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Consider a Bellman--Harris-type branching process, in which individuals evolve independently of one another, giving birth after a random time $T$ to a random number $L$ of children. In this article, we study the asymptotic behaviour of the length of the longest branches of this branching process at time $t$, both pendant branches (corresponding to individuals still alive at time $t$) and interior branches (corresponding to individuals dead before time $t$)., Comment: 13 pages, correction of an error in the previous version of that article

Likelihood-free inference is quickly emerging as a powerful tool to perform fast/effective parameter estimation. We demonstrate a technique of optimizing likelihood-free inference to make it even faster by marginalizing symmetries in a physical problem. In this approach, physical symmetries, for example, time-translation are learned using joint-embedding via self-supervised learning with symmetry data augmentations. Subsequently, parameter inference is performed using a normalizing flow where the embedding network is used to summarize the data before conditioning the parameters. We present this approach on two simple physical problems and we show faster convergence in a smaller number of parameters compared to a normalizing flow that does not use a pre-trained symmetry-informed representation., Comment: Accepted for Machine Learning and the Physical Sciences Workshop (submission 69) at NeurIPS 2023; for codes, see https://github.com/ML4GW/summer-projects-2023/blob/neurips-2023/symmetry-informed-flows/README.md

Matched-filtering detection techniques for gravitational-wave (GW) signals in ground-based interferometers rely on having well-modeled templates of the GW emission. Such techniques have been traditionally used in searches for compact binary coalescences (CBCs), and have been employed in all known GW detections so far. However, interesting science cases aside from compact mergers do not yet have accurate enough modeling to make matched filtering possible, including core-collapse supernovae and sources where stochasticity may be involved. Therefore the development of techniques to identify sources of these types is of significant interest. In this paper, we present a method of anomaly detection based on deep recurrent autoencoders to enhance the search region to unmodeled transients. We use a semi-supervised strategy that we name Gravitational Wave Anomalous Knowledge (GWAK). While the semi-supervised nature of the problem comes with a cost in terms of accuracy as compared to supervised techniques, there is a qualitative advantage in generalizing experimental sensitivity beyond pre-computed signal templates. We construct a low-dimensional embedded space using the GWAK method, capturing the physical signatures of distinct signals on each axis of the space. By introducing signal priors that capture some of the salient features of GW signals, we allow for the recovery of sensitivity even when an unmodeled anomaly is encountered. We show that regions of the GWAK space can identify CBCs, detector glitches and also a variety of unmodeled astrophysical sources.

This paper presents a work-in-progress on a learn-ing system that will provide robotics students with a personalized learning environment. This addresses both the scarcity of skilled robotics instructors, particularly in community colleges and the expensive demand for training equipment. The study of robotics at the college level represents a wide range of interests, experiences, and aims. This project works to provide students the flexibility to adapt their learning to their own goals and prior experience. We are developing a system to enable robotics instruction through a web-based interface that is compatible with less expensive hardware. Therefore, the free distribution of teaching materials will empower educators. This project has the potential to increase the number of robotics courses offered at both two- and four-year schools and universities. The course materials are being designed with small units and a hierarchical dependency tree in mind; students will be able to customize their course of study based on the robotics skills they have already mastered. We present an evaluation of a five module mini-course in robotics. Students indicated that they had a positive experience with the online content. They also scored the experience highly on relatedness, mastery, and autonomy perspectives, demonstrating strong motivation potential for this approach., Comment: 5 pages, 2 figures, conference

In this article, we will establish a number of results concerning the limiting behaviour of the longest edges in the genealogical tree generated by a continuous-time Galton-Watson (GW) process. Separately, we consider the large time behaviour of the longest pendant edges, the longest (strictly) interior edges, and the longest of all the edges. These results extend the special case of long pendant edges of birth-death processes established in Bocharov, Harris, Kominek, Mooers, and Steel [1] ., Comment: 17 pages

