We address a core partition regularity problem in Ramsey theory by proving that every finite coloring of the positive integers contains monochromatic Pythagorean pairs (i.e., $x,y\in {\mathbb N}$ such that $x^2\pm y^2=z^2$ for some $z\in {\mathbb N}$). We also show that partitions generated by level sets of multiplicative functions taking finitely many values always contain Pythagorean triples. Our proofs combine known Gowers uniformity properties of aperiodic multiplicative functions with a novel and rather flexible approach based on concentration estimates of multiplicative functions.

The impact of required durations of therapy for antibiotic orders at the time of order entry has not been reported. Requiring ordering clinicians to enter stop dates at the time of antibiotic order entry decreased DOT/1000 patient days for orders with empiric indication from 154 to 119 (–34.9 (–55.7 to –14)).

We study homotopy groups of spaces of long links in Euclidean space of codimension at least three. With multiple components, they admit split injections from homotopy groups of spheres. We show that, up to knotting, these account for all the homotopy groups in a range which depends on the dimensions of the source manifolds and target manifold and which roughly generalizes the triple-point-free range for isotopy classes. Just beyond this range, joining components sends both a parametrized long Borromean rings class and a Hopf fibration to a generator of the first nontrivial homotopy group of the space of long knots. For spaces of equidimensional long links of most source dimensions, we describe generators for the homotopy group in this degree in terms of these Borromean rings and homotopy groups of spheres. A key ingredient in most of our results is a graphing map which increases source and target dimensions by one.

Friendship occupies the last place in the five social relations in the Confucian tradition, yet it plays an important role in Confucian writings. In this article, I discuss the notion of friendship that lasts beyond death from ancient China. I examine how the friendship between Bo Ya and Zhong Ziqi finds its continuation in that of Fan Shi and Zhang Shao, insofar as one of the two friends dies in both cases. These friendly bonds are tinged with a tragic tone and have fueled the imagination of the Chinese who sublimate or amplify them in all kinds of literary genres – poetry, theater, and novel – dating back to the pre-imperial period and to the Han Dynasty. All the authors underscore the faithfulness of these characters, which they consider to be the characters’ virtue. They also emphasize the spiritual link that transcends life and death. Based on the translation of these well-known and celebrated narratives, I intend to show how the exemplary nature of friendship is enhanced or mythologized, and how intertextuality has shaped the Chinese vocabulary itself in this regard.

This is a case study of Guatemala’s judicial system, initially designed to be a pluralist model in 1984. However, it is now captured by political entrepreneurs who are undermining liberal democracy. The research warns about similar risks in other young democracies and explains the pitfalls of judicial councils and capturable courts. Although judiciaries are now seen as safeguards against authoritarianism, this study demonstrates how they can be subverted. Unlike authoritarian populists who weaken judicial institutions through popular support, this case shows how entrepreneurs rely on intimidation and capture. Using data of the growth of lawyers, I propose the entrepreneurs outnumbered the elites committed to democracy and captured the nomination process in favor of uncommitted elites leading to democratic backsliding.

Adaptation to the dynamic environment and variable task sequence is the critical ability for robot navigation and task execution. The Cyclic Networking Rapidly-exploring Random Tree (CNRRT) method is proposed to obtain the optimal path in real time and realize long-term path planning ability in a complex dynamic environment. The cyclic branch is introduced to the acyclic graph of Rapidly-exploring Random Tree (RRT) method, which forms a decentralized path network in the configuration space. An iterative searching strategy is built to search for the optimal path in the network. The branch prune, reconnection, and regrowth processes enable the decentralized network to efficiently respond to dynamic changes in the environment. The CNRRT can search for the real-time optimal path in the dynamic environment, dealing with the configuration and task changes robustly. Besides, the CNRRT is consistent for scenarios with long-term task sequence without significant performance fluctuation. Simulations and real-world comparative experiments verify the effectiveness of the proposed method.

Two characteristics that defined Bob Morris were his empathy and his humanity. As a person, not just as a teacher and scholar, these elements infused his approach to people no matter their age or status. This short appreciation considers his contributions to urban and social history, his capacity for synthesis and analysis and his sensitivity in exploring places and spaces using text, data and images. Bob Morris’ humility was the hallmark of an exceptional historian, colleague and friend.

