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Massive online user review platforms, with their star ratings and text reviews, are reshaping the information available for consumer and public service decisions. We study the leading K-12 schooling platform, GreatSchools, applying machine learning (Natural Language Processing, NLP) to 600,000 reviews that encompass the vast majority of the nation's traditional public, charter, and private schools (84,009 schools in total), supplemented with qualitative analysis of a subsample of reviews. Encompassing more than fifty million words of text, our initial analysis pre-specified eight broad topics and 27 sub-topics and coded review words into these categories. We find that parents write the vast majority of reviews and tend to write more about School Staff and School Culture than students. More generally, text reviews vary in important ways across user types (parents, students, teachers, principals), school sector (traditional public, charter, and private schools), grade level, and demographics. The partial correlation between topics and star ratings also differs across user types and sectors. Taken together, these results suggest that user reviews are less useful than they appear and less useful than with other kinds of products. Our analysis points to design features that might improve their usefulness. The variation in content and value of the reviews also has methodological implications as it shows how NLP can complement qualitative research methods with such large volumes of text.

Families are being given more and more choices of schools, from charter schools to virtual schools and private schools, through school vouchers. However, families often report not being well informed about these choices. Many report being awash in information, though not necessarily the information they want or need. State, district, and school websites, along with Facebook pages and word-of-mouth, provide additional information but not necessarily a coherent picture of the various schooling options available to families. Massive school information and review platforms add another source of information. These platforms provide access to much of the same data found on other public websites--test scores, student demographics, graduation rates, and more--combined with text reviews and star ratings provided by students, parents, educators, and other stakeholders. The authors studied the content and usefulness of user reviews from one of the most widely used platforms, GreatSchools, including 50 million words of text across more than 600,000 reviews written about 84,000 schools from 2009 to 2019. The findings suggest that user reviews have the potential to inform consumers about school choices. However, they face many hurdles, some of which have not been well recognized. The authors propose ways to improve school user reviews and discuss implications for school choice.

The problem of avoiding saturation of the coil currents is critical in large tokamaks with superconducting coils like ITER. Indeed, if the current limits are reached, a loss of control of the plasma may lead to a major disruption. Therefore, a Current Limit Avoidance (CLA) system is essential to operate safely. This paper provides the first experimental evidence that the online solution of a constrained quadratic optimization problem can offer a valid methodology to implement a CLA. Experiments are carried out on the Tokamak \`a Configuration Variable (TCV) at the Swiss Plasma Center, showing the effectiveness of the proposed approach and its suitability for real-time application in view of future reactors such as ITER., Comment: 14 pages, currently under review

The fragmentation cross sections of carbon ion beams with kinetic energies of $115 - 353~\text{MeV/u}$ impinging on thin targets of graphite (C), polyvinyl-toluene (C$_9$H$_{10}$) and PMMA (C$_2$O$_5$H$_8$) have been measured at 90$^{\text{o}}$ and 60$^{\text{o}}$ at the CNAO particle therapy center (Pavia, Italy). The presented measurements are a complete reanalysis by the FOOT collaboration of already published elemental cross section on composite targets, in order to refine the analysis, improve the systematic uncertainties and show the comparison with the FLUKA Monte Carlo code calculations. In this work, the kinetic energy at production of measured fragments has been completely redefined, together with the efficiencies computation. The new analysis strategy has been successfully validated against the Monte Carlo cross sections. Two detection arms were positioned at two different angles to perform the measurement at 90$^{\text{o}}$ and 60$^{\text{o}}$. The fragment species have been identified in charge (Z$_{id}$ = H) and mass (M$_{id}$ = $^1$H, $^2$H, $^3$H) combining the information of the deposited energy in thin plastic scintillators, of the deposited energy in a thick LYSO crystal and of the fragments Time of Flight (ToF) measurement. The ToF was also used to compute the fragments measured kinetic energy. The cross sections are presented as a function of the fragments kinetic energy at production thanks to an unfolding technique applied to the data., Comment: Corresponding Author: Marco Toppi, marco.toppi@uniroma1.it

