A study on Quantization Dimension in complete metric spaces

The primary objective of the present paper is to develop the theory of quantization dimension of an invariant measure associated with an iterated function system consisting of finite number of contractive infinitesimal similitudes in a complete metric space. This generalizes the known results on quantization dimension of self-similar measures in the Euclidean space to a complete metric space. In the last part, continuity of quantization dimension is discussed

Estimating healthcare demand for an aging population: a flexible and robust bayesian joint model

In this paper, we analyse two frequently used measures of the demand for health care, namely hospital visits and out-of-pocket health care expenditure, which have been analysed separately in the existing literature. Given that these two measures of healthcare demand are highly likely to be closely correlated, we propose a framework to jointly model hospital visits and out-of-pocket medical expenditure. Furthermore, the joint framework allows for the presence of non-linear effects of covariates using splines to capture the effects of aging on healthcare demand. Sample heterogeneity is modelled robustly with the random effects following Dirichlet process priors with explicit cross-part correlation. The findings of our empirical analysis of the U.S. Health and Retirement Survey indicate that the demand for healthcare varies with age and gender and exhibits significant cross-part correlation that provides a rich understanding of how aging affects health care demand, which is of particular policy relevance in the context of an aging population

Rendez-vous of dwarfs

We present observations of multiple system of dwarf galaxies at the Russian 6-m telescope and the GMRT (Giant Metrewave Radio Telescope). The optical observations are a part of the programme Study of Groups of Dwarf Galaxies in the Local Supercluster. The group of galaxies under consideration looks like filament of 5 dwarfs. Two faint galaxies show peculiar structure. Long slit spectrum reveals inner motions about 150 km/s in one of them. It suggests that the galaxy is on stage of ongoing interaction. Probably, we see the group in moment of its formation.Comment: 2 pages, 3 figures; to appear in the proceedings of the conference "A Universe of dwarf galaxies" (Lyon, June 14-18, 2010

Some recent developments in quantization of fractal measures

We give an overview on the quantization problem for fractal measures, including some related results and methods which have been developed in the last decades. Based on the work of Graf and Luschgy, we propose a three-step procedure to estimate the quantization errors. We survey some recent progress, which makes use of this procedure, including the quantization for self-affine measures, Markov-type measures on graph-directed fractals, and product measures on multiscale Moran sets. Several open problems are mentioned.Comment: 13 page

Entropy "floor" and effervescent heating of intracluster gas

Recent X-ray observations of clusters of galaxies have shown that the entropy of the intracluster medium (ICM), even at radii as large as half the virial radius, is higher than that expected from gravitational processes alone. This is thought to be the result of nongravitational processes influencing the physical state of the ICM. In this paper, we investigate whether heating by a central AGN can explain the distribution of excess entropy as a function of radius. The AGN is assumed to inject buoyant bubbles into the ICM, which heat the ambient medium by doing pdV work as they rise and expand. Several authors have suggested that this "effervescent heating" mechanism could allow the central regions of clusters to avoid the ``cooling catastrophe''. Here we study the effect of effervescent heating at large radii. Our calculations show that such a heating mechanism is able to solve the entropy problem. The only free parameters of the model are the time-averaged luminosity and the AGN lifetime. The results are mainly sensitive to the total energy injected into the cluster. Our model predicts that the total energy injected by AGN should be roughly proportional to the cluster mass. The expected correlation is consistent with a linear relation between the mass of the central black hole(s) and the mass of the cluster, which is reminiscent of the Magorrian relation between the black hole and bulge mass.Comment: accepted for Ap