Consider a population evolving as a critical continuous-time Galton-Watson (GW) tree. Conditional on the population surviving until a large time $T$, sample $k$ individuals uniformly at random (without replacement) from amongst those alive at time $T$. What is the genealogy of this sample of individuals? In cases where the offspring distribution has finite variance, the probabilistic properties of the joint ancestry of these $k$ particles are well understood, as seen in \cite{HJR20, J19}. In the present article, we study the joint ancestry of a sample of $k$ particles under the following regime: the offspring distribution has mean $1$ (critical) and the tails of the offspring distribution are \emph{heavy} in that $\alpha \in (1,2]$ is the supremum over indices $\beta$ such that the $\beta^{\text{th}}$ moment is finite. We show that for each $\alpha$, after rescaling time by $1/T$, there is a universal stochastic process describing the joint coalescent structure of the $k$ distinct particles. The special case $\alpha = 2$ generalises the known case of sampling from critical GW trees with finite variance where only pairwise mergers are observed and the genealogical tree is, roughly speaking, some kind of mixture of time-changed Kingman coalescents. The cases $\alpha \in (1,2)$ introduce new universal limiting partition-valued stochastic processes with interesting probabilistic structures which have representations connected to the Lauricella function and the Dirichlet distribution, and whose coalescent structures exhibit multiple-mergers of family lines. Moreover, in the case $\alpha \in (1,2)$, we show that the coalescent events of the ancestry of the $k$ particles are associated with birth events that produce giant numbers of offspring of the same order of magnitude as the entire population size, and we compute the joint law of the ancestry together with the sizes of these giant births., Comment: 47 pages

In Virginia, there has been a long-term effort to increase the number of graduates who earn career and technical education (CTE) credentials. These CTE credentials are intended to provide high school graduates with additional preparation for college and careers. In 2013, the Virginia Board of Education added a CTE credential requirement to the Standard diploma for students who entered grade 9 for the first time in 2013 or later. Graduates can complete this requirement by passing an approved assessment and do not have to take any CTE courses. The CTE credential requirement was added to the Standard diploma because graduates earning this diploma are less likely to enroll in, persist in, or complete college than graduates who earn Virginia's other main diploma, the Advanced Studies diploma. In addition, this new policy is part of the state's efforts to eliminate racial and socioeconomic inequities in Virginia public schools. Graduates who are Black or Hispanic, who are English learner students, who are in economically disadvantaged circumstances, or who receive special education services are more likely than other groups of graduates to earn the Standard diploma rather than the Advanced Studies diploma. At the request of Virginia CTE leaders, the Regional Educational Laboratory Appalachia conducted a descriptive study of attainment rates of CTE credentials, completion rates of CTE programs of study, and college enrollment rates for Standard diploma graduates from 2011 to 2017, the years before and after the policy change. Education stakeholders in Virginia and elsewhere can use the results of this study to inform their CTE policies. From 2011 to 2017, the percentage of Standard diploma graduates who earned at least one CTE credential increased from 23 percent to 91 percent. A similar increase occurred among Advanced Studies diploma graduates, even though the CTE credential requirement applied only to Standard diploma graduates. The attainment rates of CTE credentials increased for all groups of Standard diploma graduates, including groups based on demographic characteristics, federal program participation, and academic achievement. While the percentages of Standard diploma graduates who earned a CTE credential increased consistently from 2011 to 2017, their college enrollment rates dropped. The percentage of Standard diploma graduates completing a CTE program of study, which requires taking CTE courses that are not required to earn a credential but may still be helpful for later student outcomes, decreased in 2016 and 2017. The study findings suggest a need to examine workforce outcomes for Standard diploma graduates to fully understand whether this policy is meeting its intended goals. In addition, the findings suggest a need to consider other methods to address outcomes for Virginia's Standard diploma graduates, such as support for implementing practices with rigorous evidence of effectiveness for improving college and career outcomes. [For the appendixes, see ED616549. For the Study Snapshot, see ED616547.]

We provide a many-to-few formula in the general setting of non-local branching Markov processes. This formula allows one to compute expectations of k-fold sums over functions of the population at k different times. The result generalises [14] to the non-local setting, as introduced in [11] and [8]. As an application, we consider the case when the branching process is critical, and conditioned to survive for a large time. In this setting, we prove a general formula for the limiting law of the death time of the most recent common ancestor of two particles selected uniformly from the population at two different times, as t tends to infinity. Moreover, we describe the limiting law of the population sizes at two different times, in the same asymptotic regime., Comment: 29 pages, 3 figures

