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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!

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.

Federated learning allows for the training of machine learning models on multiple decentralized local datasets without requiring explicit data exchange. However, data pre-processing, including strategies for handling missing data, remains a major bottleneck in real-world federated learning deployment, and is typically performed locally. This approach may be biased, since the subpopulations locally observed at each center may not be representative of the overall one. To address this issue, this paper first proposes a more consistent approach to data standardization through a federated model. Additionally, we propose Fed-MIWAE, a federated version of the state-of-the-art imputation method MIWAE, a deep latent variable model for missing data imputation based on variational autoencoders. MIWAE has the great advantage of being easily trainable with classical federated aggregators. Furthermore, it is able to deal with MAR (Missing At Random) data, a more challenging missing-data mechanism than MCAR (Missing Completely At Random), where the missingness of a variable can depend on the observed ones. We evaluate our method on multi-modal medical imaging data and clinical scores from a simulated federated scenario with the ADNI dataset. We compare Fed-MIWAE with respect to classical imputation methods, either performed locally or in a centralized fashion. Fed-MIWAE allows to achieve imputation accuracy comparable with the best centralized method, even when local data distributions are highly heterogeneous. In addition, thanks to the variational nature of Fed-MIWAE, our method is designed to perform multiple imputation, allowing for the quantification of the imputation uncertainty in the federated scenario.

Proceedings for our meeting ``What comes beyond the Standard Models'', which covered a broad series of subjects., Comment: This is the proceedings for the 25th Workshop in Bled for "What comes beyond the Standard Models'' including also a webinar "meeting'' using Cosmovia on the same subject

Algorithmic fairness in the context of personalized recommendation presents significantly different challenges to those commonly encountered in classification tasks. Researchers studying classification have generally considered fairness to be a matter of achieving equality of outcomes between a protected and unprotected group, and built algorithmic interventions on this basis. We argue that fairness in real-world application settings in general, and especially in the context of personalized recommendation, is much more complex and multi-faceted, requiring a more general approach. We propose a model to formalize multistakeholder fairness in recommender systems as a two stage social choice problem. In particular, we express recommendation fairness as a novel combination of an allocation and an aggregation problem, which integrate both fairness concerns and personalized recommendation provisions, and derive new recommendation techniques based on this formulation. Simulations demonstrate the ability of the framework to integrate multiple fairness concerns in a dynamic way.

The explosion of conference paper submissions in AI and related fields, has underscored the need to improve many aspects of the peer review process, especially the matching of papers and reviewers. Recent work argues that the key to improve this matching is to modify aspects of the \emph{bidding phase} itself, to ensure that the set of bids over papers is balanced, and in particular to avoid \emph{orphan papers}, i.e., those papers that receive no bids. In an attempt to understand and mitigate this problem, we have developed a flexible bidding platform to test adaptations to the bidding process. Using this platform, we performed a field experiment during the bidding phase of a medium-size international workshop that compared two bidding methods. We further examined via controlled experiments on Amazon Mechanical Turk various factors that affect bidding, in particular the order in which papers are presented \cite{cabanac2013capitalizing,fiez2020super}; and information on paper demand \cite{meir2021market}. Our results suggest that several simple adaptations, that can be added to any existing platform, may significantly reduce the skew in bids, thereby improving the allocation for both reviewers and conference organizers., Comment: Camera ready version of a paper accepted to AAMAS'23: https://aamas2023.soton.ac.uk/program/accepted-papers/

Semi-supervised learning is a powerful technique for leveraging unlabeled data to improve machine learning models, but it can be affected by the presence of ``informative'' labels, which occur when some classes are more likely to be labeled than others. In the missing data literature, such labels are called missing not at random. In this paper, we propose a novel approach to address this issue by estimating the missing-data mechanism and using inverse propensity weighting to debias any SSL algorithm, including those using data augmentation. We also propose a likelihood ratio test to assess whether or not labels are indeed informative. Finally, we demonstrate the performance of the proposed methods on different datasets, in particular on two medical datasets for which we design pseudo-realistic missing data scenarios.

