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Decades of chronic underfunding and inequitable funding have been spiraling Pennsylvania's public school system into crisis--failing kids and threatening the future of the Commonwealth. The Commonwealth Court has ruled that the state's current funding system for K-12 schools is unconstitutional and the state must take action to adequately and equitably fund schools. This report provides a cautionary tale for those considering expanding existing taxpayer-funded vouchers to attend private schools in Pennsylvania or creating a new program. Pennsylvania does not need to rely only on evidence from other states in evaluating whether to establish a new taxpayer-funded school voucher program. The reason: Pennsylvania already has two existing voucher programs now funded for a combined $470 million per year, over four times more than in 2012-13, the first year of the Opportunity Scholarship Tax Credit (OSTC) program, the newer of the two new voucher programs. The legislature first provided funds for the Educational Improvement Tax Credit (EITC) program in 2001-02. This report updates a 2017 Keystone Research Center report on these two existing voucher programs, which have received about $2.6 billion in state tax credits since their inception. This report finds: (1) All students in the state do not benefit equally from Pennsylvania's voucher program--students in rural communities often don't have access and participating schools are allowed to, and do, discriminate against students; (2) By design, neither the EITC nor OSTC program requires meaningful educational or financial accountability; Scholarship organizations and schools have few reporting requirements, making it difficult to assess impact or program compliance; (3) The EITC/OSTC programs are subsidizing religious schools that have few state-required standards regarding curriculum. Some of these schools receiving public money teach creationism as science and present the Bible as factually accurate history; and (4) PA's existing voucher program subsidizes the state's most elite and expensive private schools, as well as affluent families. The inadequate accountability in Pennsylvania's $470 million OSTC and EITC programs (for 2023-24) makes clear that the state should not divert more taxpayer dollars to these programs or create a new one. At minimum, a comprehensive financial and educational audit of these programs must be done first, including to evaluate curricula schools use and make recommendations regarding basic curriculum standards. The Independent Fiscal Office (IFO) attempted to evaluate the effectiveness of these programs and reported that, due to a lack of reporting requirements, it could not do so. Pennsylvania should also prioritize fully and fairly funding public schools, which serve all of Pennsylvania's students. A public dollar spent on expanding existing or creating new voucher programs in Pennsylvania is a dollar less that can be spent to meet the court-ordered mandate to fix the unconstitutional public school funding system.

Kolmogorov GAM (K-GAM) networks are shown to be an efficient architecture for training and inference. They are an additive model with an embedding that is independent of the function of interest. They provide an alternative to the transformer architecture. They are the machine learning version of Kolmogorov's Superposition Theorem (KST) which provides an efficient representations of a multivariate function. Such representations have use in machine learning for encoding dictionaries (a.k.a. "look-up" tables). KST theory also provides a representation based on translates of the K\"oppen function. The goal of our paper is to interpret this representation in a machine learning context for applications in Artificial Intelligence (AI). Our architecture is equivalent to a topological embedding which is independent of the function together with an additive layer that uses a Generalized Additive Model (GAM). This provides a class of learning procedures with far fewer parameters than current deep learning algorithms. Implementation can be parallelizable which makes our algorithms computationally attractive. To illustrate our methodology, we use the Iris data from statistical learning. We also show that our additive model with non-linear embedding provides an alternative to transformer architectures which from a statistical viewpoint are kernel smoothers. Additive KAN models therefore provide a natural alternative to transformers. Finally, we conclude with directions for future research.

Generative methods (Gen-AI) are reviewed with a particular goal to solving tasks in Machine Learning and Bayesian inference. Generative models require one to simulate a large training dataset and to use deep neural networks to solve a supervised learning problem. To do this, we require high dimensional regression methods and tools for dimensionality reduction (a.k.a feature selection). The main advantage of Gen-AI methods is their ability to be model-free and to use deep neural networks to estimate conditional densities or posterior quantiles of interest. To illustrate generative methods, we analyze the well-known Ebola data-set. Finally, we conclude with directions for future research., Comment: arXiv admin note: substantial text overlap with arXiv:2305.14972

