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The scarcity of teachers of color (TOCs) in Pennsylvania has been well-documented. In 2018, Research for Action (RFA) reviewed the literature on the benefits of teachers of color for all students and highlighted barriers, strategies, and initiatives in "Patching the Leaky Pipeline: Recruiting and Retaining Teachers of Color in Pennsylvania." Using national survey data from 2011-12, it was found that Pennsylvania's rate of disproportionality between students of color (SOCs) and TOCs is among the highest in the nation. Later that year, in collaboration with WHYY and the Philadelphia Public School Notebook, 2016-17 data provided by the Pennsylvania Department of Education (PDE) was examined, finding that the majority of Pennsylvania schools and 37% of entire school districts employed only White teachers. A key observation in each of these studies was that, in contrast to widely available data on student race/ethnicity, there is no regular public reporting of teacher race/ethnicity in Pennsylvania. More than two years later, that is still the case. Recently, WHYY obtained seven years of teacher race/ethnicity data via records request from PDE, dating from 2013-14 through 2019-20 school years. RFA cleaned this data and merged it with student data to calculate the percentages of teachers and students by race/ethnicity at the state, county, district, and school levels for all Pennsylvania public schools. This brief presents descriptive findings of RFA's examination of this new data. The brief begins by updating prior analyses of the general distribution of teacher and student demographics across the Commonwealth. Next, the association between student and teacher demographics is examined. Finally, additional analyses are included to compare race/ethnicity between: (1) subgroups of full-time, part-time, and split-time teachers; (2) teachers of elementary, secondary, and ungraded classes, and; (3) teachers of different instructional subjects. An Appendix is included, with tables that identify schools and districts which have consistently employed the highest rates of TOCs and schools that have employed only white teachers over the past seven years, despite high rates of SOCs. [For "Patching the Leaky Pipeline: Recruiting and Retaining Teachers of Color in Pennsylvania. A PACER Policy Brief," see ED589381.]

The aim of this paper is to study a dimorphic property associated with two different sums of identically independent Bernoulli random variables having two different families of probability mass functions. In addition, we give two expressions on sums of products of degenerate Stirling numbers of the second kind and Stirling numbers of the first kind connected with those two different sums of identically independent Bernoulli random variables., Comment: 8 pages

The aim of this paper is twofold. Firstly, we investigate a finite sum involving the generalized falling factorial polynomials, in some special cases of which we express it in terms of the degenerate Stirling numbers of the second kind, the degenerate Bernoulli polynomials and the degenerate Frobenius-Euler polynomials. Secondly, we consider the degenerate Eulerian polynomials and deduce the generating function and a recurrence relation for them., Comment: 10 pages

Recently, several types of degenerate Bell polynomials have been introduced as degenerate versions of the ordinary Bell polynomials. The aim of this paper is to study some identities for the degenerate Bell polynomials and their related identities by making use of series transformation formula obtained by Boyadzhiev. In particular, this answers to the natural question about the relationship between two different types of degenerate Bell polynomials., Comment: 11 pages

Recently, Bovadzhiev studied a power series whose coefficients are binomial expressions and extended some known formulas involving classical special functions and polynomials. The aim of this paper is to adopt his ideas to express several identities involving " degenerate formal power series" as those including degenerate stirling numbers of the second kind, degenerate Bell polynomials, degenerate Fubini polynomials and degenerate poly-Bernoulli polynomials., Comment: 17 pages

Optimizing expensive to evaluate black-box functions over an input space consisting of all permutations of d objects is an important problem with many real-world applications. For example, placement of functional blocks in hardware design to optimize performance via simulations. The overall goal is to minimize the number of function evaluations to find high-performing permutations. The key challenge in solving this problem using the Bayesian optimization (BO) framework is to trade-off the complexity of statistical model and tractability of acquisition function optimization. In this paper, we propose and evaluate two algorithms for BO over Permutation Spaces (BOPS). First, BOPS-T employs Gaussian process (GP) surrogate model with Kendall kernels and a Tractable acquisition function optimization approach based on Thompson sampling to select the sequence of permutations for evaluation. Second, BOPS-H employs GP surrogate model with Mallow kernels and a Heuristic search approach to optimize expected improvement acquisition function. We theoretically analyze the performance of BOPS-T to show that their regret grows sub-linearly. Our experiments on multiple synthetic and real-world benchmarks show that both BOPS-T and BOPS-H perform better than the state-of-the-art BO algorithm for combinatorial spaces. To drive future research on this important problem, we make new resources and real-world benchmarks available to the community., Comment: Accepted at AAAI 2022

