Analytical form of the Probability Density Function of travel times in rectangular zone with Tchebyshev’s metric

Geometrical dependencies are being researched for analytical representation of the probability density function (pdf) for the travel time between a random, and a known or another random point in Tchebyshev’s metric. In the most popular case - a rectangular area of service - the pdf of this random variable depends directly on the position of the server. Two approaches have been introduced for the exact analytical calculation of the pdf: Ad-hoc approach – useful for a ‘manual’ solving of a specific case; by superposition – an algorithmic approach for the general case. The main concept of each approach is explained, and a short comparison is done to prove the faithfulness.

Sizing up your enemy: individual predation vulnerability predicts migratory probability

Partial migration, in which a fraction of a population migrate and the rest remain resident, occurs in an extensive range of species and can have powerful ecological consequences. The question of what drives differences in individual migratory tendency is a contentious one. It has been shown that the timing of partial migration is based upon a trade-off between seasonal fluctuations in predation risk and growth potential. Phenotypic variation in either individual predation risk or growth potential should thus mediate the strength of the trade-off and ultimately predict patterns of partial migration at the individual level (i.e. which individuals migrate and which remain resident). We provide cross-population empirical support for the importance of one component of this model—individual predation risk—in predicting partial migration in wild populations of bream Abramis brama, a freshwater fish. Smaller, high-risk individuals migrate with a higher probability than larger, low-risk individuals, and we suggest that predation risk maintains size-dependent partial migration in this system.

Safety and Feasibility of a Diagnostic Algorithm Combining Clinical Probability, d-Dimer Testing, and Ultrasonography for Suspected Upper Extremity Deep Venous Thrombosis: A Prospective Management Study.

BACKGROUND Although well-established for suspected lower limb deep venous thrombosis, an algorithm combining a clinical decision score, d-dimer testing, and ultrasonography has not been evaluated for suspected upper extremity deep venous thrombosis (UEDVT). OBJECTIVE To assess the safety and feasibility of a new diagnostic algorithm in patients with clinically suspected UEDVT. DESIGN Diagnostic management study. (ClinicalTrials.gov: NCT01324037) SETTING: 16 hospitals in Europe and the United States. PATIENTS 406 inpatients and outpatients with suspected UEDVT. MEASUREMENTS The algorithm consisted of the sequential application of a clinical decision score, d-dimer testing, and ultrasonography. Patients were first categorized as likely or unlikely to have UEDVT; in those with an unlikely score and normal d-dimer levels, UEDVT was excluded. All other patients had (repeated) compression ultrasonography. The primary outcome was the 3-month incidence of symptomatic UEDVT and pulmonary embolism in patients with a normal diagnostic work-up. RESULTS The algorithm was feasible and completed in 390 of the 406 patients (96%). In 87 patients (21%), an unlikely score combined with normal d-dimer levels excluded UEDVT. Superficial venous thrombosis and UEDVT were diagnosed in 54 (13%) and 103 (25%) patients, respectively. All 249 patients with a normal diagnostic work-up, including those with protocol violations (n = 16), were followed for 3 months. One patient developed UEDVT during follow-up, for an overall failure rate of 0.4% (95% CI, 0.0% to 2.2%). LIMITATIONS This study was not powered to show the safety of the substrategies. d-Dimer testing was done locally. CONCLUSION The combination of a clinical decision score, d-dimer testing, and ultrasonography can safely and effectively exclude UEDVT. If confirmed by other studies, this algorithm has potential as a standard approach to suspected UEDVT. PRIMARY FUNDING SOURCE None.

Bounds for the probability generating functional of a Gibbs point process

We derive explicit lower and upper bounds for the probability generating functional of a stationary locally stable Gibbs point process, which can be applied to summary statistics such as the F function. For pairwise interaction processes we obtain further estimates for the G and K functions, the intensity, and higher-order correlation functions. The proof of the main result is based on Stein's method for Poisson point process approximation.

