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This is the appendices for the full report, "Identifying the Nation's Lowest Performing Schools: Shifts Following the Passage of the Every Student Succeeds Act (ESSA)." This study examines state identification of schools for the most intensive support to see how changes in federal laws and regulations played out nationally and at the state level, by comparing schools identified just before and just after ESSA's implementation. Specifically, it looks at two time points: 2016-17, during which there were two distinct policy contexts, with most states operating under waivers but seven states still operating under the previous No Child Left Behind policies, and 2018-19, when all states were expected to be following ESSA regulations for the first time. Of particular interest is whether the number and characteristics of identified schools--including their average student achievement and demographics--differed when comparing the set of schools identified under ESSA with the set of schools identified just before ESSA. The appendices provide supporting details on the policy being evaluated, the study methods, and supplementary analyses for the findings presented.

For more than two decades, federal law has required states to identify schools failing to provide students with a high-quality education and has led to substantial debate about how best to do so. Appropriately identifying the lowest performing schools matters because it allows state and local education agencies to target limited resources for school improvement to where they are needed most. The Every Student Succeeds Act (ESSA) of 2015 sought to address perceived problems with school accountability systems under prior federal law. ESSA provided states with increased flexibility in how they design their "annual evaluation of school performance." It also introduced new requirements for states' subsequent "identification of schools for the most intensive support," now designated as those needing Comprehensive Support and Improvement (CSI), in part to allow states to focus on a smaller set of the lowest performing schools. This report examines if ESSA played out as policymakers expected or if there were any other, perhaps less expected, consequences for the number, types, and composition of schools that states identified. The report examines this issue by comparing schools identified for the most intensive supports just before and just after ESSA's implementation.

This article proposes an active-learning-based adaptive trajectory tracking control method for autonomous ground vehicles to compensate for modeling errors and unmodeled dynamics. The nominal vehicle model is decoupled into lateral and longitudinal subsystems, which are augmented with online Gaussian Processes (GPs), using measurement data. The estimated mean functions of the GPs are used to construct a feedback compensator, which, together with an LPV state feedback controller designed for the nominal system, gives the adaptive control structure. To assist exploration of the dynamics, the paper proposes a new, dynamic active learning method to collect the most informative samples to accelerate the training process. To analyze the performance of the overall learning tool-chain provided controller, a novel iterative, counterexample-based algorithm is proposed for calculating the induced L2 gain between the reference trajectory and the tracking error. The analysis can be executed for a set of possible realizations of the to-be-controlled system, giving robust performance certificate of the learning method under variation of the vehicle dynamics. The efficiency of the proposed control approach is shown on a high-fidelity physics simulator and in real experiments using a 1/10 scale F1TENTH electric car., Comment: Submitted to IEEE Transactions on Control Systems Technology

While the existence of an asymmetry between the two Maxwell centroids at the centre of the two foveas recorded using a foveascope, leads to the ocular dominance in good readers, the lack of asymmetry in most of the observers with dyslexia leads to their non-dominance and their difficulties in reading and writing. Indeed, the lack of asymmetry between the two main roads to the brain, i.e. the two optical nerves, leads to perturbations in the brain central connectivity, namely between the two hemispheres inducing too robust interhemispheric visual connections, beyond the critical period of 7-8 years. The symmetrical mirror-connections like b-d (observed for about 60% of children with dyslexia) or the non-symmetrical connections like b-b (35%) induce confusions and duplications in observers with dyslexia but remain erasable thanks to pulsed systems (glasses, lamps, screens. . .), using Hebbian processes in primary cortex synapses. The effect is instantaneous, non-invasive and compensates the lack of asymmetry. These systems help most of the observers with dyslexia to overcome their difficulties. The orthoptists and speech therapists can acquire and improve the mechanism to help the children to catch up, and perhaps be able to use the foveascope for an early diagnosis with young children., Comment: 8 pages, 4 figures

BPS states in type II string compactified on a Calabi-Yau threefold can typically be decomposed as moduli-dependent bound states of absolutely stable constituents, with a hierarchical structure labelled by attractor flow trees. This decomposition is best understood from the scattering diagram, an arrangement of real codimension-one loci (or rays) in the space of stability conditions where BPS states of given electromagnetic charge and fixed phase of the central charge exist. The consistency of the diagram when rays intersect determines all BPS indices in terms of the `attractor indices' carried by the initial rays. In this work we study the scattering diagram for a non-compact toric CY threefold known as local $\mathbb{F}_0$, namely the total space of the canonical bundle over $\mathbb{P}^1\times \mathbb{P}^1$. We first construct the scattering diagram for the quiver, valid near the orbifold point, and for the large volume slice, valid when both $\mathbb{P}^1$'s have large (and nearly equal) area. We then combine the insights gained from these simple limits to construct the scattering diagram along the physical slice of $\Pi$-stability conditions, which carries an action of a $\mathbb{Z}^4$ extension of the modular group $\Gamma_0(4)$. We sketch a proof of the Split Attractor Flow Tree Conjecture in this example, albeit for a restricted range of the central charge phase. Most arguments are similar to our early study of local $\mathbb{P}^2$ [arXiv:2210.10712], but complicated by the occurence of an extra mass parameter and ramification points on the $\Pi$-stability slice., Comment: 64 pages, 36 colorful figures

