Splitting schemes for coupled differential equations: Block Schur-based approaches & Partial Jacobi approximation

Coupled multi-physics problems are encountered in countless applications and pose significant numerical challenges. In a broad sense, one can categorise the numerical solution strategies for coupled problems into two classes: monolithic approaches and sequential (also known as split, decoupled, partitioned or segregated) approaches. The monolithic approaches treat the entire problem as one, whereas the sequential approaches are iterative decoupling techniques where the different sub-problems are treated separately. Although the monolithic approaches often offer the most robust solution strategies, they tend to require ad-hoc preconditioners and numerical implementations. Sequential methods, on the other hand, offer the possibility to add and remove equations from the model flexibly and rely on existing black-box solvers for each specific equation. Furthermore, when problems are non-linear, inner iterations need to be performed even in monolithic solvers, making the sequential approaches an even more viable alternative. The cost of running inner iterations to recover the multi-physics coupling could, however, easily become prohibitive. Moreover, the sequential approaches might not converge at all. In this work, we present a general formulation of splitting schemes for continuous operators with arbitrary implicit/explicit splitting, like in standard iterative methods for linear systems. By introducing a generic relaxation operator, we find the conditions for the convergence of the iterative schemes. We show how the relaxation operator can be thought of as a preconditioner and constructed based on an approximate Schur complement. We propose a Schur-based Partial Jacobi relaxation operator to stabilise the coupling and show its effectiveness. Although we mainly focus on scalar-scalar linear problems, most results are easily extended to non-linear and higher-dimensional problems. The schemes presented are not explicitly dependent on any particular discretisation methodologies. Numerical tests (1D and 2D) for two PDE systems, namely the Dual-Porosity model and a Quad-Laplacian operator, are carried out to investigate the practical implications of the theoretical results

On the flexibility of the design of Multiple Try Metropolis schemes

The Multiple Try Metropolis (MTM) method is a generalization of the classical Metropolis-Hastings algorithm in which the next state of the chain is chosen among a set of samples, according to normalized weights. In the literature, several extensions have been proposed. In this work, we show and remark upon the flexibility of the design of MTM-type methods, fulfilling the detailed balance condition. We discuss several possibilities and show different numerical results

Deep Graph Matching via Blackbox Differentiation of Combinatorial Solvers

Building on recent progress at the intersection of combinatorial optimization and deep learning, we propose an end-to-end trainable architecture for deep graph matching that contains unmodified combinatorial solvers. Using the presence of heavily optimized combinatorial solvers together with some improvements in architecture design, we advance state-of-the-art on deep graph matching benchmarks for keypoint correspondence. In addition, we highlight the conceptual advantages of incorporating solvers into deep learning architectures, such as the possibility of post-processing with a strong multi-graph matching solver or the indifference to changes in the training setting. Finally, we propose two new challenging experimental setups. The code is available at https://github.com/martius-lab/blackbox-deep-graph-matchingComment: ECCV 2020 conference pape

Appointments, pay and performance in UK boardrooms by gender

This article uses UK data to examine issues regarding the scarcity of women in boardroom positions. The article examines appointments, pay and any associated productivity effects deriving from increased diversity. Evidence of gender-bias in the appointment of women as non-executive directors is found together with mixed evidence of discrimination in wages or fees paid. However, the article finds no support for the argument that gender diverse boards enhance corporate performance. Proposals in favour of greater board diversity may be best structured around the moral value of diversity, rather than with reference to an expectation of improved company performance

Sex-specific transcriptional and proteomic signatures in schizophrenia

It has remained unclear why schizophrenia typically manifests after adolescence and which neurobiological mechanisms are underlying the cascade leading to the actual onset of the illness. Here we show that the use of induced pluripotent stem cell-derived neurons of monozygotic twins from pairs discordant for schizophrenia enhances disease-specific signal by minimizing genetic heterogeneity. In proteomic and pathway analyses, clinical illness is associated especially with altered glycosaminoglycan, GABAergic synapse, sialylation, and purine metabolism pathways. Although only 12% of all 19,462 genes are expressed differentially between healthy males and females, up to 61% of the illness-related genes are sex specific. These results on sex-specific genes are replicated in another dataset. This implies that the pathophysiology differs between males and females, and may explain why symptoms appear after adolescence when the expression of many sex-specific genes change, and suggests the need for sex-specific treatments.Peer reviewe

Analysis of a nonlinear importance sampling scheme for Bayesian parameter estimation in state-space models

