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We study of the connection between operator valued central limits for monotone, Boolean and free probability theory, which we shall call the arcsine, Bernoulli and semicircle distributions, respectively. In scalar-valued non-commutative probability these measures are known to satisfy certain arithmetic relations with respect to Boolean and free convolutions. We show that generally the corresponding operator-valued distributions satisfy the same relations only when we consider them in the fully matricial sense introduced by Voiculescu. In addition, we provide a combinatorial description in terms of moments of the operator valued arcsine distribution and we show that its reciprocal Cauchy transform satisfies a version of the Abel equation similar to the one satisfied in the scalar-valued case.

Abstract: In the last two decades the validity of clinical trials in psychiatry has been subjected to discussion. The most accepted clinical study method in the medical area, i.e. the randomized controlled trial (RCT), faces significant problems when applied to the psychiatric field. One of the causes for this scenario is the strict participant inclusion and exclusion criteria that may not represent the real world. The inconsistency of the different endpoint parameters that are used in the field is another cause. We think that psychiatric RCTs’ challenges, together with the underlying complexity of psychiatry, lead to a problematic clinical practice. Psychoactive substances are currently routinely tested outside of a formal clinical trial environment. Off-label psychoactive drugs are commonly prescribed, and other substances, such as herbal remedies, are also regularly consumed. These real-life experiments can teach us useful lessons. Real-world data (RWD) includes information about heterogeneous patient populations, and it can be measured with standardized parameters. Collecting RWD can also address the need for systematically documenting and sharing case reports’ outcomes. We suggest using digital tools to capture objective and continuous behavioral data from patients passively. New conclusions will be constantly drawn, possibly allowing more personalized treatment outcomes. The relevant nextgeneration decision support tools are already available.

Abstract: This review encapsulates an extensive variety of substances identified as mutual prodrugs or codrugs, wherein two, or sometimes three, biologically active moieties are linked using an assortment of metabolically unstable bridging entities. Following the administration of the mutual prodrugs, these undergo a bridge cleavage releasing the active molecules, which then elicit their respective biological effects. In some cases, the released drugs act synergistically, other times the biological activity of only one of the drugs is elicited, and in such cases, the accompanying drug serves only as a carrier, which may have an affinity to the desired receptor. The most promising results are commonly observed when the two released drugs are efficacious at similar concentrations and particularly when the two drugs are effective against similar diseases. For instance, the best results are observed, when two analgesics, two anticancer agents, two drugs for the treatment of cardiac conditions, etc., are the substances comprising the codrug. Mutual prodrugs/ codrugs described herein have been reported, primarily since the year 2000, as potential drugs for use against a plethora of diseases including pain, inflammation, cancer, bacterial infections, sickle cell anemia, Alzheimer’s disease, and others.

VORO++ is a software library written in C++ for computing the Voronoi tessellation, a technique in computational geometry that is widely used for analyzing systems of particles. VORO++ was released in 2009 and is based on computing the Voronoi cell for each particle individually. Here, we take advantage of modern computer hardware, and extend the original serial version to allow for multithreaded computation of Voronoi cells via the OpenMP application programming interface. We test the performance of the code, and demonstrate that we can achieve parallel efficiencies greater than 95% in many cases. The multithreaded extension follows standard OpenMP programming paradigms, allowing it to be incorporated into other programs. We provide an example of this using the VoroTop software library, performing a multithreaded Voronoi cell topology analysis of up to 102.4 million particles. Fix typo and section numbers

Planar graphs can be represented as intersection graphs of different types of geometric objects in the plane, e.g., circles (Koebe, 1936), line segments (Chalopin \& Gon{��}alves, 2009), \textsc{L}-shapes (Gon{��}alves et al, 2018). For general graphs, however, even deciding whether such representations exist is often $NP$-hard. We consider apex graphs, i.e., graphs that can be made planar by removing one vertex from them. We show, somewhat surprisingly, that deciding whether geometric representations exist for apex graphs is $NP$-hard. More precisely, we show that for every positive integer $k$, recognizing every graph class $\mathcal{G}$ which satisfies $\textsc{PURE-2-DIR} \subseteq \mathcal{G} \subseteq \textsc{1-STRING}$ is $NP$-hard, even when the input graphs are apex graphs of girth at least $k$. Here, $PURE-2-DIR$ is the class of intersection graphs of axis-parallel line segments (where intersections are allowed only between horizontal and vertical segments) and \textsc{1-STRING} is the class of intersection graphs of simple curves (where two curves share at most one point) in the plane. This partially answers an open question raised by Kratochv{\'��}l \& Pergel (2007). Most known $NP$-hardness reductions for these problems are from variants of 3-SAT. We reduce from the \textsc{PLANAR HAMILTONIAN PATH COMPLETION} problem, which uses the more intuitive notion of planarity. As a result, our proof is much simpler and encapsulates several classes of geometric graphs.