Boosting literacy among school-age children remains a national priority. Nearly one third of students in the United States have not developed the foundational reading skills needed to succeed academically, with students living in poverty, students with disabilities, and English learners especially at risk. Starting in 2010, Congress invested more than $1 billion for state literacy improvement efforts through the Striving Readers Comprehensive Literacy (SRCL) program. SRCL was intended to focus funding on disadvantaged schools, encourage schools to use evidence-based practices, and support schools and teachers in providing comprehensive literacy instruction. These efforts were expected to lead to improved literacy outcomes for students. This study assesses how well SRCL implementation was aligned with these goals, using information collected from states, districts, and schools in all 11 states awarded grants in 2017.

Carcinogenesis is a proteiform phenomenon, with tumors emerging in various locations and displaying complex, diverse shapes. At the crucial intersection of research and clinical practice, it demands precise and flexible assessment. However, current biomarkers, such as RECIST 1.1's long and short axis measurements, fall short of capturing this complexity, offering an approximate estimate of tumor burden and a simplistic representation of a more intricate process. Additionally, existing supervised AI models face challenges in addressing the variability in tumor presentations, limiting their clinical utility. These limitations arise from the scarcity of annotations and the models' focus on narrowly defined tasks. To address these challenges, we developed ONCOPILOT, an interactive radiological foundation model trained on approximately 7,500 CT scans covering the whole body, from both normal anatomy and a wide range of oncological cases. ONCOPILOT performs 3D tumor segmentation using visual prompts like point-click and bounding boxes, outperforming state-of-the-art models (e.g., nnUnet) and achieving radiologist-level accuracy in RECIST 1.1 measurements. The key advantage of this foundation model is its ability to surpass state-of-the-art performance while keeping the radiologist in the loop, a capability that previous models could not achieve. When radiologists interactively refine the segmentations, accuracy improves further. ONCOPILOT also accelerates measurement processes and reduces inter-reader variability, facilitating volumetric analysis and unlocking new biomarkers for deeper insights. This AI assistant is expected to enhance the precision of RECIST 1.1 measurements, unlock the potential of volumetric biomarkers, and improve patient stratification and clinical care, while seamlessly integrating into the radiological workflow.

It is usually assumed that the memory of any thermo-mechanical protocol applied to a glass can be erased by heating the material in the supercooled liquid. While this is true for thermally treated amorphous solids, we show that hydrostatic compression can irreversibly modify the atomic motion, thermodynamic state and structure of a prototypical metallic glass-former, in a way which depends on the degree of ergodicity reached by the material during compression. While enhanced kinetic and thermodynamic stability can be obtained by quenching the dense liquid, high-pressure annealing in the glass leads to thermal rejuvenation and complex structural rearrangements at the level of the short and medium range order. When heated above their glass transition temperature, these compressed glasses do not convert into the pristine supercooled liquid but rather transform into different systems, challenging the generally accepted idea of an equilibrium recovery controlled solely by the microscopic $\alpha$-relaxation process.

The Boulby UnderGround Screening (BUGS) facility, located at the Boulby Underground Laboratory, has significantly advanced its material screening capabilities by installing two XIA UltraLo-1800 alpha particle detectors. This study presents a comprehensive evaluation of one of these detectors, operated 1,100 meters underground at the Boulby Underground Laboratory, which provides significant shielding from cosmic radiation and maintains a low ambient radon activity of 2.30 $\pm$ 0.03 Bq/m$^3$. Our evaluation focuses on energy reconstruction accuracy, background radiation rates, and operational stability. The XIA UltraLo-1800 detector demonstrates remarkable stability in energy reconstruction, with less than 0.1 MeV variation over four years. Moreover, the implementation of a graphite-filled PTFE liner in the sample tray resulted in a significant reduction in background radiation levels compared to measurements with the original stainless steel tray, achieving an average activity of 0.15 $\pm$ 0.01 $\alpha$/cm$^2$/khr. Copper sample assays, performed before and after radon exposure, demonstrated the detector's ability to accurately identify and quantify $^{210}$Po contamination. By implementing the robust cleanliness procedures and protocols described in this article, we observed a reduction in $^{210}$Po activity from 0.504 $\pm$ 0.022 mBq to 0.336 $\pm$ 0.013 mBq, highlighting the crucial role of refined cleaning methods in minimizing background for sensitive experiments. Additionally, observations of elevated background activity levels post-high-activity sample measurements illustrate the need for careful management of assay conditions and environment to maintain low background levels. These results highlight the potential of the XIA UltraLo-1800 in enhancing the precision of material assays essential for reducing background interference in rare event experiments.

