On p-adic lattices and Grassmannians

It is well-known that the coset spaces G(k((z)))/G(k[[z]]), for a reductive group G over a field k, carry the geometric structure of an inductive limit of projective k-schemes. This k-ind-scheme is known as the affine Grassmannian for G. From the point of view of number theory it would be interesting to obtain an analogous geometric interpretation of quotients of the form G(W(k)[1/p])/G(W(k)), where p is a rational prime, W denotes the ring scheme of p-typical Witt vectors, k is a perfect field of characteristic p and G is a reductive group scheme over W(k). The present paper is an attempt to describe which constructions carry over from the function field case to the p-adic case, more precisely to the situation of the p-adic affine Grassmannian for the special linear group G=SL_n. We start with a description of the R-valued points of the p-adic affine Grassmannian for SL_n in terms of lattices over W(R), where R is a perfect k-algebra. In order to obtain a link with geometry we further construct projective k-subvarieties of the multigraded Hilbert scheme which map equivariantly to the p-adic affine Grassmannian. The images of these morphisms play the role of Schubert varieties in the p-adic setting. Further, for any reduced k-algebra R these morphisms induce bijective maps between the sets of R-valued points of the respective open orbits in the multigraded Hilbert scheme and the corresponding Schubert cells of the p-adic affine Grassmannian for SL_n.Comment: 36 pages. This is a thorough revision, in the form accepted by Math. Zeitschrift, of the previously published preprint "On p-adic loop groups and Grassmannians

Global oceanic emission of ammonia: constraints from seawater and atmospheric observations

Current global inventories of ammonia emissions identify the ocean as the largest natural source. This source depends on seawater pH, temperature, and the concentration of total seawater ammonia (NHx(sw)), which reflects a balance between remineralization of organic matter, uptake by plankton, and nitrification. Here we compare [NHx(sw)] from two global ocean biogeochemical models (BEC and COBALT) against extensive ocean observations. Simulated [NHx(sw)] are generally biased high. Improved simulation can be achieved in COBALT by increasing the plankton affinity for NHx within observed ranges. The resulting global ocean emissions is 2.5 TgN a−1, much lower than current literature values (7–23 TgN a−1), including the widely used Global Emissions InitiAtive (GEIA) inventory (8 TgN a−1). Such a weak ocean source implies that continental sources contribute more than half of atmospheric NHx over most of the ocean in the Northern Hemisphere. Ammonia emitted from oceanic sources is insufficient to neutralize sulfate aerosol acidity, consistent with observations. There is evidence over the Equatorial Pacific for a missing source of atmospheric ammonia that could be due to photolysis of marine organic nitrogen at the ocean surface or in the atmosphere. Accommodating this possible missing source yields a global ocean emission of ammonia in the range 2–5 TgN a−1, comparable in magnitude to other natural sources from open fires and soils

A Computational Comparison of Optimization Methods for the Golomb Ruler Problem

The Golomb ruler problem is defined as follows: Given a positive integer n, locate n marks on a ruler such that the distance between any two distinct pair of marks are different from each other and the total length of the ruler is minimized. The Golomb ruler problem has applications in information theory, astronomy and communications, and it can be seen as a challenge for combinatorial optimization algorithms. Although constructing high quality rulers is well-studied, proving optimality is a far more challenging task. In this paper, we provide a computational comparison of different optimization paradigms, each using a different model (linear integer, constraint programming and quadratic integer) to certify that a given Golomb ruler is optimal. We propose several enhancements to improve the computational performance of each method by exploring bound tightening, valid inequalities, cutting planes and branching strategies. We conclude that a certain quadratic integer programming model solved through a Benders decomposition and strengthened by two types of valid inequalities performs the best in terms of solution time for small-sized Golomb ruler problem instances. On the other hand, a constraint programming model improved by range reduction and a particular branching strategy could have more potential to solve larger size instances due to its promising parallelization features