For binary plug nozzle, the plug cone is exposed to high-temperature mainstream flow, making it one of the nozzle’s high-temperature components. This paper uses the Realizable k-ε turbulence model and the reverse Monte Carlo method to numerically investigate the aerodynamic and infrared radiation characteristics of the plug nozzle. Various slot cooling configurations were adopted to study the nozzle’s infrared radiation in detail. Results indicate that compared to the baseline nozzle, the plug nozzle’s performance is slightly reduced due to the decrease in effective area of flow over the plug cone. Introducing slot cooling at the rear edge provides significant infrared suppression benefits at low detection angles and notably reduces infrared radiation discrepancy with baseline nozzle at high detection angles. The cooling air from slots causes the nozzle jet to exhibit a ‘thermal layered’ feature. With the same total coolant mass flow, the ‘leading edge + trailing edge’ cooling configuration can lower the area-averaged wall temperature of the plug cone by 5.5% – 12.3%. However, its infrared radiation intensity at each detection angle on the pitch detection plane is higher than that of the ‘trailing edge’ configuration. The significance of leading-edge cooling is focused more on thermal protection for the plug. Thus, it is essential to balance coolant mass flow distribution between infrared radiation suppression and thermal protection.

The increasing size and severity of wildfires across the western United States have generated dangerous levels of PM2.5 concentrations in recent years. In a changing climate, expanding the use of prescribed fires is widely considered to be the most robust fire mitigation strategy. However, reliably forecasting the potential air quality impact from prescribed fires, which is critical in planning the prescribed fires’ location and time, at hourly to daily time scales remains a challenging problem. In this paper, we introduce a spatio-temporal graph neural network (GNN)-based forecasting model for hourly PM2.5 predictions across California. Utilizing a two-step approach, we use our forecasting model to predict the net and ambient PM2.5 concentrations, which are used to estimate wildfire contributions. Integrating the GNN-based PM2.5 forecasting model with simulations of historically prescribed fires, we propose a novel framework to forecast their air quality impact. This framework determines that March is the optimal month for implementing prescribed fires in California and quantifies the potential air quality trade-offs involved in conducting more prescribed fires outside the peak of the fire season.

Phylogenetic analysis demonstrates that Kuamaia lata, a helmetiid euarthropod from the lower Cambrian (Series 2, Stage 3) Chengjiang Konservat-Lagerstätte, nests robustly within Artiopoda, the euarthropod clade including trilobitomorphs. Microtomography of new specimens of K. lata reveals details of morphology, notably a six-segmented head and raptorial frontal appendages, the latter contrasting with filiform antennae considered to be a diagnostic character of Artiopoda. Phylogenetic analyses demonstrate that a raptorial frontal appendage is a symplesiomorphy for upper stem-group euarthropods, retained across a swathe of tree space, but evolved secondarily in K. lata from an antenna within Artiopoda. The phylogenetic position of K. lata adds support to a six-segmented head being an ancestral state for upper stem- and crown-group euarthropods.

On April 9, 2024, the Grand Chamber of the European Court of Human Rights (ECtHR or the Court) seated in Strasbourg released its judgment in the Verein KlimaSeniorinnen Schweiz v. Switzerland case, which marks the first occasion where the Court found a violation of several rights of the European Convention on Human Rights and Fundamental Freedoms (Convention) in a climate change litigation case.

Musical sources from the nineteenth century in Argentina are very scarce. The first challenge, therefore, is to locate these materials across multiple repositories. In the last 15 years, certain state policies have been introduced to unify access to information in digital and non-digital archives. However, the country's economic instability, successive changes of government and the discontinuity of public policies in reference to cultural and educational programmes continue to impede a consistent systematization of collections and catalogues of these repositories. Additionally, it is also necessary to consult other repositories – both public collections, managed by provinces rather than the national government, and private ones that may offer online resources such as catalogues, transcriptions or digitized materials. Much of the musical production in the first half of the nineteenth century occurred within religious contexts, which means that a large part of these sources is located in ecclesiastical repositories that are very difficult to access. Many lack websites, the extent of their holdings remains unknown, and in cases where catalogues do exist, they are often not digitized.

Electrophoretic characterization of nano- and micro-metre scaled bubbles and drops is increasingly important in environmental and health sciences. Despite more than a hundred years of study, the interpretation of bubble electrophoresis data remains an unresolved fundamental problem that bridges fluid mechanics and interfacial science. This paper examines, from a theoretical perspective, how the electrophoretic mobility of small drops and bubbles responds to the interfacial kinetic-exchange rate and interfacial-charge mobility: factors that have been largely overlooked, but which provide new insights on the interpretation of $\zeta$-potentials, which are routinely used to assess surface charge density. A variety of outcomes are demonstrated, each reflecting subtle balances of hydrodynamic and electrical forces, modulated by interfacial thermodynamics and transport. Among the findings is that irreversibly bound charge with low interfacial mobility furnishes rigid-sphere behaviour; whereas interfacial charge with high mobility produces the characteristically high electrophoretic mobilities of non-conducting, uniformly charged fluid spheres. Outcomes are more complex when drops and bubbles have interfacial charge that seeks local equilibrium with the immediately adjacent electrolyte. For example, the present model shows that interfacial-charge mobility regularizes the singular behaviour predicted by theories for fluid spheres bearing high, perfectly uniform surface charge.