Biologists study Diatoms, a fundamental algae, to assess the health of aquatic systems. Diatom specimens have traditionally been preserved on analog slides, where a single slide can contain thousands of these microscopic organisms. Digitization of these collections presents both metadata challenges and opportunities. This paper reports on metadata research aimed at providing access to a digital portion of the Academy of Natural Sciences' Diatom Herbarium, Drexel University. We report results of a 3-part study covering 1) a review of relevant metadata standards and a microscopy metadata framework shared by Hammer et al., 2) a baseline metadata alignment mapping current diatom metadata properties to standard metadata types, and 3) a metadata risk analysis associated with the course of standard data curation practices. This research is part of an effort involving the transfer of these digital slides to an new system, DataFed, to support global accessible. The final section of this paper includes a conclusion and discusses next steps., Comment: 13 pages, 2 figures, 1 table, to be published in MTSR 2024 conference proceedings

HIVE4MAT is a linked data interactive application for navigating ontologies of value to materials science. HIVE enables automatic indexing of textual resources with standardized terminology. This article presents the motivation underlying HIVE4MAT, explains the system architecture, reports on two evaluations, and discusses future plans., Comment: 11 pages, 1 figures, 3 tables, to be published in SeMatS 2024 workshop proceedings

Ultrawide bandgap (UWBG) semiconductors are promising for next-generation power electronics, largely attributed to their substantial bandgap and exceptional breakdown electric field. Rutile GeO2 (r-GeO2) emerges as a promising alternative, particularly because of its ambipolar dopability. However, research on r-GeO2 is still in its infancy, and further investigation into its structural properties is essential for enhancing epilayer quality. In our previous work, we identified distinct surface morphologies; square-patterned and smooth regions of epitaxial r-GeO2 films grown on r-TiO2 (001) substrates using metal-organic chemical vapor deposition (MOCVD).This research employs transmission electron microscopy (TEM) to investigate the structural characteristics of the material. The findings indicate that the square-patterned regions are crystalline, whereas the smooth regions exhibit amorphous properties. The measured lattice spacing in the (110) plane is 0.324 nm, slightly exceeding the theoretical value of 0.312 nm. This discrepancy suggests the presence of tensile strain in the r-GeO2 film, resulting from lattice mismatch or thermal expansion differences with the substrate. We also observed a threading dislocation density of 1.83*10^9 cm-2, consisting of 11.76% screw-type, 29.41% edge-type, 55.89% mixed-type dislocations, and 2.94% planar defects. These findings offer valuable insights into the growth mechanisms and defect characteristics of r-GeO2., Comment: 19 pages, 5 figures

Radiopharmaceutical therapies (RPTs) present a major opportunity to improve cancer therapy. Although many current RPTs use the same injected activity for all patients, there is interest in using absorbed dose measurements to enable personalized prescriptions. Image-based absorbed dose calculations incur uncertainties from calibration factors, partial volume effects and segmentation methods. While previously published dose estimation protocols incorporate these uncertainties, they do not account for uncertainty originating from the reconstruction process itself with the propagation of Poisson noise from projection data. This effect should be accounted for to adequately estimate the total uncertainty in absorbed dose estimates. This paper proposes a computationally practical algorithm that propagates uncertainty from projection data through clinical reconstruction algorithms to obtain uncertainties on the total measured counts within volumes of interest (VOIs). The algorithm is first validated on ${}^{177}$Lu and ${}^{225}$Ac phantom data by comparing estimated uncertainties from individual SPECT acquisitions to empirical estimates obtained from multiple acquisitions. It is then applied to (i) Monte Carlo and (ii) multi-time point ${}^{177}$Lu-DOTATATE and ${}^{225}$Ac-PSMA-617 patient data for time integrated activity (TIA) uncertainty estimation. The outcomes of this work are two-fold: (i) the proposed uncertainty algorithm is validated, and (ii) a blueprint is established for how the algorithm can be inform dosimetry protocols via TIA uncertainty estimation. The proposed algorithm is made publicly available in the open-source image reconstruction library PyTomography.