We present two methods for deriving the equations of motion for charged massive spin-3/2 particles. The first approach involves utilizing the Euler-Lagrange equations derived from a Lagrangian that describes the propagation of the first massive excitation of open superstrings. The second method entails enforcing the conditions that the trace vanishes and that the covariant derivative of the equations vanish. We very briefly comment about other spins., Comment: 11 pages. Corfu Summer Institute 2023

Mid-infrared emission features probe the properties of ionized gas, and hot or warm molecular gas. The Orion Bar is a frequently studied photodissociation region (PDR) containing large amounts of gas under these conditions, and was observed with the MIRI IFU aboard JWST as part of the "PDRs4All" program. The resulting IR spectroscopic images of high angular resolution (0.2") reveal a rich observational inventory of mid-IR emission lines, and spatially resolve the substructure of the PDR, with a mosaic cutting perpendicularly across the ionization front and three dissociation fronts. We extracted five spectra that represent the ionized, atomic, and molecular gas layers, and measured the most prominent gas emission lines. An initial analysis summarizes the physical conditions of the gas and the potential of these data. We identified around 100 lines, report an additional 18 lines that remain unidentified, and measured the line intensities and central wavelengths. The H I recombination lines originating from the ionized gas layer bordering the PDR, have intensity ratios that are well matched by emissivity coefficients from H recombination theory, but deviate up to 10% due contamination by He I lines. We report the observed emission lines of various ionization stages of Ne, P, S, Cl, Ar, Fe, and Ni, and show how certain line ratios vary between the five regions. We observe the pure-rotational H$_2$ lines in the vibrational ground state from 0-0 S(1) to 0-0 S(8), and in the first vibrationally excited state from 1-1 S(5) to 1-1 S(9). We derive H$_2$ excitation diagrams, and approximate the excitation with one thermal (~700 K) component representative of an average gas temperature, and one non-thermal component (~2700 K) probing the effect of UV pumping. We compare these results to an existing model for the Orion Bar PDR and highlight the differences with the observations., Comment: 26 pages, 12 figures, 3 tables. Submitted to A&A, under review (1st revision)

The impurity paramagnetic ion, $Cu^{2+}$ substitutes $Al$ in the $SrLaAlO_4$ single crystal lattice, this results in a $CuO_6$ elongated octahedron, the resulting measured g-factors shows four-fold axes variation condition. The aggregate frequency width of the electron spin resonance with the required minimum level of impurity concentration has been evaluated in single crystal $SrLaAlO_4$ at $20$ millikelvin. Measured parallel hyperfine constants, $A_{\scriptscriptstyle\parallel Cu}$, were determined to be $-155.7\times10^{-4}~cm^{-1},~ -163.0\times10^{-4}~cm^{-1},~ -178.3\times10^{-4}~cm^{-1} $ and$~-211.1\times10^{-4}~cm^{-1}$ at $9.072~GHz~(WGH_{4,1,1})$ for the nuclear magnetic quantum number $M_I=+\frac{3}{2},+\frac{1}{2},-\frac{1}{2}$,~and$-\frac{3}{2}$ respectively. The anisotropy of the hyperfine structure reveals a characteristics of static Jahn-Teller effect. The second-order-anisotropy-term, $\sim (\frac{spin-orbit~coupling}{10D_q})^2$, is significant and can not be disregarded, with the local strain dominating over the observed Zeeman-anisotropy-energy difference. The Bohr electron magneton, $\beta=9.23\times 10^{-24} JT^{-1}$, (within $-0.43\%$ so-called experimental error) has been found using the measured spin-Hamiltonian parameters. Measured nuclear dipolar hyperfine structure parameter $P_{\scriptscriptstyle\parallel}=12.3\times10^{-4}~cm^{-1}$ shows that the mean inverse third power of the electron distance from the nucleus is $\langle r^{-3}_q\rangle\simeq 5.23$ a.u. for $Cu^{2+}$ ion in the substituted $Al^{3+}$ ion site assuming nuclear electric quadruple moment $Q=-0.211$ barn.