Experience versus Talent Shapes the Structure of the Web

We use sequential large-scale crawl data to empirically investigate and validate the dynamics that underlie the evolution of the structure of the web. We find that the overall structure of the web is defined by an intricate interplay between experience or entitlement of the pages (as measured by the number of inbound hyperlinks a page already has), inherent talent or fitness of the pages (as measured by the likelihood that someone visiting the page would give a hyperlink to it), and the continual high rates of birth and death of pages on the web. We find that the web is conservative in judging talent and the overall fitness distribution is exponential, showing low variability. The small variance in talent, however, is enough to lead to experience distributions with high variance: The preferential attachment mechanism amplifies these small biases and leads to heavy-tailed power-law (PL) inbound degree distributions over all pages, as well as over pages that are of the same age. The balancing act between experience and talent on the web allows newly introduced pages with novel and interesting content to grow quickly and surpass older pages. In this regard, it is much like what we observe in high-mobility and meritocratic societies: People with entitlement continue to have access to the best resources, but there is just enough screening for fitness that allows for talented winners to emerge and join the ranks of the leaders. Finally, we show that the fitness estimates have potential practical applications in ranking query results

Relativistic Thermodynamics with an Invariant Energy Scale

A particular framework for Quantum Gravity is the Doubly Special Relativity (DSR) formalism that introduces a new observer independent scale, the Planck energy. Our aim in this paper is to study the effects of this energy upper bound in relativistic thermodynamics. We have explicitly computed the modified equation of state for an ideal fluid in the DSR framework. In deriving our result we exploited the scheme of treating DSR as a non-linear representation of the Lorentz group in Special Relativity.Comment: 14 pages, Latex, No figures, minor corrections, two new references added, to appear in PR

Let Your CyberAlter Ego Share Information and Manage Spam

Almost all of us have multiple cyberspace identities, and these {\em cyber}alter egos are networked together to form a vast cyberspace social network. This network is distinct from the world-wide-web (WWW), which is being queried and mined to the tune of billions of dollars everyday, and until recently, has gone largely unexplored. Empirically, the cyberspace social networks have been found to possess many of the same complex features that characterize its real counterparts, including scale-free degree distributions, low diameter, and extensive connectivity. We show that these topological features make the latent networks particularly suitable for explorations and management via local-only messaging protocols. {\em Cyber}alter egos can communicate via their direct links (i.e., using only their own address books) and set up a highly decentralized and scalable message passing network that can allow large-scale sharing of information and data. As one particular example of such collaborative systems, we provide a design of a spam filtering system, and our large-scale simulations show that the system achieves a spam detection rate close to 100%, while the false positive rate is kept around zero. This system has several advantages over other recent proposals (i) It uses an already existing network, created by the same social dynamics that govern our daily lives, and no dedicated peer-to-peer (P2P) systems or centralized server-based systems need be constructed; (ii) It utilizes a percolation search algorithm that makes the query-generated traffic scalable; (iii) The network has a built in trust system (just as in social networks) that can be used to thwart malicious attacks; iv) It can be implemented right now as a plugin to popular email programs, such as MS Outlook, Eudora, and Sendmail.Comment: 13 pages, 10 figure

Phase transition and scaling behavior of topological charged black holes in Horava-Lifshitz gravity

Gravity can be thought as an emergent phenomenon and it has a nice "thermodynamic" structure. In this context, it is then possible to study the thermodynamics without knowing the details of the underlying microscopic degrees of freedom. Here, based on the ordinary thermodynamics, we investigate the phase transition of the static, spherically symmetric charged black hole solution with arbitrary scalar curvature $2k$ in Ho\v{r}ava-Lifshitz gravity at the Lifshitz point $z=3$. The analysis is done using the canonical ensemble frame work; i.e. the charge is kept fixed. We find (a) for both $k=0$ and $k=1$, there is no phase transition, (b) while $k=-1$ case exhibits the second order phase transition within the {\it physical region} of the black hole. The critical point of second order phase transition is obtained by the divergence of the heat capacity at constant charge. Near the critical point, we find the various critical exponents. It is also observed that they satisfy the usual thermodynamic scaling laws.Comment: Minor corrections, refs. added, to appear in Class. Quant. Grav. arXiv admin note: text overlap with arXiv:1111.0973 by other author