Uniqueness of the Embedding Continuous Convolution Semigroup of a Gaussian Probability Measure on the Affine Group and an Application in Mathematical Finance

Let {μ(i)t}t≥0 ( i=1,2 ) be continuous convolution semigroups (c.c.s.) of probability measures on Aff(1) (the affine group on the real line). Suppose that μ(1)1=μ(2)1 . Assume furthermore that {μ(1)t}t≥0 is a Gaussian c.c.s. (in the sense that its generating distribution is a sum of a primitive distribution and a second-order differential operator). Then μ(1)t=μ(2)t for all t≥0 . We end up with a possible application in mathematical finance.

Importance sampling approximations to various probabilities of ruin of spectrally negative Lévy risk processes

This article provides importance sampling algorithms for computing the probabilities of various types ruin of spectrally negative Lévy risk processes, which are ruin over the infinite time horizon, ruin within a finite time horizon and ruin past a finite time horizon. For the special case of the compound Poisson process perturbed by diffusion, algorithms for computing probabilities of ruins by creeping (i.e. induced by the diffusion term) and by jumping (i.e. by a claim amount) are provided. It is shown that these algorithms have either bounded relative error or logarithmic efficiency, as t,x→∞t,x→∞, where t>0t>0 is the time horizon and x>0x>0 is the starting point of the risk process, with y=t/xy=t/x held constant and assumed either below or above a certain constant.

Diffusion-weighted magnetic resonance imaging detects significant prostate cancer with high probability

PURPOSE We prospectively assessed the diagnostic accuracy of diffusion-weighted magnetic resonance imaging for detecting significant prostate cancer. MATERIALS AND METHODS We performed a prospective study of 111 consecutive men with prostate and/or bladder cancer who underwent 3 Tesla diffusion-weighted magnetic resonance imaging of the pelvis without an endorectal coil before radical prostatectomy (78) or cystoprostatectomy (33). Three independent readers blinded to clinical and pathological data assigned a prostate cancer suspicion grade based on qualitative imaging analysis. Final pathology results of prostates with and without cancer served as the reference standard. Primary outcomes were the sensitivity and specificity of diffusion-weighted magnetic resonance imaging for detecting significant prostate cancer with significance defined as a largest diameter of the index lesion of 1 cm or greater, extraprostatic extension, or Gleason score 7 or greater on final pathology assessment. Secondary outcomes were interreader agreement assessed by the Fleiss κ coefficient and image reading time. RESULTS Of the 111 patients 93 had prostate cancer, which was significant in 80 and insignificant in 13, and 18 had no prostate cancer on final pathology results. The sensitivity and specificity of diffusion-weighted magnetic resonance imaging for detecting significant PCa was 89% to 91% and 77% to 81%, respectively, for the 3 readers. Interreader agreement was good (Fleiss κ 0.65 to 0.74). Median reading time was between 13 and 18 minutes. CONCLUSIONS Diffusion-weighted magnetic resonance imaging (3 Tesla) is a noninvasive technique that allows for the detection of significant prostate cancer with high probability without contrast medium or an endorectal coil, and with good interreader agreement and a short reading time. This technique should be further evaluated as a tool to stratify patients with prostate cancer for individualized treatment options.

Voting Power and Probability

Voting power is commonly measured using a probability. But what kind of probability is this? Is it a degree of belief or an objective chance or some other sort of probability? The aim of this paper is to answer this question. The answer depends on the use to which a measure of voting power is put. Some objectivist interpretations of probabilities are appropriate when we employ such a measure for descriptive purposes. By contrast, when voting power is used to normatively assess voting rules, the probabilities are best understood as classical probabilities, which count possibilities. This is so because, from a normative stance, voting power is most plausibly taken to concern rights and thus possibilities. The classical interpretation also underwrites the use of the Bernoulli model upon which the Penrose/Banzhaf measure is based.