Feature selection in clustering is a hard task which involves simultaneously the discovery of relevant clusters as well as relevant variables with respect to these clusters. While feature selection algorithms are often model-based through optimised model selection or strong assumptions on the data distribution, we introduce a discriminative clustering model trying to maximise a geometry-aware generalisation of the mutual information called GEMINI with a simple l1 penalty: the Sparse GEMINI. This algorithm avoids the burden of combinatorial feature subset exploration and is easily scalable to high-dimensional data and large amounts of samples while only designing a discriminative clustering model. We demonstrate the performances of Sparse GEMINI on synthetic datasets and large-scale datasets. Our results show that Sparse GEMINI is a competitive algorithm and has the ability to select relevant subsets of variables with respect to the clustering without using relevance criteria or prior hypotheses., Comment: Published in Statistics and Computing, Volume 34, article number 155, (2024), https://doi.org/10.1007/s11222-024-10467-9

We give a description of the intermediate Jacobian fibration attached to a general complex cubic fourfold $X$ containing a plane as a Lagrangian subfibration of a moduli space of torsion sheaves on the K3 surface associated to $X$ up to a cover. To do so, we propose a general construction of Lagrangian fibrations in Prym varieties as subfibrations of Beauville-Mukai systems over some loci of nodal curves in linear systems on K3 surfaces., Comment: v2: Minor corrections. Added Remark 5.14

A free boundary value problem related to the genesis of multispecies granular biofilms is presented. The granular biofilm is modelled as a spherical free boundary domain with radial symmetry. The proposed model is conceived in the framework of continuum mechanics and consists of: nonlinear hyperbolic PDEs which model the advective transport and growth of attached species that constitute the granular biofilm matrix; semilinear elliptic PDEs which govern the diffusive transport and conversion of nutrients; and semilinear elliptic PDEs describing the invasion phenomena and conversion of planktonic cells suspended in the surrounding environment. The evolution of the free boundary is governed by an ODE accounting for microbial growth, attachment, and detachment. By using the method of characteristics, the system of equations constituting the granular biofilm model is converted into an equivalent integral system. Existence and uniqueness of solutions are discussed and proved for the attachment regime using the fixed point theorem., Comment: 18 pages, preprint version

A multiscale mathematical model describing the genesis and ecology of algal-bacterial photogranules and the metals biosorption on their solid matrix within a sequencing batch reactor (SBR) is presented. The granular biofilm is modelled as a spherical free boundary domain with radial symmetry and a vanishing initial value. The free boundary evolution is governed by an ODE accounting for microbial growth, attachment and detachment phenomena. The model is based on systems of PDEs derived from mass conservation principles. Specifically, two systems of nonlinear hyperbolic PDEs model the growth of attached species and the dynamics of free adsorption sites; and two systems of quasi-linear parabolic PDEs govern the diffusive transport and conversion of nutrients and metals. The model is completed with systems of impulsive ordinary differential equations (IDEs) describing the evolution of dissolved substrates, metals, and planktonic and detached biomasses within the granular-based SBR. All main phenomena involved in the process are considered in the mathematical model. Moreover, the dual effect of metal presence on the formation process of photogranules is accounted: metal stimulates the production of EPS by sessile species and negatively affects the metabolic activities of microbial species. To describe the effects related to metal presence, a stimulation term for EPS production and an inhibition term for metal are included in all microbial kinetics. The model is used to examine the role of the microbial species and EPS in the adsorption process, and the effect of metal concentration and adsorption proprieties of biofilm components on the metal removal. Numerical results show that the model accurately describes the photogranules evolution and ecology and confirm the applicability of algal-bacterial photogranules systems for metal-rich wastewater treatment., Comment: 43 pages, 18 figures, preprint version

The object of this survey is to give an overview on the topology of singularities of holomorphic foliation germs on $(\mathbb C^2,0)$.

The Bloch sphere representation is a geometric model for all possible quantum states of a two-level system that can be used to describe the time dynamics of a qubit. As explicit application, we consider the time dynamics of a particle in a double-well potential. In particular, we adopt a recent method for off-resonant excitations, the so-called SUPER principle (Swing-UP of the quantum emitter population) driven by periodic electromagnetic fields, to the context of quantum tunnelling. We show that the tunnelling probability can be enhanced significantly when an appropriate oscillation of the potential height is introduced. Driven by a collaborative approach we call educator-developer dialogue, an updated version of the software Quantum Composer is presented. For educational purposes, we map the two lowest energy states of the 1D-Schr\"odinger equation to the Bloch sphere representation, leading to a rather clear and intuitive physical picture for the pertinent time dynamics., Comment: 19 pages, 11 figures, submitted to European Journal of Physics

A wide variety of model explanation approaches have been proposed in recent years, all guided by very different rationales and heuristics. In this paper, we take a new route and cast interpretability as a statistical inference problem. We propose a general deep probabilistic model designed to produce interpretable predictions. The model parameters can be learned via maximum likelihood, and the method can be adapted to any predictor network architecture and any type of prediction problem. Our method is a case of amortized interpretability models, where a neural network is used as a selector to allow for fast interpretation at inference time. Several popular interpretability methods are shown to be particular cases of regularised maximum likelihood for our general model. We propose new datasets with ground truth selection which allow for the evaluation of the features importance map. Using these datasets, we show experimentally that using multiple imputation provides more reasonable interpretations., Comment: 10 pages, 22 figures, published at ICLR 2023

