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Reward schemes may affect not only agents' effort, but also their incentives to gather information to reduce the riskiness of the productive activity. In a laboratory experiment using a novel task, we find that the relationship between incentives and evidence gathering depends critically on the availability of information about peers' strategies and outcomes. When no peer information is available, competitive rewards can be associated with more evidence gathering than noncompetitive rewards. In contrast, when decision-makers know what or how their peers are doing, competitive rewards schemes are associated with less active evidence gathering than noncompetitive schemes. The nature of the feedback -- whether subjects receive information about peers' strategies, outcomes, or both -- also affects subjects' incentives to engage in evidence gathering. Specifically, only combined feedback about peers' strategies and performance -- from which subjects may assess the overall relationship between evidence gathering, riskiness, and success -- is associated with less evidence gathering when rewards are based on relative performance; we find no similar effect for noncompetitive rewards.

In this manuscript we consider a special complex torus, denoted $S_{\Delta_{2k}}$ (for each $k \in \mathbb{N},\, k \geq 1$) and called the Dirac spinor torus. It is an Abelian variety of complex dimension $2^{k}$ whose covering space is the space of Dirac spinors, $\Delta_{2k}$, for the Clifford algebra $Cl(\mathbb{C}^{2k})$ associated with the vector space $\mathbb{C}^{2k}$. Fixing an isomorphism $\rho:Cl(\mathbb{C}^{2k})\rightarrow End (\Delta_{2k})$, we define Clifford multiplication on $S_{\Delta_{2k}}$ as the actions of those endomorphisms in the image of $\rho$ that preserve the full rank lattice. We analyze the properties of that Clifford multiplication on the 2-torsion points of the Dirac spinor torus. We identify the Clifford actions with permutation maps that represent all isomorphism classes of these actions on the group of 2-torsion points. We provide a structure theorem describing these isomorphism classes of Clifford actions in a way that is independent of the choice of representatives. We conclude by extending the scope of our analysis to the group of $n$-torsion points and analyzing the fixed points and translation constants of entry-permuting maps, a broader class of actions of which the Clifford actions on the 2-torsion points of $S_{\Delta_{2k}}$ is a subset.

We introduce a version of skein categories which depends on a tensor ideal in a ribbon category, thereby extending the existing theory to the setting of non-semisimple TQFTs. We obtain modified notions of skein algebras of surfaces and skein modules of 3-cobordisms for non-semisimple ribbon categories. We prove that these skein categories built from ideals coincide with factorization homology, shedding new light on the similarities and differences between the semisimple and non-semisimple settings. As a consequence, we get a skein-theoretic description of factorization homology for a large class of balanced braided categories in Pr, precisely all those which are expected to induce an oriented categorified 3-TQFT., Comment: 29 pages. Comments welcome!

We show that the quantum invariants arising from typical representations of the quantum group $U_h\mathfrak{sl}(2|1)$ are q-holonomic. In particular, this implies the existence of an underlying field theory for which this family of invariants are partition functions., Comment: 15 pages

Recent research has demonstrated the capability of behavior signals captured by smartphones and wearables for longitudinal behavior modeling. However, there is a lack of a comprehensive public dataset that serves as an open testbed for fair comparison among algorithms. Moreover, prior studies mainly evaluate algorithms using data from a single population within a short period, without measuring the cross-dataset generalizability of these algorithms. We present the first multi-year passive sensing datasets, containing over 700 user-years and 497 unique users' data collected from mobile and wearable sensors, together with a wide range of well-being metrics. Our datasets can support multiple cross-dataset evaluations of behavior modeling algorithms' generalizability across different users and years. As a starting point, we provide the benchmark results of 18 algorithms on the task of depression detection. Our results indicate that both prior depression detection algorithms and domain generalization techniques show potential but need further research to achieve adequate cross-dataset generalizability. We envision our multi-year datasets can support the ML community in developing generalizable longitudinal behavior modeling algorithms., Comment: Thirty-sixth Conference on Neural Information Processing Systems Datasets and Benchmarks Track

