Some inequalities for operator (p,h)-convex functions

Let $p$ be a positive number and $h$ a function on $\mathbb{R}^+$ satisfying $h(xy) \ge h(x) h(y)$ for any $x, y \in \mathbb{R}^+$. A non-negative continuous function $f$ on $K (\subset \mathbb{R}^+)$ is said to be {\it operator $(p,h)$-convex} if \begin{equation*}\label{def} f ([\alpha A^p + (1-\alpha)B^p]^{1/p}) \leq h(\alpha)f(A) +h(1-\alpha)f(B) \end{equation*} holds for all positive semidefinite matrices $A, B$ of order $n$ with spectra in $K$, and for any $\alpha \in (0,1)$. In this paper, we study properties of operator $(p,h)$-convex functions and prove the Jensen, Hansen-Pedersen type inequalities for them. We also give some equivalent conditions for a function to become an operator $(p,h)$-convex. In applications, we obtain Choi-Davis-Jensen type inequality for operator $(p,h)$-convex functions and a relation between operator $(p,h)$-convex functions with operator monotone functions

Subsampling MCMC - An introduction for the survey statistician

The rapid development of computing power and efficient Markov Chain Monte Carlo (MCMC) simulation algorithms have revolutionized Bayesian statistics, making it a highly practical inference method in applied work. However, MCMC algorithms tend to be computationally demanding, and are particularly slow for large datasets. Data subsampling has recently been suggested as a way to make MCMC methods scalable on massively large data, utilizing efficient sampling schemes and estimators from the survey sampling literature. These developments tend to be unknown by many survey statisticians who traditionally work with non-Bayesian methods, and rarely use MCMC. Our article explains the idea of data subsampling in MCMC by reviewing one strand of work, Subsampling MCMC, a so called pseudo-marginal MCMC approach to speeding up MCMC through data subsampling. The review is written for a survey statistician without previous knowledge of MCMC methods since our aim is to motivate survey sampling experts to contribute to the growing Subsampling MCMC literature.Comment: Accepted for publication in Sankhya A. Previous uploaded version contained a bug in generating the figures and reference

Structure of spaces of germs of holomorphic functions

Let $E$ be a Frechet (resp. Frechet-Hilbert) space. It is shown that $E\in (\Omega)$ (resp. $E\in (DN)$) if and only if [\Cal H(O_E)]'\in(\Omega) (resp. [\Cal H(O_E)]'\in (DN)). Moreover it is also shown that $E\in (DN)$ if and only if \Cal H_b(E')\in (DN). In the nuclear case these results were proved by Meise and Vogt \cite{2}

Density-dependent phonoriton states in highly excited semiconductors

The dynamical aspects of the phonoriton state in highly-photoexcited semiconductors is studied theoretically. The effect of the exciton-exciton interaction and nonbosonic character of high-density excitons are taken into account. Using Green's function method and within the Random Phase Approximation it is shown that the phonoriton dispersion and damping are very sensitive to the exciton density, characterizing the excitation degree of semiconductors.Comment: ICTP preprint IC/95/226, Latex, 10 pages, 3 figure

Situational-Context for Virtually Modeling the Elderly

The generalized aging of the population is incrementing the pressure over, frequently overextended, healthcare systems. This situations is even worse in underdeveloped, sparsely populated regions like Extremadura in Spain or Alentejo in Portugal. In this paper we propose an initial approach to use the Situational-Context, a technique to seamlessly adapt Internet of Things systems to the needs and preferences of their users, for virtually modeling the elderly. These models could be used to enhance the elderly experience when using those kind of systems without raising the need for technical skills. The proposed virtual models will also be the basis for further eldercare innovations in sparsely populated regions

Powers of ideals and convergence of Green functions with colliding poles

Let us have a family of ideals of holomorphic functions vanishing at N distinct points of a complex manifold, all tending to a single point. As is known, convergence of the ideals does not guarantee the convergence of the pluricomplex Green functions to the Green function of the limit ideal; moreover, the existence of the limit of the Green functions was unclear. Assuming that all the powers of the ideals converge to some ideals, we prove that the Green functions converge, locally uniformly away from the limit pole, to a function which is essentially the upper envelope of the scaled Green functions of the limits of the powers. As examples, we consider ideals generated by hyperplane sections of a holomorphic curve near its singular point. In particular, our result explains recently obtained asymptotics for 3-point models.Comment: 15 pages; typesetting errors fixe