Solving Feynman’s sprinkler puzzle
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Currency harmonisation in the Southern African Development Community: a pathway to addressing the PPP puzzle
Over a century since its inception, the purchasing power parity (PPP) theory, linking exchange rates to relative prices, remains one of the most widely accepted and influential theories in international economics. Despite its theoretical appeal, the empirical validity of PPP remains highly contentious. This study examines the empirical support for PPP within the Southern African Development Community (SADC) region. We employ a battery of linear and ESTAR nonlinear unit root tests, panel stationarity tests, and multivariate cointegration analysis on two distinct numéraire currencies—US dollar and the South African rand (ZAR)—alongside consumer price index (CPI) data for 14 SADC countries over the monthly period 1990:01–2022:04. To this end, we test two important hypotheses in the literature on whether the empirical validity of PPP is influenced by the: (i) ‘numéraire currency’ effect, and (ii) ‘border’ effect. Overall, our findings lend overwhelming support to both of these conjectures. Further evidence suggests that the half-life of parity reversion is significantly shorter for the ZAR-based real exchange rates. These findings imply that SADC meets the optimum currency area (OCA) requirements, making the proposed monetary union a promising prospect.
Self-reports map the landscape of task states derived from brain imaging
Psychological states influence our happiness and productivity; however, estimates of their impact have historically been assumed to be limited by the accuracy with which introspection can quantify them. Over the last two decades, studies have shown that introspective descriptions of psychological states correlate with objective indicators of cognition, including task performance and metrics of brain function, using techniques like functional magnetic resonance imaging (fMRI). Such evidence suggests it may be possible to quantify the mapping between self-reports of experience and objective representations of those states (e.g., those inferred from measures of brain activity). Here, we used machine learning to show that self-reported descriptions of experiences across tasks can reliably map the objective landscape of task states derived from brain activity. In our study, 194 participants provided descriptions of their psychological states while performing tasks for which the contribution of different brain systems was available from prior fMRI studies. We used machine learning to combine these reports with descriptions of brain function to form a ‘state-space’ that reliably predicted patterns of brain activity based solely on unseen descriptions of experience (N = 101). Our study demonstrates that introspective reports can share information with the objective task landscape inferred from brain activity.
Holomorphic embedding method for large-scale reverse osmosis desalination optimization
Large-scale optimal design problems involving nonlinear differential equations are widely applied in modeling such as craft manufacturing, chemical engineering and energy engineering. Herein we propose a fast and flexible holomorphic embedding-based method to solve nonlinear differential equations quickly, and further apply it to handle the industrial application of reverse osmosis desalination. Without solving nonlinear differential equations at each discrete point by a traditional small-step iteration approach, the proposed method determines the solution through an approximation function or approximant within segmented computational domain independently. The results of solving more than 11 million of nonlinear differential equations with various design parameters for the reverse osmosis desalination process indicate that the fast and flexible holomorphic embedding-based method is six-fold faster than several typical solvers in computational efficiency with the same level of accuracy. The proposed computational method in this work has great application potential in engineering design.
Towards replicability and sustainability in cancer research
High-quality cancer research is crucial to both save lives and improve quality of life. Spurious findings, however, impedes these laudable goals by misleading research efforts and creating research waste that is inherently difficult to counteract. Irreproducible research is intrinsically wasteful, and unsustainable over the long term. In this perspective piece, we elucidate the extent of the current replication crisis and the underlying causes, identifying practices that lend themselves to unsustainable spurious findings, and the factors that underpin these practices. Finally we outline some remedies to the problem of irreproducible research, and how we might move towards more sustainable and trustworthy research in biomedical science.
Spatial modeling algorithms for reactions and transport in biological cells
Biological cells rely on precise spatiotemporal coordination of biochemical reactions to control their functions. Such cell signaling networks have been a common focus for mathematical models, but they remain challenging to simulate, particularly in realistic cell geometries. Here we present Spatial Modeling Algorithms for Reactions and Transport (SMART), a software package that takes in high-level user specifications about cell signaling networks and then assembles and solves the associated mathematical systems. SMART uses state-of-the-art finite element analysis, via the FEniCS Project software, to efficiently and accurately resolve cell signaling events over discretized cellular and subcellular geometries. We demonstrate its application to several different biological systems, including yes-associated protein (YAP)/PDZ-binding motif (TAZ) mechanotransduction, calcium signaling in neurons and cardiomyocytes, and ATP generation in mitochondria. Throughout, we utilize experimentally derived realistic cellular geometries represented by well-conditioned tetrahedral meshes. These scenarios demonstrate the applicability, flexibility, accuracy and efficiency of SMART across a range of temporal and spatial scales.
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