Mean Curvature Flow on Ricci Solitons

We study monotonic quantities in the context of combined geometric flows. In particular, focusing on Ricci solitons as the ambient space, we consider solutions of the heat type equation integrated over embedded submanifolds evolving by mean curvature flow and we study their monotonicity properties. This is part of an ongoing project with Magni and Mantegazzawhich will treat the case of non-solitonic backgrounds \cite{a_14}.Comment: 19 page

On-line Hydraulic State Estimation in Urban Water Networks Using Reduced Models

A Predictor-Corrector (PC) approach for on-line forecasting of water usage in an urban water system is presented and demonstrated. The M5 Model-Trees algorithm is used to predict water demands and Genetic Algorithms (GAs) are used to correct (i.e., calibrate according to on-line pressure and flow rate measurements) these predicted values in real-time. The PC loop repeats itself at each subsequent time-step with the forecasting model inputs being the corrected outputs of previous iterations, thus improving the model performances over time. To meet the computational efficiency requirements of real-time hydraulic state estimation, the urban network model which is comprised of over ten thousand pipelines and nodes is reduced using a water system aggregation technique. The reduced model, which resembles the original system's hydraulic performances with high accuracy, simplifies the computation of the PC loop and facilitates the implementation of the on-line model. The developed methodology is tested against the real input data of an urban water distribution system comprised of approximately 12500 nodes and 15000 pipes.Singapore-MIT Alliance for Research and TechnologySingapore. National Research Foundatio

The Simplicial Ricci Tensor

The Ricci tensor (Ric) is fundamental to Einstein's geometric theory of gravitation. The 3-dimensional Ric of a spacelike surface vanishes at the moment of time symmetry for vacuum spacetimes. The 4-dimensional Ric is the Einstein tensor for such spacetimes. More recently the Ric was used by Hamilton to define a non-linear, diffusive Ricci flow (RF) that was fundamental to Perelman's proof of the Poincare conjecture. Analytic applications of RF can be found in many fields including general relativity and mathematics. Numerically it has been applied broadly to communication networks, medical physics, computer design and more. In this paper, we use Regge calculus (RC) to provide the first geometric discretization of the Ric. This result is fundamental for higher-dimensional generalizations of discrete RF. We construct this tensor on both the simplicial lattice and its dual and prove their equivalence. We show that the Ric is an edge-based weighted average of deficit divided by an edge-based weighted average of dual area -- an expression similar to the vertex-based weighted average of the scalar curvature reported recently. We use this Ric in a third and independent geometric derivation of the RC Einstein tensor in arbitrary dimension.Comment: 19 pages, 2 figure

Construction of two whole genome radiation hybrid panels for dromedary (Camelus dromedarius): 5000RAD and 15000RAD

The availability of genomic resources including linkage information for camelids has been very limited. Here, we describe the construction of a set of two radiation hybrid (RH) panels (5000RAD and 15000RAD) for the dromedary (Camelus dromedarius) as a permanent genetic resource for camel genome researchers worldwide. For the 5000RAD panel, a total of 245 female camel-hamster radiation hybrid clones were collected, of which 186 were screened with 44 custom designed marker loci distributed throughout camel genome. The overall mean retention frequency (RF) of the final set of 93 hybrids was 47.7%. For the 15000RAD panel, 238 male dromedary-hamster radiation hybrid clones were collected, of which 93 were tested using 44 PCR markers. The final set of 90 clones had a mean RF of 39.9%. This 15000RAD panel is an important high-resolution complement to the main 5000RAD panel and an indispensable tool for resolving complex genomic regions. This valuable genetic resource of dromedary RH panels is expected to be instrumental for constructing a high resolution camel genome map. Construction of the set of RH panels is essential step toward chromosome level reference quality genome assembly that is critical for advancing camelid genomics and the development of custom genomic tools

a cross-sectional study in six European cities

Background: The relationship between socioeconomic position (SEP) and adolescent physical activity is uncertain, as most evidence is limited to specific settings and a restricted number of SEP indicators. This study aimed to assess the magnitude of socioeconomic differences in adolescent vigorous physical activity (VPA) across various European countries using a wide range of SEP indicators, including family-based (education, family affluence, perceived social standing, parents’ employment, housing tenure) and adolescent-based (academic performance and pocket money) ones. Methods: We used data from a survey among 10,510 students aged 14–17 from 50 schools in six European cities: Namur (BE), Tampere (FI), Hannover (DE), Latina (IT), Amersfoort (NL), Coimbra (PT). The questionnaire included socio-demographic characteristics and the amount of time spent in VPA. Results: The mean time spent practicing VPA was 60.4 min per day, with lower values for Namur (BE) and Latina (IT), and higher values for Amersfoort (NL). In the multivariable analysis, both categories of SEP indicators (family-based and adolescent based indicators) were independently associated with VPA. For each SEP indicator, lower levels of VPA were recorded in lower socioeconomic groups. In the total sample, each additional category of low SEP was associated with a decrease in mean VPA of about 4 min per day. Conclusions: This study showed that across European cities adolescent VPA is positively related to both family-based SEP and adolescents’ own SEP. When analysing socioeconomic differences in adolescent VPA, one should consider the use of multiple indicators of SEP.publishersversionpublishe

