Study of the apsidal precession of the Physical Symmetrical Pendulum

We study the apsidal precession of a Physical Symmetrical Pendulum (Allais' precession) as a generalization of the precession corresponding to the Ideal Spherical Pendulum (Airy's Precession). Based on the Hamilton-Jacobi formalism and using the technics of variation of parameters along with the averaging method, we obtain approximate solutions, in terms of which the motion of both systems admits a simple geometrical description. The method developed in this paper is considerably simpler than the standard one in terms of elliptical functions and the numerical agreement with the exact solutions is excellent. In addition, the present procedure permits to show clearly the origin of the Airy's and Allais' precession, as well as the effect of the spin of the Physical Pendulum on the Allais' precession. Further, the method can be extended to the study of the asymmetrical pendulum in which an exact solution is not possible anymore.Comment: 20 pages, 8 figures, LaTeX2

Cake Cutting Algorithms for Piecewise Constant and Piecewise Uniform Valuations

Cake cutting is one of the most fundamental settings in fair division and mechanism design without money. In this paper, we consider different levels of three fundamental goals in cake cutting: fairness, Pareto optimality, and strategyproofness. In particular, we present robust versions of envy-freeness and proportionality that are not only stronger than their standard counter-parts but also have less information requirements. We then focus on cake cutting with piecewise constant valuations and present three desirable algorithms: CCEA (Controlled Cake Eating Algorithm), MEA (Market Equilibrium Algorithm) and CSD (Constrained Serial Dictatorship). CCEA is polynomial-time, robust envy-free, and non-wasteful. It relies on parametric network flows and recent generalizations of the probabilistic serial algorithm. For the subdomain of piecewise uniform valuations, we show that it is also group-strategyproof. Then, we show that there exists an algorithm (MEA) that is polynomial-time, envy-free, proportional, and Pareto optimal. MEA is based on computing a market-based equilibrium via a convex program and relies on the results of Reijnierse and Potters [24] and Devanur et al. [15]. Moreover, we show that MEA and CCEA are equivalent to mechanism 1 of Chen et. al. [12] for piecewise uniform valuations. We then present an algorithm CSD and a way to implement it via randomization that satisfies strategyproofness in expectation, robust proportionality, and unanimity for piecewise constant valuations. For the case of two agents, it is robust envy-free, robust proportional, strategyproof, and polynomial-time. Many of our results extend to more general settings in cake cutting that allow for variable claims and initial endowments. We also show a few impossibility results to complement our algorithms.Comment: 39 page

Link and subgraph likelihoods in random undirected networks with fixed and partially fixed degree sequence

The simplest null models for networks, used to distinguish significant features of a particular network from {\it a priori} expected features, are random ensembles with the degree sequence fixed by the specific network of interest. These "fixed degree sequence" (FDS) ensembles are, however, famously resistant to analytic attack. In this paper we introduce ensembles with partially-fixed degree sequences (PFDS) and compare analytic results obtained for them with Monte Carlo results for the FDS ensemble. These results include link likelihoods, subgraph likelihoods, and degree correlations. We find that local structural features in the FDS ensemble can be reasonably well estimated by simultaneously fixing only the degrees of few nodes, in addition to the total number of nodes and links. As test cases we use a food web, two protein interaction networks (\textit{E. coli, S. cerevisiae}), the internet on the autonomous system (AS) level, and the World Wide Web. Fixing just the degrees of two nodes gives the mean neighbor degree as a function of node degree, $_k$, in agreement with results explicitly obtained from rewiring. For power law degree distributions, we derive the disassortativity analytically. In the PFDS ensemble the partition function can be expanded diagrammatically. We obtain an explicit expression for the link likelihood to lowest order, which reduces in the limit of large, sparse undirected networks with $L$ links and with $k_{\rm max} \ll L$ to the simple formula $P(k,k') = kk'/(2L + kk')$. In a similar limit, the probability for three nodes to be linked into a triangle reduces to the factorized expression $P_{\Delta}(k_1,k_2,k_3) = P(k_1,k_2)P(k_1,k_3)P(k_2,k_3)$.Comment: 17 pages, includes 11 figures; first revision: shortened to 14 pages (7 figures), added discussion of subgraph counts, deleted discussion of directed network

Pharmacological activation of a novel p53-dependent S-phase checkpoint involving CHK-1.

We have recently shown that induction of the p53 tumour suppressor protein by the small-molecule RITA (reactivation of p53 and induction of tumour cell apoptosis; 2,5-bis(5-hydroxymethyl-2-thienyl)furan) inhibits hypoxia-inducible factor-1α and vascular endothelial growth factor expression in vivo and induces p53-dependent tumour cell apoptosis in normoxia and hypoxia. Here, we demonstrate that RITA activates the canonical ataxia telangiectasia mutated/ataxia telangiectasia and Rad3-related DNA damage response pathway. Interestingly, phosphorylation of checkpoint kinase (CHK)-1 induced in response to RITA was influenced by p53 status. We found that induction of p53, phosphorylated CHK-1 and γH2AX proteins was significantly increased in S-phase. Furthermore, we found that RITA stalled replication fork elongation, prolonged S-phase progression and induced DNA damage in p53 positive cells. Although CHK-1 knockdown did not significantly affect p53-dependent DNA damage or apoptosis induced by RITA, it did block the ability for DNA integrity to be maintained during the immediate response to RITA. These data reveal the existence of a novel p53-dependent S-phase DNA maintenance checkpoint involving CHK-1