Impurity $Fe^{3+}$ ion electron spin resonance (ESR) spectroscopy using multiple dielectric modes in a $SrTiO_3$ dielectric resonator has been performed with a tuneable DC magnetic field of up to $1.6~T$. The $Ti^{4+}(d^0)$ ion is substituted by $Fe^{3+}$ ion forming $FeO_6$ octahedral complex with an iron-oxygen-vacancy $(Fe^{3+}-V_O)$. In such a metal-ligand complex, a giant g-factor of $g_{\scriptscriptstyle\parallel F} = 5.51$ was observed in the ferroelectric phase at $20~mK$. The the change of $Fe^{3+}$ ion center-symmetry in the $FeO_6$ complex as a soft-mode characteristics of ferroelectric phase transition and the influences of iron-oxygen-vacancy $(Fe^{3+}-V_O)$, interactively sensitive to asymmetry in the octahedral rotational parameter $\Phi$ in $SrTi0_3$.

To construct asymptotically-Euclidean Einstein's initial data sets, we introduce the localized seed-to-solution method, which projects from approximate to exact solutions of the Einstein constraints. The method enables us to glue together initial data sets in multiple asymptotically-conical regions, and in particular construct data sets that exhibit the gravity shielding phenomenon, specifically that are localized in a cone and exactly Euclidean outside of it. We achieve optimal shielding in the sense that the metric and extrinsic curvature { are controlled at a super-harmonic rate, regardless of how slowly they decay (even} beyond the standard ADM formalism), and the gluing domain can be a collection of arbitrarily narrow nested cones. We also uncover several notions of independent interest: silhouette functions, localized ADM modulator, and relative energy-momentum vector. An axisymmetric example is provided numerically., Comment: 10 pages

Densified silica can be obtained by different pressure and temperature paths and for different stress conditions, hydrostatic or including shear. The density is usually the macroscopic parameter used to characterize the different compressed silica samples. The aim of our present study is to compare structural modifications for silica glass, densified from several routes. For this, densified silica glasses are prepared from cold and high temperature (up to 1020 $^\circ$C) compressions. The different densified glasses obtained in our study are characterized by micro-Raman spectroscopy. Intertetrahedral angles from the main band relative to the bending mode decreases and their values are larger for densified samples from high temperature compression than those samples from cold compression. The relative amount of 3-membered rings deduced from the D2 line area increases as a function of density for cold compression. The temperature increase during the compression process induces a decrease of the 3 fold ring population. Moreover, 3 fold rings are more deformed and stressed for densified samples at room temperature at the expense of those densified at high temperature. Temperature plays a main role in the reorganization structure during the densification and leads to obtaining a more relaxed structure with lower stresses than glasses densified from cold compression. The role of hydrostatic or non-hydrostatic applied stresses on the glass structure is discussed. From the Sen and Thorpe central force model, intertetrahedral angle average value and their distribution are estimated.

*Caveat: we learned post-factum that most of these results are not novel. We are keeping this paper for continuity reasons.* Given finite-dimensional complex representations $V$ and $V'$ of a simply-connected semisimple compact Lie group $G$, we determine the dimension of the $G$-invariant subspace of $\mathrm{adj}(G)\otimes V\otimes V'$, of $\mathrm{adj}(G)\otimes S^2 V$, and of $\mathrm{adj}(G)\otimes\Lambda^2 V$, where $\mathrm{adj}(G)$ is the adjoint representation. In other words we derive the multiplicity with which summands of $\mathrm{adj}(G)$ appear in a tensor product $V \otimes V'$ or (anti)symmetric square $S^2 V$ or $\Lambda^2 V$. We find in particular that the dimension of the $G$-invariant subspace of $\mathrm{adj}(G)\otimes S^2 V$ is larger than (resp. smaller or equal to) that of $\mathrm{adj}(G)\otimes\Lambda^2 V$ for a symplectic (resp. orthogonal) representation $V$., Comment: 14 pages. The $\mu = \overline{\nu}$ case of our Theorem 1.3, as well as our Theorem 1.4, already appear in the literature; we added the relevant references

