Numerical solution of the Dirichlet initial boundary value problem for the heat equation in exterior 3-dimensional domains using integral equations

A numerical method for the Dirichlet initial boundary value problem for the heat equation in the exterior and unbounded region of a smooth closed simply connected 3-dimensional domain is proposed and investigated. This method is based on a combination of a Laguerre transformation with respect to the time variable and an integral equation approach in the spatial variables. Using the Laguerre transformation in time reduces the parabolic problem to a sequence of stationary elliptic problems which are solved by a boundary layer approach giving a sequence of boundary integral equations of the first kind to solve. Under the assumption that the boundary surface of the solution domain has a one-to-one mapping onto the unit sphere, these integral equations are transformed and rewritten over this sphere. The numerical discretisation and solution are obtained by a discrete projection method involving spherical harmonic functions. Numerical results are included.

A method of fundamental solutions for radially symmetric and axisymmetric backward heat conduction problems

We propose and investigate an application of the method of fundamental solutions (MFS) to the radially symmetric and axisymmetric backward heat conduction problem (BHCP) in a solid or hollow cylinder. In the BHCP, the initial temperature is to be determined from the temperature measurements at a later time. This is an inverse and ill-posed problem, and we employ and generalize the MFS regularization approach [B.T. Johansson and D. Lesnic, A method of fundamental solutions for transient heat conduction, Eng. Anal. Boundary Elements 32 (2008), pp. 697–703] for the time-dependent heat equation to obtain a stable and accurate numerical approximation with small computational cost.

Maltreatment, psychiatric symptoms and human immunodeficiency virus/sexual transmitted infection risk behavior among youth with alcohol and other drug use problems: A person-centered analysis

Multi-problem youth undergoing treatment for substance use problems are at high behavioral risk for exposure to sexually transmitted infections (STIs), including human immunodeficiency virus (HIV). Specific risk factors include childhood adversities such as maltreatment experiences and subsequent forms of psychopathology. The current study used a person-centered analytical approach to examine how childhood maltreatment experiences were related to patterns of psychiatric symptoms and HIV/STI risk behaviors in a sample of adolescents (N = 408) receiving treatment services. Data were collected in face-to-face interviews at two community-based facilities. Descriptive statistics and Latent Profile Analysis (LPA) were used to (a) classify adolescents into groups based on past year psychiatric symptoms, and (b) examine relations between class membership and forms of childhood maltreatment experiences, as well as past year sexual risk behavior (SRB). ^ LPA results indicated significant heterogeneity in psychiatric symptoms among the participants. The three classes generated via the optimal LPA solution included: (a) a low psychiatric symptoms class, (b) a high alcohol symptoms class and (c) a high internalizing symptoms class. Class membership was associated significantly with adolescents’ self-reported scores for childhood sexual abuse and emotional neglect. ANOVAs documented significant differences in mean scores for multiple indices of SRB indices by class membership, demonstrating differential risk for HIV/STI exposure across classes. The two classes characterized by elevated psychiatric symptom profiles and more severe maltreatment histories were at increased behavioral risk for HIV/STI exposure, compared to the low psychiatric symptoms class. The high internalizing symptoms class reported the highest scores for most of the indices of SRB assessed. The heterogeneity of psychiatric symptom patterns documented in the current study has important implications for HIV/STI prevention programs implemented with multi-problem youth. The results highlight complex relations between childhood maltreatment experiences, psychopathology and multiple forms of health risk behavior among adolescents. The results underscore the importance of further integration between substance abuse treatment and HIV/STI risk reduction efforts to improve morbidity and mortality among vulnerable youth. ^

Treatment attrition among racial /ethnic minority adolescents participating in a brief motivational intervention for substance use problems: The influence of individual, social, cultural, and treatment factors

