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For decades, differential equations have been used to model various problems in the natural sciences and engineering. However, ordinary differential equations (ODEs) are usually not analytically solvable, so many numerical approaches have been developed to produce approximate solutions. More recently, it has been proposed that neural networks can learn solutions of ODEs and thus provide faster and more accurate numerical approximations. Here, we propose a novel approach of having neural networks learn solutions to ODEs via the Picard formulation. We show, through examples, that this approach produces approximations that are at least as reliable as earlier approaches.

Molecular Dynamics (MD) is the numerical simulation of a large system of interacting molecules, and one of the key components of a MD simulation is the numerical estimation of the solutions to a system of nonlinear differential equations. Such systems are very sensitive to discretization and round-off error, and correspondingly, standard techniques such as Runge-Kutta methods can lead to poor results. However, MD systems are conservative, which means that we can use Hamiltonian mechanics and symplectic transformations (also known as canonical transformations) in analyzing and approximating solutions. This is standard in MD applications, leading to numerical techniques known as symplectic integrators, and often, these techniques are developed for well-understood Hamiltonian systems such as Hills lunar equation. In this presentation, we explore how well symplectic techniques developed for well understood systems (specifically, Hills Lunar equation) address discretization errors in MD systems which fail for one or more reasons.

Transforming food systems is essential to bring about a healthier, equitable, sustainable, and resilient future, including achieving global development and sustainability goals. To date, no comprehensive framework exists to track food systems transformation and their contributions to global goals. In 2021, the Food Systems Countdown to 2030 Initiative (FSCI) articulated an architecture to monitor food systems across five themes: 1 diets, nutrition, and health; 2 environment, natural resources, and production; 3 livelihoods, poverty, and equity; 4 governance; and 5 resilience and sustainability. Each theme comprises three-to-five indicator domains. This paper builds on that architecture, presenting the inclusive, consultative process used to select indicators and an application of the indicator framework using the latest available data, constructing the first global food systems baseline to track transformation. While data are available to cover most themes and domains, critical indicator gaps exist such as off-farm livelihoods, food loss and waste, and governance. Baseline results demonstrate every region or country can claim positive outcomes in some parts of food systems, but none are optimal across all domains, and some indicators are independent of national income. These results underscore the need for dedicated monitoring and transformation agendas specific to food systems. Tracking these indicators to 2030 and beyond will allow for data-driven food systems governance at all scales and increase accountability for urgently needed progress toward achieving global goals.

In this study, we evaluated the validity of selfreported posttraumatic growth (PTG) by assessing the relation between perceived growth and actual growth from pre-to posttrauma. Undergraduate students completed measures tapping typical PTG domains at Time 1 and Time 2 (2 months later). We compared change in those measures with scores on the Posttraumatic Growth Inventory (PTGI; Tedeschi & Calhoun, 1996) for those participants who reported a traumatic event between Time 1 and Time 2 (n = 122). PTGI scores generally were unrelated to actual growth in PTG-related domains. Moreover, perceived growth was associated with increased distress from pre-to posttrauma, whereas actual growth was related to decreased distress, a pattern suggesting that perceived and actual growth reflect different processes. Finally, perceived (but not actual) growth was related to positive reinterpretation coping. Thus, the PTGI, and perhaps other retrospective measures, does not appear to measure actual pre-to posttrauma change.

Although adequate representation of specific subgroups (eg, women and the elderly) in randomized controlled trials (RCTs) has been under intense scrutiny, there are few data on representation by race. Using all RCTs cited by the 2007 American Heart Association guidelines for cardiovascular disease prevention in women (although trials were included whether or not there were female participants), we explored the extent to which information on race was reported in the baseline characteristics. Race/ethnicity categories were whites, blacks, Asians, Hispanics, and “others.” Overall, 156 trials were analyzed. Demographic data on race/ethnicity were reported in 55 (35%) trials and increased significantly over time (1970s, 12.5%; 1980s, 25%; 1990s, 30.5%; 2000s, 46.2%; P for trend = .011). Among the 55 trials reporting any race/ethnicity information, trial inclusion of whites, blacks, Asians, Hispanics, and “others” was reported in 27%, 13%, 14%, 5%, and 10% of trials, respectively, and increased over time ( P for trend < .05 for all). Trials enrolling subjects only in the United States or globally, including the US, were more likely to report race composition than trials that included no US sites (US only 64% vs global 62% vs non-US 21%, P < .01). Industry- and federal/foundation-funded RCTs reported race with similar frequency (industry 36% vs federal 34% vs both 24%, P = .44). When we isolated our analyses to trials that were funded by the National Institutes of Health, 12 (67%) of 18 RCTs reported race/ethnicity as a baseline characteristic. Although reporting the race/ethnic composition of study populations is increasing over time, two thirds of all RCTs supporting a recent American Heart Association () guideline failed to publish any information on race. A necessary first requirement in translating RCT evidence to patients of all races is information regarding racial demographics. Such information should be strongly encouraged in future publications.

Recalling the pain of adolescent romantic relationship breakups often conjures up memories of weeks spent ruminating and depressed, wondering whether a relationship like that would ever be found again. Although relationship breakups are stressful, most people do eventually stop thinking about their expartner, their mood eventually improves, and they realize that there are \"other fish in the sea.\" In fact, most people date more than one person-and in fact may marry more than one person-in their lifetimes. In retrospect, early relationships may never have had much of a chance. Poor partner selection, a poor fit between partners, or just a general lack of knowledge about how to make a relationship work can make it difficult for adolescent romances to endure. Ideally, years of trial and error in romantic relationships enable individuals to grow in their capacity to select and sustain satisfying, stable romantic relationships.