Generating natural language specifications from UML class diagrams

Early phases of software development are known to be problematic, difficult to manage and errors occurring during these phases are expensive to correct. Many systems have been developed to aid the transition from informal Natural Language requirements to semistructured or formal specifications. Furthermore, consistency checking is seen by many software engineers as the solution to reduce the number of errors occurring during the software development life cycle and allow early verification and validation of software systems. However, this is confined to the models developed during analysis and design and fails to include the early Natural Language requirements. This excludes proper user involvement and creates a gap between the original requirements and the updated and modified models and implementations of the system. To improve this process, we propose a system that generates Natural Language specifications from UML class diagrams. We first investigate the variation of the input language used in naming the components of a class diagram based on the study of a large number of examples from the literature and then develop rules for removing ambiguities in the subset of Natural Language used within UML. We use WordNet,a linguistic ontology, to disambiguate the lexical structures of the UML string names and generate semantically sound sentences. Our system is developed in Java and is tested on an independent though academic case study

State based model of long-term potentiation and synaptic tagging and capture

Recent data indicate that plasticity protocols have not only synapse-specific but also more widespread effects. In particular, in synaptic tagging and capture (STC), tagged synapses can capture plasticity-related proteins, synthesized in response to strong stimulation of other synapses. This leads to long-lasting modification of only weakly stimulated synapses. Here we present a biophysical model of synaptic plasticity in the hippocampus that incorporates several key results from experiments on STC. The model specifies a set of physical states in which a synapse can exist, together with transition rates that are affected by high- and low-frequency stimulation protocols. In contrast to most standard plasticity models, the model exhibits both early- and late-phase LTP/D, de-potentiation, and STC. As such, it provides a useful starting point for further theoretical work on the role of STC in learning and memory

Mutations in pericentrin cause Seckel syndrome with defective ATR-dependent DNA damage signaling

Large brain size is one of the defining characteristics of modern humans. Seckel syndrome (MIM 210600), a disorder of markedly reduced brain and body size, is associated with defective ATR-dependent DNA damage signaling. Only a single hypomorphic mutation of ATR has been identified in this genetically heterogeneous condition. We now report that mutations in the gene encoding pericentrin (PCNT)--resulting in the loss of pericentrin from the centrosome, where it has key functions anchoring both structural and regulatory proteins--also cause Seckel syndrome. Furthermore, we find that cells of individuals with Seckel syndrome due to mutations in PCNT (PCNT-Seckel) have defects in ATR-dependent checkpoint signaling, providing the first evidence linking a structural centrosomal protein with DNA damage signaling. These findings also suggest that other known microcephaly genes implicated in either DNA repair responses or centrosomal function may act in common developmental pathways determining human brain and body size

Preventing type 2 diabetes mellitus in Qatar by reducing obesity, smoking, and physical inactivity: mathematical modeling analyses.

BACKGROUND: The aim of this study was to estimate the impact of reducing the prevalence of obesity, smoking, and physical inactivity, and introducing physical activity as an explicit intervention, on the burden of type 2 diabetes mellitus (T2DM), using Qatar as an example. METHODS: A population-level mathematical model was adapted and expanded. The model was stratified by sex, age group, risk factor status, T2DM status, and intervention status, and parameterized by nationally representative data. Modeled interventions were introduced in 2016, reached targeted level by 2031, and then maintained up to 2050. Diverse intervention scenarios were assessed and compared with a counter-factual no intervention baseline scenario. RESULTS: T2DM prevalence increased from 16.7% in 2016 to 24.0% in 2050 in the baseline scenario. By 2050, through halting the rise or reducing obesity prevalence by 10-50%, T2DM prevalence was reduced by 7.8-33.7%, incidence by 8.4-38.9%, and related deaths by 2.1-13.2%. For smoking, through halting the rise or reducing smoking prevalence by 10-50%, T2DM prevalence was reduced by 0.5-2.8%, incidence by 0.5-3.2%, and related deaths by 0.1-0.7%. For physical inactivity, through halting the rise or reducing physical inactivity prevalence by 10-50%, T2DM prevalence was reduced by 0.5-6.9%, incidence by 0.5-7.9%, and related deaths by 0.2-2.8%. Introduction of physical activity with varying intensity at 25% coverage reduced T2DM prevalence by 3.3-9.2%, incidence by 4.2-11.5%, and related deaths by 1.9-5.2%. CONCLUSIONS: Major reductions in T2DM incidence could be accomplished by reducing obesity, while modest reductions could be accomplished by reducing smoking and physical inactivity, or by introducing physical activity as an intervention

Determinants of medication adherence to antihypertensive medications among a Chinese population using Morisky medication adherence scale