The amplitude of a pulse that propagates in a homogeneous material whose properties are instantaneously changed periodically in time will undergo an exponential increase, due to the interference between the reflected and transmitted pulses generated at each sudden switch. Here we resolve the issue by designing suitable reciprocal PT-symmetric space-time microstructures both in the one-dimensional and two-dimensional case, so that the interference between the scattered waves is such that the overall amplitude of the wave will be constant in time in each constituent material. Remarkably, for the geometries here proposed, a pulse will propagate with constant amplitude regardless of the impedance between the constituent materials, and for some, regardless of the wave speed mismatch. Given that the energy associated with the wave will increase exponentially in time, this creates the possibility to exploit the stable propagation of the pulse to accumulate energy for harvesting.

In representative democracies, the election of new representatives in regular election cycles is meant to prevent corruption and other misbehavior by elected officials and to keep them accountable in service of the ``will of the people." This democratic ideal can be undermined when candidates are dishonest when campaigning for election over these multiple cycles or rounds of voting. Much of the work on COMSOC to date has investigated strategic actions in only a single round. We introduce a novel formal model of \emph{pandering}, or strategic preference reporting by candidates seeking to be elected, and examine the resilience of two democratic voting systems to pandering within a single round and across multiple rounds. The two voting systems we compare are Representative Democracy (RD) and Flexible Representative Democracy (FRD). For each voting system, our analysis centers on the types of strategies candidates employ and how voters update their views of candidates based on how the candidates have pandered in the past. We provide theoretical results on the complexity of pandering in our setting for a single cycle, formulate our problem for multiple cycles as a Markov Decision Process, and use reinforcement learning to study the effects of pandering by both single candidates and groups of candidates across a number of rounds.

The Brazil Bolsa Familia (BF) program is a conditional cash transfer program aimed to reduce short-term poverty by direct cash transfers and to fight long-term poverty by increasing human capital among poor Brazilian people. Eligibility for Bolsa Familia benefits depends on a cutoff rule, which classifies the BF study as a regression discontinuity (RD) design. Extracting causal information from RD studies is challenging. Following Li et al (2015) and Branson and Mealli (2019), we formally describe the BF RD design as a local randomized experiment within the potential outcome approach. Under this framework, causal effects can be identified and estimated on a subpopulation where a local overlap assumption, a local SUTVA and a local ignorability assumption hold. We first discuss the potential advantages of this framework over local regression methods based on continuity assumptions, which concern the definition of the causal estimands, the design and the analysis of the study, and the interpretation and generalizability of the results. A critical issue of this local randomization approach is how to choose subpopulations for which we can draw valid causal inference. We propose a Bayesian model-based finite mixture approach to clustering to classify observations into subpopulations where the RD assumptions hold and do not hold. This approach has important advantages: a) it allows to account for the uncertainty in the subpopulation membership, which is typically neglected; b) it does not impose any constraint on the shape of the subpopulation; c) it is scalable to high-dimensional settings; e) it allows to target alternative causal estimands than the average treatment effect (ATE); and f) it is robust to a certain degree of manipulation/selection of the running variable. We apply our proposed approach to assess causal effects of the Bolsa Familia program on leprosy incidence in 2009.

Agents care not only about the outcomes of collective decisions but also about how decisions are made. In many cases, both the outcome and the procedure affect whether agents see a decision as legitimate, justifiable, or acceptable. We propose a novel model for collective decisions that takes into account both the preferences of the agents and their higher order concerns about the process of preference aggregation. To this end we (1) propose natural, plausible preference structures and establish key properties thereof, (2) develop mechanisms for aggregating these preferences to maximize the acceptability of decisions, and (3) characterize the performance of our acceptance-maximizing mechanisms. We apply our general approach to the specific setting of dichotomous choice, and compare the worst-case rates of acceptance achievable among populations of agents of different types. We also show in the special case of rule selection, i.e., amendment procedures, the method proposed by Abramowitz, Shapiro, and Talmon (2021) achieves universal acceptance with certain agent types.

