New Strings for Old Veneziano Amplitudes III. Symplectic Treatment

A d-dimensional rational polytope P is a polytope whose vertices are located at the nodes of d-dimensional Z-lattice. Consider a number of points inside the inflated polytope (with coefficient of inflation k, k=1,2, 3...). The Ehrhart polynomial of P counts the number of such lattice points (nodes) inside the inflated P and (may be) at its faces (including vertices). In Part I (hep-th/0410242) of our four parts work we noticed that the Veneziano amplitude is just the Laplace transform of the generating function (considered as a partition function in the sence of statistical mechanics) for the Ehrhart polynomial for the regular inflated simplex obtained as a deformation retract of the Fermat (hyper) surface living in complex projective space. This observation is sufficient for development of new symplectic (this work) and supersymmetric (hep-th/0411241)physical models reproducing the Veneziano (and Veneziano-like) amplitudes. General ideas (e.g.those related to the properties of Ehrhart polynomials) are illustrated by simple practical examples (e.g. use of mirror symmetry for explanation of available experimental data on pion-pion scattering) worked out in some detail. Obtained final results are in formal accord with those earlier obtained by Vergne [PNAS 93 (1996) 14238].Comment: 48 pages J.Geom.Phys.(in press, available on line

Persistent decline over 3 years in physical function predicts 15-year mortality in ambulatory older men

Objectives: Physical function measurements can predict important adverse outcomes in older persons, but little is known about the predictive value of longitudinal changes in these measurements. This study evaluated the effects of transient and persistent decline over three years from baseline in physical function on 12 year mortality. Methods: This community-based cohort study included ambulatory men aged ≥71, living in the community of Merelbeke (municipality of Ghent, Belgium). Participants’ physical function and decline from baseline were assessed annually over three years using the following measurements and cut-off points: Timed Up and Go (2 sec), Chair Rise (1 sec), Balance (1 point), Grip strength (6kg), General Health (Short Form-36 item; 15 points), Physical Function (Short Form-36 item; 20 points) and Activities of Daily Living (ADL; Rapid Disability Rating Scale-2 questions; 2 points). Decline was considered persistent or transient based on whether the decline was still present at the end of year three. Results: Of 162 older men with complete annual physical function assessments from 1997 until 2000, 107 (66%) died within the subsequent 12 years. Mortality risk increased with persistent decline in Timed Up and Go (HR=2.15, 95%CI=1.24–3.73), Grip strength (HR=3.39, 95% CI=1.45–7.93), Physical Function (HR=2.51, 95%CI=1.43–4.41), General Health (HR=3.07, 95%CI=1.69–5.60), and ADL score (HR=3.30, 95%CI=1.43–7.63), compared with no decline. Decline in the last year in Chair Rise time (HR=2.63, 95%CI=1.39–4.98) and Balance (HR=2.39, 95%CI=1.10–5.18) also predicted death. Conclusions: Persistent decline in physical function affects mortality risk in ambulatory older men

Neighborhood Deprivation, Individual Socioeconomic Status, and Cognitive Function in Older People: Analyses from the English Longitudinal Study of Ageing

To assess the relationship between cognitive function, socioeconomic status, and neighborhood deprivation (lack of local resources of all types, financial and otherwise). DESIGN : Nationally representative cross-section. SETTING : The English Longitudinal Study of Ageing (ELSA). PARTICIPANTS : Seven thousand one hundred twenty-six community-dwelling individuals aged 52 and older and resident in urban areas. MEASUREMENTS : Individual cognitive function score and index of multiple deprivation (IMD) at the Super Output Area level, adjusting for health, lifestyle, and sociodemographic confounders. Analyses were conducted separately according to sex and age group (52–69 and ≥70). RESULTS : IMD affected cognitive function independent of the effects of education and socioeconomic status. For example, in fully adjusted models, women aged 70 and older had a standardized cognitive function score ( z -score) that was 0.20 points (95% confidence interval (CI)=0.01–0.39) lower in the bottom 20% of wealth than the top 20%, 0.44 points (95% CI=0.20–0.69) lower in the least-educated group than in the most educated, and 0.31 points (95% CI 0.15–0.48) lower if resident lived in an area in the bottom 20% of IMD than in the top 20%. CONCLUSION : In community-based older people in urban neighborhoods, neighborhood deprivation—living in a neighborhood with high levels of deprivation, compared with national levels—is associated with cognitive function independent of individual socioeconomic circumstances. The mechanisms underlying this relationship are unclear and warrant further investigation.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66217/1/j.1532-5415.2007.01557.x.pd

