments μn=∫a btndψ(t) exist for n=0,±1,±2,⋯, is called a strong positive measure on [a,b]. If 0≤akernel polynomials associated with these L-orthogonal polynomials. As applications, we consider the quadrature rules associated with these kernel polynomials. Associated eigenvalue problems and numerical evaluation of the nodes and weights of such quadrature rules are also considered. © 2010 IMACS. Published by Elsevier B.V. All rights reserved.

Asymptotic integral kernel for ensembles of random normal matrices with radial potentials

The method of steepest descent is used to study the integral kernel of a family of normal random matrix ensembles with eigenvalue distribution P-N (z(1), ... , z(N)) = Z(N)(-1)e(-N)Sigma(N)(i=1) V-alpha(z(i)) Pi(1 <= i<j <= N) vertical bar z(i) - z(j)vertical bar(2), where V-alpha(z) = vertical bar z vertical bar(alpha), z epsilon C and alpha epsilon inverted left perpendicular0, infinity inverted right perpendicular. Asymptotic formulas with error estimate on sectors are obtained. A corollary of these expansions is a scaling limit for the n-point function in terms of the integral kernel for the classical Segal-Bargmann space. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3688293]

Reproducing kernel Hilbert spaces associated with kernels on topological spaces

We analyze reproducing kernel Hilbert spaces of positive definite kernels on a topological space X being either first countable or locally compact. The results include versions of Mercer's theorem and theorems on the embedding of these spaces into spaces of continuous and square integrable functions.

Weighted Fourier–Laplace transforms in reproducing kernel Hilbert spaces on the sphere

We study the action of a weighted Fourier–Laplace transform on the functions in the reproducing kernel Hilbert space (RKHS) associated with a positive definite kernel on the sphere. After defining a notion of smoothness implied by the transform, we show that smoothness of the kernel implies the same smoothness for the generating elements (spherical harmonics) in the Mercer expansion of the kernel. We prove a reproducing property for the weighted Fourier–Laplace transform of the functions in the RKHS and embed the RKHS into spaces of smooth functions. Some relevant properties of the embedding are considered, including compactness and boundedness. The approach taken in the paper includes two important notions of differentiability characterized by weighted Fourier–Laplace transforms: fractional derivatives and Laplace–Beltrami derivatives.

ANOVA kernels and RKHS of zero mean functions for model-based sensitivity analysis

Given a reproducing kernel Hilbert space (H,〈.,.〉)(H,〈.,.〉) of real-valued functions and a suitable measure μμ over the source space D⊂RD⊂R, we decompose HH as the sum of a subspace of centered functions for μμ and its orthogonal in HH. This decomposition leads to a special case of ANOVA kernels, for which the functional ANOVA representation of the best predictor can be elegantly derived, either in an interpolation or regularization framework. The proposed kernels appear to be particularly convenient for analyzing the effect of each (group of) variable(s) and computing sensitivity indices without recursivity.

An integral security kernel

As the user base of the Internet has grown tremendously, the need for secure services has increased accordingly. Most secure protocols, in digital business and other fields, use a combination of symmetric and asymmetric cryptography, random generators and hash functions in order to achieve confidentiality, integrity, and authentication. Our proposal is an integral security kernel based on a powerful mathematical scheme from which all of these cryptographic facilities can be derived. The kernel requires very little resources and has the flexibility of being able to trade off speed, memory or security; therefore, it can be efficiently implemented in a wide spectrum of platforms and applications, either software, hardware or low cost devices. Additionally, the primitives are comparable in security and speed to well known standards.

Perturbed Proximal Point Algorithm with Nonquadratic Kernel

Let H be a real Hilbert space and T be a maximal monotone operator on H. A well-known algorithm, developed by R. T. Rockafellar [16], for solving the problem (P) ”To find x ∈ H such that 0 ∈ T x” is the proximal point algorithm. Several generalizations have been considered by several authors: introduction of a perturbation, introduction of a variable metric in the perturbed algorithm, introduction of a pseudo-metric in place of the classical regularization, . . . We summarize some of these extensions by taking simultaneously into account a pseudo-metric as regularization and a perturbation in an inexact version of the algorithm.

Mechanisms Predisposing Penile Fracture And Long-term Outcomes On Erectile And Voiding Functions.

Purpose. To determine the mechanisms predisposing penile fracture as well as the rate of long-term penile deformity and erectile and voiding functions. Methods. All fractures were repaired on an emergency basis via subcoronal incision and absorbable suture with simultaneous repair of eventual urethral lesion. Patients' status before fracture and voiding and erectile functions at long term were assessed by periodic follow-up and phone call. Detailed history included cause, symptoms, and single-question self-report of erectile and voiding functions. Results. Among the 44 suspicious cases, 42 (95.4%) were confirmed, mean age was 34.5 years (range: 18-60), mean follow-up 59.3 months (range 9-155). Half presented the classical triad of audible crack, detumescence, and pain. Heterosexual intercourse was the most common cause (28 patients, 66.7%), followed by penile manipulation (6 patients, 14.3%), and homosexual intercourse (4 patients, 9.5%). Woman on top was the most common heterosexual position (n = 14, 50%), followed by doggy style (n = 8, 28.6%). Four patients (9.5%) maintained the cause unclear. Six (14.3%) patients had urethral injury and two (4.8%) had erectile dysfunction, treated by penile prosthesis and PDE-5i. No patient showed urethral fistula, voiding deterioration, penile nodule/curve or pain. Conclusions. Woman on top was the potentially riskiest sexual position (50%). Immediate surgical treatment warrants long-term very low morbidity.

