An Integro-Differential Equation of the Fractional Form: Cauchy Problem and Solution

Producción CientíficaWe solve the Cauchy problem defined by the fractional partial differential equation [∂tt − κD]u = 0, with D the pseudo-differential Riesz operator of first order, and certain initial conditions. The solution of the Cauchy problem resulting from the substitution of the Gaussian pulse u(x, 0) by the Dirac delta distribution ϕ(x) = μδ(x) is obtained as corollary.MINECO grant MTM2014-57129-C2-1-P

Envisioning a Marine Biodiversity Observation Network

Humans depend on diverse ocean ecosystems for food, jobs, and sustained well-being, yet many stressors threaten marine life. Extensive research has demonstrated that maintaining biodiversity promotes ocean health and service provision; therefore, monitoring the status and trends of marine biodiversity is important for effective ecosystem management. However, there is no systematic sustained program for evaluating ocean biodiversity. Coordinating existing monitoring and building a proactive marine biodiversity observation network will support efficient, economical resource management and conservation and should be a high priority. A synthesis of expert opinions suggests that, to be most effective, a marine biodiversity observation network should integrate biological levels, from genes to habitats; link biodiversity observations to abiotic environmental variables; site projects to incorporate environmental forcing and biogeography; and monitor adaptively to address emerging issues. We summarize examples illustrating how to leverage existing data and infrastructure to meet these goals

Sporadic implementation of UK familial mammographic surveillance guidelines 15 years after original publication

This work is published under the standard license to publish agreement. After 12 months the work will become freely available and the license terms will switch to a Creative Commons Attribution 4.0 International (CC BY 4.0).: D.G.E. is supported by the NIHR Manchester Biomedical Research centre (ISBRC-1215-20007). M.T. is supported by the NIHR Cambridge Biomedical Research centr

Discovery of Design Methodologies

In this paper we present an AI-based approach for the discovery of design methodologies for multi-disciplinary design situations. The approach is based on simulating the design process using a multi-agent system that mimics the behavior of the design team. The system activates the pieces of design knowledge when they become applicable. The use of knowledge by agents is recorded by tracing the steps that the agents have taken during a design project. Many traces are generated by solving a large number of design projects that differ in their requirements. A set of design methodologies is constructed by using clustering techniques to generalize the traces. These methodologies can be used to guide design teams through design projects

Review of Inverse Laplace Transform Algorithms for Laplace-Space Numerical Approaches

A boundary element method (BEM) simulation is used to compare the efficiency of numerical inverse Laplace transform strategies, considering general requirements of Laplace-space numerical approaches. The two-dimensional BEM solution is used to solve the Laplace-transformed diffusion equation, producing a time-domain solution after a numerical Laplace transform inversion. Motivated by the needs of numerical methods posed in Laplace-transformed space, we compare five inverse Laplace transform algorithms and discuss implementation techniques to minimize the number of Laplace-space function evaluations. We investigate the ability to calculate a sequence of time domain values using the fewest Laplace-space model evaluations. We find Fourier-series based inversion algorithms work for common time behaviors, are the most robust with respect to free parameters, and allow for straightforward image function evaluation re-use across at least a log cycle of time

A stable pattern of EEG spectral coherence distinguishes children with autism from neuro-typical controls - a large case control study

<p>Abstract</p> <p>Background</p> <p>The autism rate has recently increased to 1 in 100 children. Genetic studies demonstrate poorly understood complexity. Environmental factors apparently also play a role. Magnetic resonance imaging (MRI) studies demonstrate increased brain sizes and altered connectivity. Electroencephalogram (EEG) coherence studies confirm connectivity changes. However, genetic-, MRI- and/or EEG-based diagnostic tests are not yet available. The varied study results likely reflect methodological and population differences, small samples and, for EEG, lack of attention to group-specific artifact.</p> <p>Methods</p> <p>Of the 1,304 subjects who participated in this study, with ages ranging from 1 to 18 years old and assessed with comparable EEG studies, 463 children were diagnosed with autism spectrum disorder (ASD); 571 children were neuro-typical controls (C). After artifact management, principal components analysis (PCA) identified EEG spectral coherence factors with corresponding loading patterns. The 2- to 12-year-old subsample consisted of 430 ASD- and 554 C-group subjects (n = 984). Discriminant function analysis (DFA) determined the spectral coherence factors' discrimination success for the two groups. Loading patterns on the DFA-selected coherence factors described ASD-specific coherence differences when compared to controls.</p> <p>Results</p> <p>Total sample PCA of coherence data identified 40 factors which explained 50.8% of the total population variance. For the 2- to 12-year-olds, the 40 factors showed highly significant group differences (<it>P </it>< 0.0001). Ten randomly generated split half replications demonstrated high-average classification success (C, 88.5%; ASD, 86.0%). Still higher success was obtained in the more restricted age sub-samples using the jackknifing technique: 2- to 4-year-olds (C, 90.6%; ASD, 98.1%); 4- to 6-year-olds (C, 90.9%; ASD 99.1%); and 6- to 12-year-olds (C, 98.7%; ASD, 93.9%). Coherence loadings demonstrated reduced short-distance and reduced, as well as increased, long-distance coherences for the ASD-groups, when compared to the controls. Average spectral loading per factor was wide (10.1 Hz).</p> <p>Conclusions</p> <p>Classification success suggests a stable coherence loading pattern that differentiates ASD- from C-group subjects. This might constitute an EEG coherence-based phenotype of childhood autism. The predominantly reduced short-distance coherences may indicate poor local network function. The increased long-distance coherences may represent compensatory processes or reduced neural pruning. The wide average spectral range of factor loadings may suggest over-damped neural networks.</p

Cost-Effectiveness of Gene-Specific Prevention Strategies for Ovarian and Breast Cancer.