This paper presents the measurements of the angular differential cross sections for the forward production of He, Li, Be, B, C and N nuclei in the fragmentation process of a 400$\text{MeV/nucleon}$ $^{16}\text{O}$ beam interacting with a graphite target. Due to the limited data available in this energy regime, these measurements of nuclear fragmentation cross sections are relevant to improve nuclear interaction models for Particle Therapy and space radioprotection applications. The data analyzed in this paper were collected during a measurement campaign carried out at the GSI Helmholtz Center for Heavy Ion Research facility in Darmstadt (Germany) in 2021 by the FOOT collaboration. The results are compared with similar results found in the literature and with a previous FOOT measurement of the same process, using the same setup, from a previous pilot run performed at GSI in 2019. The pilot run data, however, had limited statistics and only allowed for the measurement of elemental fragmentation cross sections integrated in the setup acceptance. The 2021 data set, with statistics more than 100 times larger compared to the data collected in 2019, enabled the measurement of angular differential cross sections, fully exploiting the granularity of the FOOT $\Delta \text{E}$-TOF system. Furthermore, a better comprehension of the FOOT apparatus allowed to improve the analysis techniques, leading to a reduction in the final systematic uncertainties.

This work presents the existence and uniqueness of solution to a free boundary value problem related to biofilm growth. The problem consists of a system of nonlinear hyperbolic partial differential equations governing the microbial species growth, and a system of parabolic partial differential equations describing the substrate dynamics. The free boundary evolution is governed by an ordinary differential equation that accounts for the thickness of the biofilm. We use the method of characteristics and fixed point strategies to prove the existence and uniqueness theorem in small and all times. All the equations are converted into integral equations, in particular this transformation is made for the parabolic equations by using the Green's functions. We consider Dirichlet-Neumann and Neumann-Robin boundary conditions for the substrates equations and their extension to the case with variable

We present the stability analysis of two free boundary problems arising in biofilm modelling. The first, introduced in the 1980s by Wanner and Gujer, is related to the competition between autotrophic and heterotrophic bacteria in a biofilm bioreactor. It is a free boundary problem consisting of a system of hyperbolic PDEs modelling biofilm growth and the competition between species, a parabolic system accounting for substrate consumption, and an ODE for biofilm thickness. The second, also based on the former, arises from the modelling of trace-metal precipitation in biofilms, with a special focus on the role of sulfate-reducing bacteria in the methane production process. The analysis is made into two steps, the first one being the existence and uniqueness of the stationary solutions. The second one allows to show that the calssical solutions converge to the stationary solutions by using a semigroup approach and the energy method. We also extend the study to the precipitation model, in which the substrates are modelled by a parabolic system with variable diffusion coefficients.

We introduce and study the analytic relative Jacobian sheaf for a Lagrangian fibration of a hyperk\"ahler manifold. When the fibration has irreducible fibers in codimension 1 and a relative principal polarization, we show that it is isomorphic to the relative Albanese sheaf which acts on the Lagrangian fibration. We apply this to OG10 Lagrangian fibrations associated to a smooth cubic fourfold constructed by Laza-Sacc\`a-Voisin and Sacc\`a. For sufficiently general cubic fourfolds, we compute the Tate-Shafarevich group parametrizing twists of the original Lagrangian fibration in terms of certain degree twists and Brauer twists. Among the main tools we use are perverse sheaves, decomposition theorem, Hodge modules and Deligne cohomology., Comment: Comments are welcome

Algorithmic fairness in recommender systems requires close attention to the needs of a diverse set of stakeholders that may have competing interests. Previous work in this area has often been limited by fixed, single-objective definitions of fairness, built into algorithms or optimization criteria that are applied to a single fairness dimension or, at most, applied identically across dimensions. These narrow conceptualizations limit the ability to adapt fairness-aware solutions to the wide range of stakeholder needs and fairness definitions that arise in practice. Our work approaches recommendation fairness from the standpoint of computational social choice, using a multi-agent framework. In this paper, we explore the properties of different social choice mechanisms and demonstrate the successful integration of multiple, heterogeneous fairness definitions across multiple data sets.