The Bayesian estimation of the unknown parameters of state-space (dynamical) systems has received considerable attention over the past decade, with a handful of powerful algorithms being introduced. In this paper we tackle the theoretical analysis of the recently proposed nonlinear population Monte Carlo (NPMC). This is an iterative importance sampling scheme whose key features, compared to conventional importance samplers, are (i) the approximate computation of the importance weights (IWs) assigned to the Monte Carlo samples and (ii) the nonlinear transformation of these IWs in order to prevent the degeneracy problem that flaws the performance of conventional importance samplers. The contribution of the present paper is a rigorous proof of convergence of the nonlinear IS (NIS) scheme as the number of Monte Carlo samples, M, increases. Our analysis reveals that the NIS approximation errors converge to 0 almost surely and with the optimal Monte Carlo rate of M [superíndice - ­½]. Moreover, we prove that this is achieved even when the mean estimation error of the IWs remains constant, a property that has been termed exact approximation in the Markov chain Monte Carlo literature. We illustrate these theoretical results by means of a computer simulation example involving the estimation of the parameters of a state-space model typically used for target tracking.This research has been partially supported by the Spanish Ministry of Economy and Competitiveness (projects TEC2015-69868-C2-1-R ADVENTURE and FIS2013-40653-P), the Spanish Ministry of Education, Culture and Sport (mobility award PRX15/00378) and the Office of Naval Research (ONR) Global (Grant Award no. N62909-15-1-2011)

Basin-scale phenology and effects of climate variability on global timing of initial seaward migration of Atlantic salmon (Salmo salar)

Migrations between different habitats are key events in the lives of many organisms. Such movements involve annually recurring travel over long distances usually triggered by seasonal changes in the environment. Often, the migration is associated with travel to or from reproduction areas to regions of growth. Young anadromous Atlantic salmon (Salmo salar) emigrate from freshwater nursery areas during spring and early summer to feed and grow in the North Atlantic Ocean. The transition from the freshwater (parr') stage to the migratory stage where they descend streams and enter salt water (smolt') is characterized by morphological, physiological and behavioural changes where the timing of this parr-smolt transition is cued by photoperiod and water temperature. Environmental conditions in the freshwater habitat control the downstream migration and contribute to within- and among-river variation in migratory timing. Moreover, the timing of the freshwater emigration has likely evolved to meet environmental conditions in the ocean as these affect growth and survival of the post-smolts. Using generalized additive mixed-effects modelling, we analysed spatio-temporal variations in the dates of downstream smolt migration in 67 rivers throughout the North Atlantic during the last five decades and found that migrations were earlier in populations in the east than the west. After accounting for this spatial effect, the initiation of the downstream migration among rivers was positively associated with freshwater temperatures, up to about 10 degrees C and levelling off at higher values, and with sea-surface temperatures. Earlier migration occurred when river discharge levels were low but increasing. On average, the initiation of the smolt seaward migration has occurred 2.5days earlier per decade throughout the basin of the North Atlantic. This shift in phenology matches changes in air, river, and ocean temperatures, suggesting that Atlantic salmon emigration is responding to the current global climate changes

Inducible cAMP Early Repressor (ICER) and Brain Functions

The inducible cAMP early repressor (ICER) is an endogenous repressor of cAMP-responsive element (CRE)-mediated gene transcription and belongs to the CRE-binding protein (CREB)/CRE modulator (CREM)/activating transcription factor 1 (ATF-1) gene family. ICER plays an important role in regulating the neuroendocrine system and the circadian rhythm. Other aspects of ICER function have recently attracted heightened attention. Being a natural inducible CREB antagonist, and more broadly, an inducible repressor of CRE-mediated gene transcription, ICER regulates long-lasting plastic changes that occur in the brain in response to incoming stimulation. This review will bring together data on ICER and its functions in the brain, with a special emphasis on recent findings highlighting the involvement of ICER in the regulation of long-term plasticity underlying learning and memory

The Perils of Gender Beliefs for Men Leaders as Change Agents for Gender Equality

This article examines the potentially damaging role that gender beliefs can play in hindering women's equal representation in leadership positions. Based on a secondary analysis of a large‐scale EU‐wide survey (Eurobarometer 76.1), the article shows that essentialist gender beliefs lower support for equality interventions such as quotas or targets, particularly among men as leaders. The results show that discriminatory gender beliefs partially mediate this relationship and produce a more negative effect among men leaders. The paper contributes to understanding the role essentialist gender beliefs often lay the groundwork for gender discriminatory beliefs. Those in turn hinder support for effective gender equality measures. Gender essentialist beliefs can be held by everyone but are more prevalent among men leaders. We conclude that greater gender balance in leadership cannot be achieved without tackling underlying gender beliefs, particularly among men leaders since they are called upon to enact change. We thereby argue that simply asking for men to become change agents for gender equality is not an effective strategy if underlying gender beliefs are left unchallenged