We provide a statistical analysis of the recent controversy between Vladimir Kramnik (ex chess world champion) and Hikaru Nakamura. Hikaru Nakamura is a chess prodigy and a five-time United States chess champion. Kramnik called into question Nakamura's 45.5 out of 46 win streak in an online blitz contest at chess.com. We assess the weight of evidence using a priori assessment of Viswanathan Anand and the streak evidence. Based on this evidence, we show that Nakamura has a 99.6 percent chance of not cheating. We study the statistical fallacies prevalent in both their analyses. On the one hand Kramnik bases his argument on the probability of such a streak is very small. This falls precisely into the Prosecutor's Fallacy. On the other hand, Nakamura tries to refute the argument using a cherry-picking argument. This violates the likelihood principle. We conclude with a discussion of the relevant statistical literature on the topic of fraud detection and the analysis of streaks in sports data.

Recently, nanofluidics experiments have been used to characterize the behavior of single DNA molecules confined to narrow slits etched with arrays of nanopits. Analysis of the experimental data relies on analytical estimates of the underlying free-energy landscape. In this study we use computer simulations to explicitly calculate the free energy and test the approximations employed in such analytical models. Specifically, Monte Carlo simulations were used to study a polymer confined to complex geometry consisting of a nanoslit with two square nanopits embedded in one of the surfaces. The two-dimensional Weighted Histogram Analysis Method (WHAM2D) is used to calculate the free energy, $F$, as a function of the sum ($\lambda_1$) and the difference ($\lambda_2$) of the length of the polymer contour contained in the two nanopits. We find the variation of the free-energy function with respect to confinement dimensions to be comparable to the analytical predictions that employ a simplistic theoretical model. However, there are some noteworthy quantitative discrepancies, particularly between the predicted and observed variation of $F$ with respect to $\lambda_1$. Our study provides a useful lesson on the limitations of using simplistic analytical expressions for polymer free-energy landscapes to interpret results for experiments of DNA confined to a complex geometry and points to the value of carrying out accurate numerical calculations of the free energy instead., Comment: 14 pages, 9 figures

Modeling of the collimator-detector response (CDR) in SPECT reconstruction enables improved resolution and accuracy, and is thus important for quantitative imaging applications such as dosimetry. The implementation of CDR modeling, however, can become a computational bottleneck when there are substantial components of septal penetration and scatter in the acquired data, since a direct convolution-based approach requires large 2D kernels. This work proposes a 1D convolution and rotation-based CDR model that reduces reconstruction times but maintains consistency with models that employ 2D convolutions. To enable open-source development and use of these models in image reconstruction, we release a SPECTPSFToolbox repository for the PyTomography project on GitHub.

Generative Bayesian Computation (GBC) methods are developed to provide an efficient computational solution for maximum expected utility (MEU). We propose a density-free generative method based on quantiles that naturally calculates expected utility as a marginal of quantiles. Our approach uses a deep quantile neural estimator to directly estimate distributional utilities. Generative methods assume only the ability to simulate from the model and parameters and as such are likelihood-free. A large training dataset is generated from parameters and output together with a base distribution. Our method a number of computational advantages primarily being density-free with an efficient estimator of expected utility. A link with the dual theory of expected utility and risk taking is also discussed. To illustrate our methodology, we solve an optimal portfolio allocation problem with Bayesian learning and a power utility (a.k.a. fractional Kelly criterion). Finally, we conclude with directions for future research.

Gene therapy is poised to transition from niche to mainstream medicine, with recombinant adeno-associated virus (rAAV) as the vector of choice. However, this requires robust, scalable, industrialized production to meet demand and provide affordable patient access, which has thus far failed to materialize. Closing the chasm between demand and supply requires innovation in biomanufacturing to achieve the essential step change in rAAV product yield and quality. Omics provides a rich source of mechanistic knowledge that can be applied to HEK293, the prevailing cell line for rAAV production. In this review, the findings from a growing number of disparate studies that apply genomics, epigenomics, transcriptomics, proteomics, and metabolomics to HEK293 bioproduction are explored. Learnings from CHO-Omics, application of omics approaches to improve CHO bioproduction, provide context for the potential of "HEK-Omics" as a multiomics-informed approach providing actionable mechanistic insights for improved transient and stable production of rAAV and other recombinant products in HEK293., Comment: 41 pages, 1 figure, 1 table