The present study has the primary aim of examining the predictors of treatment attrition among racial/ethnic minority adolescents with substance use problems. This study explores the potential differential influence of specific individual, social, cultural, and treatment factors on treatment attrition within three racial/ethnic subgroups of adolescents. Participants: A unique feature of the study is the use of a racial/ethnic minority sample (N=453), [U.S.-born Hispanics (n = 262), Foreign-born Hispanics (n = 117), and African-Americans (n = 74)]. Multivariate logit analyses were used to examine the influence of specific factors on treatment attrition among the full sample of adolescents, as well as within each racial/ethnic subgroup. Consistent with expectations, multivariate logit analyses reveal that, the specific factors associated with attrition varied across the three racial/ethnic subgroups. Having parents with problem substance use, being on the waitlist, and being court mandated to treatment emerged as predictors of attrition among the US-born Hispanics, while only Conduct Disorder was significantly associated with greater attrition among foreign-born Hispanics. Finally, among African-Americans, parental crack/cocaine use, parental abstinence from alcohol, and being on the waitlist were predictive of attrition. Multiple factors were associated with treatment attrition among racial/ethnic minority adolescents with specific factors differentially predicting attrition within each racial/ethnic subgroup. African-American youth were more than twice as likely as their Hispanic counterparts to leave treatment prematurely. It is critically important to understand the predictors of attrition among racial/ethnic minority youth in order to better meet the needs of youth most at risk of dropping out. ^

Treatment attrition among racial/ethnic minority adolescents participating in a brief motivational intervention for substance use problems : the influence of individual, social, cultural, and treatment factors

The present study has the primary aim of examining the predictors of treatment attrition among racial/ethnic minority adolescents with substance use problems. This study explores the potential differential influence of specific individual, social, cultural, and treatment factors on treatment attrition within three racial/ethnic subgroups of adolescents. Participants: A unique feature of the study is the use of a racial/ethnic minority sample (N=453), [U.S.-born Hispanics (n = 262), Foreign-born Hispanics (n = 117), and African- Americans (n = 74)]. Multivariate logit analyses were used to examine the influence of specific factors on treatment attrition among the full sample of adolescents, as well as within each racial/ethnic subgroup. Consistent with expectations, multivariate logit analyses reveal that, the specific factors associated with attrition varied across the three racial/ethnic subgroups. Having parents with problem substance use, being on the waitlist, and being court mandated to treatment emerged as predictors of attrition among the US-born Hispanics, while only Conduct Disorder was significantly associated with greater attrition among foreign-born Hispanics. Finally, among African-Americans, parental crack/cocaine use, parental abstinence from alcohol, and being on the waitlist were predictive of attrition. Multiple factors were associated with treatment attrition among racial/ethnic minority adolescents with specific factors differentially predicting attrition within each racial/ethnic subgroup. African-American youth were more than twice as likely as their Hispanic counterparts to leave treatment prematurely. It is critically important to understand the predictors of attrition among racial/ethnic minority youth in order to better meet the needs of youth most at risk of dropping out.

Maltreatment, Psychiatric Symptoms and Human Immunodeficiency Virus/Sexual Transmitted Infection Risk Behavior Among Youth with Alcohol and Other Drug Use Problems: A Person-Centered Analysis

Multi-problem youth undergoing treatment for substance use problems are at high behavioral risk for exposure to sexually transmitted infections (STIs), including human immunodeficiency virus (HIV). Specific risk factors include childhood adversities such as maltreatment experiences and subsequent forms of psychopathology. The current study used a person-centered analytical approach to examine how childhood maltreatment experiences were related to patterns of psychiatric symptoms and HIV/STI risk behaviors in a sample of adolescents (N = 408) receiving treatment services. Data were collected in face-to-face interviews at two community-based facilities. Descriptive statistics and Latent Profile Analysis (LPA) were used to (a) classify adolescents into groups based on past year psychiatric symptoms, and (b) examine relations between class membership and forms of childhood maltreatment experiences, as well as past year sexual risk behavior (SRB). LPA results indicated significant heterogeneity in psychiatric symptoms among the participants. The three classes generated via the optimal LPA solution included: (a) a low psychiatric symptoms class, (b) a high alcohol symptoms class and (c) a high internalizing symptoms class. Class membership was associated significantly with adolescents’ self-reported scores for childhood sexual abuse and emotional neglect. ANOVAs documented significant differences in mean scores for multiple indices of SRB indices by class membership, demonstrating differential risk for HIV/STI exposure across classes. The two classes characterized by elevated psychiatric symptom profiles and more severe maltreatment histories were at increased behavioral risk for HIV/STI exposure, compared to the low psychiatric symptoms class. The high internalizing symptoms class reported the highest scores for most of the indices of SRB assessed. The heterogeneity of psychiatric symptom patterns documented in the current study has important implications for HIV/STI prevention programs implemented with multi-problem youth. The results highlight complex relations between childhood maltreatment experiences, psychopathology and multiple forms of health risk behavior among adolescents. The results underscore the importance of further integration between substance abuse treatment and HIV/STI risk reduction efforts to improve morbidity and mortality among vulnerable youth.

