On a matrix with integer eigenvalues and its relation to conditional Poisson sampling

A special non-symmetric N × N matrix with eigenvalues 0, 1, 2, . . . ,N − 1 is presented. The matrix appears in sampling theory. Its right eigenvectors, if properly normalized, give the inclusion probabilities of the Conditional Poisson design (for all different fixed sample sizes). The explicit expressions for the right eigenvectors become complicated for N large. Nevertheless, the left eigenvectors have a simple analytic form. An inversion of the left eigenvector matrix produces the right eigenvectors − the inclusion probabilities. Finally, a more general matrix with similar properties is defined and expressions for its left and right eigenvectors are derived

Stochastic Calculus for a Time-changed Semimartingale and the Associated Stochastic Differential Equations

It is shown that under a certain condition on a semimartingale and a time-change, any stochastic integral driven by the time-changed semimartingale is a time-changed stochastic integral driven by the original semimartingale. As a direct consequence, a specialized form of the Ito formula is derived. When a standard Brownian motion is the original semimartingale, classical Ito stochastic differential equations driven by the Brownian motion with drift extend to a larger class of stochastic differential equations involving a time-change with continuous paths. A form of the general solution of linear equations in this new class is established, followed by consideration of some examples analogous to the classical equations. Through these examples, each coefficient of the stochastic differential equations in the new class is given meaning. The new feature is the coexistence of a usual drift term along with a term related to the time-change.Comment: 27 pages; typos correcte

Mixtures in non stable Levy processes

We analyze the Levy processes produced by means of two interconnected classes of non stable, infinitely divisible distribution: the Variance Gamma and the Student laws. While the Variance Gamma family is closed under convolution, the Student one is not: this makes its time evolution more complicated. We prove that -- at least for one particular type of Student processes suggested by recent empirical results, and for integral times -- the distribution of the process is a mixture of other types of Student distributions, randomized by means of a new probability distribution. The mixture is such that along the time the asymptotic behavior of the probability density functions always coincide with that of the generating Student law. We put forward the conjecture that this can be a general feature of the Student processes. We finally analyze the Ornstein--Uhlenbeck process driven by our Levy noises and show a few simulation of it.Comment: 28 pages, 3 figures, to be published in J. Phys. A: Math. Ge

Levy-Student Distributions for Halos in Accelerator Beams

We describe the transverse beam distribution in particle accelerators within the controlled, stochastic dynamical scheme of the Stochastic Mechanics (SM) which produces time reversal invariant diffusion processes. This leads to a linearized theory summarized in a Shchr\"odinger--like (\Sl) equation. The space charge effects have been introduced in a recent paper~\cite{prstab} by coupling this \Sl equation with the Maxwell equations. We analyze the space charge effects to understand how the dynamics produces the actual beam distributions, and in particular we show how the stationary, self--consistent solutions are related to the (external, and space--charge) potentials both when we suppose that the external field is harmonic (\emph{constant focusing}), and when we \emph{a priori} prescribe the shape of the stationary solution. We then proceed to discuss a few new ideas~\cite{epac04} by introducing the generalized Student distributions, namely non--Gaussian, L\'evy \emph{infinitely divisible} (but not \emph{stable}) distributions. We will discuss this idea from two different standpoints: (a) first by supposing that the stationary distribution of our (Wiener powered) SM model is a Student distribution; (b) by supposing that our model is based on a (non--Gaussian) L\'evy process whose increments are Student distributed. We show that in the case (a) the longer tails of the power decay of the Student laws, and in the case (b) the discontinuities of the L\'evy--Student process can well account for the rare escape of particles from the beam core, and hence for the formation of a halo in intense beams.Comment: revtex4, 18 pages, 12 figure