Investigating Off-shell Stability of Anti-de Sitter Space in String Theory

We propose an investigation of stability of vacua in string theory by studying their stability with respect to a (suitable) world-sheet renormalization group (RG) flow. We prove geometric stability of (Euclidean) anti-de Sitter (AdS) space (i.e., $\mathbf{H}^n$) with respect to the simplest RG flow in closed string theory, the Ricci flow. AdS space is not a fixed point of Ricci flow. We therefore choose an appropriate flow for which it is a fixed point, prove a linear stability result for AdS space with respect to this flow, and then show this implies its geometric stability with respect to Ricci flow. The techniques used can be generalized to RG flows involving other fields. We also discuss tools from the mathematics of geometric flows that can be used to study stability of string vacua.Comment: 29 pages, references added in this version to appear in Classical and Quantum Gravit

The association of adolescents' smoking with the physical activity levels of their friends

Funding Information: This study is part of the SILNE-R project (Enhancing the Effectiveness of Programs and Strategies to Prevent Smoking by Adolescents: A Realist Evaluation Comparing Seven European Countries), which is supported by the European Union‘s Horizon 2020 research and innovation programme, under grant agreement 635,056. The funder was not involved and did not have any input in the design, analysis and reporting of this study. Publisher Copyright: © 2023Background: Smoking is inversely related to people's Physical Activity Level (PAL). As the behavior of friends may affect the choices and behavior of adolescents, having friends with a high PAL may potentially protect against adolescent smoking. This study aims to assess whether adolescents' smoking is associated with the PAL of their friends. Methods: SILNE-R survey data of 11.918 adolescents from 55 different schools in 7 European cities was used to determine weekly smoking, individual PAL, PAL of friends, school PAL, and smoking of friends. Multilevel, multivariable logistic regression analysis were used to assess the association between the PAL of friends and weekly smoking. Several socio-demographic variables were included as covariates in the analysis. Results: Our results indicated that 10.8% of the respondents was smoking weekly. Weekly smoking was most common among adolescents whose friends had a PAL of 0–42.0 min per day (14.5%). Respondents were significantly more likely to be smoking weekly if their friends were on average 0–42 min vs. 80–180 min physically active (OR 1.27 [95% CI 1.04–1.55]). This association existed independently of the individual PAL of respondents. Stratification for smoking of friends yielded equal results, although the association appeared to be somewhat stronger for those with smoking friends (OR 1.38 [95% CI 1.06–1.82]). Conclusion: Adolescents are less likely to smoke weekly if they associate with friends who spend >80 min per day on physical activity. Initiatives aimed at the prevention of smoking among adolescents may benefit from organizing group-based physical activity programs.publishersversionpublishe

On the nonlinear stability of mKdV breathers

A mathematical proof for the stability of mKdV breathers is announced. This proof involves the existence of a nonlinear equation satisfied by all breather profiles, and a new Lyapunov functional which controls the dynamics of small perturbations and instability modes. In order to construct such a functional, we work in a subspace of the energy one. However, our proof introduces new ideas in order to attack the corresponding stability problem in the energy space. Some remarks about the sine-Gordon case are also considered.Comment: 7 p

Diffusion of particles moving with constant speed

The propagation of light in a scattering medium is described as the motion of a special kind of a Brownian particle on which the fluctuating forces act only perpendicular to its velocity. This enforces strictly and dynamically the constraint of constant speed of the photon in the medium. A Fokker-Planck equation is derived for the probability distribution in the phase space assuming the transverse fluctuating force to be a white noise. Analytic expressions for the moments of the displacement $$ along with an approximate expression for the marginal probability distribution function $P(x,t)$ are obtained. Exact numerical solutions for the phase space probability distribution for various geometries are presented. The results show that the velocity distribution randomizes in a time of about eight times the mean free time ($8t^*$) only after which the diffusion approximation becomes valid. This factor of eight is a well known experimental fact. A persistence exponent of $0.435 \pm 0.005$ is calculated for this process in two dimensions by studying the survival probability of the particle in a semi-infinite medium. The case of a stochastic amplifying medium is also discussed.Comment: 9 pages, 9 figures(Submitted to Phys. Rev. E