Central limit approximations for Markov population processes with countably many types

When modelling metapopulation dynamics, the influence of a single patch on the metapopulation depends on the number of individuals in the patch. Since there is usually no obvious natural upper limit on the number of individuals in a patch, this leads to systems in which there are countably infinitely many possible types of entity. Analogous considerations apply in the transmission of parasitic diseases. In this paper, we prove central limit theorems for quite general systems of this kind, together with bounds on the rate of convergence in an appropriately chosen weighted $\ell_1$ norm.Comment: 24 page

A Delicate Balance of Life Tenure and Independence: Conditional Resignations from the Federal Bench

Judicial selection, including judicial resignations, nominations, and confirmations, is comprised of a patchwork of traditions, rules, and constitutional provisions. The Constitution does not explicitly detail a formalized process at any stage of the appointments process, but checks and balances have organically developed and changed over time as the process has become more politicized. The question becomes, then, whether conditional resignations comport with this system or the Framers’ intent. At the Supreme Court level, conditional resignations are rare. Only a handful of conditional resignations have ever been submitted. At the court of appeals and district court levels, it is unclear how widespread this practice is. Neither Congress nor the President has prohibited conditional resignations. Indeed, resignations subject to a date certain have generally been accepted. This Comment explores the constitutionality of conditional resignations within the context of judicial selection. It also includes a discussion of the politicization of judicial selection for the federal bench and explores the constitutional limits of conditional resignations. Next, this Comment discusses the next natural step for judicial selection—that is, regulation. If the judiciary tips the delicate balance by submitting problematic conditional resignations, attempts to regulate judicial departures may naturally follow. This Comment ultimately concludes that conditional resignations protect judicial permanency in office by providing another check and balance in the patchwork of traditions, rules, and constitutional requirements in the appointments process. As an extension of these changes, the conditional resignation can be interpreted as judges asserting more control over their life tenure and independence

A law of large numbers approximation for Markov population processes with countably many types

When modelling metapopulation dynamics, the influence of a single patch on the metapopulation depends on the number of individuals in the patch. Since the population size has no natural upper limit, this leads to systems in which there are countably infinitely many possible types of individual. Analogous considerations apply in the transmission of parasitic diseases. In this paper, we prove a law of large numbers for quite general systems of this kind, together with a rather sharp bound on the rate of convergence in an appropriately chosen weighted ℓ 1 nor

Central limit approximations for Markov population processes with countably many types

When modelling metapopulation dynamics, the influence of a single patch on the metapopulation depends on the number of individuals in the patch. Since there is usually no obvious natural upper limit on the number of individuals in a patch, this leads to systems in which there are countably infinitely many possible types of entity. Analogous considerations apply in the transmission of parasitic diseases. In this paper, we prove central limit theorems for quite general systems of this kind, together with bounds on the rate of convergence in an appropriately chosen weighted $\ell_1$ norm

To feed or not to feed in palliative medicine

The problem of malnutrition concerns most patients in the advanced stages of cancer. Nutrition and food are synonymous with the continuation of life for patients and their families and friends. In this paper, the methods of oral, enteral and parenteral nutrition are discussed, together with their advantages and the controversies connected with them and their effects on survival time and the quality of life.The problem of malnutrition concerns most patients in the advanced stages of cancer. Nutrition and food are synonymous with the continuation of life for patients and their families and friends. In this paper, the methods of oral, enteral and parenteral nutrition are discussed, together with their advantages and the controversies connected with them and their effects on survival time and the quality of life

Coloring random graphs

We study the graph coloring problem over random graphs of finite average connectivity $c$. Given a number $q$ of available colors, we find that graphs with low connectivity admit almost always a proper coloring whereas graphs with high connectivity are uncolorable. Depending on $q$, we find the precise value of the critical average connectivity $c_q$. Moreover, we show that below $c_q$ there exist a clustering phase $c\in [c_d,c_q]$ in which ground states spontaneously divide into an exponential number of clusters and where the proliferation of metastable states is responsible for the onset of complexity in local search algorithms.Comment: 4 pages, 1 figure, version to app. in PR