We consider asymptotically Euclidean, initial data sets for Einstein's field equations and solve the localization problem at infinity, also called gluing problem. We achieve optimal gluing and optimal decay, in the sense that we encompass solutions with possibly arbitrarily low decay at infinity and establish (super-)harmonic estimates within possibly arbitrarily narrow conical domains. In the localized seed-to-solution method (as we call it), we define a variational projection operator which associates the solution to the Einstein constraints that is closest to any given localized seed data set (as we call it). Our main contribution concerns the derivation of harmonic estimates for the linearized Einstein operator and its formal adjoint which, in particular, includes new analysis on the linearized scalar curvature operator. The statement of harmonic estimates requires the notion of energy-momentum modulators (as we call them), which arise as correctors to the localized seed data sets. For the Hamiltonian and momentum operators, we introduce a notion of harmonic-spherical decomposition and we uncover stability conditions on the localization function, which are localized Poincare and Hardy-type inequalities and, for instance, hold for arbitrarily narrow gluing domains. Our localized seed-to-solution method builds upon the gluing techniques pioneered by Carlotto, Chrusciel, Corvino, Delay, Isenberg, Maxwell, and Schoen, while providing a proof of a conjecture by Carlotto and Schoen on the localization problem and generalize P. LeFloch and Nguyen's theorem on the asymptotic localization problem., Comment: 91 pages

During reading, dyslexic readers exhibit more and longer fixations than normal readers. However, there is no significant difference when dyslexic and control readers perform only visual tasks on a string of letters, showing the importance of cognitive processes in reading. This linguistic and cognitive processing demand in reading is often perturbed for dyslexic readers by perceived additional letter and word mirror-images superposed to the primary images on the primary cortex, inducing an internal visual crowding. Here we show that whereas for a normal reader, the number and the duration of fixations remain invariant whatever the nature of the lighting, the excess of fixations and total duration of reading can be controlled for a dyslexic reader using the Hebbian mechanisms to erase the extra images in an optimized pulse-width lighting. The number of fixations can be reduced by a factor of about 1.8, recovering the normal reader records., Comment: 8 pages, 6 figures

The aim of this paper is to give new insights about families of integrable systems lifting a Hamiltonian $S^1$-space. Specifically, we study one-parameter families $(M^4,\omega,F_t=(J,H_t))_{0 \leq t \leq 1}$ of systems with a fixed Hamiltonian $S^1$-space $(M,\omega,J)$ and which are semitoric for certain values of the parameter $t$, with a focus on such families in which one singular point undergoes a Hamiltonian-Hopf bifurcation (also called nodal trade in the context of semitoric systems, and more generally almost toric fibrations). Beyond semitoric systems, we also study families containing hypersemitoric systems, and we investigate the local theory of a nodal trade.\\Building on and generalizing the ideas of a previous paper, we show how such families can be used to find explicit semitoric systems with certain desired invariants (bundled in the marked semitoric polygon). This allows us to make progress on the semitoric minimal model program by understanding and coming up with explicit systems for each strictly minimal type (i.e., those not admitting any toric or semitoric type blowdown). In order to obtain these systems, we develop strategies for constructing and understanding explicit examples of semitoric (and hypersemitoric) systems in general. One strategy we make use of is to start from a well-understood system (such as a toric system) and to explicitly induce Hamiltonian-Hopf bifurcations to produce focus-focus singular points. This is an expanded version of the technique used in the aforementioned previous paper, in order to apply it to semitoric systems which include non-trivial isotropy spheres in the underlying $S^1$-space (i.e., $\mathbb{Z}_k$-spheres), which occurs in several of the strictly minimal systems.\\In particular, we give an explicit one-parameter family of systems on $\mathbb{CP}^2$ which transitions between being of toric type, semitoric type, and hypersemitoric type depending on the value of the parameter. We study this system at each stage, computing the marked semitoric polygon of the semitoric system and determining several properties of the hypersemitoric system, including the existence of a unique flap and two parabolic orbits. Furthermore, we study the transitions between these stages.\\We also come up with new explicit semitoric systems on all Hirzebruch surfaces which, together with the previous systems and the systems already contained in the literature, gives an explicit model for every type of strictly minimal system. Moreover, we show how to obtain every strictly minimal system by applying sequences of alternating toric type blowups and blowdowns to simple explicit systems. In particular, we obtain that every strictly minimal semitoric polygon can be obtained from a semitoric system which is part of a family $(M,\omega,F_t=(J,H_t))$ which is semitoric for all but a finite number of values of $t$, called a semitoric family., Comment: 125 pages, 53 figures. Exposition and formatting improved

Star formation rate functions (SFRFs) give an instantaneous view of the distribution of star formation rates (SFRs) in galaxies at different epochs. They are a complementary and more stringent test for models than the galaxy stellar mass function, which gives an integrated view of the past star formation activity. However, the exploration of SFRFs has been limited thus far due to difficulties in assessing the SFR from observed quantities and probing the SFRF over a wide range of SFRs. We overcome these limitations thanks to an original method that predicts the infrared luminosity from the rest-frame UV/optical color of a galaxy and then its SFR over a wide range of stellar masses and redshifts. We applied this technique to the deep imaging survey HSC-CLAUDS combined with near-infrared and UV photometry. We provide the first SFR functions with reliable measurements in the high- and low-SFR regimes up to $z=2$ and compare our results with previous observations and four state-of-the-art hydrodynamical simulations., Comment: 29 pages, 19 figures