Data compilation on the biological response to ocean acidification: environmental and experimental context of data sets and related literature

The exponential growth of studies on the biological response to ocean acidification over the last few decades has generated a large amount of data. To facilitate data comparison, a data compilation hosted at the data publisher PANGAEA was initiated in 2008 and is updated on a regular basis (doi:10.1594/PANGAEA.149999). By January 2015, a total of 581 data sets (over 4 000 000 data points) from 539 papers had been archived. Here we present the developments of this data compilation five years since its first description by Nisumaa et al. (2010). Most of study sites from which data archived are still in the Northern Hemisphere and the number of archived data from studies from the Southern Hemisphere and polar oceans are still relatively low. Data from 60 studies that investigated the response of a mix of organisms or natural communities were all added after 2010, indicating a welcomed shift from the study of individual organisms to communities and ecosystems. The initial imbalance of considerably more data archived on calcification and primary production than on other processes has improved. There is also a clear tendency towards more data archived from multifactorial studies after 2010. For easier and more effective access to ocean acidification data, the ocean acidification community is strongly encouraged to contribute to the data archiving effort, and help develop standard vocabularies describing the variables and define best practices for archiving ocean acidification data.

Codomain Rigidity of the Dirichlet to Neumann Operator for the Riemannian Wave Equation

We study the Dirichlet to Neumann operator for the Riemannian wave equation on a compact Riemannian manifold. If the Riemannian manifold is modelled as an elastic medium, this operator represents the data available to an observer on the boundary of the manifold when the manifold is set into motion through boundary vibrations. We study the Dirichlet to Neumann operator when vibrations are imposed and data recorded on disjoint sets, a useful setting for applications. We prove that this operator determines the Dirichlet to Neumann operator where sources and observations are on the same set, provided a spectral condition on the Laplace-Beltrami operator for the manifold is satisfied. We prove this by providing an implementable procedure for determining a portion of the Riemannian manifold near the area where sources are applied. Drawing on established results, an immediate corollary is that a compact Riemannian manifold can be reconstructed from the Dirichlet to Neumann operator where sources and observations are on disjoint sets.

Codomain Rigidity of the Dirichlet to Neumann Operator for the Riemannian Wave Equation

We study the Dirichlet to Neumann operator for the Riemannian wave equation on a compact Riemannian manifold. If the Riemannian manifold is modelled as an elastic medium, this operator represents the data available to an observer on the boundary of the manifold when the manifold is set into motion through boundary vibrations. We study the Dirichlet to Neumann operator when vibrations are imposed and data recorded on disjoint sets, a useful setting for applications. We prove that this operator determines the Dirichlet to Neumann operator where sources and observations are on the same set, provided a spectral condition on the Laplace-Beltrami operator for the manifold is satisfied. We prove this by providing an implementable procedure for determining a portion of the Riemannian manifold near the area where sources are applied. Drawing on established results, an immediate corollary is that a compact Riemannian manifold can be reconstructed from the Dirichlet to Neumann operator where sources and observations are on disjoint sets.

Fixed-boundary constituencies and the principle of equal representation in Ireland

The process of constituency boundary revision in Ireland, designed to satisfy what is perceived as a rigid requirement that a uniform deputy-population ratio be maintained across constituencies, has traditionally consumed a great deal of the time of politicians and officials. For almost two decades after a High Court ruling in 1961, the process was a political one, was highly contentious, and was marked by serious allegations of ministerial gerrymandering. The introduction in 1979 of constituency commissions made up of officials neutralised, for the most part, charges that the system had become too politicised, but it continued the process of micro-management of constituency boundaries. This article suggests that the continuing problems caused by this system – notably, the permanently changing nature of constituency boundaries and resulting difficulties of geographical identification – could be resolved by reversion to the procedure that is normal in proportional representation systems: periodic post-census allocation of seats to constituencies whose boundaries are based on those of recognised local government units and which are stable over time. This reform, replacing the principle of redistricting by the principle of reapportionment, would result in more recognisable constituencies, more predictable boundary trajectories over time, and a more efficient, fairer, and speedier process of revision.