Two-component System Vicrk Regulates Functions Associated With Establishment Of Streptococcus Sanguinis In Biofilms.

Streptococcus sanguinis is a commensal pioneer colonizer of teeth and an opportunistic pathogen of infectious endocarditis. The establishment of S. sanguinis in host sites likely requires dynamic fitting of the cell wall in response to local stimuli. In this study, we investigated the two-component system (TCS) VicRK in S. sanguinis (VicRKSs), which regulates genes of cell wall biogenesis, biofilm formation, and virulence in opportunistic pathogens. A vicK knockout mutant obtained from strain SK36 (SKvic) showed slight reductions in aerobic growth and resistance to oxidative stress but an impaired ability to form biofilms, a phenotype restored in the complemented mutant. The biofilm-defective phenotype was associated with reduced amounts of extracellular DNA during aerobic growth, with reduced production of H2O2, a metabolic product associated with DNA release, and with inhibitory capacity of S. sanguinis competitor species. No changes in autolysis or cell surface hydrophobicity were detected in SKvic. Reverse transcription-quantitative PCR (RT-qPCR), electrophoretic mobility shift assays (EMSA), and promoter sequence analyses revealed that VicR directly regulates genes encoding murein hydrolases (SSA_0094, cwdP, and gbpB) and spxB, which encodes pyruvate oxidase for H2O2 production. Genes previously associated with spxB expression (spxR, ccpA, ackA, and tpK) were not transcriptionally affected in SKvic. RT-qPCR analyses of S. sanguinis biofilm cells further showed upregulation of VicRK targets (spxB, gbpB, and SSA_0094) and other genes for biofilm formation (gtfP and comE) compared to expression in planktonic cells. This study provides evidence that VicRKSs regulates functions crucial for S. sanguinis establishment in biofilms and identifies novel VicRK targets potentially involved in hydrolytic activities of the cell wall required for these functions.

Monte Carlo Simulation Of The Response Functions Of Cdte Detectors To Be Applied In X-ray Spectroscopy.

In this work, the energy response functions of a CdTe detector were obtained by Monte Carlo (MC) simulation in the energy range from 5 to 160keV, using the PENELOPE code. In the response calculations the carrier transport features and the detector resolution were included. The computed energy response function was validated through comparison with experimental results obtained with (241)Am and (152)Eu sources. In order to investigate the influence of the correction by the detector response at diagnostic energy range, x-ray spectra were measured using a CdTe detector (model XR-100T, Amptek), and then corrected by the energy response of the detector using the stripping procedure. Results showed that the CdTe exhibits good energy response at low energies (below 40keV), showing only small distortions on the measured spectra. For energies below about 80keV, the contribution of the escape of Cd- and Te-K x-rays produce significant distortions on the measured x-ray spectra. For higher energies, the most important correction is the detector efficiency and the carrier trapping effects. The results showed that, after correction by the energy response, the measured spectra are in good agreement with those provided by a theoretical model of the literature. Finally, our results showed that the detailed knowledge of the response function and a proper correction procedure are fundamental for achieving more accurate spectra from which quality parameters (i.e., half-value layer and homogeneity coefficient) can be determined.

Data collapse, scaling functions, and analytical solutions of generalized growth models

We consider a nontrivial one-species population dynamics model with finite and infinite carrying capacities. Time-dependent intrinsic and extrinsic growth rates are considered in these models. Through the model per capita growth rate we obtain a heuristic general procedure to generate scaling functions to collapse data into a simple linear behavior even if an extrinsic growth rate is included. With this data collapse, all the models studied become independent from the parameters and initial condition. Analytical solutions are found when time-dependent coefficients are considered. These solutions allow us to perceive nontrivial transitions between species extinction and survival and to calculate the transition's critical exponents. Considering an extrinsic growth rate as a cancer treatment, we show that the relevant quantity depends not only on the intensity of the treatment, but also on when the cancerous cell growth is maximum.

Charm and longitudinal structure functions within the Kharzeev-Levin-Nardi model

We use the Kharzeev-Levin-Nardi (KLN) model of the low x gluon distributions to fit recent HERA data on F(L) and F(2)(c)(F(2)(b)). Having checked that this model gives a good description of the data, we use it to predict F(L) and F(2)(c) to be measured in a future electron-ion collider. The results are similar to those obtained with the de Florian-Sassot and Eskola-Paukkunen-Salgado nuclear gluon distributions. The conclusion of this exercise is that the KLN model, simple as it is, may still be used as an auxiliary tool to make estimates for both heavy-ion and electron-ion collisions.