IMPORTANCE: Pathogenic variants (PVs) in BRCA1, BRCA2, PALB2, RAD51C, RAD51D, and BRIP1 cancer susceptibility genes (CSGs) confer an increased ovarian cancer (OC) risk, with BRCA1, BRCA2, PALB2, RAD51C, and RAD51D PVs also conferring an elevated breast cancer (BC) risk. Risk-reducing surgery, medical prevention, and BC surveillance offer the opportunity to prevent cancers and deaths, but their cost-effectiveness for individual CSGs remains poorly addressed. OBJECTIVE: To estimate the cost-effectiveness of prevention strategies for OC and BC among individuals carrying PVs in the previously listed CSGs. DESIGN, SETTING, AND PARTICIPANTS: In this economic evaluation, a decision-analytic Markov model evaluated the cost-effectiveness of risk-reducing salpingo-oophorectomy (RRSO) and, where relevant, risk-reducing mastectomy (RRM) compared with nonsurgical interventions (including BC surveillance and medical prevention for increased BC risk) from December 1, 2022, to August 31, 2023. The analysis took a UK payer perspective with a lifetime horizon. The simulated cohort consisted of women aged 30 years who carried BRCA1, BRCA2, PALB2, RAD51C, RAD51D, or BRIP1 PVs. Appropriate sensitivity and scenario analyses were performed. EXPOSURES: CSG-specific interventions, including RRSO at age 35 to 50 years with or without BC surveillance and medical prevention (ie, tamoxifen or anastrozole) from age 30 or 40 years, RRM at age 30 to 40 years, both RRSO and RRM, BC surveillance and medical prevention, or no intervention. MAIN OUTCOMES AND MEASURES: The incremental cost-effectiveness ratio (ICER) was calculated as incremental cost per quality-adjusted life-year (QALY) gained. OC and BC cases and deaths were estimated. RESULTS: In the simulated cohort of women aged 30 years with no cancer, undergoing both RRSO and RRM was most cost-effective for individuals carrying BRCA1 (RRM at age 30 years; RRSO at age 35 years), BRCA2 (RRM at age 35 years; RRSO at age 40 years), and PALB2 (RRM at age 40 years; RRSO at age 45 years) PVs. The corresponding ICERs were -£1942/QALY (-$2680/QALY), -£89/QALY (-$123/QALY), and £2381/QALY ($3286/QALY), respectively. RRSO at age 45 years was cost-effective for RAD51C, RAD51D, and BRIP1 PV carriers compared with nonsurgical strategies. The corresponding ICERs were £962/QALY ($1328/QALY), £771/QALY ($1064/QALY), and £2355/QALY ($3250/QALY), respectively. The most cost-effective preventive strategy per 1000 PV carriers could prevent 923 OC and BC cases and 302 deaths among those carrying BRCA1; 686 OC and BC cases and 170 deaths for BRCA2; 464 OC and BC cases and 130 deaths for PALB2; 102 OC cases and 64 deaths for RAD51C; 118 OC cases and 76 deaths for RAD51D; and 55 OC cases and 37 deaths for BRIP1. Probabilistic sensitivity analysis indicated both RRSO and RRM were most cost-effective in 96.5%, 89.2%, and 84.8% of simulations for BRCA1, BRCA2, and PALB2 PVs, respectively, while RRSO was cost-effective in approximately 100% of simulations for RAD51C, RAD51D, and BRIP1 PVs. CONCLUSIONS AND RELEVANCE: In this cost-effectiveness study, RRSO with or without RRM at varying optimal ages was cost-effective compared with nonsurgical strategies for individuals who carried BRCA1, BRCA2, PALB2, RAD51C, RAD51D, or BRIP1 PVs. These findings support personalizing risk-reducing surgery and guideline recommendations for individual CSG-specific OC and BC risk management

Similarity solutions for unsteady shear-stress-driven flow of Newtonian and power-law fluids : slender rivulets and dry patches

Unsteady flow of a thin film of a Newtonian fluid or a non-Newtonian power-law fluid with power-law index N driven by a constant shear stress applied at the free surface, on a plane inclined at an angle α to the horizontal, is considered. Unsteady similarity solutions representing flow of slender rivulets and flow around slender dry patches are obtained. Specifically, solutions are obtained for converging sessile rivulets (0 < α < π/2) and converging dry patches in a pendent film (π/2 < α < π), as well as for diverging pendent rivulets and diverging dry patches in a sessile film. These solutions predict that at any time t, the rivulet and dry patch widen or narrow according to |x|3/2, and the film thickens or thins according to |x|, where x denotes distance down the plane, and that at any station x, the rivulet and dry patch widen or narrow like |t|−1, and the film thickens or thins like |t|−1, independent of N