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Understanding patterns and mechanisms underlying local adaptation is becoming increasingly important for species conservation amid anthropogenically driven environmental change. Alpine systems are experiencing particularly intense pressure from environmental change resulting from increased rates of warming and corresponding loss of snow and ice. We integrate morphological and genetic analyses to identify traits important for local adaptation in one of the highest elevation breeding birds in North America, the Sierra Nevada Gray-crowned Rosy Finch. We performed an in-depth analysis of how traits with known links to thermoregulation in birds such as wing length, bill size, and feather microstructure vary between two populations at sites with contrasting climate and environmental conditions. We identified loci underlying these traits using a genome-wide association study and further examined regions of the genome related to altitude adaptation and cold tolerance using F ST outlier tests. Together, these results indicate that temperature, food availability, and alpine landscape features may impose multifaceted and potentially conflicting selective pressures on morphological traits important to adaptation in alpine birds. Overall, this work represents one of the first in-depth analyses of the genetic basis of adaptation in an alpine specialist songbird. 

This paper aims to introduce a new paradigm for mathematics literacy. By integrating computational thinking and coding into curricular units from The Algebra Project, we engaged middle school students in creativity, imagination, and self-expression in the mathematics classroom. We refined instruments to measure the development of student voice, agency, and belongingness. In the context of the mathematics classroom, there is potential for an earned insurgency to arise when these attributes of mathematical identity are amplified, leading students to engage in a learning community that rejects the repressive logic of the current racialized, classed, and otherwise oppressive mathematics education 

Abstract The hydrogen atom is a touchstone for the foundations, evolution and frontiers of quantum theory^1–9. Key spectral lines of this atom have been determined to remarkable precision^10,11. Our research focuses on the study of antihydrogen, the antimatter counterpart of hydrogen. We test fundamental symmetries of nature (such as simultaneous charge conjugation, parity inversion, and time reversal or CPT symmetry) through precision comparisons of these atomic systems¹². Recent 1S–2S spectroscopic measurements on trapped antihydrogen have achieved relative precisions of parts per trillion (refs. ^13,14). However, the ground-state hyperfine splitting, which is sensitive to the internal structure of the antiproton, has only been measured to 400 parts per million (ppm). Here we report a 4 ppm measurement of the antihydrogen ground-state hyperfine splitting energya_1S, advancing the state-of-the-art precision¹⁵by two orders of magnitude. From microwave spectroscopy experiments with roughly 24,000 anti-atoms, we determine$${a}_{1{\rm{S}}}/h=\mathrm{1,420,404.8}\pm 1.1(\mathrm{stat.})\pm 5.6\,(\mathrm{sys.})\,\text{kHz}$$ $a_{1S}/h=\mathrm{1,420,404.8}\pm 1.1\left(\mathrm{stat.}\right)\pm 5.6\left(\mathrm{sys.}\right)\text{kHz}$in a 1-T magnetic field, consistent with expectations for hydrogen¹¹. At this level, our measurement is sensitive to the internal structure of the antiproton, which contributes at about 40 ppm and is approaching the limit of existing theoretical analyses¹⁶. The gains we report are the product of marked advances in magnetic trap field control, stabilization and characterization; anti-atom spin-state manipulation; and improved antihydrogen accumulation rate¹⁷. 

Abstract Antihydrogen, the bound state of a positron and an antiproton, is the only pure anti-atomic system ever studied. It is produced exclusively in the laboratory, as it has never been observed in nature. This unique system is of great interest for searching for tentative differences between matter and antimatter. Antihydrogen has been routinely trapped since 2010 and accumulated since 2017, enabling, for example, the first precision spectroscopic study of the anti-atom in 2018 and the first observation of the influence of gravity in 2023. Here we report an eight-fold increase in the trapping rate of antihydrogen, enabled by sympathetic cooling of positrons with laser-cooled beryllium ions. With beryllium sympathetic cooling, we now accumulate over 15000 antihydrogen atoms in under seven hours. This technique transforms our ability to study systematic and sidereal effects in existing experiments while paving the way for studies that would otherwise remain out of reach. 

This chapter provides a brief review of recent developments on two nonlocal operators: fractional Laplacian and fractional time derivative. We start by accounting for several applications of these operators in imaging science, geophysics, harmonic maps, and deep (machine) learning. Various notions of solutions to linear fractional elliptic equations are provided and numerical schemes for fractional Laplacian and fractional time derivative are discussed. Special emphasis is given to exterior optimal control problems with a linear elliptic equation as constraints. In addition, optimal control problems with interior control and state constraints are considered. We also provide a discussion on fractional deep neural networks, which is shown to be a minimization problem with fractional in time ordinary differential equation as constraint. The paper concludes with a discussion on several open problems.