<b>Background and objectives</b> Poor adherence to medications is one of the major public health challenges. Only one-third of the population reported successful control of blood pressure, mostly caused by poor drug adherence. However, there are relatively few reports studying the adherence levels and their associated factors among Chinese patients. This study aimed to study the adherence profiles and the factors associated with antihypertensive drug adherence among Chinese patients.<p></p> <b>Methods</b> A cross-sectional study was conducted in an outpatient clinic located in the New Territories Region of Hong Kong. Adult patients who were currently taking at least one antihypertensive drug were invited to complete a self-administered questionnaire, consisting of basic socio-demographic profile, self-perceived health status, and self-reported medication adherence. The outcome measure was the Morisky Medication Adherence Scale (MMAS-8). Good adherence was defined as MMAS scores greater than 6 points (out of a total score of 8 points).<p></p> <b>Results</b> From 1114 patients, 725 (65.1%) had good adherence to antihypertensive agents. Binary logistic regression analysis was conducted. Younger age, shorter duration of antihypertensive agents used, job status being employed, and poor or very poor self-perceived health status were negatively associated with drug adherence.<p></p> <b>Conclusion</b> This study reported a high proportion of poor medication adherence among hypertensive subjects. Patients with factors associated with poor adherence should be more closely monitored to optimize their drug taking behavior

Deletion of Insulin-Degrading Enzyme Elicits Antipodal, Age-Dependent Effects on Glucose and Insulin Tolerance

Insulin-degrading enzyme (IDE) is widely recognized as the principal protease responsible for the clearance and inactivation of insulin, but its role in glycemic control in vivo is poorly understood. We present here the first longitudinal characterization, to our knowledge, of glucose regulation in mice with pancellular deletion of the IDE gene (IDE-KO mice).IDE-KO mice and wild-type (WT) littermates were characterized at 2, 4, and 6 months of age in terms of body weight, basal glucose and insulin levels, and insulin and glucose tolerance. Consistent with a functional role for IDE in insulin clearance, fasting serum insulin levels in IDE-KO mice were found to be ∼3-fold higher than those in wild-type (WT) controls at all ages examined. In agreement with previous observations, 6-mo-old IDE-KO mice exhibited a severe diabetic phenotype characterized by increased body weight and pronounced glucose and insulin intolerance. In marked contrast, 2-mo-old IDE-KO mice exhibited multiple signs of improved glycemic control, including lower fasting glucose levels, lower body mass, and modestly enhanced insulin and glucose tolerance relative to WT controls. Biochemically, the emergence of the diabetic phenotype in IDE-KO mice correlated with age-dependent reductions in insulin receptor (IR) levels in muscle, adipose, and liver tissue. Primary adipocytes harvested from 6-mo-old IDE-KO mice also showed functional impairments in insulin-stimulated glucose uptake.Our results indicate that the diabetic phenotype in IDE-KO mice is not a primary consequence of IDE deficiency, but is instead an emergent compensatory response to chronic hyperinsulinemia resulting from complete deletion of IDE in all tissues throughout life. Significantly, our findings provide new evidence to support the idea that partial and/or transient inhibition of IDE may constitute a valid approach to the treatment of diabetes

Grifonin-1: A Small HIV-1 Entry Inhibitor Derived from the Algal Lectin, Griffithsin

Background: Griffithsin, a 121-residue protein isolated from a red algal Griffithsia sp., binds high mannose N-linked glycans of virus surface glycoproteins with extremely high affinity, a property that allows it to prevent the entry of primary isolates and laboratory strains of T- and M-tropic HIV-1. We used the sequence of a portion of griffithsin's sequence as a design template to create smaller peptides with antiviral and carbohydrate-binding properties. Methodology/Results: The new peptides derived from a trio of homologous β-sheet repeats that comprise the motifs responsible for its biological activity. Our most active antiviral peptide, grifonin-1 (GRFN-1), had an EC50 of 190.8±11.0 nM in in vitro TZM-bl assays and an EC50 of 546.6±66.1 nM in p24gag antigen release assays. GRFN-1 showed considerable structural plasticity, assuming different conformations in solvents that differed in polarity and hydrophobicity. Higher concentrations of GRFN-1 formed oligomers, based on intermolecular β-sheet interactions. Like its parent protein, GRFN-1 bound viral glycoproteins gp41 and gp120 via the N-linked glycans on their surface. Conclusion: Its substantial antiviral activity and low toxicity in vitro suggest that GRFN-1 and/or its derivatives may have therapeutic potential as topical and/or systemic agents directed against HIV-1