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For a very long time, computational approaches to the design of new materials have relied on an iterative process of finding a candidate material and modeling its properties. AI has played a crucial role in this regard, helping to accelerate the discovery and optimization of crystal properties and structures through advanced computational methodologies and data-driven approaches. To address the problem of new materials design and fasten the process of new materials search, we have applied latest generative approaches to the problem of crystal structure design, trying to solve the inverse problem: by given properties generate a structure that satisfies them without utilizing supercomputer powers. In our work we propose two approaches: 1) conditional structure modification: optimization of the stability of an arbitrary atomic configuration, using the energy difference between the most energetically favorable structure and all its less stable polymorphs and 2) conditional structure generation. We used a representation for materials that includes the following information: lattice, atom coordinates, atom types, chemical features, space group and formation energy of the structure. The loss function was optimized to take into account the periodic boundary conditions of crystal structures. We have applied Diffusion models approach, Flow matching, usual Autoencoder (AE) and compared the results of the models and approaches. As a metric for the study, physical PyMatGen matcher was employed: we compare target structure with generated one using default tolerances. So far, our modifier and generator produce structures with needed properties with accuracy 41% and 82% respectively. To prove the offered methodology efficiency, inference have been carried out, resulting in several potentially new structures with formation energy below the AFLOW-derived convex hulls.

A Koszul duality-type correspondence between coderived categories of conilpotent differential graded Lie coalgebras and their Chevalley-Eilenberg differential graded algebras is established. This gives an interpretation of Lie coalgebra cohomology as a certain kind of derived functor. A similar correspondence is proved for coderived categories of commutative cofibrant differential graded algebras and their Harrison differential graded Lie coalgebras., Comment: 23 pages

Distributing long-distance entanglement is a fundamental goal that is necessary for a variety of tasks such as quantum communication, distributed quantum computing, and quantum metrology. Currently quantum repeater schemes typically aim to distribute one ebit at a time, the equivalent of one Bell pair's worth of entanglement. Here we present a method to distribute a macroscopic amount of entanglement across long-distances using a number of operations that scales only linearly with the chain length. The scheme involves ensembles of qubits and entangling them with an $S^z S^z$ interaction, which can be realized using atomic gas ensembles coupled by a shared optical mode. Using only local measurements on the intermediate ensembles, this leaves the ensembles at the ends of the chain entangled. We show that there are particular ``magic'' interaction times that allow for distribution of entanglement with perfect fidelity, with no degradation with chain length. The scheme is deterministic, such that with suitable local conditional unitary corrections, the same entangled state can always be prepared with good approximation.

We consider the remote state restoring and perfect transfer of the zero-order coherence matrix (PTZ) in a spin system governed by the XXZ-Hamiltonian conserving the excitation number. The restoring tool is represented by several nonzero Larmor frequencies in the Hamiltonian. To simplify the analysis we use two approximating models including either step-wise or pulse-type time-dependence of the Larmor frequencies. Restoring in spin chains with up to 20 nodes is studied. Studying PTZ, we consider the zigzag and rectangular configurations and optimize the transfer of the 0-order coherence matrix using geometrical parameters of the communication line as well as the special unitary transformation of the extended receiver. Overall observation is that XXZ-chains require longer time for state transfer than XX-chains, which is confirmed by the analytical study of the evolution under the nearest-neighbor approximation. We demonstrate the exponential increase of the state-transfer time with the spin chain length., Comment: 22 pages, 13 figures. arXiv admin note: text overlap with arXiv:2401.09569

There are reasons to suggest that a number of mental disorders may be related to alteration in the neural complexity (NC). Thus, quantitative analysis of NC could be helpful in classifying mental and understanding conditions. Here, focusing on a methodological procedure, we have worked with young individuals, typical and with attention-deficit/hyperactivity disorder (ADHD) whose NC was assessed using q-statistics applied to the electroencephalogram (EEG). The EEG was recorded while subjects performed the visual Attention Network Test (ANT) and during a short pretask period of resting state. Time intervals of the EEG amplitudes that passed a threshold were collected from task and pretask signals from each subject. The data were satisfactorily fitted with a stretched $q$-exponential including a power-law prefactor(characterized by the exponent c), thus determining the best $(c, q)$ for each subject, indicative of their individual complexity. We found larger values of $q$ and $c$ in ADHD subjects as compared with the typical subjects both at task and pretask periods, the task values for both groups being larger than at rest. The $c$ parameter was highly specific in relation to DSM diagnosis for inattention, where well-defined clusters were observed. The parameter values were organized in four well-defined clusters in $(c, q)$-space. As expected, the tasks apparently induced greater complexity in neural functional states with likely greater amount of internal information processing. The results suggest that complexity is higher in ADHD subjects than in typical pairs. The distribution of values in the $(c, q)$-space derived from $q$-statistics seems to be a promising biomarker for ADHD diagnosis., Comment: 12 pages,5 figures

