Intermittent random walks for an optimal search strategy: One-dimensional case

We study the search kinetics of an immobile target by a concentration of randomly moving searchers. The object of the study is to optimize the probability of detection within the constraints of our model. The target is hidden on a one-dimensional lattice in the sense that searchers have no a priori information about where it is, and may detect it only upon encounter. The searchers perform random walks in discrete time n=0,1,2, ..., N, where N is the maximal time the search process is allowed to run. With probability \alpha the searchers step on a nearest-neighbour, and with probability (1-\alpha) they leave the lattice and stay off until they land back on the lattice at a fixed distance L away from the departure point. The random walk is thus intermittent. We calculate the probability P_N that the target remains undetected up to the maximal search time N, and seek to minimize this probability. We find that P_N is a non-monotonic function of \alpha, and show that there is an optimal choice \alpha_{opt}(N) of \alpha well within the intermittent regime, 0 < \alpha_{opt}(N) < 1, whereby P_N can be orders of magnitude smaller compared to the "pure" random walk cases \alpha =0 and \alpha = 1.Comment: 19 pages, 5 figures; submitted to Journal of Physics: Condensed Matter; special issue on Chemical Kinetics Beyond the Textbook: Fluctuations, Many-Particle Effects and Anomalous Dynamics, eds. K.Lindenberg, G.Oshanin and M.Tachiy

Guidance on Design and Construction of the Built Environment Against Wildland Urban Interface Fire Hazard: A Review

Wildland-Urban Interface (WUI) fires, a worldwide problem, are gaining more importance over time due to climate change and increased urbanization in WUI areas. Some jurisdictions have provided standards, codes and guidelines, which may greatly help planning, prevention and protection against wildfires. This work presents a wide systematic review of standards, codes and guidelines for the design and construction of the built environment against WUI fire hazard from North American, European, Oceanic countries, alongside with trans-national codes. The main information reviewed includes: the definition of WUI hazards, risk areas and related severity classes, the influence of land and environmental factors, the requirements for building materials, constructions, utilities, fire protection measures and road access. Some common threads among the documents reviewed have been highlighted. They include similar attempts at: (a) defining WUI risk areas and severity classes, (b) considering land factors including the defensible space (also known as ignition zones), (c) prescribing requirements for buildings and access. The main gaps highlighted in the existing standards/guidelines include lacks of detailed and widespread requirements for resources, fire protection measures, and lacks of taking into account environmental factors in detail. The main design and construction principles contained in the reviewed documents are largely based on previous research and/or good practices. Hence, the main contributions of this paper consist in: (a) systematically disseminate these guidance concepts, (b) setting a potential basis for the development of standards/guidelines in other jurisdictions lacking dedicated WUI fire design guidance, (c) highlighting gaps in existing standards/guidelines to be addressed by current and future research

Is loss in femorotibial cartilage thickness related to severity of contra-lateral radiographic knee osteoarthritis? – Longitudinal data from the Osteoarthritis Initiative

SummaryObjectiveAnti-catabolic disease modifying drugs (DMOADs) aim to reduce cartilage loss in knee osteoarthritis (KOA). Testing such drugs in clinical trials requires sufficient rates of loss in the study participants to occur, preferably at a mild disease stage where cartilage can be preserved. Here we analyze a “progression” model in mild radiographic KOA (RKOA), based on contra-lateral radiographic status.MethodsWe studied 837 participants (62.4 ± 9 yrs; 30 ± 4.9 kg/m²; 61.8% women) from the Osteoarthritis Initiative (OAI) with mild to moderate RKOA (Kellgren Lawrence grade [KLG] 2–3) and with/without Osteoarthritis Research Society International (OARSI) atlas radiographic joint space narrowing (JSN). These had quantitative measurements of subregional femorotibial cartilage thickness from magnetic resonance imaging (MRI) at baseline and 1-year follow-up. They were stratified by contra-lateral knee status: no (KLG 0/1), definite (KLG2) and moderate RKOA (KLG 3/4).ResultsKLG2 knees with JSN and moderate contra-lateral RKOA had (P = 0.008) greater maximum subregional cartilage loss −220 μm [95% confidence interval (CI) −255, −184 μm] than those without contra-lateral RKOA −164 μm [−187, −140 μm]. Their rate of subregional cartilage loss was similar and not significantly different (P = 0.61) to that in KLG 3 knees without contra-lateral RKOA (−232 μm; [−266; −198 μm]). The effect of contra-lateral RKOA status was less in KLG2 knees without JSN, and in KLG3 knees.ConclusionKLG2 knees with JSN and moderate contra-lateral RKOA, display relatively high rates of subregional femorotibial cartilage loss, despite being at a relatively mild stage of RKOA. They may therefore provide a unique opportunity for recruitment in clinical trials that explore the efficacy of anti-catabolic DMOADs on structural progression

Massless particles on supergroups and AdS3 x S3 supergravity

Firstly, we study the state space of a massless particle on a supergroup with a reparameterization invariant action. After gauge fixing the reparameterization invariance, we compute the physical state space through the BRST cohomology and show that the quadratic Casimir Hamiltonian becomes diagonalizable in cohomology. We illustrate the general mechanism in detail in the example of a supergroup target GL(1|1). The space of physical states remains an indecomposable infinite dimensional representation of the space-time supersymmetry algebra. Secondly, we show how the full string BRST cohomology in the particle limit of string theory on AdS3 x S3 renders the quadratic Casimir diagonalizable, and reduces the Hilbert space to finite dimensional representations of the space-time supersymmetry algebra (after analytic continuation). Our analysis provides an efficient way to calculate the Kaluza-Klein spectrum for supergravity on AdS3 x S3. It may also be a step towards the identification of an interesting and simpler subsector of logarithmic supergroup conformal field theories, relevant to string theory.Comment: 16 pages, 10 figure