We investigate the $q$-holonomic properties of a class of link invariants based on quantum group representations with vanishing quantum dimensions, motivated by the search for the invariants' realization in physics. Some of the best known invariants of this type, constructed from `typical' representations of the unrolled quantum group $\mathcal U^H_{\zeta_{2r}}(\mathfrak{sl}_2)$ at a $2r$-th root of unity, were introduced by Akutsu-Deguchi-Ohtsuki (ADO). We prove that the ADO invariants for $r\geq 2$ are a $q$-holonomic family, implying in particular that they satisfy recursion relations that are independent of $r$. In the case of a knot, we prove that the $q$-holonomic recursion ideal of the ADO invariants is contained in the recursion ideal of the colored Jones polynomials, the subject of the celebrated AJ Conjecture. (Combined with a recent result of S. Willetts, this establishes an isomorphism of the ADO and Jones recursion ideals. Our results also confirm a recent physically-motivated conjecture of Gukov-Hsin-Nakajima-Park-Pei-Sopenko.), Comment: 42 pages, 2 figures

The impact of COVID-19 on students has been enormous, with an increase in worries about fiscal and physical health, a rapid shift to online learning, and increased isolation. In addition to these changes, students with disabilities/health concerns may face accessibility problems with online learning or communication tools, and their stress may be compounded by additional risks such as financial stress or pre-existing conditions. To our knowledge, no one has looked specifically at the impact of COVID-19 on students with disabilities/health concerns. In this paper, we present data from a survey of 147 students with and without disabilities collected in late March to early April of 2020 to assess the impact of COVID-19 on these students' education and mental health. Our findings show that students with disabilities/health concerns were more concerned about classes going online than their peers without disabilities. In addition, students with disabilities/health concerns also reported that they have experienced more COVID-19 related adversities compared to their peers without disabilities/health concerns. We argue that students with disabilities/health concerns in higher education need confidence in the accessibility of the online learning tools that are becoming increasingly prevalent in higher education not only because of COVID-19 but also more generally. In addition, educational technologies will be more accessible if they consider the learning context, and are designed to provide a supportive, calm, and connecting learning environment., Comment: 15 pages

Extending recent investigations on the structure of Tukey types of ultrafilters on $\mathcal{P}(\omega)$ to Boolean algebras in general, we classify the spectra of Tukey types of ultrafilters for several classes of Boolean algebras, including interval algebras, tree algebras, and pseudo-tree algebras., Comment: 18 pages

We show that the analysis of the time evolution of the occupation of site and momentum modes of harmonically trapped lattice hard-core bosons, under driven dipole oscillations, allows one to determine the energy of the lowest one-particle excitations of the system in equilibrium. The analytic solution of a single particle in the absence of a lattice is used to identify which function of those time-dependent observables is best fit for the analysis, as well as to relate the dynamic response of the system to its single-particle spectrum. In the presence of the lattice and of multiple particles, a much richer and informative dynamical response is observed under the drive., Comment: 5 pages, 3 figures, as published

Context. The Crab nebula has been used as a celestial calibration source of the X-ray flux and spectral shape for many years by X-ray astronomy missions. However, the object is often too bright for current and future missions equipped with instruments with improved sensitivity. Aims. We use G21.5-0.9 as a viable, fainter substitute to the Crab, which is another pulsar-wind nebula with a time-constant powerlaw spectrum with a flux of a few milli Crab in the X-ray band. Using this source, we conduct a cross-calibration study of the instruments onboard currently active observatories: Chandra ACIS, Suzaku XIS, Swift XRT, XMM-Newton EPIC (MOS and pn) for the soft-band, and INTEGRAL IBIS-ISGRI, RXTE PCA, and Suzaku HXD-PIN for the hard band. Methods. We extract spectra from all the instruments and fit them under the same astrophysical assumptions. We compare the spectral parameters of the G21.5-0.9 model: power-law photon index, H-equivalent column density of the interstellar photoelectric absorption, flux in the soft (2-8 keV) or hard (15-50 keV) energy band. Results. We identify the systematic differences in the best-fit parameter values unattributable to the statistical scatter of the data alone. We interpret these differences as due to residual cross-calibration problems. The differences can be as large as 20% and 9% for the soft-band flux and power-law index, respectively, and 46% for the hard-band flux. The results are plotted and tabulated as a useful reference for future calibration and scientific studies using multiple missions., Comment: 16 pages, 21 figures, and 6 tables. A&A in press