Gauss proposed the problem of how to enumerate the number of solutions for placing $N$ queens on an $N\times N$ chess board, so no two queens attack each other. The N-queen problem is a classic problem in combinatorics. We describe a variety of Monte Carlo (MC) methods for counting the number of solutions. In particular, we propose a quantile re-ordering based on the Lorenz curve of a sum that is related to counting the number of solutions. We show his approach leads to an efficient polynomial-time solution. Other MC methods include vertical likelihood Monte Carlo, importance sampling, slice sampling, simulated annealing, energy-level sampling, and nested-sampling. Sampling binary matrices that identify the locations of the queens on the board can be done with a Swendsen-Wang style algorithm. Our Monte Carlo approach counts the number of solutions in polynomial time.

Each year as tuition costs increase, more students rely on financial aid to attend institutions of higher education. Financial aid packages, which are created to encourage individual investments in education, consist of a variety of types of funding assistance and aid packages, and are highly tailored to individual students. In general, financial aid includes need- based grants, merit-based awards, and subsidized loans. A mix of federal, state and local governments, as well as private organizations, finance these programs and many are contingent on student actions or characteristics. The ramifications of the diversity of funding programs within aid packages has received little attention from policy makers. This is unfortunate because certain programs may have behavioral consequences for students beyond decreasing the cost of attendance. For example, federal work- study funding provides funds to students conditional on their commitment to working while in school. This job and time requirement may affect student performance in positive or negative ways. Analyzing the efficacy of the federal work-study program is important because it may have adverse effects on student outcomes if working involves a substantial time trade-off with time spent learning. At the same time, working while in school may provide a means for students to gain knowledge and skills that reinforce their academic experience and prepare them for success in academics and the labor market.

Independent Component Estimation (ICE) has many applications in modern day machine learning as a feature engineering extraction method. Horseshoe-type priors are used to provide scalable algorithms that enables both point estimates via expectation-maximization (EM) and full posterior sampling via Markov Chain Monte Carlo (MCMC) algorithms. Our methodology also applies to flow-based methods for nonlinear feature extraction and deep learning. We also discuss how to implement conditional posteriors and envelope-based methods for optimization. Through this hierarchy representation, we unify a number of hitherto disparate estimation procedures. We illustrate our methodology and algorithms on a numerical example. Finally, we conclude with directions for future research., Comment: 23 pages, 2 figures

Negative probabilities arise primarily in physics, statistical quantum mechanics and quantum computing. Negative probabilities arise as mixing distributions of unobserved latent variables in Bayesian modeling. Our goal is to provide a link between these two viewpoints. Bartlett provides a definition of negative probabilities based on extraordinary random variables and properties of their characteristic function. A version of Bayes rule is given with negative mixing weights. The classic half coin distribution and Polya-Gamma mixing is discussed. Heisenberg's principle of uncertainty and the duality of scale mixtures of Normals is also discussed. A number of examples of dual densities with negative mixing measures are provided including the Linnik and Wigner distributions. Finally, we conclude with directions for future research.

Meeting students' basic food and nutrition requirements is an essential role of public schools and critical to student learning. Yet as with other support services in schools -- such as transportation and janitorial services -- school boards or school administrators who are worried about the bottom line may turn to outside companies to manage or replace in-house district school food programs. In 2004, about 70% of Pennsylvania school districts self-operated their food service programs. But by 2019, that number dropped to 47%, as more districts chose management companies to run their school food programs. This report relies on a mix of rigorous statistical analysis and interview-based qualitative research and finds that contracting out food services -- their management or the entire operation -- does not yield the financial benefits school districts are promised by contractors.