The fundamental nature of Dark Matter is a central theme of the Snowmass 2021 process, extending across all Frontiers. In the last decade, advances in detector technology, analysis techniques and theoretical modeling have enabled a new generation of experiments and searches while broadening the types of candidates we can pursue. Over the next decade, there is great potential for discoveries that would transform our understanding of dark matter. In the following, we outline a road map for discovery developed in collaboration among the Frontiers. A strong portfolio of experiments that delves deep, searches wide, and harnesses the complementarity between techniques is key to tackling this complicated problem, requiring expertise, results, and planning from all Frontiers of the Snowmass 2021 process., Comment: 10 pages, 5 figures. Version prepared for inclusion in the Snowmass Book. Extended version at arXiv:2210.01770. v2: fixed authors and affiliations

The fundamental nature of Dark Matter is a central theme of the Snowmass 2021 process, extending across all frontiers. In the last decade, advances in detector technology, analysis techniques and theoretical modeling have enabled a new generation of experiments and searches while broadening the types of candidates we can pursue. Over the next decade, there is great potential for discoveries that would transform our understanding of dark matter. In the following, we outline a road map for discovery developed in collaboration among the frontiers. A strong portfolio of experiments that delves deep, searches wide, and harnesses the complementarity between techniques is key to tackling this complicated problem, requiring expertise, results, and planning from all Frontiers of the Snowmass 2021 process., Comment: v3: fixed authorlist (on arXiv only)

This is the Snowmass2021 Energy Frontier (EF) Beyond the Standard Model (BSM) report. It combines the EF topical group reports of EF08 (Model-specific explorations), EF09 (More general explorations), and EF10 (Dark Matter at Colliders). The report includes a general introduction to BSM motivations and the comparative prospects for proposed future experiments for a broad range of potential BSM models and signatures, including compositeness, SUSY, leptoquarks, more general new bosons and fermions, long-lived particles, dark matter, charged-lepton flavor violation, and anomaly detection., Comment: 108 pages + 38 pages references and appendix, 37 figures, Report of the Topical Group on Beyond the Standard Model Physics at Energy Frontier for Snowmass 2021. The first nine authors are the Conveners, with Contributions from the other authors

We investigate the genealogy of a sample of $k\geq1$ particles chosen uniformly without replacement from a population alive at large times in a critical discrete-time Galton-Watson process in a varying environment (GWVE). We will show that subject to an explicit deterministic time-change involving only the mean and variances of the varying offspring distributions, the sample genealogy always converges to the same universal genealogical structure; it has the same tree topology as Kingman's coalescent, and the coalescent times of the $k-1$ pairwise mergers look like a mixture of independent identically distributed times. Our approach uses $k$ distinguished \emph{spine} particles and a suitable change of measure under which (a) the spines form a uniform sample without replacement, as required, but additionally (b) there is $k$-size biasing and discounting according to the population size. Our work significantly extends the spine techniques developed in Harris, Johnston, and Roberts \emph{[Annals Applied Probability, 2020]} for genealogies of uniform samples of size $k$ in near-critical continuous-time Galton-Watson processes, as well as a two-spine GWVE construction in Cardona and Palau \emph{[Bernoulli, 2021]}. Our results complement recent works by Kersting \emph{[Proc. Steklov Inst. Maths., 2022]} and Boenkost, Foutel-Rodier, and Schertzer \emph{[arXiv:2207.11612]}.

Dark matter is estimated to make up ~84% of all normal/baryonic matter, but cannot be directly imaged. Despite the fact that dark matter cannot be directly observed yet, its influence on the motion of stars and gas in spiral galaxies have been detected. One way to show motion in galaxies are rotation curves that are plots of velocity measurements of how fast stars and gas move in a galaxy around the center of mass. According to Newton's Law of Gravitation, the rotational velocity is an indication of the amount of visible and non-visible mass in the galaxy. Given that the visible matter is measurable using photometry, dark matter mass can therefore be estimated, offering an insight into the size distribution in galaxies. In order to gain a greater appreciation of the research scientists' findings about dark matter, their method should be easily reproduced by any curious individual. Our interactive workshop is an excellent educational tool to investigate how dark matter impacts the rotation of visible matter by providing a guide to produce galactic rotation curves. The Python-based notebooks are set up to walk you through the whole process of producing rotation curves using an online database (SPARC) and to allow you to learn about each component of the galaxy. The three steps of the rotation curve building process is plotting the measured velocity data, constructing the rotation curves for each component, and fitting the total velocity to the measured values., Comment: 6 pages, 1 table