Compressive force generation by a bundle of living biofilaments

To study the compressional forces exerted by a bundle of living stiff filaments pressing on a surface, akin to the case of an actin bundle in filopodia structures, we have performed particulate Molecular Dynamics simulations of a grafted bundle of parallel living (self-assembling) filaments, in chemical equilibrium with a solution of their constitutive monomers. Equilibrium is established as these filaments, grafted at one end to a wall of the simulation box, grow at their chemically active free end and encounter the opposite confining wall of the simulation box. Further growth of filaments requires bending and thus energy, which automatically limit the populations of longer filaments. The resulting filament sizes distribution and the force exerted by the bundle on the obstacle are analyzed for different grafting densities and different sub- or supercritical conditions, these properties being compared with the predictions of the corresponding ideal confined bundle model. In this analysis, non-ideal effects due to interactions between filaments and confinement effects are singled out. For all state points considered at the same temperature and at the same gap width between the two surfaces, the force per filament exerted on the opposite wall appears to be a function of a rescaled free monomer density $\hat{\rho}_1^{\rm eff}$. This quantity can be estimated directly from the characteristic length of the exponential filament size distribution $P$ observed in the size domain where these grafted filaments are not in direct contact with the wall. We also analyze the dynamics of the filament contour length fluctuations in terms of effective polymerization ($U$) and depolymerization ($W$) rates, where again it is possible to disentangle non-ideal and confinement effects.Comment: 24 pages, 7 figure

Topological phase transition between non-high symmetry critical phases and curvature function renormalization group

The interplay between topology and criticality has been a recent interest of study in condensed matter physics. A unique topological transition between certain critical phases has been observed as a consequence of the edge modes living at criticalities. In this work, we generalize this phenomenon by investigating possible transitions between critical phases which are non-high symmetry in nature. We find the triviality and non-triviality of these critical phases in terms of the decay length of the edge modes and also characterize them using the winding numbers. The distinct non-high symmetry critical phases are separated by multicritical points with linear dispersion at which the winding number exhibits the quantized jump, indicating a change in the topology (number of edge modes) at the critical phases. Moreover, we reframe the scaling theory based on the curvature function, i.e. curvature function renormalization group method to efficiently address the non-high symmetry criticalities and multicriticalities. Using this we identify the conventional topological transition between gapped phases through non-high symmetry critical points, and also the unique topological transition between critical phases through multicritical points. The renormalization group flow, critical exponents and correlation function of Wannier states enable the characterization of non-high symmetry criticalities along with multicriticalities.Comment: 12 pages + supplementary (4 pages), 13 figures. Comments are welcom

THE EFFECT OF ACTIGRAPHY MEASURED PHYSICAL ACTIVITY ON EXECUTIVE FUNCTION IN OLDER ADULTS

Executive function (i.e., decision making, self-control, planning) is important for facilitating independent living in older adults. Physical activity may preserve executive function, but previous research has demonstrated sex differences in both physical activity and executive function among older adults. Few studies have investigated sex differences in the association between the two. We examined associations between objectively measured physical activity and executive function with attention to sex differences. We recruited N = 204 participants (Mage =71, SD=6.36; 57% women) with (n=47) and without (n=157) Alzheimer’s disease from the University of Kansas Alzheimer’s Disease Research Center. We used wrist-worn accelerometers (Actigraph GT9X) to measure physical activity 24 hours a day for 7 days in a free-living environment. We categorized physical activity as moderate to vigorous (MVPA) based on the Montoye (2020) Adult Vector Magnitude cut-points. We evaluated sex differences in the association between executive function and MVPA using multiple regression with an interaction term, adjusting for age, education, and dementia status. We used a composite score to combine tests of executive function (Digit Symbol Substitution, Stroop Interference, Trail making Part B, and Verbal Fluency). Results indicated, older age and lower education were associated with lower executive function scores (β=-2.12, p < 0.001; B=2.13, p < .05). In contrast to previous research, we did not find evidence for sex differences in the MVPA, executive function, nor the association between the two in our sample. Future research should investigate whether individualized exercise-based interventions and treatment between men and women may differentially benefit cognitive function

Simulated trading in a two-good economy on a network

With the upturn in living standards and increasing work stress, people have started to pay more attention to how happy they feel in their daily lives. Evaluating people\u27s happiness is becoming increasingly important in scientific fields. The focus of this thesis is to build a rational happiness function and to do simulations on several kinds of social networks related to the real world in a trading model with only two types of goods but no common currency. The purpose of the simulations is to seek the equilibrium points of the trading system. For this model, the parameters in the function and the shape of networks are key factors that affect the experimental results

The optimization problem of quantile and poverty measures estimation based on calibration

New calibrated estimators of quantiles and poverty measures are proposed. These estimators combine the incorporation of auxiliary information provided by auxiliary variables related to the variable of interest by calibration techniques with the selection of optimal calibration points under simple random sampling without replacement. The problem of selecting calibration points that minimize the asymptotic variance of the quantile estimator is addressed. Once the problem is solved, the definition of the new quantile estimator requires that the optimal estimator of the distribution function on which it is based verifies the properties of the distribution function. Through a theorem, the nondecreasing monotony property for the optimal estimator of the distribution function is established and the corresponding optimal estimator can be defined. This optimal quantile estimator is also used to define new estimators for poverty measures. Simulation studies with real data from the Spanish living conditions survey compares the performance of the new estimators against various methods proposed previously, where some resampling techniques are used for the variance estimation. Based on the results of the simulation study, the proposed estimators show a good performance and are a reasonable alternative to other estimators.Ministerio de Educacion y Cienci