Fast and Accurate Computation of Orbital Collision Probability for Short-Term Encounters

International audienceThis article provides a new method for computing the probability of collision between two spherical space objects involved in a short-term encounter under Gaussian-distributed uncertainty. In this model of conjunction, classical assumptions reduce the probability of collision to the integral of a two-dimensional Gaussian probability density function over a disk. The computational method presented here is based on an analytic expression for the integral, derived by use of Laplace transform and D-finite functions properties. The formula has the form of a product between an exponential term and a convergent power series with positive coefficients. Analytic bounds on the truncation error are also derived and are used to obtain a very accurate algorithm. Another contribution is the derivation of analytic bounds on the probability of collision itself, allowing for a very fast and - in most cases - very precise evaluation of the risk. The only other analytical method of the literature - based on an approximation - is shown to be a special case of the new formula. A numerical study illustrates the efficiency of the proposed algorithms on a broad variety of examples and favorably compares the approach to the other methods of the literature

The Tychonoff uniqueness theorem for the G-heat equation

In this paper, we obtain the Tychonoff uniqueness theorem for the G-heat equation

Uniqueness of nontrivially complete monotonicity for a class of functions involving polygamma functions

For $m,n\in\mathbb{N}$, let $f_{m,n}(x)=\bigr[\psi^{(m)}(x)\bigl]^2+\psi^{(n)}(x)$ on $(0,\infty)$. In the present paper, we prove using two methods that, among all $f_{m,n}(x)$ for $m,n\in\mathbb{N}$, only $f_{1,2}(x)$ is nontrivially completely monotonic on $(0,\infty)$. Accurately, the functions $f_{1,2}(x)$ and $f_{m,2n-1}(x)$ are completely monotonic on $(0,\infty)$, but the functions $f_{m,2n}(x)$ for $(m,n)\ne(1,1)$ are not monotonic and does not keep the same sign on $(0,\infty)$.Comment: 9 page

Vertical migration, feeding and colouration in the mesopelagic shrimp Sergestes arcticus

Intraspecific variation in vertical distribution, timing of vertical migration, and colouration of the mesopelagic shrimp Sergestes arcticus were studied in the >400 m deep part of Masfjorden, Norway. Very few individuals were caught in the upper strata during daytime, and larger individuals occurred deeper during the day than smaller ones. Vertical migration was prominent and no overall trend of increasing length with depth was found at night. Small individuals arrived in the upper layers earlier than larger ones. Animal colouration assessed by digital photography revealed significant variance in individual redness. Depth of capture was the most important factor explaining colouration, with increasing degree of redness with depth. Assessing the gut fullness of the transparent shrimps provided a rapid way of estimating feeding activity and showed that feeding took place mainly at night

The Measure of the Orthogonal Polynomials Related to Fibonacci Chains: The Periodic Case

The spectral measure for the two families of orthogonal polynomial systems related to periodic chains with N-particle elementary unit and nearest neighbour harmonic interaction is computed using two different methods. The interest is in the orthogonal polynomials related to Fibonacci chains in the periodic approximation. The relation of the measure to appropriately defined Green's functions is established.Comment: 19 pages, TeX, 3 scanned figures, uuencoded file, original figures on request, some misprints corrected, tbp: J. Phys.

Biogeographic variation in the microbiome of the ecologically important sponge, Carteriospongia foliascens

Sponges are well known for hosting dense and diverse microbial communities, but how these associations vary with biogeography and environment is less clear. Here we compared the microbiome of an ecologically important sponge species, Carteriospongia foliascens, over a large geographic area and identified environmental factors likely responsible for driving microbial community differences between inshore and offshore locations using co-occurrence networks (NWs). The microbiome of C. foliascens exhibited exceptionally high microbial richness, with more than 9,000 OTUs identified at 97% sequence similarity. A large biogeographic signal was evident at the OTU level despite similar phyla level diversity being observed across all geographic locations. The C. foliascens bacterial community was primarily comprised of Gammaproteobacteria (34.2% ± 3.4%) and Cyanobacteria (32.2% ± 3.5%), with lower abundances of Alphaproteobacteria, Bacteroidetes, unidentified Proteobacteria, Actinobacteria, Acidobacteria and Deltaproteobacteria. Co-occurrence NWs revealed a consistent increase in the proportion of Cyanobacteria over Bacteroidetes between turbid inshore and oligotrophic offshore locations, suggesting that the specialist microbiome of C. foliascens is driven by environmental factors

