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

LEARNING ARITHMETIC READ-ONCE FORMULAS*

Abstract. A formula is read-once if each variable appears at most once in it. An arithmetic read-once formula is one in which the operators are addition, subtraction, multiplication, and division. We present polynomial time algorithms for exact learning of arithmetic read-once formulas over a field. We present a membership and equivalence query algorithm that identifies arithmetic read-once formulas over an arbitrary field. We present a randomized membership query algorithm (i.e., a randomized black box interpolation algorithm) that identifies such formulas over finite fields with at least 2n + 5 elements (where n is the number of variables) and over infinite fields. We also show the existence of nonuniform deterministic membership query algorithms for arbitrary read-once formulas over fields of characteristic 0, and division-free read-once formulas over fields that have at least 2n + elements. For our algorithms, we assume we are able to perform efficiently arithmetic operations on field elements and compute square roots in the field. It is shown that the ability to compute square roots is necessary in the sense that the problem of computing n square roots in a field can be reduced to the problem of identifying an arithmetic formula over n variables in that field. Our equivalence queries are of a slightly nonstandard form, in which counterexamples are required not to be inputs on which the formula evaluates to 0/0. This assumption is shown to be necessary for fields of size o(n! log n) in the sense that we prove there exists no polynomial time identification algorithm that uses only membership and standard equivalence queries

An ANGPTL4-ceramide-protein kinase Cζ axis mediates chronic glucocorticoid exposure-induced hepatic steatosis and hypertriglyceridemia in mice.

Chronic or excess glucocorticoid exposure causes lipid disorders such as hypertriglyceridemia and hepatic steatosis. Angptl4 (angiopoietin-like 4), a primary target gene of the glucocorticoid receptor in hepatocytes and adipocytes, is required for hypertriglyceridemia and hepatic steatosis induced by the synthetic glucocorticoid dexamethasone. Angptl4 has also been shown to be required for dexamethasone-induced hepatic ceramide production. Here, we further examined the role of ceramide-mediated signaling in hepatic dyslipidemia caused by chronic glucocorticoid exposure. Using a stable isotope-labeling technique, we found that dexamethasone treatment induced the rate of hepatic de novo lipogenesis and triglyceride synthesis. These dexamethasone responses were compromised in Angptl4-null mice (Angptl4-/-). Treating mice with myriocin, an inhibitor of the rate-controlling enzyme of de novo ceramide synthesis, serine palmitoyltransferase long-chain base subunit 1 (SPTLC1)/SPTLC2, decreased dexamethasone-induced plasma and liver triglyceride levels in WT but not Angptl4-/- mice. We noted similar results in mice infected with adeno-associated virus-expressing small hairpin RNAs targeting Sptlc2. Protein phosphatase 2 phosphatase activator (PP2A) and protein kinase Cζ (PKCζ) are two known downstream effectors of ceramides. We found here that mice treated with an inhibitor of PKCζ, 2-acetyl-1,3-cyclopentanedione (ACPD), had lower levels of dexamethasone-induced triglyceride accumulation in plasma and liver. However, small hairpin RNA-mediated targeting of the catalytic PP2A subunit (Ppp2ca) had no effect on dexamethasone responses on plasma and liver triglyceride levels. Overall, our results indicate that chronic dexamethasone treatment induces an ANGPTL4-ceramide-PKCζ axis that activates hepatic de novo lipogenesis and triglyceride synthesis, resulting in lipid disorders

Explicit kinetic heterogeneity: mechanistic models for interpretation of labeling data of heterogeneous cell populations

Estimation of division and death rates of lymphocytes in different conditions is vital for quantitative understanding of the immune system. Deuterium, in the form of deuterated glucose or heavy water, can be used to measure rates of proliferation and death of lymphocytes in vivo. Inferring these rates from labeling and delabeling curves has been subject to considerable debate with different groups suggesting different mathematical models for that purpose. We show that the three models that are most commonly used are in fact mathematically identical and differ only in their interpretation of the estimated parameters. By extending these previous models, we here propose a more mechanistic approach for the analysis of data from deuterium labeling experiments. We construct a model of "kinetic heterogeneity" in which the total cell population consists of many sub-populations with different rates of cell turnover. In this model, for a given distribution of the rates of turnover, the predicted fraction of labeled DNA accumulated and lost can be calculated. Our model reproduces several previously made experimental observations, such as a negative correlation between the length of the labeling period and the rate at which labeled DNA is lost after label cessation. We demonstrate the reliability of the new explicit kinetic heterogeneity model by applying it to artificially generated datasets, and illustrate its usefulness by fitting experimental data. In contrast to previous models, the explicit kinetic heterogeneity model 1) provides a mechanistic way of interpreting labeling data; 2) allows for a non-exponential loss of labeled cells during delabeling, and 3) can be used to describe data with variable labeling length

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

Metabolic effects of diets differing in glycaemic index depend on age and endogenous GIP