Half‐Cauchy and Power Cauchy Distributions: Ordinary Differential Equations

In this chapter, homogenous ordinary differential equations (ODES) of different orders were obtained for the probability density function, quantile function, survival function inverse survival function, hazard function and reversed hazard functions of half‐Cauchy and power Cauchy distributions. This is possible since the aforementioned probability functions are differentiable. Differentiation and modified product rule were used to obtain the required ordinary differential equations, whose solutions are the respective probability functions. The different conditions necessary for the existence of the ODEs were obtained and it is almost in consistent with the support that defined the various probability functions considered. The parameters that defined each distribution greatly affect the nature of the ODEs obtained. This method provides new ways of classifying and approximating other probability distributions apart from half‐Cauchy and power Cauchy distributions considered in this chapter. In addition, the result of the quantile function can be compared with quantile approximation using the quantile mechanics

Genome-Wide Search Reveals the Existence of a Limited Number of Thyroid Hormone Receptor Alpha Target Genes in Cerebellar Neurons

Thyroid hormone (T3) has a major influence on cerebellum post-natal development. The major phenotypic landmark of exposure to low levels of T3 during development (hypothyroidism) in the cerebellum is the retarded inward migration of the most numerous cell type, granular neurons. In order to identify the direct genetic regulation exerted by T3 on cerebellar neurons and their precursors, we used microarray RNA hybridization to perform a time course analysis of T3 induced gene expression in primary cultures of cerebellar neuronal cell. These experiments suggest that we identified a small set of genes which are directly regulated, both in vivo and in vitro, during cerebellum post-natal development. These modest changes suggest that T3 does not acts directly on granular neurons and mainly indirectly influences the cellular interactions taking place during development

Hepatitis Vaccination of Men Who Have Sex with Men at Gay Pride Events

Prevention researchers have advocated primary prevention such as vaccination in alternative venues. However, there have been major questions about both the attendance of, and the ability to, vaccinate high-risk individuals in such settings. The current study seeks to assess the feasibility of vaccinating high-risk men who have sex with men (MSM) at Gay Pride events. The research questions are: Do gay men who are sampled at Gay Pride events engage in more or less risky behavior than gay men sampled at other venues? Do the gay men who receive hepatitis vaccinations at Gay Pride engage in more or less risky behavior than gay men at Gay Pride who do not receive hepatitis vaccination? Of the 3689 MSM that completed the Field Risk Assessment (FRA), 1095/3689 = 29.68% were recruited at either the 2006 or 2007 Long Beach, California Gay Pride events. The remaining, 2594/3689 = 70.32% were recruited at Long Beach gay bars, gay community organizations and institutions, and through street recruitment in various gay enclaves in the Long Beach area. Logistic regression analysis yielded eight factors that were associated with non-attendance of Gay Pride: Age, had sex while high in the last 12 months, had unprotected anal intercourse (UAI) in the last 12 months, had sex for drugs/money in the last 12 months, been diagnosed with a sexually transmitted infection (STI) in the last 12 months, used nitrites (poppers) in the last 12 months, and used methamphetamine in the last 12 months. Identifying as White, Asian, or African American compared to Hispanic was also associated with non-attendance. Bivariate analysis indicated that, of the MSM sampled at Gay Pride, 280/1095 = 25.57% received a hepatitis vaccination there. The MSM sampled at Gay Pride who reported engaging in UAI or having used any stimulant (cocaine, crack-cocaine, or methamphetamine) in the last 12 months were more likely to receive hepatitis vaccination on-site. The results provide evidence for the viability of successfully vaccinating high-risk MSM at Gay Pride events. However, it is vital that no-cost vaccinations are also funded in other community settings such as STI clinics, drug treatment programs, prisons, universities, and other community resource centers in order to reach those additional high-risk MSM who do not attend Gay Pride

20-Year Risks of Breast-Cancer Recurrence after Stopping Endocrine Therapy at 5 Years

The administration of endocrine therapy for 5 years substantially reduces recurrence rates during and after treatment in women with early-stage, estrogen-receptor (ER)-positive breast cancer. Extending such therapy beyond 5 years offers further protection but has additional side effects. Obtaining data on the absolute risk of subsequent distant recurrence if therapy stops at 5 years could help determine whether to extend treatment