We present the results of a simulation study into the properties of 12 different estimators of the Hurst parameter, $H$, or the fractional integration parameter, $d$, in long memory time series. We compare and contrast their performance on simulated Fractional Gaussian Noises and fractionally integrated series with lengths between 100 and 10,000 data points and $H$ values between 0.55 and 0.90 or $d$ values between 0.05 and 0.40. We apply all 12 estimators to the Campito Mountain data and estimate the accuracy of their estimates using the Beran goodness of fit test for long memory time series. MCS code: 37M10, Comment: Submitted to the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org)

This final report summarizes the activities and evaluation of Project Outcomes, a program developed at the University of Kentucky to prepare personnel to work with young children and their families in inclusive settings. The program was built around three unique components: (1) individual program plans were developed for each student; (2) each course was offered in an alternative format, such as distance learning, weekend courses, summer institutes, and night courses; and (3) the project focused on developing partnerships with families. The outcomes of the project were: (1) an increased number of early childhood personnel trained to work in both urban and rural areas; (2) increased educational opportunities for nontraditional students; and (3) increased opportunities for collaboration between professionals and families. The project accomplished all of its outcomes at a cost of about $5,520 per student. Students in rural and urban settings were able to take courses together, and of the 28 students who have finished or are nearing graduation, all are working with young children birth to 8, with the majority working in inclusive programs for children who are birth to five. Included are lists of courses offered throughout the life of the project, inservices attended and conducted, professional conference presentations given, and research conducted. (SG)

We analyze 205 ks of imaging data of the active binary, Capella, obtained with the Chandra High Resolution Camera Imager (HRC-I) to determine whether Capella shows any variability at timescales < 50 ks. We find that a clear signal for variability is present for timescales < 20 ks, and that the light curves show evidence for excess fluctuation over that expected from a purely Poisson process. This overdispersion is consistent with variability at the 2-7% level, and suggests that the coronae on the binary components of Capella are composed of low-density plasma and low-lying loops., Comment: submitted to The Astronomical Journal

The University of Kentucky has been providing graduate-level distance learning programs in moderate and severe disabilities and early childhood special education since 1989 through the Training Rural Educators in Kentucky (TREK) Projects. To document the effectiveness of the program, a follow-up survey was conducted in 1998 with an emphasis on the program's impact on students with disabilities, other teachers, and school districts. Surveys were returned from 29 former and current TREK participants. Results indicate that a significant number of participants had achieved an advanced degree or additional certification in some area of special education. A majority of respondents who indicated a job change felt that the change was due to their completion of the TREK course. On a scale of 1 (not useful) to 5 (very useful), the range of scores across all courses was 4.4. Components of the three delivery formats--on-site, satellite, and compressed video--were rated, with the satellite and combination approach tying for preferred format, followed by compressed video and on-site. A greater percentage of participants were implementing best practices for children with disabilities after taking TREK courses, and a majority of these participants shared information about the practices with other adults. Nineteen respondents reported that systemic changes in their places of employment resulted from the knowledge they gained in the TREK program. The emphasis on research-based decision making resulted in TREK participants becoming agents of change in their rural districts on behalf of children with disabilities. (TD)