We consider the problem of determining a binary ground truth using advice from a group of independent reviewers (experts) who express their guess about a ground truth correctly with some independent probability (competence). In this setting, when all reviewers are competent (competence greater than one-half), the Condorcet Jury Theorem tells us that adding more reviewers increases the overall accuracy, and if all competences are known, then there exists an optimal weighting of the reviewers. However, in practical settings, reviewers may be noisy or incompetent, i.e., competence below half, and the number of experts may be small, so the asymptotic Condorcet Jury Theorem is not practically relevant. In such cases we explore appointing one or more chairs (judges) who determine the weight of each reviewer for aggregation, creating multiple levels. However, these chairs may be unable to correctly identify the competence of the reviewers they oversee, and therefore unable to compute the optimal weighting. We give conditions when a set of chairs is able to weight the reviewers optimally, and depending on the competence distribution of the agents, give results about when it is better to have more chairs or more reviewers. Through numerical simulations we show that in some cases it is better to have more chairs, but in many cases it is better to have more reviewers.

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. Some of these metrics 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 clustering context where the number of clusters is a priori unknown., Comment: To be published in Neural Information Processing Systems 2022

Fairness-aware recommender systems that have a provider-side fairness concern seek to ensure that protected group(s) of providers have a fair opportunity to promote their items or products. There is a ``cost of fairness'' borne by the consumer side of the interaction when such a solution is implemented. This consumer-side cost raises its own questions of fairness, particularly when personalization is used to control the impact of the fairness constraint. In adopting a personalized approach to the fairness objective, researchers may be opening their systems up to strategic behavior on the part of users. This type of incentive has been studied in the computational social choice literature under the terminology of ``bossiness''. The concern is that a bossy user may be able to shift the cost of fairness to others, improving their own outcomes and worsening those for others. This position paper introduces the concept of bossiness, shows its application in fairness-aware recommendation and discusses strategies for reducing this strategic incentive.

We prove that projective hyperk\"{a}hler manifolds of K3$^{[n]}$-type admitting a non-trivial symplectic birational self-map of finite order are isomorphic to moduli spaces of stable (twisted) coherent sheaves on K3 surfaces. Motivated by this result, we analyze the reflections on the movable cone of moduli spaces of sheaves and determine when they come from a birational involution., Comment: 21 pages, v2: Theorem A significantly improved, Theorem B updated to reflect one of its consequences. v3: The numerical criterion in Lemma 4.13 (and formerly Theorem C) has been significantly simplified. Feedback from anonymous referees incorporated. Comments are still very welcome!

Truss structures composed of members that work exclusively in tension or in compression appear in several problems of science and engineering, e.g., in the study of the resisting mechanisms of masonry structures, as well as in the design of spider web-inspired web structures. This work generalizes previous results on the existence of cable webs that are able to support assigned sets of nodal forces under tension. We extend such a problem to the limit analysis of compression-only 'strut nets' subjected to fixed and variable nodal loads. These systems provide discrete element models of masonry bodies, which lie inside the polygon/polyhedron with vertices at the points of application of the given forces ('underlying masonry structures'). It is assumed that fixed nodal forces are combined with variable forces growing proportionally to a scalar multiplier (load multiplier), and that the supporting strut net is subjected to kinematic constraints at given nodal positions., Comment: 20 pages, 10 figures

We analyzed the first 255 PCR-confirmed cases of monkeypox occurred in Italy in 2022. Preliminary estimates indicate: mean incubation period of 9.1 days (95%CI of the mean: 6.5-10.9); mean generation time of 12.5 days (95%CI of the mean: 7.5-17.3); reproduction number in the MSM community of 2.43 (95%CI: 1.82-3.26)., Comment: 3 pages, 1 figure, 1 table, supplementary material

A body $\Theta$ containing two phases, which may form a periodic composite with microstructure much smaller that the body, or which may have structure on a length scale comparable to the body, is subjected to slowly time varying boundary conditions that would produce an approximate uniform field in $\Theta$ were it filled with homogeneous material. Here slowly time varying means that the wavelengths and attenuation lengths of waves at the frequencies associated with the time variation are much larger than the size of $\Theta$, so that we can make a quasistatic approximation. At least one of the two phase does not have an instantaneous response but rather depends on fields at prior times. The fields may be those associated with electricity, magnetism, fluid flow in porous media, or antiplane elasticity. We find, subject to these approximations, that the time variation of the boundary conditions can be designed so boundary measurements at a specific time $t=t_0$ exactly yield the volume fractions of the phases, independent of the detailed geometric configuration of the phases. Moreover, for specially tailored time variations, the volume fraction can be exactly determined frommeasurements at any time $t$, not just at the specific time $t=t_0$. We also show how time varying boundary conditions, not oscillating at the single frequency $\omega_0$, can be designed to exactly retrieve the response at $\omega_0$., Comment: 35 pages, 8 figures