Synthetic data is a useful resource for algorithmic research. It allows for the evaluation of systems under a range of conditions that might be difficult to achieve in real world settings. In recommender systems, the use of synthetic data is somewhat limited; some work has concentrated on building user-item interaction data at large scale. We believe that fairness-aware recommendation research can benefit from simulated data as it allows the study of protected groups and their interactions without depending on sensitive data that needs privacy protection. In this paper, we propose a novel type of data for fairness-aware recommendation: synthetic recommender system outputs that can be used to study re-ranking algorithms.

Aggregating the preferences of multiple agents into a collective decision is a common step in many important problems across areas of computer science including information retrieval, reinforcement learning, and recommender systems. As Social Choice Theory has shown, the problem of designing algorithms for aggregation rules with specific properties (axioms) can be difficult, or provably impossible in some cases. Instead of designing algorithms by hand, one can learn aggregation rules, particularly voting rules, from data. However, the prior work in this area has required extremely large models, or been limited by the choice of preference representation, i.e., embedding. We recast the problem of designing a good voting rule into one of learning probabilistic versions of voting rules that output distributions over a set of candidates. Specifically, we use neural networks to learn probabilistic social choice functions from the literature. We show that embeddings of preference profiles derived from the social choice literature allows us to learn existing voting rules more efficiently and scale to larger populations of voters more easily than other work if the embedding is tailored to the learning objective. Moreover, we show that rules learned using embeddings can be tweaked to create novel voting rules with improved axiomatic properties. Namely, we show that existing voting rules require only minor modification to combat a probabilistic version of the No Show Paradox.

Fast emitting polymeric scintillators are requested in advanced applications where high-speed detectors with large signal-to-noise ratio are needed. However, their low density implies a weak stopping power of high energy radiations, thus a limited light output and sensitivity. To enhance their performances, polymeric scintillators can be loaded with dense nanoparticles (NPs). We investigate the properties of a series of polymeric scintillators by means of photoluminescence and scintillation spectroscopy, comparing standard scintillators with a composite system loaded with dense hafnium dioxide (HfO2) NPs. The nanocomposite shows a scintillation yield enhancement of +100% with unchanged time response. We provide for the first time an interpretation of this effect, pointing out the local effect of NPs in the generation of emissive states upon interaction with the ionizing radiation. The obtained results indicate that coupling of fast conjugated emitters with optically inert dense NPs could allow to surpass the actual limits of pure polymeric scintillators., Comment: 14 pages, 4 figures

This work addresses the certification of the local robustness of vision-based two-stage 6D object pose estimation. The two-stage method for object pose estimation achieves superior accuracy by first employing deep neural network-driven keypoint regression and then applying a Perspective-n-Point (PnP) technique. Despite advancements, the certification of these methods' robustness remains scarce. This research aims to fill this gap with a focus on their local robustness on the system level--the capacity to maintain robust estimations amidst semantic input perturbations. The core idea is to transform the certification of local robustness into neural network verification for classification tasks. The challenge is to develop model, input, and output specifications that align with off-the-shelf verification tools. To facilitate verification, we modify the keypoint detection model by substituting nonlinear operations with those more amenable to the verification processes. Instead of injecting random noise into images, as is common, we employ a convex hull representation of images as input specifications to more accurately depict semantic perturbations. Furthermore, by conducting a sensitivity analysis, we propagate the robustness criteria from pose to keypoint accuracy, and then formulating an optimal error threshold allocation problem that allows for the setting of a maximally permissible keypoint deviation thresholds. Viewing each pixel as an individual class, these thresholds result in linear, classification-akin output specifications. Under certain conditions, we demonstrate that the main components of our certification framework are both sound and complete, and validate its effects through extensive evaluations on realistic perturbations. To our knowledge, this is the first study to certify the robustness of large-scale, keypoint-based pose estimation given images in real-world scenarios., Comment: 25 pages, 10 figures, 5 tables