USNO Bright Star Catalog (UBSC) is a new astrometric catalog of 1423 brightest stars covering the entire sky, which is published online. It is nearly complete to $V=3$ mag except for three stellar systems. A combined astrometric solution of the Hipparcos Intermediate Astrometry Data and two dedicated ground-based campaigns in 2013 -- 2020 is the basis for this catalog. The astrometric parameters for each star include position coordinates, parallax, proper motion components, and their covariances on the Hipparcos mean epoch 1991.25. 64 percent of the catalog are flagged as known or suspected double or binary stars. UBSC lists 68 stars missing in Gaia EDR3 and another 114 stars without Gaia parallaxes or proper motions. The formal precision achieved for proper motions is comparable to that of Gaia., Comment: Accepted for publication in AJ. Astrometric catalog of 1423 bright stars will be published online

A program to build a lepton-collider Higgs factory, to precisely measure the couplings of the Higgs boson to other particles, followed by a higher energy run to establish the Higgs self-coupling and expand the new physics reach, is widely recognized as a primary focus of modern particle physics. We propose a strategy that focuses on a new technology and preliminary estimates suggest that can lead to a compact, affordable machine. New technology investigations will provide much needed enthusiasm for our field, resulting in trained workforce. This cost-effective, compact design, with technologies useful for a broad range of other accelerator applications, could be realized as a project in the US. Its technology innovations, both in the accelerator and the detector, will offer unique and exciting opportunities to young scientists. Moreover, cost effective compact designs, broadly applicable to other fields of research, are more likely to obtain financial support from our funding agencies., Comment: 11 pages, 2 figures, contribution to Snowmass 2021

We present the United States Naval Observatory (USNO) Bright-Star Astrometric Database (UBAD), a current-epoch high-accuracy astrometric catalog. The catalog consists of 364 bright northern hemisphere stars, including all but five such stars with either $V < 3.5$ or with $I < 3.2$ and $V < 6$, as well as a large fraction of slightly fainter stars; 36 of the brightest catalog stars are not included in Gaia Early Data Release 3 (EDR3). Observations were conducted with the USNO, Flagstaff Station, Kaj Strand 61-inch Astrometric Reflector. Target stars were imaged through a small 12.5-magnitude neutral-density spot, while the remainder of the stars in the field of view were unattenuated. This allowed for unsaturated images of the bright target stars to be calibrated directly against much fainter reference stars from Gaia EDR3. The median position errors are 1.9 mas in both right ascension and declination at the catalog epoch of 2017.0, with 90% of catalog stars having errors less than 2.6 mas; systematic errors are 1 -- 3 mas. Combining UBAD observations with Hipparcos-2 positions yields proper motions with median errors of 0.045 and 0.049 mas year$^{-1}$ in right ascension and declination, respectively, with 90% of stars having errors less than 0.1 mas year$^{-1}$; systematic errors are about 0.1 mas year$^{-1}$. Single-frame accuracy for positions of the target stars is typically 5 -- 6 mas. Gaia EDR3 astrometry for these bright stars, which are heavily saturated in the Gaia observations, is validated over the magnitude range $2 \lesssim G \lesssim 6$., Comment: 22 pages, 26 figures, published in The Astronomical Journal

In Virginia, all high school students can earn either a Standard diploma or an Advanced Studies diploma, the latter being a college preparatory diploma. Starting in 2017, the Virginia Department of Education (VDOE) began requiring students graduating with the Standard diploma to earn a career and technical education (CTE) credential to encourage them to pursue opportunities that enhance their career readiness. This is likely to be particularly important for students graduating with the Standard diploma, as they have been shown to have limited success in postsecondary education. This study examined the CTE credentials Virginia high school graduates most commonly earned from 2011 through 2017. The five most commonly earned CTE credentials in Virginia remained the same during this time period, but the percentage of students earning the Workplace Readiness Skills (WRS) and W!se Financial Literacy Certification credentials increased. Both of these credentials cover broad skills relevant to a wide range of jobs, as opposed to a specific occupation or industry. Although the new CTE requirement applies only to Standard diploma graduates, there were few differences in the top 10 credentials by diploma type, both in terms of which credentials were most common as well as the rates at which students earned these credentials. Regardless of diploma type, in 2017, 9 of the top 10 credentials were broad credentials that were not narrowly aligned to a specific occupation or industry. This study also looked at the top 10 credentials earned by 2017 Standard diploma graduates across a variety of student subgroups, including English learner students, economically disadvantaged students, students with disabilities, and racial/ethnic subgroups. English learner students and students with disabilities earned the top 10 credentials at lower rates than other Standard diploma graduates. Student credential-earning rates differed the most by geographic region, both in terms of which credentials appeared in the top 10 and the percentage of students earning the top 10 credentials. This study highlights the need for additional analyses to help CTE stakeholders and policymakers understand the value of different types of CTE credentials. In particular, Virginia and other states might explore the relative value of broad CTE credentials that apply to a wide range of jobs and have become increasingly prevalent in Virginia compared with CTE credentials that are more narrowly aligned with a specific occupation or industry.