We have analyzed Chandra calibration observations of Betelgeuse (alpha Ori, M2Iab, m_V=0.58, 131 pc) obtained at the aimpoint locations of the HRC-I (8 ks), HRC-S (8 ks), and ACIS-I (5 ks). Betelgeuse is undetected in all the individual observations as well as cumulatively. We derive upper limits to the X-ray count rates and compute the corresponding X-ray flux and luminosity upper limits for coronal plasma that may potentially exist in the atmosphere of Betelgeuse over a range of temperatures, T=0.3-10 MK. We place a flux limit at the telescope of fx ~ 4x10^(-15) ergs s^(-1) cm^(-2) at T=1 MK. The upper limit is lowered by a factor of ~3 at higher temperatures, roughly an order of magnitude lower than that obtained previously. Assuming that the entire stellar surface is active, these fluxes correspond to a surface flux limit that ranges from 30-7000 ergs s^(-1) cm^(-2) at T=1 MK, to ~1 ergs s^(-1) cm^(-2) at higher temperatures, five orders of magnitude below the quiet Sun X-ray surface flux. We discuss the implications of our analysis in the context of models of a buried corona and a pervasive magnetic carpet. We rule out the existence of a solar-like corona on Betelgeuse, but cannot rule out the presence of low-level emission on the scale of coronal holes., Comment: 19 pages, 4 figures. Submitted to the ApJ. This is the revised version, in response to the referee's report

We present the X-ray point source population in the nearby Virgo elliptical galaxy NGC 4636 from 3 Chandra/ACIS observations, totaling 193 ks, taken over 3 years. Using wavelet decomposition, we detect 318 point sources. Here, we use a subset of the 277 sources with >10 net cts (>1.2E37 erg/s, 0.5-2 keV, >1.5 arcmin of center). Between 1.5-6 arcmin from the center, 25% are likely background sources (AGN) and the rest are LMXBs within the galaxy, while at >6 arcmin, background sources dominate. We present a color-color diagram based on ratios of X-ray flux, which yields a tighter source distribution, and shows a large population of sources which are likely LMXBs and black hole candidates. We explore short and long-term variability (over time-scales of 1 day to 3 yr): 54 sources (24%) in the common ACIS fields show significant variability between observations. Of these, 37 are detected with >10 net counts only once and thus may be "transient". About 10% of sources in each observation show significant short-term variability. The cumulative luminosity function for the point sources can be represented as a power-law of slope 1.14. Between 1.5-6 arcmin of the center, 48 of the 129 X-ray point sources (37%) with >10 net counts are matched with optical globular cluster (GC) candidates (matches could be as high as 50% since many of the optical sources are AGN). 70% of matched sources are associated with the redder GC candidates, those that are thought to have near-solar metal abundance. The fraction of GC candidates matched with point sources decreases with decreasing GC luminosity. The X-ray luminosities of the matched point sources are not correlated with the luminosity or color of the host GC candidates. Finally, we estimate an upper limit of 4.5E37 erg/s to the current X-ray luminosity of the historical supernova SN1939A., Comment: Accepted for publication in the Astrophysical Journal; 19 pages, 15 figures, 3 tables. Version with full quality figures can be obtained at http://hea-www.harvard.edu/~jpbrown/ngc4636_astroph.pdf

The ability to conduct field-based research is a particularly valuable tool for special education teachers working in isolated rural areas. To address this need, the University of Kentucky's Developmental and Behavioral Disorders Program focuses on preparing graduate-level special education personnel to work in diverse settings; provide consultation, inservice training, and information dissemination; and analyze and conduct applied research. In addition to this on-campus program, distance learning coursework is offered through the Training Rural Educators in Kentucky (TREK) projects. All students must complete three courses that teach research and related skills: an advanced course in applied behavioral analysis; a course focusing on instructional methodology; and a course in single-subject research design. Rural research is facilitated through a graduate course that focuses on instructional issues and methodologies: group instruction, instructive feedback, embedded skill instruction, and observational learning. These skills are utilized and implemented by students in their own classroom setting. The thesis requirement of a classroom research project trains rural educators who are geographically and professionally isolated to independently solve classroom problems. Teachers acquire the skills needed to objectively analyze the classroom environment and student behaviors, generate hypotheses, implement and modify behavioral and instructional programming, and use research results to defend or discard classroom practices. Two examples include a teacher research project and a collaborative study conducted by a program graduate and a faculty member. Practical applications and issues in rural research are summarized. (SAS)