Aggregating signals from a collection of noisy sources is a fundamental problem in many domains including crowd-sourcing, multi-agent planning, sensor networks, signal processing, voting, ensemble learning, and federated learning. The core question is how to aggregate signals from multiple sources (e.g. experts) in order to reveal an underlying ground truth. While a full answer depends on the type of signal, correlation of signals, and desired output, a problem common to all of these applications is that of differentiating sources based on their quality and weighting them accordingly. It is often assumed that this differentiation and aggregation is done by a single, accurate central mechanism or agent (e.g. judge). We complicate this model in two ways. First, we investigate the setting with both a single judge, and one with multiple judges. Second, given this multi-agent interaction of judges, we investigate various constraints on the judges' reporting space. We build on known results for the optimal weighting of experts and prove that an ensemble of sub-optimal mechanisms can perform optimally under certain conditions. We then show empirically that the ensemble approximates the performance of the optimal mechanism under a broader range of conditions.

Chang'e-3(CE-3) has been the first spacecraft to soft-land on the Moon since the Soviet Union's Luna 24 in 1976. The spacecraft arrived at Mare Imbrium on December 14, 2013 and the same day, Yutu lunar rover separated from lander to start its exploration of the surface and the subsurface around the landing site. The rover was equipped, among other instruments, with two Lunar Penetrating Radar systems (LPR) having a working frequency of 60 and 500 MHz. The radars acquired data for about two weeks while the rover was slowly moving along a path of about 114 m. At Navigation point N0209 the rover got stacked into the lunar soil and after that only data at fixed position could be collected. The low frequency radar data have been analyzed by different authors and published in two different papers, which reported totally controversial interpretations of the radar cross sections. The present study is devoted to resolve such controversy carefully analyzing and comparing the data collected on the Moon by Yutu rover and on Earth by a prototype of LRP mounted onboard a model of the CE-3 lunar rover. Such analysis demonstrates that the deep radar features previously ascribed to the lunar shallow stratigraphy are not real reflectors, rather they are signal artefacts probably generated by the system and its electromagnetic interaction with the metallic rover.

Video content is present in an ever-increasing number of fields, both scientific and commercial. Sports, particularly soccer, is one of the industries that has invested the most in the field of video analytics, due to the massive popularity of the game and the emergence of new markets. Previous state-of-the-art methods on soccer matches video summarization rely on handcrafted heuristics to generate summaries which are poorly generalizable, but these works have yet proven that multiple modalities help detect the best actions of the game. On the other hand, machine learning models with higher generalization potential have entered the field of summarization of general-purpose videos, offering several deep learning approaches. However, most of them exploit content specificities that are not appropriate for sport whole-match videos. Although video content has been for many years the main source for automatizing knowledge extraction in soccer, the data that records all the events happening on the field has become lately very important in sports analytics, since this event data provides richer context information and requires less processing. We propose a method to generate the summary of a soccer match exploiting both the audio and the event metadata. The results show that our method can detect the actions of the match, identify which of these actions should belong to the summary and then propose multiple candidate summaries which are similar enough but with relevant variability to provide different options to the final editor. Furthermore, we show the generalization capability of our work since it can transfer knowledge between datasets from different broadcasting companies, different competitions, acquired in different conditions, and corresponding to summaries of different lengths

We consider the problem of finding a net that supports prescribed forces applied at prescribed points, yet avoids certain obstacles, with all the elements of the net under compression (strut net) or under tension (cable web). In the case of masonry structures, for instance, this consists in finding a strut net that supports the forces, is contained within the physical structure, and avoids regions that may be not accessible due, for instance, to the presence of holes. We solve such a problem in the two-dimensional case, where the prescribed forces are applied at the vertices of a convex polygon, and we treat the cases of both single and multiple obstacles. By approximating the obstacles by polygonal regions, the task reduces to identifying the feasible domain in a linear programming problem. For a single obstacle we show how the region $\Gamma$ available to the obstacle can be enlarged as much as possible in the sense that there is no other strut net, having a region $\Gamma_1$ available to the obstacle with $\Gamma_1 \subset\Gamma$. The case where some of the forces are reactive, unprescribed but reacting to the other prescribed forces, is also treated. It again reduces to identifying the feasible domain in a linear programming problem. Finally, one may allow a subset of the reactive forces to each act not at a prescribed point, but rather at any point on a prescribed line segment. Then the task reduces to identifying the feasible domain in a quadratic programming problem., Comment: 22 pages, 12 figures, 3 supplemental videos