Proof of a conjecture of Polya on the zeros of successive derivatives of real entire functions

We prove Polya's conjecture of 1943: For a real entire function of order greater than 2, with finitely many non-real zeros, the number of non-real zeros of the n-th derivative tends to infinity with n. We use the saddle point method and potential theory, combined with the theory of analytic functions with positive imaginary part in the upper half-plane.Comment: 26 page

An objective based classification of aggregation techniques for wireless sensor networks

Wireless Sensor Networks have gained immense popularity in recent years due to their ever increasing capabilities and wide range of critical applications. A huge body of research efforts has been dedicated to find ways to utilize limited resources of these sensor nodes in an efficient manner. One of the common ways to minimize energy consumption has been aggregation of input data. We note that every aggregation technique has an improvement objective to achieve with respect to the output it produces. Each technique is designed to achieve some target e.g. reduce data size, minimize transmission energy, enhance accuracy etc. This paper presents a comprehensive survey of aggregation techniques that can be used in distributed manner to improve lifetime and energy conservation of wireless sensor networks. Main contribution of this work is proposal of a novel classification of such techniques based on the type of improvement they offer when applied to WSNs. Due to the existence of a myriad of definitions of aggregation, we first review the meaning of term aggregation that can be applied to WSN. The concept is then associated with the proposed classes. Each class of techniques is divided into a number of subclasses and a brief literature review of related work in WSN for each of these is also presented

Accelerated in vivo proliferation of memory phenotype CD4+ T-cells in human HIV-1 infection irrespective of viral chemokine co-receptor tropism.

CD4(+) T-cell loss is the hallmark of HIV-1 infection. CD4 counts fall more rapidly in advanced disease when CCR5-tropic viral strains tend to be replaced by X4-tropic viruses. We hypothesized: (i) that the early dominance of CCR5-tropic viruses results from faster turnover rates of CCR5(+) cells, and (ii) that X4-tropic strains exert greater pathogenicity by preferentially increasing turnover rates within the CXCR4(+) compartment. To test these hypotheses we measured in vivo turnover rates of CD4(+) T-cell subpopulations sorted by chemokine receptor expression, using in vivo deuterium-glucose labeling. Deuterium enrichment was modeled to derive in vivo proliferation (p) and disappearance (d*) rates which were related to viral tropism data. 13 healthy controls and 13 treatment-naive HIV-1-infected subjects (CD4 143-569 cells/ul) participated. CCR5-expression defined a CD4(+) subpopulation of predominantly CD45R0(+) memory cells with accelerated in vivo proliferation (p = 2.50 vs 1.60%/d, CCR5(+) vs CCR5(-); healthy controls; P<0.01). Conversely, CXCR4 expression defined CD4(+) T-cells (predominantly CD45RA(+) naive cells) with low turnover rates. The dominant effect of HIV infection was accelerated turnover of CCR5(+)CD45R0(+)CD4(+) memory T-cells (p = 5.16 vs 2.50%/d, HIV vs controls; P<0.05), naïve cells being relatively unaffected. Similar patterns were observed whether the dominant circulating HIV-1 strain was R5-tropic (n = 9) or X4-tropic (n = 4). Although numbers were small, X4-tropic viruses did not appear to specifically drive turnover of CXCR4-expressing cells (p = 0.54 vs 0.72 vs 0.44%/d in control, R5-tropic, and X4-tropic groups respectively). Our data are most consistent with models in which CD4(+) T-cell loss is primarily driven by non-specific immune activation

Clinical care recommendations for cardiologists treating adults with myotonic dystrophy

Myotonic dystrophy is an inherited systemic disorder affecting skeletal muscle and the heart. Genetic testing for myotonic dystrophy is diagnostic and identifies those at risk for cardiac complications. The 2 major genetic forms of myotonic dystrophy, type 1 and type 2, differ in genetic etiology yet share clinical features. The cardiac management of myotonic dystrophy should include surveillance for arrhythmias and left ventricular dysfunction, both of which occur in progressive manner and contribute to morbidity and mortality. To promote the development of care guidelines for myotonic dystrophy, the Myotonic Foundation solicited the input of care experts and organized the drafting of these recommendations. As a rare disorder, large scale clinical trial data to guide the management of myotonic dystrophy are largely lacking. The following recommendations represent expert consensus opinion from those with experience in the management of myotonic dystrophy, in part supported by literature-based evidence where available

Clinical care recommendations for cardiologists treating adults with myotonic dystrophy

Myotonic dystrophy is an inherited systemic disorder affecting skeletal muscle and the heart. Genetic testing for myotonic dystrophy is diagnostic and identifies those at risk for cardiac complications. The 2 major genetic forms of myotonic dystrophy, type 1 and type 2, differ in genetic etiology yet share clinical features. The cardiac management of myotonic dystrophy should include surveillance for arrhythmias and left ventricular dysfunction, both of which occur in progressive manner and contribute to morbidity and mortality. To promote the development of care guidelines for myotonic dystrophy, the Myotonic Foundation solicited the input of care experts and organized the drafting of these recommendations. As a rare disorder, large scale clinical trial data to guide the management of myotonic dystrophy are largely lacking. The following recommendations represent expert consensus opinion from those with experience in the management of myotonic dystrophy, in part supported by literature-based evidence where available