A distance-learning personnel-preparation course on transdisciplinary services for students with low incidence disabilities was developed through collaboration among four Kentucky institutions of higher learning. The course, "Transdisciplinary Services to Students with Deafblindness and Other Multiple Disabilities," was delivered to eight Kentucky locations using compressed video (two-way audio and two-way visual). This technology was chosen because it provided for direct student interaction, eliminated the need for specialists to travel to deliver lectures, and promoted class activities such as discussion. The course was viewed by 60 students enrolled in the University of Kentucky, Morehead State University, Breschia College, and the University of Louisville. In a postcourse evaluation, the overall rating was in the upper quartile. The advantages of the course were that Kentucky students had equal access to the same best-practice information, and the regional exchange of experience and dialogue provided all students with information needed to implement the concepts anywhere in the state. While technology and diversity were crucial contributors to the course's value, they were also at the heart of the challenges encountered. Recommendations to address these challenges include development by collaborating faculty of a common philosophy of instruction that includes appropriate interactive instructional activities and an understanding of the student body; guidance for students on use of the technology and rules related to mutual respect and on-line interaction; guidelines related to student on-line time that assure equal access yet effectively manage class time; and ongoing evaluation to continually adjust content and presentation. Two tables present evaluation findings. (TD)

Afterschool and competency-based learning are increasingly emerging as student-centered, supportive learning models to prepare students for college and career. This white paper explores the intersection and relationship between these two fields, recommends ideal policy environments for implementing successful programs, provides real-world examples, and shines a spotlight on emerging trends for the future.

This publication is a series of in-depth case studies to examine how three programs which serve a disconnected youth population are utilizing data as a tool for continuous program improvement and ongoing accountability. The report features the following programs: (1) Roca, an organization in Massachusetts which engages the highest-risk youth in Chelsea, East Boston, Revere, and Springfield through transformational relationships (intensive relationship building) and moving them into educational, employment, and life skills programming; (2) Our Piece of the Pie, a youth development agency operating in Hartford, Connecticut offering a relationship-centered approach to help young people access and attain a mix of the educational, employment, and personal skills that contribute to their success; and (3) Diploma Plus, a national network of public schools which engages students through performance-based system that includes competency-based assessment, supportive school culture, and a future focus on postsecondary/career education. "Beyond the Numbers" investigates three programs with a proven record of success with the disconnected youth population and catalogues their elements of success in data collection and use to effectively engage this population. The report distills the key lessons learned both for practitioners and policymakers aiming to improve outcomes for the disconnected youth population and raises important policy questions concerning financing, data sharing, and the standardization of outcomes. (Contains 10 footnotes.)

Youth development approaches have grown in popularity, yet the appropriateness of these strategies for adolescents with serious behavior problems has rarely been addressed. Life-course research examining the onset and developmental course of problem behaviors suggests that youth with different patterns of behavior problems may not equally benefit from youth development interventions. This paper reviews contemporary perspectives on the positive youth development approach in light of multidisciplinary life-course research regarding the development of disruptive behavior problems. The wraparound case-management model is described as a potential framework for applying this research to support youth with serious behavior problems.

