Virtual reality (VR) is a technology that allows to interact with recreated digital environments and situations with enhanced realism. VR has shown good acceptability and promise in different mental health conditions. No systematic review has evaluated the use of VR in Bipolar Disorder (BD). This PRISMA-compliant systematic review searched PubMed and Web of Science databases (PROSPERO: CRD42023467737) to identify studies conducted in individuals with BD in which VR was used. Results were systematically synthesized around four categories (cognitive and functional evaluation, clinical assessment, response to VR and safety/acceptability). Eleven studies were included (267 individuals, mean age = 36.6 years, 60.7% females). Six studies using VR to carry out a cognitive evaluation detected impairments in neuropsychological performance and delayed reaction times. VR was used to assess emotional regulation. No differences in well-being between VR-based and physical calm rooms were found. A VR-based stress management program reduced subjective stress, depression, and anxiety levels. VR-based cognitive remediation improved cognition, depressive symptoms, and emotional awareness. 48.7% of the individuals with BD considered VR-based cognitive remediation ‘excellent’, whereas 28.2% considered it ‘great’. 87.2% of individuals did not report any side effects. 81.8% of studies received a global quality rating of moderate. Emerging data point towards a promising use of VR in BD as an acceptable assessment/intervention tool. However, multiple unstudied domains as comorbidity, relapse and prodromal symptoms should be investigated. Research on children and adolescents is also recommended. Further research and replication of findings are required to disentangle which VR-interventions for which populations and outcomes are effective.

Physics-informed neural networks (PINNs) and their variants have been very popular in recent years as algorithms for the numerical simulation of both forward and inverse problems for partial differential equations. This article aims to provide a comprehensive review of currently available results on the numerical analysis of PINNs and related models that constitute the backbone of physics-informed machine learning. We provide a unified framework in which analysis of the various components of the error incurred by PINNs in approximating PDEs can be effectively carried out. We present a detailed review of available results on approximation, generalization and training errors and their behaviour with respect to the type of the PDE and the dimension of the underlying domain. In particular, we elucidate the role of the regularity of the solutions and their stability to perturbations in the error analysis. Numerical results are also presented to illustrate the theory. We identify training errors as a key bottleneck which can adversely affect the overall performance of various models in physics-informed machine learning.

Beta-lactam therapeutic drug monitoring has been growing in prevalence in the acute care hospital setting. Expansion of its use to outpatient parenteral antimicrobial therapy requires careful consideration of potential logistical and therapeutic barriers.

This is a survey of the theory of adaptive finite element methods (AFEMs), which are fundamental to modern computational science and engineering but whose mathematical assessment is a formidable challenge. We present a self-contained and up-to-date discussion of AFEMs for linear second-order elliptic PDEs and dimension d > 1, with emphasis on foundational issues. After a brief review of functional analysis and basic finite element theory, including piecewise polynomial approximation in graded meshes, we present the core material for coercive problems. We start with a novel a posteriori error analysis applicable to rough data, which delivers estimators fully equivalent to the solution error. They are used in the design and study of three AFEMs depending on the structure of data. We prove linear convergence of these algorithms and rate-optimality provided the solution and data belong to suitable approximation classes. We also address the relation between approximation and regularity classes. We finally extend this theory to discontinuous Galerkin methods as prototypes of non-conforming AFEMs, and beyond coercive problems to inf-sup stable AFEMs.

Much research has focused on executive function (EF) impairments in psychopathy, a severe personality disorder characterized by a lack of empathy, antisocial behavior, and a disregard for social norms and moral values. However, it is still unclear to what extent EF deficits are present across psychopathy factors and, more importantly, which EF domains are impaired. The current meta-analysis answers these questions by synthesizing the results of 50 studies involving 5,694 participants from 12 different countries. Using multilevel random-effects models, we pooled effect sizes (Cohen's d) for five different EF domains: overall EF, inhibition, planning, shifting, and working memory. Moreover, differences between psychopathy factors were evaluated. Our analyses revealed small deficits in overall EF, inhibition, and planning performance. However, a closer inspection of psychopathy factors indicated that EF deficits were specific to lifestyle/antisocial traits, such as disinhibition. Conversely, interpersonal/affective traits, such as boldness, showed no deficits and in some cases even improved EF performance. These findings suggest that EF deficits are not a key feature of psychopathy per se, but rather are related to antisociality and disinhibitory traits. Potential brain correlates of these findings as well as implications for future research and treatment are discussed.