Variationelle Zeitdiskretisierungen höherer Ordnung der Konvektions-Diffusions-Reaktions-Gleichungen in zeitabhängigen Gebieten

Wir betrachten zeitabhängige Konvektions-Diffusions-Reaktions-Gleichungen in zeitabhängi- gen Gebieten, wobei die Bewegung des Gebietsrandes bekannt ist. Die zeitliche Entwicklung des Gebietes wird durch die ALE-Formulierung behandelt, die die Nachteile der klassischen Euler- und Lagrange-Betrachtungsweisen behebt. Die Position des Randes und seine Geschwindigkeit werden dabei so in das Gebietsinnere fortgesetzt, dass starke Gitterdeformationen verhindert werden. Als Zeitdiskretisierungen höherer Ordnung werden stetige Galerkin-Petrov-Verfahren (cGP) und unstetige Galerkin-Verfahren (dG) auf Probleme in zeitabhängigen Gebieten angewendet. Weiterhin werden das C 1 -stetige Galerkin-Petrov-Verfahren und das C 0 -stetige Galerkin- Verfahren vorgestellt. Deren Lösungen lassen sich auch in zeitabhängigen Gebieten durch ein einfaches einheitliches Postprocessing aus der Lösung des cGP-Problems bzw. dG-Problems erhalten. Für Problemstellungen in festen Gebieten und mit zeitlich konstanten Konvektions- und Reaktionstermen werden Stabilitätsresultate sowie optimale Fehlerabschätzungen für die nachbereiteten Lösungen der cGP-Verfahren und der dG-Verfahren angegeben. Für zeitabhängige Konvektions-Diffusions-Reaktions-Gleichungen in zeitabhängigen Gebieten präsentieren wir konservative und nicht-konservative Formulierungen, wobei eine besondere Aufmerksamkeit der Behandlung der Zeitableitung und der Gittergeschwindigkeit gilt. Stabilität und optimale Fehlerschätzungen für die in der Zeit semi-diskretisierten konservativen und nicht-konservativen Formulierungen werden vorgestellt. Abschließend wird das volldiskretisierte Problem betrachtet, wobei eine Finite-Elemente-Methode zur Ortsdiskretisierung der Konvektions-Diffusions-Reaktions-Gleichungen in zeitabhängigen Gebieten im ALE-Rahmen einbezogen wurde. Darüber hinaus wird eine lokale Projektionsstabilisierung (LPS) eingesetzt, um der Konvektionsdominanz Rechnung zu tragen. Weiterhin wird numerisch untersucht, wie sich die Approximation der Gebietsgeschwindigkeit auf die Genauigkeit der Zeitdiskretisierungsverfahren auswirkt.

Differential Evolution: A Tool for Global Optimization

This report describes a tool for global optimization that implements the Differential Evolution optimization algorithm as a new Excel add-in. The tool takes a step beyond Excel’s Solver add-in, because Solver often returns a local minimum, that is, a minimum that is less than or equal to nearby points, while Differential Evolution solves for the global minimum, which includes all feasible points. Despite complex underlying mathematics, the tool is relatively easy to use, and can be applied to practical optimization problems, such as establishing pricing and awards in a hotel loyalty program. The report demonstrates an example of how to develop an optimum approach to that problem.

Problems of optimal transportation on the circle and their mechanical applications

We consider a mechanical problem concerning a 2D axisymmetric body moving forward on the plane and making slow turns of fixed magnitude about its axis of symmetry. The body moves through a medium of non-interacting particles at rest, and collisions of particles with the body's boundary are perfectly elastic (billiard-like). The body has a blunt nose: a line segment orthogonal to the symmetry axis. It is required to make small cavities with special shape on the nose so as to minimize its aerodynamic resistance. This problem of optimizing the shape of the cavities amounts to a special case of the optimal mass transfer problem on the circle with the transportation cost being the squared Euclidean distance. We find the exact solution for this problem when the amplitude of rotation is smaller than a fixed critical value, and give a numerical solution otherwise. As a by-product, we get explicit description of the solution for a class of optimal transfer problems on the circle.

Riemann-Hilbert problems for poly-Hardy space on the unit ball

In this paper, we focus on a Riemann–Hilbert boundary value problem (BVP) with a constant coefficients for the poly-Hardy space on the real unit ball in higher dimensions. We first discuss the boundary behaviour of functions in the poly-Hardy class. Then we construct the Schwarz kernel and the higher order Schwarz operator to study Riemann–Hilbert BVPs over the unit ball for the poly- Hardy class. Finally, we obtain explicit integral expressions for their solutions. As a special case, monogenic signals as elements in the Hardy space over the unit sphere will be reconstructed in the case of boundary data given in terms of functions having values in a Clifford subalgebra. Such monogenic signals represent the generalization of analytic signals as elements of the Hardy space over the unit circle of the complex plane.