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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

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

In the last decade, recent successes in deep clustering majorly involved the Mutual Information (MI) as an unsupervised objective for training neural networks with increasing regularisations. While the quality of the regularisations have been largely discussed for improvements, little attention has been dedicated to the relevance of MI as a clustering objective. In this paper, we first highlight how the maximisation of MI does not lead to satisfying clusters. We identified the Kullback-Leibler divergence as the main reason of this behaviour. Hence, we generalise the mutual information by changing its core distance, introducing the Generalised Mutual Information (GEMINI): a set of metrics for unsupervised neural network training. Unlike MI, some GEMINIs do not require regularisations when training as they are geometry-aware thanks to distances or kernels in the data space. Finally, we highlight that GEMINIs can automatically select a relevant number of clusters, a property that has been little studied in deep discriminative clustering context where the number of clusters is a priori unknown., Comment: Submitted for review at the IEEE Transactions on Pattern Analysis and Machine Intelligence. This article is an extension of an original NeurIPS 2022 article [arXiv:2210.06300]

The abrupt decline in the Total Fertility Rate (TFR) of Puerto Rico since 2000 makes the prospect of a sustained population decline a real possibility. From 2000 to 2021 the TFR declined from 2.1 to 0.9 children per woman, one of the lowest in the world. Population projections produced by the United States Census Bureau and the United Nations Population Division show that the island population may decline from 3.8 millions in 2000 to slightly above 2 million by 2050, a dramatic 47% population decline in 50 years. As dire as this prospect may be, this may be an optimistic scenario. Both projections have the TFR increasing to 1.5 by 2050, but a fertility projection conducted by us show that fertility can remain much closer to 1.0 until 2050. Bayesian Hierarchical Probabilistic Theory has been used by the United Nations to incorporate a way to measure the uncertainty and to estimate the projection parameters. However, the assumption that the fertility level in countries with low fertility will eventually increase to 2.1 has been widely criticized as unrealistic and not supported by evidence. We modified the assumptions used by the United Nations considering countries with TFR similar to Puerto Rico and find that by 2050 Puerto Rico may have a TFR of 1.1 bounded by a 95% credibility interval (0.56,1.77). This indicates that there may be a larger population decline than what current projections show.

Nudging is a behavioral strategy aimed at influencing people's thoughts and actions. Nudging techniques can be found in many situations in our daily lives, and these nudging techniques can targeted at human fast and unconscious thinking, e.g., by using images to generate fear or the more careful and effortful slow thinking, e.g., by releasing information that makes us reflect on our choices. In this paper, we propose and discuss a value-based AI-human collaborative framework where AI systems nudge humans by proposing decision recommendations. Three different nudging modalities, based on when recommendations are presented to the human, are intended to stimulate human fast thinking, slow thinking, or meta-cognition. Values that are relevant to a specific decision scenario are used to decide when and how to use each of these nudging modalities. Examples of values are decision quality, speed, human upskilling and learning, human agency, and privacy. Several values can be present at the same time, and their priorities can vary over time. The framework treats values as parameters to be instantiated in a specific decision environment.