Data from the Connecticut Department of Higher Education and the National Association of Colleges and Employers were used to explore effects of college major on differences by race and gender in estimated starting salaries of 2006 bachelor degree recipients from Connecticut colleges and universities. Females' relatively high presence in majors with low average starting salaries and low presence in majors with high average starting salaries suggest that gender earnings differences will persist. Racial distributions across majors for men indicate that average starting salaries for Whites, American Indian/Alaska Natives, and Asian/Pacific Islanders will be higher than those for Blacks and Hispanics, and that racial earnings differences will persist even as educational attainment becomes more equal. For women, increasing graduation rates of non-Whites should significantly reduce racial earnings inequality as White and American Indian/Alaska Native women are predicted to have lower average starting salaries than Blacks, Hispanics, and Asian/Pacific Islanders based on distributions across majors. (Contains 3 tables and 2 figures.)

This compendium identifies and describes schools, programs, and policies that link secondary and postsecondary education to help students earn college credit or take college-level courses while in high school. It raises issues for practitioners and policymakers to consider as these program grow and target a wider range of students. This compendium is designed to help national, state, and local policymakers and practitioners better understand what Secondary-Post-Secondary Learning Options (SPLOs) are, the various ways they are structured, and their impact on student outcomes. By helping policymakers gain a better understanding of successful or effective interventions, they can implement policies that will support student preparation for and access to postsecondary education. By profiling SPLOs, practitioners can learn what models and strategies are effective with various student populations. The authors were driven by the following guiding questions: (1) Is there evidence that these different models of SPLOs are effective at increasing academic performance, closing the achievement gap, and increasing entry to and retention in postsecondary education, particularly for first-generation, low-income, or students of color and students with disabilities?; (2) Do financing mechanisms support equity and access by all students? Is there evidence that these programs are cost effective?; (3) Are college courses for high school students as rigorous and at the same level as regular college courses?; (4) What evidence exists to demonstrate that these programs meet their respective goals of serving a specific target population or solving a specific problem?; (5) Who should pay for high school students to take these courses and what are some of the financing structures? Should federal student aid dollars be used to support high school students?; and (6) On what outcomes should these programs be measured: high school graduation or grades, attainment of college credit, entry to postsecondary education, and/or completion of degree? Unfortunately, due to limitations in the data, AYPF was unable to answer many of these questions. Instead, the available data allowed the authors to consider the following program characteristics and issues: type of student served; sources of funding; course rigor, as it is related to program location, teacher and faculty preparation, prerequisites for participation, and program length; extra supports; formal sanctioning; transferability of credit; and data. The authors conclude that there is evidence to support the effectiveness of SPLOs, yet as the field grows, the research must become more rigorous in order to answer additional specific questions on who benefits and in what ways.

This study examined the use of interactive videodisc technology in a physical education methods course. It was designed to: (1) evaluate the use of interactive videodisc technology by physical education majors; (2) describe the amounts and type of control utilized by learners using interactive videodisc technology in a controlled learning situation; (3) evaluate potential problems of the use of interactive videodisc technology with novice users; and (4) describe student attitudes toward the use of interactive video. Subjects were enrolled in a physical education methods course, and were studying playground equipment and use of playground equipment with physically handicapped students. After a pretest on the instructional material, subjects viewed the interactive videodisc and, through controls incorporated in the HyperCard-based computer program, were able to stop to take notes and/or to review any of the video segments. At the conclusion of the videodisc segment, subjects were tested again and the results correlated with subject actions (stopping the disk, reviewing the material, and time on task) which occurred during the viewing of the instructional material. Subject actions were also correlated by gender. Results indicated that females stopped the videodisc and reviewed segments more often, and spent more time on task than males. Subjects' scores on the posttest reflected these differences. It is concluded that the level of user control is an area that must be addressed when developing interactive videodisc materials for instruction use. (DB)

The article focuses on the characteristics, use, harmfulness, and regulation of nicotine pouches. Topics discussed include their diverse characteristics, marketing strategies, and regulatory challenges, emphasizing the need for caution due to their similarities to traditional tobacco products and limited data on their impact.