We investigate obstruction classes of moduli spaces of sheaves on K3 surfaces. We extend previous results by Caldararu, explicitly determining the obstruction class and its order in the Brauer group. Our main theorem establishes a short exact sequence relating the Brauer group of the moduli space to that of the underlying K3 surface. This provides a criterion for when the moduli space is fine, generalising well-known results for K3 surfaces. Additionally, we explore applications to Ogg-Shafarevich theory for Beauville-Mukai systems. Furthermore, we investigate birational equivalences of Beauville-Mukai systems on elliptic K3 surfaces, presenting a complete characterisation of such equivalences., Comment: 29 pages, comments are welcome!

School rating websites are increasingly used by parents to assess the quality and fit of U.S. K-12 schools for their children. These online reviews often contain detailed descriptions of a school's strengths and weaknesses, which both reflect and inform perceptions of a school. Existing work on these text reviews has focused on finding words or themes that underlie these perceptions, but has stopped short of using the textual reviews as leading indicators of school performance. In this paper, we investigate to what extent the language used in online reviews of a school is predictive of changes in the attributes of that school, such as its socio-economic makeup and student test scores. Using over 300K reviews of 70K U.S. schools from a popular ratings website, we apply language processing models to predict whether schools will significantly increase or decrease in an attribute of interest over a future time horizon. We find that using the text improves predictive performance significantly over a baseline model that does not include text but only the historical time-series of the indicators themselves, suggesting that the review text carries predictive power. A qualitative analysis of the most predictive terms and phrases used in the text reviews indicates a number of topics that serve as leading indicators, such as diversity, changes in school leadership, a focus on testing, and school safety.

Trees are convenient models for obtaining explainable predictions on relatively small datasets. Although there are many proposals for the end-to-end construction of such trees in supervised learning, learning a tree end-to-end for clustering without labels remains an open challenge. As most works focus on interpreting with trees the result of another clustering algorithm, we present here a novel end-to-end trained unsupervised binary tree for clustering: Kauri. This method performs a greedy maximisation of the kernel KMeans objective without requiring the definition of centroids. We compare this model on multiple datasets with recent unsupervised trees and show that Kauri performs identically when using a linear kernel. For other kernels, Kauri often outperforms the concatenation of kernel KMeans and a CART decision tree.

This study investigates the role of spatial segregation, prompted by competition avoidance, as a key mechanism for emergent coexistence within microbial communities. Recognizing these communities as complex adaptive systems, we challenge the sufficiency of mean-field pairwise interaction models and consider the impact of spatial dynamics. We developed an individual-based spatial simulation depicting bacterial movement through a pattern of random walks influenced by competition avoidance, leading to the formation of spatially segregated clusters. This model was integrated with a Lotka-Volterra metapopulation framework focused on competitive interactions. Our findings reveal that spatial segregation combined with low diffusion rates and high compositional heterogeneity among patches can lead to emergent coexistence in microbial communities. This reveals a novel mechanism underpinning the formation of stable, coexisting microbe clusters, which is nonetheless incapable of promoting coexistence in the case of isolated pairs of species. This study underscores the importance of considering spatial factors in understanding the dynamics of microbial ecosystems.