Questions of ‘how best to acquire data’ are essential to modelling and prediction in the natural and social sciences, engineering applications, and beyond. Optimal experimental design (OED) formalizes these questions and creates computational methods to answer them. This article presents a systematic survey of modern OED, from its foundations in classical design theory to current research involving OED for complex models. We begin by reviewing criteria used to formulate an OED problem and thus to encode the goal of performing an experiment. We emphasize the flexibility of the Bayesian and decision-theoretic approach, which encompasses information-based criteria that are well-suited to nonlinear and non-Gaussian statistical models. We then discuss methods for estimating or bounding the values of these design criteria; this endeavour can be quite challenging due to strong nonlinearities, high parameter dimension, large per-sample costs, or settings where the model is implicit. A complementary set of computational issues involves optimization methods used to find a design; we discuss such methods in the discrete (combinatorial) setting of observation selection and in settings where an exact design can be continuously parametrized. Finally we present emerging methods for sequential OED that build non-myopic design policies, rather than explicit designs; these methods naturally adapt to the outcomes of past experiments in proposing new experiments, while seeking coordination among all experiments to be performed. Throughout, we highlight important open questions and challenges.

This overview is devoted to splitting methods, a class of numerical integrators intended for differential equations that can be subdivided into different problems easier to solve than the original system. Closely connected with this class of integrators are composition methods, in which one or several low-order schemes are composed to construct higher-order numerical approximations to the exact solution. We analyse in detail the order conditions that have to be satisfied by these classes of methods to achieve a given order, and provide some insight about their qualitative properties in connection with geometric numerical integration and the treatment of highly oscillatory problems. Since splitting methods have received considerable attention in the realm of partial differential equations, we also cover this subject in the present survey, with special attention to parabolic equations and their problems. An exhaustive list of methods of different orders is collected and tested on simple examples. Finally, some applications of splitting methods in different areas, ranging from celestial mechanics to statistics, are also provided.

Este artículo teoriza las relaciones entre la ciudadanía y el Estado ecuatoriano durante el primer año y medio de la pandemia COVID-19. Basado en una metodología cualitativa de entrevistas, las perspectivas de los participantes revelan relaciones contradictorias con el gobierno características de los estados de seguridad neoliberales, pero también de patrones (pos)coloniales persistentes de exclusión racista y clasista: por un lado, un sentido de abandono del Estado, particularmente en salud pública y educación; y por otro lado, la fuerza represiva del Estado en su uso de medidas militares y policiales y de estados de excepción. Proponemos el término estado disperso para referirnos a estas tendencias opuestas de simultánea ausencia y presencia estatal. Argumentamos que las respuestas ciudadanas a la ausencia estatal incluyen cierta aceptación del retorno de las funciones educativas y sanitarias a comunidades, hogares e individuos, provocando de todas maneras nuevas formas de adaptación y creatividad cultural. En cuanto a la presencia represiva del Estado, los participantes expresaron apoyo considerable hacia medidas estatales autoritarias, frecuentemente justificadas por discursos esencialistas sobre el carácter de la ciudadanía nacional.

Drylands provide multiple essential services to human society, and dryland vegetation is one of the foundations of these services. There is a paradox, however, in the vegetation productivity–precipitation relationship in drylands. Although water is the most limiting resource in these systems, a strong relationship between precipitation and productivity does not always occur. Such a paradox affects our understanding of dryland vegetation dynamics and hinders our capacity to predict dryland vegetation responses under future climates. In this perspective, we examine the possible causes of the dryland precipitation–productivity paradox. We argue that the underlying reasons depend on the location and scale of the study. Sometimes multiple factors may interact, resulting in a less significant relationship between vegetation growth and water availability. This means that when we observe a poor correlation between vegetation growth and water availability, there are potentially missing sources of water input or a lack of consideration of other important processes. The paradox could also be related to the inaccurate measurement of vegetation productivity and water availability indicators. Incorporating these complexities into predictive models will help us better understand the complex relationship between water availability and dryland ecosystem processes and improve our ability to predict how these ecosystems will respond to the multiple facets of climate change.

A partition calculation method (PCM) for calculating the diffraction efficiency of multilayer Fresnel zone plate with high aspect ratio is proposed. In contrast to the traditional theory, PCM designs and evaluates Fresnel zone plate (FZP) considering material pairs, all zone widths, thicknesses and X-ray energy more completely. The results obtained through PCM are validated by comparing them with the complex amplitude superposition theory and coupled wave theory numerical results. The PCM satisfies the requirements of the theoretical investigation of FZP with small outermost zone width (drN) and large thickness (t). Combining proper numerical analysis with the experimental conditions will present a great potential to break through the imaging performance of X-ray microscopy.