In this note, we derive a finite summation formula and an infinite summation formula involving Harmonic numbers of order up to some order by means of several definite integrals, Comment: 6 pages

Supervised learning-based methods yield robust denoising results, yet they are inherently limited by the need for large-scale clean/noisy paired datasets. The use of unsupervised denoisers, on the other hand, necessitates a more detailed understanding of the underlying image statistics. In particular, it is well known that apparent differences between clean and noisy images are most prominent on high-frequency bands, justifying the use of low-pass filters as part of conventional image preprocessing steps. However, most learning-based denoising methods utilize only one-sided information from the spatial domain without considering frequency domain information. To address this limitation, in this study we propose a frequency-sensitive unsupervised denoising method. To this end, a generative adversarial network (GAN) is used as a base structure. Subsequently, we include spectral discriminator and frequency reconstruction loss to transfer frequency knowledge into the generator. Results using natural and synthetic datasets indicate that our unsupervised learning method augmented with frequency information achieves state-of-the-art denoising performance, suggesting that frequency domain information could be a viable factor in improving the overall performance of unsupervised learning-based methods., Comment: Accepted to BMVC 2021

We explore the connection between the $\gamma$-ray and radio emission in the jet of the blazar 0716$+$714 by using 15, 37, and 230 GHz radio and 0.1$-$200 GeV $\gamma$-ray light curves spanning 10.5 years (2008$-$2019). We find significant positive and negative correlations between radio and $\gamma$-ray fluxes in different time ranges. The time delays between radio and $\gamma$-ray emission suggest that the observed $\gamma$-ray flares originated from multiple regions upstream of the radio core, within a few parsecs from the central engine. Using time-resolved 43 GHz VLBA maps we identified 14 jet components moving downstream along the jet. Their apparent speeds range from 6 to 26 $c$, showing notable variations in their position angles upstream the stationary component ($\sim$0.53 mas from the core). The brightness temperature declines as function of distance from the core according to a power-law which becomes shallower at the location of the stationary component. We also find that the periods at which significant correlations between radio and $\gamma$-ray emission occur overlap with the times when the jet was oriented to the north. Our results indicate that the passage of a propagating disturbance (or shock) through the radio core and the orientation of the jet might be responsible for the observed correlation between the radio and $\gamma$-ray variability. We present a scenario that connects the positive correlation and the unusual anti-correlation by combining the production of a flare and a dip at $\gamma$-rays by a strong moving shock at different distances from the jet apex., Comment: 26 pages, 13 figures, 5 tables, Accepted for publication in ApJ

In this paper, we consider the problem of representing any polynomial in terms of the ordered Bell and degenerate ordered Bell polynomials, and more generally of the higher-order ordered Bell and higher-order degenerate ordered Bell polynomials. We derive explicit formulas with the help of umbral calculus and illustrate our results with some examples., Comment: 20 pages. arXiv admin note: substantial text overlap with arXiv:2108.05049, arXiv:2109.13700

The United States is plagued by large disparities in life outcomes between racial and ethnic groups. Researchers have documented how gaps in outcomes are related to gaps in access to opportunity, both in education and otherwise. Yet, as documented in this report, too often state policymakers still fail to provide equitable learning opportunities to their students. The Civil Rights Data Collection (CRDC) is administered biennially by the U.S. Department of Education's Office of Civil Rights. This data set provides dozens of indicators related to access to educational opportunity from virtually every public school in the nation. To determine the extent to which high school students have access to schools that provide quality educational opportunities, we analyzed 14 CRDC indicators. From these 14 indicators, we generated composite indices of three broad domains of access to educational opportunity for high school students: (1) Access to Quality Educators Index; (2) Access to College and Career Readiness Curriculum Index; and (3) Access to Positive School Climate Index.