In many causal studies, outcomes are censored by death, in the sense that they are neither observed nor defined for units who die. In such studies, the focus is usually on the stratum of always survivors up to a single fixed time s. Building on a recent strand of the literature, we propose an extended framework for the analysis of longitudinal studies, where units can die at different time points, and the main endpoints are observed and well defined only up to the death time. We develop a Bayesian longitudinal principal stratification framework, where units are cross classified according to the longitudinal death status. Under this framework, the focus is on causal effects for the principal strata of units that would be alive up to a time point s irrespective of their treatment assignment, where these strata may vary as a function of s. We can get precious insights into the effects of treatment by inspecting the distribution of baseline characteristics within each longitudinal principal stratum, and by investigating the time trend of both principal stratum membership and survivor-average causal effects. We illustrate our approach for the analysis of a longitudinal observational study aimed to assess, under the assumption of strong ignorability of treatment assignment, the causal effects of a policy promoting start ups on firms survival and hiring policy, where firms hiring status is censored by death.

Ensemble methods combine the predictions of several base models. We study whether or not including more models always improves their average performance. This question depends on the kind of ensemble considered, as well as the predictive metric chosen. We focus on situations where all members of the ensemble are a priori expected to perform as well, which is the case of several popular methods such as random forests or deep ensembles. In this setting, we show that ensembles are getting better all the time if, and only if, the considered loss function is convex. More precisely, in that case, the average loss of the ensemble is a decreasing function of the number of models. When the loss function is nonconvex, we show a series of results that can be summarised as: ensembles of good models keep getting better, and ensembles of bad models keep getting worse. To this end, we prove a new result on the monotonicity of tail probabilities that may be of independent interest. We illustrate our results on a medical prediction problem (diagnosing melanomas using neural nets) and a "wisdom of crowds" experiment (guessing the ratings of upcoming movies).

Contraction assay based on surface measurement have been widely used to evaluate cell contractility in 3D models. This method is straightforward and requires no specific equipment, but it does not provide quantitative data about contraction forces generated by cells. We expanded this method with a new biomechanical model, based on the work-energy theorem, to provide non-destructive longitudinal monitoring of contraction forces generated by cells in 3D.We applied this method on hydrogels seeded with either fibroblasts or osteoblasts. Hydrogel mechanical characteristics were modulated to enhance (condition HCA$_{High}$: hydrogel contraction assay high contraction) or limit (condition HCA$_{Low}$: hydrogel contraction assay low contraction) cell contractile behaviors. Macroscopic measures were further correlated with cell contractile behavior and descriptive analysis of their physiology in response to different mechanical environments. Fibroblasts and osteoblasts contracted their matrix up to 47% and 77% respectively. Contraction stress peaked at day 5 with 1.1 10$^{-14}$Pa for fibroblasts and 3.5 10$^{-14}$Pa for osteoblasts, which correlated with cell attachment and spreading. Negligible contraction was seen in HCA$_{Low}$. Both fibroblasts and osteoblasts expressed $\alpha$-SMA contractile fibers in HCA$_{High}$ and HCA$_{Low}$. Failure to contract HCA$_{Low}$ was attributed to increased cross-linking and resistance to proteolytic degradation of the hydrogel.

In clinical trials, patients may discontinue treatments prematurely, breaking the initial randomization and, thus, challenging inference. Stakeholders in drug development are generally interested in going beyond the Intention-To-Treat (ITT) analysis, which provides valid causal estimates of the effect of treatment assignment but does not inform on the effect of the actual treatment receipt. Our study is motivated by an RCT in oncology, where patients assigned the investigational treatment may discontinue it due to adverse events. We propose adopting a principal stratum strategy and decomposing the overall ITT effect into principal causal effects for groups of patients defined by their potential discontinuation behavior. We first show how to implement a principal stratum strategy to assess causal effects on a survival outcome in the presence of continuous time treatment discontinuation, its advantages, and the conclusions one can draw. Our strategy deals with the time-to-event intermediate variable that may not be defined for patients who would not discontinue; moreover, discontinuation time and the primary endpoint are subject to censoring. We employ a flexible model-based Bayesian approach to tackle these complexities, providing easily interpretable results. We apply this Bayesian principal stratification framework to analyze synthetic data of the motivating oncology trial. We simulate data under different assumptions that reflect real scenarios where patients' behavior depends on critical baseline covariates. Supported by a simulation study, we shed light on the role of covariates in this framework: beyond making structural and parametric assumptions more credible, they lead to more precise inference and can be used to characterize patients' discontinuation behavior, which could help inform clinical practice and future protocols.