Aims/hypothesis High- vs low-glycaemic index (GI) diets unfavourably affect body fat mass and metabolic markers in rodents. Different effects of these diets could be age-dependent, as well as mediated, in part, by carbohydrate-induced stimulation of glucose-dependent insulinotrophic polypeptide (GIP) signalling. Methods Young-adult (16 weeks) and aged (44 weeks) male wild-type (C57BL/6J) and GIP-receptor knockout (Gipr −/− ) mice were exposed to otherwise identical high-carbohydrate diets differing only in GI (20–26 weeks of intervention, n = 8–10 per group). Diet-induced changes in body fat distribution, liver fat, locomotor activity, markers of insulin sensitivity and substrate oxidation were investigated, as well as changes in the gene expression of anorexigenic and orexigenic hypothalamic factors related to food intake. Results Body weight significantly increased in young-adult high- vs low-GI fed mice (two-way ANOVA, p < 0.001), regardless of the Gipr genotype. The high-GI diet in young-adult mice also led to significantly increased fat mass and changes in metabolic markers that indicate reduced insulin sensitivity. Even though body fat mass also slightly increased in high- vs low-GI fed aged wild-type mice (p < 0.05), there were no significant changes in body weight and estimated insulin sensitivity in these animals. However, aged Gipr −/− vs wild-type mice on high-GI diet showed significantly lower cumulative net energy intake, increased locomotor activity and improved markers of insulin sensitivity. Conclusions/interpretation The metabolic benefits of a low-GI diet appear to be more pronounced in younger animals, regardless of the Gipr genotype. Inactivation of GIP signalling in aged animals on a high-GI diet, however, could be beneficial

Reconciling Estimates of Cell Proliferation from Stable Isotope Labeling Experiments.

Stable isotope labeling is the state of the art technique for in vivo quantification of lymphocyte kinetics in humans. It has been central to a number of seminal studies, particularly in the context of HIV-1 and leukemia. However, there is a significant discrepancy between lymphocyte proliferation rates estimated in different studies. Notably, deuterated (2)H2-glucose (D2-glucose) labeling studies consistently yield higher estimates of proliferation than deuterated water (D2O) labeling studies. This hampers our understanding of immune function and undermines our confidence in this important technique. Whether these differences are caused by fundamental biochemical differences between the two compounds and/or by methodological differences in the studies is unknown. D2-glucose and D2O labeling experiments have never been performed by the same group under the same experimental conditions; consequently a direct comparison of these two techniques has not been possible. We sought to address this problem. We performed both in vitro and murine in vivo labeling experiments using identical protocols with both D2-glucose and D2O. This showed that intrinsic differences between the two compounds do not cause differences in the proliferation rate estimates, but that estimates made using D2-glucose in vivo were susceptible to difficulties in normalization due to highly variable blood glucose enrichment. Analysis of three published human studies made using D2-glucose and D2O confirmed this problem, particularly in the case of short term D2-glucose labeling. Correcting for these inaccuracies in normalization decreased proliferation rate estimates made using D2-glucose and slightly increased estimates made using D2O; thus bringing the estimates from the two methods significantly closer and highlighting the importance of reliable normalization when using this technique

Molecular characterization of extended spectrum β -lactamases enterobacteriaceae causing lower urinary tract infection among pediatric population.

The β-lactam antibiotics have traditionally been the main treatment of Enterobacteriaceae infections, nonetheless, the emergence of species producing β- Lactamases has rendered this class of antibiotics largely ineffective. There are no published data on etiology of urinary tract infections (UTI) and antimicrobial resistance profile of uropathogens among children in Qatar. The aim of this study is to determine the phenotypic and genotypic profiles of antimicrobial resistant Enterobacteriaceae among children with UTI in Qatar. Bacteria were isolated from 727 urine positive cultures, collected from children with UTI between February and June 2017 at the Pediatric Emergency Center, Doha, Qatar. Isolated bacteria were tested for antibiotic susceptibility against sixteen clinically relevant antibiotics using phoenix and Double Disc Synergy Test (DDST) for confirmation of extended-spectrum beta-lactamase (ESBL) production. Existence of genes encoding ESBL production were identified using polymerase chain reaction (PCR). Statistical analysis was done using non-parametric Kappa statistics, Pearson chi-square test and Jacquard's coefficient. 201 (31.7%) of samples were confirmed as Extended Spectrum β -Lactamases (ESBL) Producing Enterobacteriaceae. The most dominant pathogen was 166 (83%) followed by 22 (11%). Resistance was mostly encoded by CTX-M (59%) genes, primarily CTX-MG1 (89.2%) followed by CTX-MG9 (7.7%). 37% of isolated bacteria were harboring multiple genes (2 genes or more). isolates were categorized into 11 clusters, while were grouped into five clonal clusters according to the presence and absence of seven genes namely TEM, SHV, CTX-MG1, CTX-MG2, CTX-MG8 CTX-MG9 CTX-MG25. Our data indicates an escalated problem of ESBL in pediatrics with UTI, which mandates implementation of regulatory programs to reduce the spread of ESBL producing Enterobacteriaceae in the community. The use of cephalosporins, aminoglycosides (gentamicin) and trimethoprim/sulfamethoxazole is compromised in Qatar among pediatric population with UTI, leaving carbapenems and amikacin as the therapeutic option for severe infections caused by ESBL producers