We report the measurement of the helicity asymmetry $E$ for the $p\pi^0$ and $n\pi^+$ final states using, for the first time, an elliptically polarized photon beam in combination with a longitudinally polarized target at the Crystal Ball experiment at MAMI. The results agree very well with data that were taken with a circularly polarized photon beam, showing that it is possible to simultaneously measure polarization observables that require linearly (e.g.~$G$) and circularly polarized photons (e.g.~$E$) and a longitudinally polarized target. The new data cover a photon energy range 270 - 1400 MeV for the $p\pi^0$ final state (230 - 842 MeV for the $n\pi^+$ final state) and the full range of pion polar angles, $\theta$, providing the most precise measurement of the observable $E$. A moment analysis gives a clear observation of the $p\eta$ cusp in the $p\pi^0$ final state.

We introduce a comprehensive framework for analyzing convergence rates for infinite dimensional linear programming problems (LPs) within the context of the moment-sum-of-squares hierarchy. Our primary focus is on extending the existing convergence rate analysis, initially developed for static polynomial optimization, to the more general and challenging domain of the generalized moment problem. We establish an easy-to-follow procedure for obtaining convergence rates. Our methodology is based on, firstly, a state-of-the-art degree bound for Putinar's Positivstellensatz, secondly, quantitative polynomial approximation bounds, and, thirdly, a geometric Slater condition on the infinite dimensional LP. We address a broad problem formulation that encompasses various applications, such as optimal control, volume computation, and exit location of stochastic processes. We illustrate the procedure at these three problems and, using a recent improvement on effective versions of Putinar's Positivstellensatz, we improve existing convergence rates.

We define Hochschild cohomology of the second kind for differential graded (dg) or curved algebras as a derived functor in a compactly generated derived category of the second kind, and show that it is invariant under Morita equivalence of the second kind. A bimodule version of Koszul duality is constructed and used to show that Hochschild cohomology of the second kind is preserved under (nonconilpotent) Koszul duality. Hochschild cohomology of the second kind of an algebra often computes the ordinary Hochschild cohomology of geometrically meaningful dg categories. Examples include the category of infinity local systems on a topological space, the bounded derived category of a complex algebraic manifold and the category of matrix factorizations., Comment: 23 pages

A new data set for the helicity-dependent differential cross section of the single-meson photoproduction reaction $\gamma p \to p \pi^{0}$ was obtained for the photon energy interval 150-400 MeV. The experiment was performed at the A2 tagged photon facility of the Mainz Microtron MAMI using a circularly polarized photon beam and a longitudinally polarized proton target. The reaction products were detected with the large acceptance Crystal Ball/TAPS calorimeter covering 97\% of the full solid angle. These new results, obtained with a fine energy and polar angle binning, greatly increase both the existing quantity and quality of the data available for this observable. A moment analysis, based on a finite expansion in Legendre polynomials, was applied to these data by using a bootstrap-based fitting method to correctly account for their systematic uncertainties. From the resulting decomposition of the differential cross sections, the $E2/M1$ ratio for the $N\to \Delta(1232)$ transition was determined to be $[-2.38 \pm 0.16{\hbox{ (stat.+sys.)}} \pm 0.10 {\hbox{ (model)}}] \%$. Combining this value with previous results also allowed us to evaluate the most precise available estimate of the $E2/M1$ ratio to be used for all further reference and model comparisons., Comment: 16 pages, 14 figures