We generalise the notion of the Tate-Shafarevich group of an elliptic K3 surface with a section to the Tate-Shafarevich group of a K3 surface endowed with a linear system. The construction, which uses Grothendieck's special Brauer group, provides an efficient way to deal with moduli spaces of twisted sheaves supported on curves in a K3 surface., Comment: 26 pages. Improved and corrected version taking referee's comment into account

We use twisted relative Picard varieties to split Brauer classes on projective varieties over algebraically closed fields by torsors for a fixed abelian scheme independent of the Brauer class. The construction is also used to prove that the index of an unramified Brauer class divides a fixed power of its period., Comment: 19 pages. Introduction rewritten, references added, results unchanged

Time-of-Flight Positron Emission Tomography is a medical imaging technique, based on the detection of two back-to-back {\gamma}-photons generated from radiotracers injected in the body. Its limit is the ability of employed scintillation detectors to discriminate in time the arrival of {\gamma}-pairs, i.e. the coincidence time resolution (CTR). A CTR < 50 ps that would enable fast imaging with ultralow radiotracer dose. Monolithic materials do not have simultaneously the required high light output and fast emission characteristics, thus the concept of scintillating heterostructure is proposed, where the device is made of a dense scintillator coupled to a fast-emitting light material. Here we present a composite polymeric scintillator, whose density has been increased upon addition of hafnium oxide nanoparticles. This enhanced by +300% its scintillation yield, surpassing commercial plastic scintillators. The nanocomposite is coupled to bismuth germanate oxide (BGO) realizing a multilayer scintillator. We observed the energy sharing between its components, which activate the nanocomposite fast emission enabling a net CTR improvement of 25% with respect to monolithic BGO. These results demonstrate that a controlled loading with dense nanomaterials is an excellent strategy to enhance the performance of polymeric scintillators for their use in advanced radiation detection and imaging technologies.

In causal inference studies, interest often lies in understanding the mechanisms through which a treatment affects an outcome. One approach is principal stratification (PS), which introduces well-defined causal effects in the presence of confounded post-treatment variables, or mediators, and clearly defines the assumptions for identification and estimation of those effects. The goal of this paper is to extend the PS framework to studies with continuous treatments and continuous post-treatment variables, which introduces a number of unique challenges both in terms of defining causal effects and performing inference. This manuscript provides three key methodological contributions: 1) we introduce novel principal estimands for continuous treatments that provide valuable insights into different causal mechanisms, 2) we utilize Bayesian nonparametric approaches to model the joint distribution of the potential mediating variables based on both Gaussian processes and Dirichlet process mixtures to ensure our approach is robust to model misspecification, and 3) we provide theoretical and numerical justification for utilizing a model for the potential outcomes to identify the joint distribution of the potential mediating variables. Lastly, we apply our methodology to a novel study of the relationship between the economy and arrest rates, and how this is potentially mediated by police capacity.

Fairness problems in recommender systems often have a complexity in practice that is not adequately captured in simplified research formulations. A social choice formulation of the fairness problem, operating within a multi-agent architecture of fairness concerns, offers a flexible and multi-aspect alternative to fairness-aware recommendation approaches. Leveraging social choice allows for increased generality and the possibility of tapping into well-studied social choice algorithms for resolving the tension between multiple, competing fairness concerns. This paper explores a range of options for choice mechanisms in multi-aspect fairness applications using both real and synthetic data and shows that different classes of choice and allocation mechanisms yield different but consistent fairness / accuracy tradeoffs. We also show that a multi-agent formulation offers flexibility in adapting to user population dynamics., Comment: arXiv admin note: text overlap with arXiv:2303.00968