The Multi Unit Spectroscopic Explorer (MUSE) is a second-generation VLT panoramic integral-field spectrograph currently in manufacturing, assembly and integration phase. MUSE has a field of 1x1 arcmin2 sampled at 0.2x0.2 arcsec2 and is assisted by the VLT ground layer adaptive optics ESO facility using four laser guide stars. The instrument is a large assembly of 24 identical high performance integral field units, each one composed of an advanced image slicer, a spectrograph and a 4kx4k detector. In this paper we review the progress of the manufacturing and report the performance achieved with the first integral field unit., Comment: 10 pages, 5 figures

The spectrum of BPS states in type IIA string theory compactified on a Calabi-Yau threefold famously jumps across codimension-one walls in complexified K\"ahler moduli space, leading to an intricate chamber structure. The Split Attractor Flow Conjecture posits that the BPS index $\Omega_z(\gamma)$ for given charge $\gamma$ and moduli $z$ can be reconstructed from the attractor indices $\Omega_*(\gamma_i)$ counting BPS states of charge $\gamma_i$ in their respective attractor chamber, by summing over a finite set of decorated rooted flow trees known as attractor flow trees. If correct, this provides a classification (or dendroscopy) of the BPS spectrum into different topologies of nested BPS bound states, each having a simple chamber structure. Here we investigate this conjecture for the simplest, albeit non-compact, Calabi-Yau threefold, namely the canonical bundle over the projective plane $P^2$. Since the K\"ahler moduli space has complex dimension one and the attractor flow preserves the argument of the central charge, attractor flow trees coincide with scattering sequences of rays in a two-dimensional slice of the scattering diagram in the space of stability conditions on the derived category of compactly supported coherent sheaves on $K_{P^2}$. We combine previous results on the scattering diagram of $K_{P^2}$ in the large volume slice with new results near the orbifold point $\mathbb{C}^3/\mathbb{Z}_3$, and prove that the Split Attractor Flow Conjecture holds true on the physical slice of $\Pi$-stability conditions. In particular, while there is an infinite set of initial rays related by the group $\Gamma_1(3)$ of auto-equivalences, only a finite number of possible decompositions $\gamma=\sum_i\gamma_i$ contribute to the index $\Omega_z(\gamma)$ for any $\gamma$ and $z$, with constituents $\gamma_i$ related by spectral flow to the fractional branes at the orbifold point., Comment: 61+23 pages, 32 figures; v3: final version to appear in Comm. Math. Phys

We study the zeros of sections of the form $T_k s_k$ of a large power $L^{\otimes k} \to M$ of a holomorphic positive Hermitian line bundle over a compact K\''ahler manifold $M$, where $s_k$ is a random holomorphic section of $L^{\otimes k}$ and $T_k$ is a Berezin-Toeplitz operator, in the limit $k \to +\infty$. In particular, we compute the second order approximation of the expectation of the distribution of these zeros. In a ball of radius of order $k^{-\frac{1}{2}}$ around $x \in M$, assuming that the principal symbol $f$ of $T_k$ is real-valued and vanishes transversally, we show that this expectation exhibits two drastically different behaviors depending on whether $f(x) = 0$ or $f(x) \neq 0$. These different regimes are related to a similar phenomenon about the convergence of the normalized Fubini-Study forms associated with $T_k$: they converge to the K\''ahler form in the sense of currents as $k\rightarrow + \infty$, but not as differential forms (even pointwise). This contrasts with the standard case $f=1$, in which the convergence is in the $\mathscr{C}^{\infty}$-topology. From this, we are able to recover the zero set of $f$ from the zeros of $T_k s_k$.

The dark entoptic Maxwell spot centroids seen through a blue filter, which coincide with the blue cone-free areas centered on the foveas, are shown to exhibit a structure. When observing through the green part of a blue-green exchange filter in a foveascope, after a fixation through the blue part, a small orange disc is seen around the centre of the pale green memory afterimage corresponding to the blue cone-free area. Using artificial pupils with different diameters, we show that this small circular pattern corresponds to the Airy disc due to the Fraunhofer diffraction through the pupil. Typically, for an eye with a 3 millimeter diameter pupil, the Airy disc exhibits a diameter of about 8 micrometers at the centre of the usual 100-150 micrometer Maxwell centroid. Fixation tests show that the towering central maximum of the Airy pattern irradiance corresponds to the preferred locus of the fixation of the eye near the centre of the blue cone-free area of the fovea. The locus of fixation in human vision thus appears to be located in the only area of the fovea where the large chromatic dispersion is cancelled, optimising the eye acuity., Comment: 10 pages, 6 figures