An exact analytical solution for generalized growth models driven by a Markovian dichotomic noise

Logistic growth models are recurrent in biology, epidemiology, market models, and neural and social networks. They find important applications in many other fields including laser modelling. In numerous realistic cases the growth rate undergoes stochastic fluctuations and we consider a growth model with a stochastic growth rate modelled via an asymmetric Markovian dichotomic noise. We find an exact analytical solution for the probability distribution providing a powerful tool with applications ranging from biology to astrophysics and laser physics

Predictors of in-hospital mortality and complications in very elderly patients undergoing emergency surgery

INTRODUCTION: With the increasing aging population demographics and life expectancies the number of very elderly patients (age ≥ 80) undergoing emergency surgery is expected to rise. This investigation examines the outcomes in very elderly patients undergoing emergency general surgery, including predictors of in-hospital mortality and morbidity. METHODS: A retrospective study of patients aged 80 and above undergoing emergency surgery between 2008 and 2010 at a tertiary care facility in Canada was conducted. Demographics, comorbidities, surgical indications, and perioperative risk assessment data were collected. Outcomes included length of hospitalization, discharge destination, and in-hospital mortality and morbidity. Multivariable logistic regression was used to identify predictors of in-hospital mortality and complications. RESULTS: Of the 170 patient admissions, the mean age was 84 years and the in-hospital mortality rate was 14.7%. Comorbidities were present in 91% of this older patient population. Over 60% of the patients required further services or alternate level of care on discharge. American Society of Anesthesiologist Physical Status (ASA) Classification (OR 5.30, 95% CI 1.774-15.817, p = 0.003) and the development of an in-hospital complications (OR 2.51, 95% CI 1.210-5.187, p = 0.013) were independent predictors of postoperative mortality. Chronological age or number of comorbidities was not predictive of surgical outcome. CONCLUSIONS: Mortality, complication rates and post-discharge care requirements were high in very elderly patients undergoing emergency general surgery. Advanced age and medical comorbidities alone should not be the limiting factors for surgical referral or treatment. This study illustrates the importance of preventing an in-hospital complication in this very vulnerable population. ASA class is a robust tool which is predictive of mortality in the very elderly population and can be used to guide patient and family counseling in the emergency setting

Loop Representations for 2+1 Gravity on a Torus

We study the loop representation of the quantum theory for 2+1 dimensional general relativity on a manifold, $M = {\cal T}^2 \times {\cal R}$, where ${\cal T}^2$ is the torus, and compare it with the connection representation for this system. In particular, we look at the loop transform in the part of the phase space where the holonomies are boosts and study its kernel. This kernel is dense in the connection representation and the transform is not continuous with respect to the natural topologies, even in its domain of definition. Nonetheless, loop representations isomorphic to the connection representation corresponding to this part of the phase space can still be constructed if due care is taken. We present this construction but note that certain ambiguities remain; in particular, functions of loops cannot be uniquely associated with functions of connections.Comment: 24 journal or 52 preprint pages, revtex, SU-GP-93/3-

Some Orthogonal Polynomials Arising from Coherent States

We explore in this paper some orthogonal polynomials which are naturally associated to certain families of coherent states, often referred to as nonlinear coherent states in the quantum optics literature. Some examples turn out to be known orthogonal polynomials but in many cases we encounter a general class of new orthogonal polynomials for which we establish several qualitative results.Comment: 21 page