To help students leave high school on a path toward success in the labor market, education policymakers and practitioners often focus on improving career and technical education (CTE) opportunities in high school. Understanding the alignment between high school CTE programs and the labor market is an important step in this process. To support CTE improvement efforts, this study quantitatively assessed the alignment between West Virginia's high school CTE programs and the labor market, with a focus on alignment to regional high-demand occupations that require moderate occupational preparation. These "high-demand study occupations" are the 20 occupations in each region of West Virginia with the largest number of long-term projected employment openings from 2014 to 2024 that require more than a high school diploma (for example, a license or work-related experience) but less than a bachelor's degree. The study found that 70 percent of West Virginia's long-term projected employment openings typically require some occupational preparation beyond a high school diploma but less than a bachelor's degree. Further, 93 percent of the regional long-term projected employment openings in high-demand study occupations were served by at least one aligned CTE program in the same region. However, students in only 53 percent of the state's CTE programs were in a program that aligned to at least one high-demand study occupation within their region. West Virginia stakeholders can use the findings to improve their CTE system's alignment and better prepare students for a postsecondary career. This study also serves as an example for policymakers and practitioners in other states who are interested in quantifying their CTE system's alignment in order to make data-informed decisions. [For the appendixes, see ED605045; for the snapshot, see ED605046.]

The number of parameters in deep neural networks (DNNs) is scaling at about 5$\times$ the rate of Moore's Law. To sustain this growth, photonic computing is a promising avenue, as it enables higher throughput in dominant general matrix-matrix multiplication (GEMM) operations in DNNs than their electrical counterpart. However, purely photonic systems face several challenges including lack of photonic memory and accumulation of noise. In this paper, we present an electro-photonic accelerator, ADEPT, which leverages a photonic computing unit for performing GEMM operations, a vectorized digital electronic ASIC for performing non-GEMM operations, and SRAM arrays for storing DNN parameters and activations. In contrast to prior works in photonic DNN accelerators, we adopt a system-level perspective and show that the gains while large are tempered relative to prior expectations. Our goal is to encourage architects to explore photonic technology in a more pragmatic way considering the system as a whole to understand its general applicability in accelerating today's DNNs. Our evaluation shows that ADEPT can provide, on average, 5.73$\times$ higher throughput per Watt compared to the traditional systolic arrays (SAs) in a full-system, and at least 6.8$\times$ and $2.5\times$ better throughput per Watt, compared to state-of-the-art electronic and photonic accelerators, respectively.

Increasing demand for algorithms that can learn quickly and efficiently has led to a surge of development within the field of artificial intelligence (AI). An important paradigm within AI is reinforcement learning (RL), where agents interact with environments by exchanging signals via a communication channel. Agents can learn by updating their behaviour based on obtained feedback. The crucial question for practical applications is how fast agents can learn to respond correctly. An essential figure of merit is therefore the learning time. While various works have made use of quantum mechanics to speed up the agent's decision-making process, a reduction in learning time has not been demonstrated yet. Here we present a RL experiment where the learning of an agent is boosted by utilizing a quantum communication channel with the environment. We further show that the combination with classical communication enables the evaluation of such an improvement, and additionally allows for optimal control of the learning progress. This novel scenario is therefore demonstrated by considering hybrid agents, that alternate between rounds of quantum and classical communication. We implement this learning protocol on a compact and fully tunable integrated nanophotonic processor. The device interfaces with telecom-wavelength photons and features a fast active feedback mechanism, allowing us to demonstrate the agent's systematic quantum advantage in a setup that could be readily integrated within future large-scale quantum communication networks., Comment: 10 pages, 4 figures