With the outbreak of the COVID-19 pandemic, various studies have focused on predicting the trajectory and risk factors of the virus and its variants. Building on previous work that addressed this problem using genetic and epidemiological data, we introduce a method, Geo Score, that also incorporates geographic, socioeconomic, and demographic data to estimate infection and mortality risk by region and time. We employ gradient descent to find the optimal weights of the factors' significance in determining risk. Such spatiotemporal risk prediction is important for informed public health decision-making so that individuals are aware of the risks of travel during an epidemic or pandemic, and, perhaps more importantly, so that policymakers know how to triage limited resources during a crisis. We apply our method to New York City COVID-19 data from 2020, predicting ZIP code-level COVID-19 risk for 2021., Comment: 16 pages, 19 figures, completed as a part of MIT PRIMES program, to be presented in Joint Mathematics Meetings 2024

In this paper, we give an algorithm for describing the Weinstein presentation of Weinstein subdomains obtained by carving out regular Lagrangians. Our work generalizes previous work in dimension three and requires a novel Legendrian isotopy move (the ``boat move") that changes the local index of Reeb chords in a front projection. As applications, we describe presentations for certain exotic Weinstein subdomains and give explicit descriptions of $P$-loose Legendrians., Comment: 28 pages, 21 figures, comments welcome!

Regional Educational Laboratory Southwest partnered with the Arkansas Department of Education to examine Arkansas's middle school and high school indicators of postsecondary readiness and success, building on an earlier study of these indicators (Hester et al., 2021). Academic indicators include attaining proficiency on state academic examinations, grade point average, enrollment in advanced courses, and community service learning. Behavioral indicators include attendance, suspension, and expulsion. Using data on statewide grade 6 cohorts from 2008/09 and 2009/10, the study examined the percentages of students who attained the readiness and success indicators and the percentages of students who attained postsecondary readiness and success outcomes by gender, race/ethnicity, eligibility for the National School Lunch Program, English learner student status, disability status, age, and district locale. The study also examined whether the predictive accuracy, specificity, and strength of the indicators varied by these student groups. This document presents the following three appendixes that accompany the study: (1) Data and Methods; (2) Supporting analyses; and (3) Supplemental analyses. [For the full report, see ED624014.]

Regional Educational Laboratory Southwest partnered with the Arkansas Department of Education (ADE) to examine Arkansas's middle and high school indicators of postsecondary readiness and success, building on an earlier study of these indicators (Hester et al., 2021). Academic indicators include attaining proficiency on state achievement tests, grade point average, enrollment in advanced courses, and community service learning. Behavioral indicators include attendance, suspension, and expulsion. Using data on statewide grade 6 cohorts from 2008/09 and 2009/10, the study examined the percentages of students who attained the readiness and success indicators and the percentages of students who attained postsecondary readiness and success outcomes by gender, race/ethnicity, eligibility for the National School Lunch Program, English learner student status, disability status, age, and district locale. The study also examined whether the predictive accuracy, specificity, and strength of the indicators varied by these student groups. Three key findings emerged. First, the attainment of indicators of postsecondary readiness and success differed substantially for nearly all student groups, with the number of substantial differences on academic indicators exceeding those on behavioral indicators. The largest number of substantial differences in the attainment of academic indicators were between Black and White students, between students eligible and ineligible for the National School Lunch Program (an indicator of economic disadvantage), and between students who entered grade 6 before and after age 13. Second, attainment of postsecondary readiness and success outcomes varied substantially across student groups, with the largest differences between students with and without a disability. Third, predictive accuracy (the percentage of students with the same predicted and actual outcomes) and strength (the relative importance of a single indicator) were similar across student groups in most cases. Leaders at ADE and in Arkansas districts can use these findings to identify appropriate indicators of postsecondary readiness and success and to target supports toward student groups who most need them. These findings can help leaders identify and address disparities such as inequitable access to resources and supportive learning environments. [For the appendixes, see ED624015.]