Working Out the Kinks: Creating Solutions to Assist Health Care Workers to Take Vital Signs Through Effective Cable Management

EPICS (Engineering Projects in Community Service) is a service-learning design program run through Purdue University. It strives to teach students design skills through providing solutions for individuals, communities, and organizations in the surrounding area while mirroring engineering industry standards. BME (Bio-medical Engineering) is a team within EPICS that strives to serve community partners through biomedical applications. Members of a health care team often spend valuable time organizing cables associated with machines used to take patients’ vital signs. Due to time constraints and the fast-paced work environment, these cables may be mismanaged and damaged. The BME team is working on a solution to ensure that relevant cords will be easily managed, damage will be minimized, and most importantly, health care professionals’ time will be saved

Estado y prioridades de conservación de los anfibios del departamento del Quindío, Colombia

stat i prioritats de conservació dels amfibis del departament del Quindío, Colòmbia En aquest article presentem una avaluació de l’estat i les prioritats de conservació dels amfibis al Quindío amb l’objectiu de proposar accions per conservar-los. Vam generar una llista d’espècies d’amfibis del departament, vam modelar la distribució potencial de les espècies amenaçades amb l’algoritme de màxima entropia de MaxEnt i en vam avaluar la representativitat en el Sistema Departamental d’Àrees Protegides del Quindío (SIDAPQ). A més a més, vam prioritzar les àrees per a la conservació dels amfibis amb l’algoritme ILV4 adjacency de ConsNet. Vam registrar 45 espècies d’amfibis, el 24,4% de les quals es troben incloses en alguna categoria d’amenaça de la Llista Vermella de la UICN. Els amfibis amenaçats van presentar una distribució i uns registres superiors al 50% dins del SIDAPQ. Les àrees prioritzades per assolir objectius de representativitat del 10, 20 i 30% de la distribució dels amfibis estan totalment fragmentades i només tenen el 30% de la distribució prioritzada al SIDAPQ. Davant d’aquest escenari, proposem una estratègia de conservació de caràcter paisatgístic que inclogui els agroecosistemes, tractant de mantenir-ne l’heterogeneïtat i eliminant-ne o disminuint-ne els factors d’amenaça.Conservation status and priorities of amphibians from the Quindío Department, Colombia We reviewed the conservation status and priorities for amphibians from the Quindío region of Colombia, with the purpose of proposing conservation actions. We modeled the potential distribution of threatened species using the maximum entropy algorithm in MaxEnt and evaluated representability in the Departmental System of Protected Areas for Quindío (Spanish acronym: SIDAPQ). We prioritized areas for amphibian conservation using the algorithm ILV4 adjacency in ConsNet. We recorded 45 species, 24.4% of which are included in threatened categories on the IUCN Red List. Over 50% of the distribution and records of the threatened amphibians occurred inside the SIDAPQ. Prioritized areas to achieve representation goals of 10, 20 and 30% of amphibian distribution are highly fragmented and have only approximately 30% of prioritized distribution in the SIDAPQ. Considering this scenario we propose a conservation strategy on the landscape level that includes agroecosystems, maintaining their heterogeneity and eliminating or mitigating threat factors.En este artículo presentamos una evaluación del estado y prioridades de conservación de los anfibios en el Quindío con el objetivo de proponer acciones para su conservación. Generamos una lista de especies de anfibios del departamento, modelamos la distribución potencial de las especies amenazadas con el algoritmo de máxima entropía de MaxEnt y evaluamos su representatividad en el Sistema Departamental de Áreas Protegidas del Quindío (SIDAPQ). Además, priorizamos las áreas para la conservación de los anfibios con el algoritmo ILV4 adjacency de ConsNet. Registramos 45 especies de anfibios, el 24,4% de las cuales se encuentran incluidas en alguna categoría de amenaza de la Lista Roja de la UICN. Los anfibios amenazados presentaron una distribución y unos registros superiores al 50% dentro del SIDAPQ. Las áreas priorizadas para alcanzar los objetivos de representatividad del 10, 20 y 30% de la distribución de los anfibios están altamente fragmentadas y sólo tienen el 30% de la distribución priorizada en el SIDAPQ. Ante este escenario, proponemos una estrategia de conservación de carácter paisajístico que incluya los agroecosistemas, tratando de mantener su heterogeneidad y eliminando o mitigando los factores de amenaza

Limits on the Dipole Moments of the τ\tau-Lepton via the Process $e^{+}e^{-}\to \tau^+ \tau^- \gamma in a Left-Right Symmetric Model

Limits on the anomalous magnetic moment and the electric dipole moment of the $\tau$ lepton are calculated through the reaction $e^{+}e^{-}\to \tau^+ \tau^- \gamma$ at the $Z_1$-pole and in the framework of a left-right symmetric model. The results are based on the recent data reported by the L3 Collaboration at CERN LEP. Due to the stringent limit of the model mixing angle $\phi$, the effect of this angle on the dipole moments is quite small.Comment: 15 pages, 3 figure