We analyze exactly marginal deformations of 3d N=4 Lagrangian gauge theories, especially mixed-branch operators with both electric and magnetic charges. These mixed-branch moduli can either belong to products of electric and magnetic current supermultiplets, or be single-trace (non-factorizable). Apart from some exceptional quivers that have additional moduli, 3d N=4 theories described by genus g quivers with nonabelian unitary gauge groups have exactly g single-trace mixed moduli, which preserve the global flavour symmetries. This partly explains why only linear and circular quivers have known AdS_4 supergravity duals. Indeed, for g>1, AdS_4 gauged supergravities cannot capture the entire g-dimensional moduli space even if one takes into account the quantization moduli of boundary conditions. Likewise, in a general Lagrangian theory, we establish (using the superconformal index) that the number of single-trace mixed moduli is bounded below by the genus of a graph encoding how nonabelian gauge groups act on hypermultiplets., Comment: 53 pages. v2: Lower bound strengthened, Section 5 added with classes of examples, references corrected. v3: comment on star-shaped quivers (matches published version)

We study the plane-symmetric collision of two gravitational waves and describe the global spacetime geometry generated by this collision. To this end, we formulate the characteristic initial value problem for the Einstein equations, when Goursat data describing the incoming waves are prescribed on two null hypersurfaces. We then construct a global solution representing a cyclic spacetime based on junction conditions associated with a prescribed singularity scattering map (a notion recently introduced by the authors). From a mathematical analysis standpoint, this amounts to a detailed analysis of the Goursat and Fuchsian initial value problems associated with singular hyperbolic equations, when junction conditions at interfaces are prescribed. In our construction, we introduce a partition into monotonicity diamonds (that is, suitable spacetime domains) and we construct the solution by concatenating domains across interfaces of timelike, null, or spacelike type., Comment: 34 pages: second half of the original arXiv:2005.11324 (now shortened)

Gamma-ray Bursts (GRBs) are the most powerful transients in the Universe, over-shining for a few seconds all other $\gamma$-ray sky sources. Their emission is produced within narrowly collimated relativistic jets launched after the core-collapse of massive stars or the merger of compact binaries. THESEUS will open a new window for the use of GRBs as cosmological tools by securing a statistically significant sample of high-$z$ GRBs, as well as by providing a large number of GRBs at low-intermediate redshifts extending the current samples to low luminosities. The wide energy band and unprecedented sensitivity of the Soft X-ray Imager (SXI) and X-Gamma rays Imaging Spectrometer (XGIS) instruments provide us a new route to unveil the nature of the prompt emission. For the first time, a full characterisation of the prompt emission spectrum from 0.3 keV to 10 MeV with unprecedented large count statistics will be possible revealing the signatures of synchrotron emission. SXI spectra, extending down to 0.3 keV, will constrain the local metal absorption and, for the brightest events, the progenitors' ejecta composition. Investigation of the nature of the internal energy dissipation mechanisms will be obtained through the systematic study with XGIS of the sub-second variability unexplored so far over such a wide energy range. THESEUS will follow the spectral evolution of the prompt emission down to the soft X-ray band during the early steep decay and through the plateau phase with the unique ability of extending above 10 keV the spectral study of these early afterglow emission phases., Comment: Submitted to Experimental Astronomy

Multi-messenger astrophysics is becoming a major avenue to explore the Universe, with the potential to span a vast range of redshifts. The growing synergies between different probes is opening new frontiers, which promise profound insights into several aspects of fundamental physics and cosmology. In this context, THESEUS will play a central role during the 2030s in detecting and localizing the electromagnetic counterparts of gravitational wave and neutrino sources that the unprecedented sensitivity of next generation detectors will discover at much higher rates than the present. Here, we review the most important target signals from multi-messenger sources that THESEUS will be able to detect and characterize, discussing detection rate expectations and scientific impact., Comment: Submitted to Experimental Astronomy