The Texas Education Agency launched the Grow Your Own (GYO) grant program in 2018 to encourage districts to develop or expand existing high-quality education and training courses for high school students and to support district-employed paraprofessionals (including instructional aides and long-term substitute teachers) to pursue certifications that would allow them to enter full-time teaching roles. This study aimed to help state education leaders in Texas understand the progress of districts in implementing the GYO program and the early outcomes of participants. This study analyzed data from 2015/16 through 2020/21 for districts that received GYO funding in the first two grant cycles and districts in the same geographic locales within the same regions that did not receive GYO funding (comparison districts). The study found that the majority of districts awarded a GYO grant were in rural areas and small towns. GYO districts were more likely to have a smaller enrollment and had a higher average percentage of Hispanic students than comparison districts. The findings suggest that the program appeared to meet the Texas Education Agency's goal of providing opportunities to students and paraprofessionals in rural and small school settings and students of color to participate in GYO activities. The study also found that the percentage of students completing education and training courses in GYO districts was low (about 10 percent) during the grant years, and the percentage was similar in comparison districts before and after the grant awards. A disproportionate share of students who completed education and training courses in GYO districts were female. Although it is too soon to tell whether the GYO program will, over time, increase the size and diversity of the state's teacher pool, leaders at the Texas Education Agency can use these early findings to both understand the progress of districts in achieving the GYO grant program aims and help identify aspects of the program that might need further investigation. [For the appendices to this report, see ED623385.]

This report leverages state educational agency data to explore the association between Alabama Science in Motion (ASIM) implementation and student outcomes. We conducted this study in Alabama to evaluate the potential of teacher implementation of ASIM lab activities to improve high school level student achievement in science. This study follows a correlational design aimed at establishing the statistical association between a single metric of teacher preparation and student outcomes. Unlike experimental and quasi-experimental studies, it does not compare treatment and control groups. It focuses entirely on students exposed to the program (in this case, the implementation of ASIM labs)--and the differences in outcomes among them that can be attributed to the metrics of program implementation--making appropriate adjustments for differences in student and school characteristics and pretest scores. This study addresses the following questions: (1) Is there an association between ASIM implementation and science achievement for students in grade 11?; (2) Does the association of ASIM implementation with student achievement vary across student groups?; and (3) Where can improvement efforts be applied in the ASIM process to produce greater program effectiveness? [This report was funded by the University of Montevallo.]

Photoproduction of $\pi^0\pi^{\pm}$-pairs from quasifree nucleons bound in the deuteron has been investigated to study the helicity dependence of this reaction. Measurements with a liquid deuterium target were used to extract the unpolarized cross sections for reactions on protons and neutrons. A deuterated, longitudinally polarized solid-butanol target, together with a circularly polarized photon beam, determined the double polarization observable $E$. From these results the spin-dependent cross sections $\sigma_{1/2}$ and $\sigma_{3/2}$, corresponding to the anti-parallel and parallel spin configurations of the beam photon and target nucleon, have been derived. The measurements were performed at the Mainz MAMI accelerator with tagged, circularly-polarized photon beams produced via bremsstrahlung from longitudinally polarized electron beams. The reaction products were detected with an almost $4\pi$ solid-angle covering calorimeter composed of the Crystal Ball and TAPS detectors, supplemented by plastic scintillation detectors for charged particle identification. The results are sensitive to sequential decays of nucleon resonances via intermediate states and also to the decay of nucleon resonances by emission of charged $\rho$ mesons, and are compared to recent model results., Comment: 9 pages, 6 figures

We study several notions of dimension for (pre-)triangulated categories naturally arising from topology and symplectic geometry. We prove new bounds on these dimensions and raise several questions for further investigation. For instance, we relate the Rouquier dimension of the wrapped Fukaya category of either the cotangent bundle of smooth manifold $M$ or more generally a Weinstein domain $X$ to quantities of geometric interest. These quantities include the minimum number of critical values of a Morse function on $M$, the Lusternik-Schnirelmann category of $M$, the number of distinct action values of a Hamiltonian diffeomorphism of $X$, and the smallest $n$ such that $X$ admits a Weinstein embedding into $\mathbb{R}^{2n+1}$. Along the way, we introduce a notion of the Lusternik-Schnirelmann category for dg-categories and construct exact Lagrangian cobordisms for restriction to a Liouville subdomain., Comment: 38 Pages