Bayesian hierarchical models are commonly employed for inference in count datasets, as they account for multiple levels of variation by incorporating prior distributions for parameters at different levels. Examples include Beta-Binomial, Negative-Binomial (NB), Dirichlet-Multinomial (DM) distributions. In this paper, we address two crucial challenges that arise in various Bayesian count models: inference for the concentration parameter in the ratio of Gamma functions and the inability of these models to effectively handle excessive zeros and small nonzero counts. We propose a novel class of prior distributions that facilitates conjugate updating of the concentration parameter in Gamma ratios, enabling full Bayesian inference for the aforementioned count distributions. We use DM models as our running examples. Our methodology leverages fast residue computation and admits closed-form posterior moments. Additionally, we recommend a default horseshoe type prior which has a heavy tail and substantial mass around zero. It admits continuous shrinkage, making the posterior highly adaptable to sparsity or quasi-sparsity in the data. Furthermore, we offer insights and potential generalizations to other count models facing the two challenges. We demonstrate the usefulness of our approach on both simulated examples and on real-world applications. Finally, we conclude with directions for future research.

Our goal is to provide a review of deep learning methods which provide insight into structured high-dimensional data. Rather than using shallow additive architectures common to most statistical models, deep learning uses layers of semi-affine input transformations to provide a predictive rule. Applying these layers of transformations leads to a set of attributes (or, features) to which probabilistic statistical methods can be applied. Thus, the best of both worlds can be achieved: scalable prediction rules fortified with uncertainty quantification, where sparse regularization finds the features., Comment: arXiv admin note: text overlap with arXiv:1808.08618

There is a need for open-source libraries in emission tomography that (i) use modern and popular backend code to encourage community contributions and (ii) offer support for the multitude of reconstruction techniques available in recent literature, such as those that employ artificial intelligence. The purpose of this research was to create and evaluate a GPU-accelerated, open-source, and user-friendly image reconstruction library, designed to serve as a central platform for the development, validation, and deployment of various tomographic reconstruction algorithms. PyTomography was developed using Python and inherits the GPU-accelerated functionality of PyTorch and parallelproj for fast computations. Its flexible and modular design decouples system matrices, likelihoods, and reconstruction algorithms, simplifying the process of integrating new imaging modalities using various python tools. Example use cases demonstrate the software capabilities in parallel hole SPECT and listmode PET imaging. Overall, we have developed and publicly share PyTomography, a highly optimized and user-friendly software for medical image reconstruction, with a class hierarchy that fosters the development of novel imaging applications., Comment: 28 pages, 7 figures

We propose a neural network-based approach to calculate the value of a chess square-piece combination. Our model takes a triplet (Color, Piece, Square) as an input and calculates a value that measures the advantage/disadvantage of having this piece on this square. Our methods build on recent advances in chess AI, and can accurately assess the worth of positions in a game of chess. The conventional approach assigns fixed values to pieces $(\symking=\infty, \symqueen=9, \symrook=5, \symbishop=3, \symknight=3, \sympawn=1)$. We enhance this analysis by introducing marginal valuations. We use deep Q-learning to estimate the parameters of our model. We demonstrate our method by examining the positioning of Knights and Bishops, and also provide valuable insights into the valuation of pawns. Finally, we conclude by suggesting potential avenues for future research.

President Biden's recent announcement regarding student debt relief has brought the issue to center stage across Pennsylvania and the U.S. Access to quality higher education is so important to Pennsylvania's individuals and families, yet the high cost of college in the state has both limited who has access to a good education and, for those attending college, weighed down students with crushing amounts of debt. Carrying such a debt burden at the start of one's career hinders Pennsylvanians' choices, careers, and life decisions and holds back our economy. This research examines the student debt crisis in Pennsylvania. It analyzes publicly available data on Pennsylvania and looks at the financial and economic implications of student debt for Pennsylvania families, students, and regions. Among the findings are: (1) Low state funding and the high cost of college sets Pennsylvania up for a statewide student loan crisis; (2) Outstanding student loan debt has skyrocketed in the last two decades, and Pennsylvania graduates have high amounts of debt compared to other states; (3) Some communities are hit harder by the student loan crisis; (4) For-profit colleges have poor student outcomes; (5) Pennsylvania students are using nonfederal loans at higher rates than much of the nation; and (6) Student loan debt is dragging down the economy. Policy solutions for Pennsylvania conclude the report.

