Extending JumpProcess.jl for fast point process simulation with time-varying intensities

Point processes model the occurrence of a countable number of random points over some support. They can model diverse phenomena, such as chemical reactions, stock market transactions and social interactions. We show that JumpProcesses.jl is a fast, general-purpose library for simulating point processes. JumpProcesses.jl was first developed for simulating jump processes via stochastic simulation algorithms (SSAs) (including Doob's method, Gillespie's methods, and Kinetic Monte Carlo methods). Historically, jump processes have been developed in the context of dynamical systems to describe dynamics with discrete jumps. In contrast, the development of point processes has been more focused on describing the occurrence of random events. In this paper, we bridge the gap between the treatment of point and jump process simulation. The algorithms previously included in JumpProcesses.jl can be mapped to three general methods developed in statistics for simulating evolutionary point processes. Our comparative exercise revealed that the library initially lacked an efficient algorithm for simulating processes with variable intensity rates. We, therefore, extended JumpProcesses.jl with a new simulation algorithm, Coevolve, that enables the rapid simulation of processes with locally-bounded variable intensity rates. It is now possible to efficiently simulate any point process on the real line with a non-negative, left-continuous, history-adapted and locally bounded intensity rate coupled or not with differential equations. This extension significantly improves the computational performance of JumpProcesses.jl when simulating such processes, enabling it to become one of the few readily available, fast, general-purpose libraries for simulating evolutionary point processes

Handgrip strength predicts persistent walking recovery after hip fracture surgery

Background In older people, hip fractures often lead to disability and death. We evaluated handgrip strength, an objective measure of physical function for bedridden patients, as a predictor of walking recovery in the year after fracture surgery. Methods This multicenter prospective cohort study included 504 patients, aged 70 years or more, who were admitted to the hospital for hip fracture surgery and were formerly able to walk independently. A multidimensional geriatric evaluation that included a physical examination, Short Portable Mental Status Questionnaire, Geriatric Depression Scale, Charlson Index, Basic Activities of Daily Living, and grip strength was administered at the time of admission. Follow-ups were performed every 3 months for 1 year after surgery to assess functional status and survival. The walking recovery probability was evaluated using multivariable logistic regression models. Results The mean age of the participants was 85.3 ± 5.5 years, and 76.1% of the participants were women. The mean grip strength was greater in men (β: 6.6 ± 0.62, P <.001) and was directly related to the Short Portable Mental Status Questionnaire results (P <.001), Basic Activities of Daily Living results (P <.001), serum vitamin D levels (P =.03), and time before surgery (P <.001), whereas it was inversely related to age (P <.001), Geriatric Depression Scale score (P <.001), and Charlson Index (P <.001). After adjusting for confounders, the grip strength was directly associated with the probability of both incident and persistent walking recovery (odds ratio highest tertile vs lowest tertile, 2.84, confidence interval, 1.76-4.59 and 2.79, confidence interval, 1.35-5.79, respectively). Conclusions In older patients with hip fractures, early grip strength evaluation might provide important prognostic information regarding the patient's future functional trajectory. © 2013 Elsevier Inc. All rights reserved

Setting and analysis of the multi-configuration time-dependent Hartree-Fock equations

In this paper we motivate, formulate and analyze the Multi-Configuration Time-Dependent Hartree-Fock (MCTDHF) equations for molecular systems under Coulomb interaction. They consist in approximating the N-particle Schrodinger wavefunction by a (time-dependent) linear combination of (time-dependent) Slater determinants. The equations of motion express as a system of ordinary differential equations for the expansion coefficients coupled to nonlinear Schrodinger-type equations for mono-electronic wavefunctions. The invertibility of the one-body density matrix (full-rank hypothesis) plays a crucial role in the analysis. Under the full-rank assumption a fiber bundle structure shows up and produces unitary equivalence between convenient representations of the equations. We discuss and establish existence and uniqueness of maximal solutions to the Cauchy problem in the energy space as long as the density matrix is not singular. A sufficient condition in terms of the energy of the initial data ensuring the global-in-time invertibility is provided (first result in this direction). Regularizing the density matrix breaks down energy conservation, however a global well-posedness for this system in L^2 is obtained with Strichartz estimates. Eventually solutions to this regularized system are shown to converge to the original one on the time interval when the density matrix is invertible.Comment: 48 pages, 1 figur

Moths Behaving like Butterflies. Evolutionary Loss of Long Range Attractant Pheromones in Castniid Moths: A Paysandisia archon Model

Background: In the course of evolution butterflies and moths developed two different reproductive behaviors. Whereas butterflies rely on visual stimuli for mate location, moths use the"female calling plus male seduction" system, in which females release long-range sex pheromones to attract conspecific males. There are few exceptions from this pattern but in all cases known female moths possess sex pheromone glands which apparently have been lost in female butterflies. In the day-flying moth family Castniidae ("butterfly-moths"), which includes some important crop pests, no pheromones have been found so far. Methodology/Principal Findings: Using a multidisciplinary approach we described the steps involved in the courtship of P. archon, showing that visual cues are the only ones used for mate location; showed that the morphology and fine structure of the antennae of this moth are strikingly similar to those of butterflies, with male sensilla apparently not suited to detect female-released long range pheromones; showed that its females lack pheromone-producing glands, and identified three compounds as putative male sex pheromone (MSP) components of P. archon, released from the proximal halves of male forewings and hindwings. Conclusions/Significance: This study provides evidence for the first time in Lepidoptera that females of a moth do not produce any pheromone to attract males, and that mate location is achieved only visually by patrolling males, which may release a pheromone at short distance, putatively a mixture of Z,E-farnesal, E,E-farnesal, and (E,Z)-2,13-octadecadienol. The outlined behavior, long thought to be unique to butterflies, is likely to be widespread in Castniidae implying a novel, unparalleled butterfly-like reproductive behavior in moths. This will also have practical implications in applied entomology since it signifies that the monitoring/control of castniid pests should not be based on the use of female-produced pheromones, as it is usually done in many moths

Strong compactness in Sobolev spaces

We prove a strong compactness criterion in Sobolev spaces: given a sequence $(u_n)$ in W_{\textrm{loc}}^{1,p}(\Rd), converging in $L_{\textrm{loc}}^{p}$ to a map u\in W_{\textrm{loc}}^{1,p}(\Rd) and such that |\n u_n | \le f almost everywhere, for some f\in L_{\textrm{loc}}^{p}(\Rd), we provide a necessary and sufficient condition under which $(u_n)$ converges strongly to $u$ in W_{\textrm{loc}}^{1,p}(\Rd). In addition we prove a pointwise version of the criterion, according to which, given $(u_n)$ and $u$ as above, but with no boundedness assumptions on the sequence of gradients, we have \n u_n \to \n u pointwise almost everywhere

A version of Olech's lemma in a problem of the calculus of variations

This paper studies the solutions of the minimum problem for a functional of the gradient under linear boundary conditions. A necessary and sufficient condition, based on the facial structure of the epigraph of the integrand, is provided for the continuous dependence of the solutions on boundary data

A fungal metabolite as the male wing gland pheromone of the bumble-bee wax moth, Aphomia sociella L.

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