THESEUS, one of the two space mission concepts being studied by ESA as candidates for next M5 mission within its Comsic Vision programme, aims at fully exploiting Gamma-Ray Bursts (GRB) to solve key questions about the early Universe, as well as becoming a cornerstone of multi-messenger and time-domain astrophysics. By investigating the first billion years of the Universe through high-redshift GRBs, THESEUS will shed light on the main open issues in modern cosmology, such as the population of primordial low mass and luminosity galaxies, sources and evolution of cosmic re-ionization, SFR and metallicity evolution up to the "cosmic dawn" and across Pop-III stars. At the same time, the mission will provide a substantial advancement of multi-messenger and time-domain astrophysics by enabling the identification, accurate localisation and study of electromagnetic counterparts to sources of gravitational waves and neutrinos, which will be routinely detected in the late '20s and early '30s by the second and third generation Gravitational Wave (GW) interferometers and future neutrino detectors, as well as of all kinds of GRBs and most classes of other X/gamma-ray transient sources. In all these cases, THESEUS will provide great synergies with future large observing facilities in the multi-messenger domain. A Guest Observer programme, comprising Target of Opportunity (ToO) observations, will expand the science return of the mission, to include, e.g., solar system minor bodies, exoplanets, and AGN., Comment: Submitted to Experimental Astronomy. arXiv admin note: text overlap with arXiv:2102.08702

Given a quantum semitoric system composed of pseudodifferential operators, Berezin-Toeplitz operators, or a combination of both, we obtain explicit formulas for recovering, from the semiclassical asymptotics of the joint spectrum, all symplectic invariants of the underlying classical semitoric system. Our formulas are based on the possibility to obtain good quantum numbers for joint eigenvalues from the bare data of the joint spectrum. In the spectral region corresponding to regular values of the momentum map, the algorithms developed by Dauge, Hall and the second author [27] produce such labellings. In our proof, it was crucial to extend these algorithms to the boundary of the spectrum, which led to the new notion of asymptotic half-lattices, and to globalize the resulting labellings. Using the construction given by Pelayo and the second author in [79], our results prove that semitoric systems are completely spectrally determined in an algorithmic way~: from the joint spectrum of a quantum semitoric system one can construct a representative of the isomorphism class of the underlying classical semitoric system. In particular, this recovers the uniqueness result obtained by Pelayo and the authors in [62,61], and completes it with the explicit computation of all invariants, including the twisting index. In the cases of the spin-oscillator and the coupled angular momenta, we implement the algorithms and illustrate numerically the computation of the invariants from the joint spectrum., Comment: Exposition improved. 115 pages, 32 figures

It is more and more common to explore the genome at diverse levels and not only at a single omic level. Through integrative statistical methods, omics data have the power to reveal new biological processes, potential biomarkers, and subgroups of a cohort. The matrix factorization (MF) is a unsupervised statistical method that allows giving a clustering of individuals, but also revealing relevant omic variables from the various blocks. Here, we present PIntMF (Penalized Integrative Matrix Factorization), a model of MF with sparsity, positivity and equality constraints.To induce sparsity in the model, we use a classical Lasso penalization on variable and individual matrices. For the matrix of samples, sparsity helps for the clustering, and normalization (matching an equality constraint) of inferred coefficients is added for a better interpretation. Besides, we add an automatic tuning of the sparsity parameters using the famous glmnet package. We also proposed three criteria to help the user to choose the number of latent variables. PIntMF was compared to other state-of-the-art integrative methods including feature selection techniques in both synthetic and real data. PIntMF succeeds in finding relevant clusters as well as variables in two types of simulated data (correlated and uncorrelated). Then, PIntMF was applied to two real datasets (Diet and cancer), and it reveals interpretable clusters linked to available clinical data. Our method outperforms the existing ones on two criteria (clustering and variable selection). We show that PIntMF is an easy, fast, and powerful tool to extract patterns and cluster samples from multi-omics data.

We describe the asymptotic behaviour of the quantum propagator generated by a Berezin-Toeplitz operator with real-valued principal symbol. We also give precise asymptotics for smoothed spectral projectors associated with the operator in the autonomous case; this leads us to introducting quantum states associated with immersed Lagrangian submanifolds. These descriptions involve geometric quantities of two origins, coming from lifts of the Hamiltonian flow to the prequantum bundle and the canonical bundle respectively. The latter are the main contribution of this article and are connected to the Maslov indices appearing in trace formulas, as will be explained in a forthcoming paper.

Genome-Wide Association Studies (GWAS) explain only a small fraction of heritability for most complex human phenotypes. Genomic heritability estimates the variance explained by the SNPs on the whole genome using mixed models and accounts for the many small contributions of SNPs in the explanation of a phenotype. This paper approaches heritability from a machine learning perspective, and examines the close link between mixed models and ridge regression. Our contribution is twofold. First, we propose estimating genomic heritability using a predictive approach via ridge regression and Generalized Cross Validation (GCV). We show that this is consistent with classical mixed model based estimation. Second, we derive simple formulae that express prediction accuracy as a function of the ratio n/p, where n is the population size and p the total number of SNPs. These formulae clearly show that a high heritability does not imply an accurate prediction when p>n. Both the estimation of heritability via GCV and the prediction accuracy formulae are validated using simulated data and real data from UK Biobank.