Generative Bayesian Computation (GBC) methods are developed for Casual Inference. Generative methods are simulation-based methods that use a large training dataset to represent posterior distributions as a map (a.k.a. optimal transport) to a base distribution. They avoid the use of MCMC by replacing the conditional posterior inference problem with a supervised learning problem. We further propose the use Quantile ReLU networks which are density free and hence apply in a variety of Econometric settings where data generating processes are specified by deterministic latent variables updates or as moment constraints. Generative approaches directly simulate large samples of observables and unobservable (parameters, latent variables) and then apply high-dimensional quantile regression to learn a nonlinear transport map from base distribution to parameter inference. We illustrate our methodology in the field of causal inference. Our approach can also handle nonlinearity and heterogeneity. Finally, we conclude with the directions for future research., Comment: arXiv admin note: text overlap with arXiv:2305.14972

Bayesian Generative AI (BayesGen-AI) methods are developed and applied to Bayesian computation. BayesGen-AI reconstructs the posterior distribution by directly modeling the parameter of interest as a mapping (a.k.a. deep learner) from a large simulated dataset. This provides a generator that we can evaluate at the observed data and provide draws from the posterior distribution. This method applies to all forms of Bayesian inference including parametric models, likelihood-free models, prediction and maximum expected utility problems. Bayesian computation is then equivalent to high dimensional non-parametric regression. Bayes Gen-AI main advantage is that it is density-free and therefore provides an alternative to Markov Chain Monte Carlo. It has a number of advantages over vanilla generative adversarial networks (GAN) and approximate Bayesian computation (ABC) methods due to the fact that the generator is simpler to learn than a GAN architecture and is more flexible than kernel smoothing implicit in ABC methods. Design of the Network Architecture requires careful selection of features (a.k.a. dimension reduction) and nonlinear architecture for inference. As a generic architecture, we propose a deep quantile neural network and a uniform base distribution at which to evaluate the generator. To illustrate our methodology, we provide two real data examples, the first in traffic flow prediction and the second in building a surrogate for satellite drag data-set. Finally, we conclude with directions for future research., Comment: arXiv admin note: text overlap with arXiv:2209.02163

In Bayesian inference, the approximation of integrals of the form $\psi = \mathbb{E}_{F}{l(X)} = \int_{\chi} l(\mathbf{x}) d F(\mathbf{x})$ is a fundamental challenge. Such integrals are crucial for evidence estimation, which is important for various purposes, including model selection and numerical analysis. The existing strategies for evidence estimation are classified into four categories: deterministic approximation, density estimation, importance sampling, and vertical representation (Llorente et al., 2020). In this paper, we show that the Riemann sum estimator due to Yakowitz (1978) can be used in the context of nested sampling (Skilling, 2006) to achieve a $O(n^{-4})$ rate of convergence, faster than the usual Ergodic Central Limit Theorem. We provide a brief overview of the literature on the Riemann sum estimators and the nested sampling algorithm and its connections to vertical likelihood Monte Carlo. We provide theoretical and numerical arguments to show how merging these two ideas may result in improved and more robust estimators for evidence estimation, especially in higher dimensional spaces. We also briefly discuss the idea of simulating the Lorenz curve that avoids the problem of intractable $\Lambda$ functions, essential for the vertical representation and nested sampling.

For acute ischemic stroke (AIS) patients with large vessel occlusions, clinicians must decide if the benefit of mechanical thrombectomy (MTB) outweighs the risks and potential complications following an invasive procedure. Pre-treatment computed tomography (CT) and angiography (CTA) are widely used to characterize occlusions in the brain vasculature. If a patient is deemed eligible, a modified treatment in cerebral ischemia (mTICI) score will be used to grade how well blood flow is reestablished throughout and following the MTB procedure. An estimation of the likelihood of successful recanalization can support treatment decision-making. In this study, we proposed a fully automated prediction of a patient's recanalization score using pre-treatment CT and CTA imaging. We designed a spatial cross attention network (SCANet) that utilizes vision transformers to localize to pertinent slices and brain regions. Our top model achieved an average cross-validated ROC-AUC of 77.33 $\pm$ 3.9\%. This is a promising result that supports future applications of deep learning on CT and CTA for the identification of eligible AIS patients for MTB., Comment: Medical Imaging with Deep Learning 2022 accepted short paper Jun 2022