Abstract Using 20 quasi-biennial oscillation (QBO)-resolving models from phases 5/6 of the Coupled Model Intercomparison Project (CMIP5/6), this study examines the projected Southern Hemisphere (SH) extratropical response to the QBO. Nine of the 22 models simulate decelerated circumpolar westerlies during easterly QBO (EQBO) in the historical climate as is observed, though only ∼30% of the observed change is reproduced in the multimodel ensemble mean (MME) of these high-skill models. These high-skill models project an enhanced stratospheric QBO teleconnection for both emissions scenarios. Further, the stratospheric wind anomaly in high latitudes is projected to move to midlatitudes in future scenarios. The climatological subtropical jet is projected to strengthen, while tropical easterlies are projected to weaken. As a consequence, upward wave activity in the future appears to become more sensitive to the QBO phase. Enhanced upward propagation of waves in mid- to high latitudes during EQBO are much stronger in future scenarios than in historical simulations. The anomalous downwelling over the Antarctic, as part of the Brewer–Dobson deep branch response to EQBO, is also projected to strengthen, corresponding to increased warm anomalies. In future scenarios, the areal extent of the deep convective response to EQBO over the Maritime Continent widens and includes a sharper reduction in outgoing longwave radiation, albeit with southward expansion from Indonesia to Australia. The enhancement and spatial shift in the stratospheric polar vortex pathway and tropical convection pathway subsequently lead to changes in the tropospheric QBO signal. An annular mode–like response forms in the troposphere and near-surface in the present climate, whereas this pattern shifts farther equatorward in future projections with circulation anomalies in the tropical Indian Ocean amplifying. Significance Statement The influence of the equatorial stratospheric quasi-biennial oscillation (QBO) has been reported to intensify in the Northern Hemisphere under climate change, even as the QBO wind magnitude weakens. It is still unknown whether the influence of the QBO on the Southern Hemisphere intensifies or weakens in a warm climate. Using simulations from multiple models, this study finds that the influence of the QBO on the Southern Hemisphere is projected to strengthen in most models even as the QBO weakens. Two QBO pathways are explored, including the stratospheric polar vortex route and the tropical convection pathway, both of which are projected to amplify in both the moderate- and high-emissions scenarios. In addition to the amplification of the QBO signals in the Southern Hemisphere extratropics, an equatorward shift of the maximum anomalies is also projected. That is, the maximum easterly anomalies in the Antarctic stratosphere during easterly QBO and the annular mode–like pattern in the troposphere or the near-surface shifts farther equatorward.

The following article presents a literature review around the concepts of subjective well-being and perceived social support. The search was carried out in Google Scholar and it was considered that they were works presented in journals of academic prestige. In addition, some research was investigated that established relationships between these concepts in adolescence. The work was carried out within the framework of an evaluative proposal for the subject Health Psychology, whose axis focuses on the approach of concepts of Positive Psychology. In this sense, it is of interest to note that this branch of psychology proposes the study of those factors that promote and enhance optimal psychological functioning. Conceptual definitions were contrasted around subjective well-being and perceived social support, outlining possible psychometric measurement instruments for both concepts. Finally, there was a difficulty in finding articles that related both constructs around this population, raising some questions regarding the adequacy of the instruments. El siguiente artículo presenta una revisión bibliográfica en torno a los constructos bienestar subjetivo y apoyo social percibido. La búsqueda se realizó en Google Scholar y se consideró que los mismos fuesen trabajos presentados en revistas de prestigio académico. Además, se pesquisaron algunas investigaciones que establecían relaciones entre dichos conceptos en la adolescencia. El trabajo se realizó en el marco de una propuesta evaluativa para la materia Psicología de la Salud, cuyo eje se centra en el abordaje de conceptos propios de la Psicología Positiva. En este sentido, resulta de interés señalar que dicha rama de la psicología propone el estudio de aquellos factores que promueven y potencia el funcionamiento psicológico óptimo. Se contrastaron definiciones conceptuales en torno al bienestar subjetivo y apoyo social percibido, reseñando posibles instrumentos de medición psicométrica para ambos conceptos. Por último, se observó una dificultad para encontrar artículos que relacionaran ambos constructos en torno a dicha población, planteando algunas preguntas al respecto de la adecuación de los instrumentos.