Modern datacenter applications are prone to high tail latencies since their requests typically follow highly-dispersive distributions. Delivering fast interrupts is essential to reducing tail latency. Prior work has proposed both OS- and system-level solutions to reduce tail latencies for microsecond-scale workloads through better scheduling. Unfortunately, existing approaches like customized dataplane OSes, require significant OS changes, experience scalability limitations, or do not reach the full performance capabilities hardware offers. The emergence of new hardware features like UINTR exposed new opportunities to rethink the design paradigms and abstractions of traditional scheduling systems. We propose LibPreemptible, a preemptive user-level threading library that is flexible, lightweight, and adaptive. LibPreemptible was built with a set of optimizations like LibUtimer for scalability, and deadline-oriented API for flexible policies, time-quantum controller for adaptiveness. Compared to the prior state-of-the-art scheduling system Shinjuku, our system achieves significant tail latency and throughput improvements for various workloads without modifying the kernel. We also demonstrate the flexibility of LibPreemptible across scheduling policies for real applications experiencing varying load levels and characteristics., Comment: Accepted by HPCA2024

The notion of one-sided localization in the homotopy invariant context is developed for dg algebras and dg categories. Applications include a simple construction of derived localization of dg algebras and dg categories, and a refinement of Drinfeld's quotient of pretriangulated dg categories., Comment: 11 pages

A study was conducted to evaluate the impact of CAPIT Reading on student early literacy achievement. The study utilized a quasi-experimental comparison group design using data from 12 elementary schools in a suburban school district in Oklahoma during the 2019-20 school year. CAPIT Reading is a comprehensive PK-2 literacy solution that includes a digital phonics curriculum and teacher professional development. Four schools used CAPIT to supplement their literacy instruction for kindergarten students while eight schools did not. The study linked CAPIT usage data and district demographic and achievement data to estimate the impact of CAPIT on the Letter Word Sounds Fluency (LWSF) and Early Literacy Composite scores of the aimsweb reading assessment administered by the district in August and January. We found a positive impact of CAPIT Reading on student early reading achievement on the aimsweb assessment for kindergarten students estimated at 4.4 test score points for the aimsweb Early Literacy Composite score (effect size 0.17, p = 0.01) and 7.8 points for the LWSF score (effect size 0.29, p < 0.001). This impact on the LWSF score is equivalent to a 29% increase in growth for the average CAPIT student from the fall to winter tests. We found limited evidence of differential impact favoring student subgroups, meaning that this positive impact for CAPIT users did not vary according to student characteristics such as eligibility for free and reduced-price lunch, race, or gender. We found that the impact on aimsweb overall was marginally greater for special education students by 4.9 points (p = 0.09) and that the impact on LWSF scores was greater for English Language Learners by 7.4 points (p = 0.09). Impact of CAPIT reading does not vary significantly across other student groups. [This paper was produced by Evidentally, Inc.]

We construct a monoidal model structure on the category of all curved coalgebras and show that it is Quillen equivalent, via the extended bar-cobar adjunction, to another model structure we construct on the category of curved algebras. When the coalgebras under consideration are conilpotent and the algebras are dg, i.e. uncurved, this corresponds to the ordinary dg Koszul duality of Positselski and Keller-Lef\`evre. As an application we construct global noncommutative moduli spaces for flat connections on vector bundles, holomorphic structures on almost complex vector bundles, dg modules over a dg algebra, objects in a dg category, and others., Comment: 78 pages. v2: section 4.5 rewritten, other minor changes

Given any toric subvariety $Y$ of a smooth toric variety $X$ of codimension $k$, we construct a length $k$ resolution of $\mathcal O_Y$ by line bundles on $X$. Furthermore, these line bundles can all be chosen to be direct summands of the pushforward of $\mathcal O_X$ under the map of toric Frobenius. The resolutions are built from a stratification of a real torus that was introduced by Bondal and plays a role in homological mirror symmetry. As a corollary, we obtain a virtual analogue of Hilbert's syzygy theorem for smooth projective toric varieties conjectured by Berkesch, Erman, and Smith. Additionally, we prove that the Rouquier dimension of the bounded derived category of coherent sheaves on a toric variety is equal to the dimension of the variety, settling a conjecture of Orlov for these examples. We also prove Bondal's claim that the pushforward of the structure sheaf under toric Frobenius generates the derived category of a smooth toric variety and formulate a refinement of Uehara's conjecture that this remains true for arbitrary line bundles., Comment: 64 pages, 15 figures. Some minor changes following referee report. Version accepted to Forum of Mathematics, Pi