Probably Safe or Live

This paper presents a formal characterisation of safety and liveness properties \`a la Alpern and Schneider for fully probabilistic systems. As for the classical setting, it is established that any (probabilistic tree) property is equivalent to a conjunction of a safety and liveness property. A simple algorithm is provided to obtain such property decomposition for flat probabilistic CTL (PCTL). A safe fragment of PCTL is identified that provides a sound and complete characterisation of safety properties. For liveness properties, we provide two PCTL fragments, a sound and a complete one. We show that safety properties only have finite counterexamples, whereas liveness properties have none. We compare our characterisation for qualitative properties with the one for branching time properties by Manolios and Trefler, and present sound and complete PCTL fragments for characterising the notions of strong safety and absolute liveness coined by Sistla

Chronic traumatic encephalopathy in contact sports: A systematic review of all reported pathological cases

© 2015 Maroon et al. Chronic traumatic encephalopathy (CTE) is a neurodegenerative disease associated with head trauma. Although initially believed to affect only boxers, the at-risk population has expanded to encompass a much wider demographic, including American football players, hockey players, wrestlers, and military veterans. This expansion has garnered considerable media attention and public concern for the potential neurodegenerative effects of head trauma. The main aim of this systematic review is to give a complete overview of the common findings and risk factors for CTE as well as the status quo regarding the incidence and prevalence of CTE. This systematic review was performed using PubMed and MEDLINE and includes all neuropathologically confirmed cases of CTE in the medical literature to date, from the first published case in 1954 to August 1, 2013 (n = 153). The demographics, including the primary source of mTBI (mild Traumatic Brain Injury), age and cause of death, ApoE genotype, and history of substance abuse, when listed, were obtained from each case report. The demographics of American football players found to have CTE are also presented separately in order to highlight the most prevalent group of CTE cases reported in recent years. These 153 case reports of CTE represent the largest collection to date. We found that a history of mTBI was the only risk factor consistently associated with CTE. In addition, we found no relationships between CTE and age of death or abnormal ApoE allele. Suicide and the presence of premorbid dementia was not strongly associated with CTE. We conclude that the incidence of CTE remains unknown due to the lack of large, longitudinal studies. Furthermore, the neuropathological and clinical findings related to CTE overlap with many common neurodegenerative diseases. Our review reveals significant limitations of the current CTE case reporting and questions the widespread existence of CTE in contact sports

Assessing an Extension Plant Pest Diagnostic Center for Commercial Clients: Satisfaction, Savings, and Success

The descriptive-correlational study reported here sought to assess the effectiveness of the Extension Plant Pest Diagnostic Center (PPDC) for Tennessee\u27s commercial clients. These clients are served through one-on-one consultation regarding their individual plant or household and structural pest problems through submitted samples. The results from a mailed questionnaire showed that the majority of PPDC clients felt that the information was quick enough for their needs. While one-third of the 61 respondents stated that the PPDC recommendations saved them money, only one in 10 estimated the amount of money they saved. Suggestions for future PPDC evaluation studies are discussed

Property (RD) for Hecke pairs

As the first step towards developing noncommutative geometry over Hecke C*-algebras, we study property (RD) (Rapid Decay) for Hecke pairs. When the subgroup H in a Hecke pair (G,H) is finite, we show that the Hecke pair (G,H) has (RD) if and only if G has (RD). This provides us with a family of examples of Hecke pairs with property (RD). We also adapt Paul Jolissant's works in 1989 to the setting of Hecke C*-algebras and show that when a Hecke pair (G,H) has property (RD), the algebra of rapidly decreasing functions on the set of double cosets is closed under holomorphic functional calculus of the associated (reduced) Hecke C*-algebra. Hence they have the same K_0-groups.Comment: A short note added explaining other methods to prove that the subalgebra of rapidly decreasing functions is smooth. This is the final version as published. The published version is available at: springer.co

A Short Counterexample Property for Safety and Liveness Verification of Fault-tolerant Distributed Algorithms

Distributed algorithms have many mission-critical applications ranging from embedded systems and replicated databases to cloud computing. Due to asynchronous communication, process faults, or network failures, these algorithms are difficult to design and verify. Many algorithms achieve fault tolerance by using threshold guards that, for instance, ensure that a process waits until it has received an acknowledgment from a majority of its peers. Consequently, domain-specific languages for fault-tolerant distributed systems offer language support for threshold guards. We introduce an automated method for model checking of safety and liveness of threshold-guarded distributed algorithms in systems where the number of processes and the fraction of faulty processes are parameters. Our method is based on a short counterexample property: if a distributed algorithm violates a temporal specification (in a fragment of LTL), then there is a counterexample whose length is bounded and independent of the parameters. We prove this property by (i) characterizing executions depending on the structure of the temporal formula, and (ii) using commutativity of transitions to accelerate and shorten executions. We extended the ByMC toolset (Byzantine Model Checker) with our technique, and verified liveness and safety of 10 prominent fault-tolerant distributed algorithms, most of which were out of reach for existing techniques.Comment: 16 pages, 11 pages appendi