After decades of decline, Scranton can capitalize on the unprecedented federal emergency relief provided to schools and communities in the pandemic and its wake. To do so, Scranton must recognize and address the threat to the city's public school system. Great public schools are the lifeblood of any thriving community, attracting and retaining families and businesses. State funding is critical to Scranton because, as a low-income community, it has a limited tax base and a student body that research shows is more expensive to educate. However, for decades, Pennsylvania has underfunded its K-12 education. This report offers a diagnosis and prescription for renewal. The prescription for renewal starts with capitalizing on federal resources to restore critical educational programming, including reinstating Pre-K and maintaining reasonable class sizes, and to achieve the goal of "competitive compensation" highlighted in the Recovery Plan. With educational programming stabilized--like finances already have been--the City of Scranton, its school district, and its people must come together with other communities across the state to get the Pennsylvania Legislature to step up to its constitutional responsibility for adequately and equitably funding schools.

In this paper, we propose Forest-PLS, a feature selection method for analyzing policy effect heterogeneity in a more flexible and comprehensive manner than is typically available with conventional methods. In particular, our method is able to capture policy effect heterogeneity both within and across subgroups of the population defined by observable characteristics. To achieve this, we employ partial least squares to identify target components of the population and causal forests to estimate personalized policy effects across these components. We show that the method is consistent and leads to asymptotically normally distributed policy effects. To demonstrate the efficacy of our approach, we apply it to the data from the Pennsylvania Reemployment Bonus Experiments, which were conducted in 1988-1989. The analysis reveals that financial incentives can motivate some young non-white individuals to enter the labor market. However, these incentives may also provide a temporary financial cushion for others, dissuading them from actively seeking employment. Our findings highlight the need for targeted, personalized measures for young non-white male participants.

Experiments using nanofluidic devices have proven effective in characterizing the physical properties of polymers confined to small cavities. Two recent studies using such methods examined the organization and dynamics of two DNA molecules in box-like cavities with strong confinement in one direction and with square and elliptical cross sections in the lateral plane. Motivated by these experiments, we employ Monte Carlo and Brownian dynamics simulations to study the physical behaviour of two polymers confined to small cavities with shapes comparable to those used in the experiments. We quantify the effects of varying the following polymer properties and confinement dimensions on the organization and dynamics of the polymers: the polymer width, the polymer contour length ratio, the cavity cross-sectional area, and the degree of cavity elongation for cavities with rectangular and elliptical cross sections. We find that the tendency for polymers to segregate is enhanced by increasing polymer width. For sufficiently small cavities, increasing cavity elongation promotes segregation and localization of identical polymers to opposite sides of the cavity along its long axis. A free-energy barrier controls the rate of polymers swapping positions, and the observed dynamics are roughly in accord with predictions of a simple theoretical model. Increasing the contour length difference between polymers significantly affects their organization in the cavity. In the case of a large linear polymer co-trapped with a small ring polymer in an elliptical cavity, the small polymer tends to lie near the lateral confining walls, and especially at the cavity poles for highly elongated ellipses., Comment: 19 pages, 15 figures, 4 pages of supplemental info

How likely is it that Magnus Carlsen will achieve an Elo rating of $2900$? This has been a goal of Magnus and is of great current interest to the chess community. Our paper uses probabilistic methods to address this question. The probabilistic properties of Elo's rating system have long been studied, and we provide an application of such methods. By applying a Brownian motion model of Stern as a simple tool we provide answers. Our research also has fundamental bearing on the choice of the $K$-factor used in Elo's system for GrandMaster (GM) chess play. Finally, we conclude with a discussion of policy issues involved with the choice of $K$-factor.