Analytic curves in algebraic varieties over number fields

We establish algebraicity criteria for formal germs of curves in algebraic varieties over number fields and apply them to derive a rationality criterion for formal germs of functions, which extends the classical rationality theorems of Borel-Dwork and P\'olya-Bertrandias valid over the projective line to arbitrary algebraic curves over a number field. The formulation and the proof of these criteria involve some basic notions in Arakelov geometry, combined with complex and rigid analytic geometry (notably, potential theory over complex and $p$-adic curves). We also discuss geometric analogues, pertaining to the algebraic geometry of projective surfaces, of these arithmetic criteria.Comment: 55 pages. To appear in "Algebra, Arithmetic, and Geometry: In Honor of Y.i. Manin", Y. Tschinkel & Yu. Manin editors, Birkh\"auser, 200

Interpolation of tracking data in a fluid environment

Interpolation of geolocation or Argos tracking data is a necessity for habitat use analyses of marine vertebrates. In a fluid marine environment, characterized by curvilinear structures, linearly interpolated track data are not realistic. Based on these two facts, we interpolated tracking data from albatrosses, penguins, boobies, sea lions, fur seals and elephant seals using six mathematical algorithms. Given their popularity in mathematical computing, we chose Bézier, hermite and cubic splines, in addition to a commonly used linear algorithm to interpolate data. Performance of interpolation methods was compared with different temporal resolutions representative of the less-precise geolocation and the more-precise Argos tracking techniques. Parameters from interpolated sub-sampled tracks were compared with those obtained from intact tracks. Average accuracy of the interpolated location was not affected by the interpolation method and was always within the precision of the tracking technique used. However, depending on the species tested, some curvilinear interpolation algorithms produced greater occurrences of more accurate locations, compared with the linear interpolation method. Total track lengths were consistently underestimated but were always more accurate using curvilinear interpolation than linear interpolation. Curvilinear algorithms are safe to use because accuracy, shape and length of the tracks are either not different or are slightly enhanced and because analyses always remain conservative. The choice of the curvilinear algorithm does not affect the resulting track dramatically so it should not preclude their use. We thus recommend using curvilinear interpolation techniques because of the more realistic fluid movements of animals. We also provide some guidelines for choosing an algorithm that is most likely to maximize track quality for different types of marine vertebrates

Thermal strategies of king penguins during prolonged fasting in water

Most animals experience periods of unfavourable conditions, challenging their daily energy balance. During breeding, king penguins fast voluntarily for up to 1.5 months in the colony, after which they replenish their energy stores at sea. However, at sea, birds might encounter periods of low foraging profitability, forcing them to draw from previously stored energy (e.g. subcutaneous fat). Accessing peripheral fat stores requires perfusion, increasing heat loss and thermoregulatory costs. Hence, how these birds balance the conflicting demands of nutritional needs and thermoregulation is unclear. We investigated the physiological responses of king penguins to fasting in cold water by: (1) monitoring tissue temperatures, as a proxy of tissue perfusion, at four distinct sites (deep and peripheral); and (2) recording their oxygen consumption rate while birds floated inside a water tank. Despite frequent oscillations, temperatures of all tissues often reached near-normothermic levels, indicating that birds maintained perfusion to peripheral tissues throughout their fasting period in water. The oxygen consumption rate of birds increased with fasting duration in water, while it was also higher when the flank tissue was warmer, indicating greater perfusion. Hence, fasting king penguins in water maintained peripheral perfusion, despite the associated greater heat loss and, therefore, thermoregulatory costs, probably to access subcutaneous fat stores. Hence, the observed normothermia in peripheral tissues of king penguins at sea, upon completion of a foraging bout, is likely explained by their nutritional needs: depositing free fatty acids (FFA) in subcutaneous tissues after profitable foraging or mobilizing FFA to fuel metabolism when foraging success was insufficient

On Charge-3 Cyclic Monopoles

We determine the spectral curve of charge 3 BPS su(2) monopoles with C_3 cyclic symmetry. The symmetry means that the genus 4 spectral curve covers a (Toda) spectral curve of genus 2. A well adapted homology basis is presented enabling the theta functions and monopole data of the genus 4 curve to be given in terms of genus 2 data. The Richelot correspondence, a generalization of the arithmetic mean, is used to solve for this genus 2 curve. Results of other approaches are compared.Comment: 34 pages, 16 figures. Revision: Abstract added and a few small change

KMS states and conformal measures

From a non-constant holomorphic map on a connected Riemann surface we construct an 'etale second countable locally compact Hausdorff groupoid whose associated groupoid C*-algebra admits a one-parameter group of automorphisms with the property that its KMS states corresponds to conformal measures in the sense of Sullivan. In this way certain quadratic polynomials give rise to quantum statistical models with a phase transition arising from spontaneous symmetry breaking.Comment: The last section revised. This version will appear in Comm. Math. Phy