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We investigate the role of constraints in the computational complexity of min-max optimization. The work of Daskalakis, Skoulakis, and Zampetakis [2021] was the first to study min-max optimization through the lens of computational complexity, showing that min-max problems with nonconvex-nonconcave objectives are PPAD-hard. However, their proof hinges on the presence of joint constraints between the maximizing and minimizing players. The main goal of this paper is to understand the role of these constraints in min-max optimization. The first contribution of this paper is a fundamentally new proof of their main result, which improves it in multiple directions: it holds for degree 2 polynomials, it is essentially tight in the parameters, and it is much simpler than previous approaches, clearly highlighting the role of constraints in the hardness of the problem. Second, we show that with general constraints (i.e., the min player and max player have different constraints), even convex-concave min-max optimization becomes PPAD-hard. Along the way, we also provide PPAD-membership of a general problem related to quasi-variational inequalities, which has applications beyond our problem.

The world is facing a multitude of challenges that hinder the development of human civilization and the well-being of humanity on the planet. The Sustainable Development Goals (SDGs) were formulated by the United Nations in 2015 to address these global challenges by 2030. Natural language processing techniques can help uncover discussions on SDGs within research literature. We propose a completely automated pipeline to 1) fetch content from the Scopus database and prepare datasets dedicated to five groups of SDGs; 2) perform topic modeling, a statistical technique used to identify topics in large collections of textual data; and 3) enable topic exploration through keywords-based search and topic frequency time series extraction. For topic modeling, we leverage the stack of BERTopic scaled up to be applied on large corpora of textual documents (we find hundreds of topics on hundreds of thousands of documents), introducing i) a novel LLM-based embeddings computation for representing scientific abstracts in the continuous space and ii) a hyperparameter optimizer to efficiently find the best configuration for any new big datasets. We additionally produce the visualization of results on interactive dashboards reporting topics' temporal evolution. Results are made inspectable and explorable, contributing to the interpretability of the topic modeling process. Our proposed LLM-based topic modeling pipeline for big-text datasets allows users to capture insights on the evolution of the attitude toward SDGs within scientific abstracts in the 2006-2023 time span. All the results are reproducible by using our system; the workflow can be generalized to be applied at any point in time to any big corpus of textual documents., Comment: 27 pages, 8 figures, 5 tables

We classify geometrically integral regular del Pezzo surfaces which are not geometrically normal over imperfect fields of positive characteristic. Based on this classification, we show that a three-dimensional terminal del Pezzo fibration onto a curve over an algebraically closed field always admits a section. Moreover, we prove that the total space is rational if the base curve is rational and the anticanonical degree of a fibre is at least five., Comment: 37 pages, comments are welcome

For every $d \geq 4$, we construct a $d$-dimensional, log canonical, $K$-trivial variety with the property that two general fibers of its Albanese morphism are not birational. This provides a strong counterexample to the Beauville--Bogomolov decomposition in the log canonical setting. This construction can also be adapted to construct a smooth quasi-projective variety of logarithmic Kodaira dimension 0 whose quasi-Albanese morphism has maximal variation. On the positive side, we show that the Albanese morphism for log canonical pairs with nef anti-canonical class is a locally stable family of pairs., Comment: 22 pages, title changed and minor changes. comments are still welcome

Due to its exceptional dimensional stability in harsh thermal conditions and excellent mechanical and optical properties, Corning ultra-low expansion (ULE) glass is the material of choice in many high-demanding fields such as aerospace, astronomy, and advanced optics. This material has recently attracted renewed attention with the advent of femtosecond laser technology, with a particular focus on the interaction of ultrafast pulses and the material itself. Phenomena like the formation of self-assembled nanogratings and their thermal stability as well as the darkening of laser-affected zones have then been characterized. This paper presents how to exploit femtosecond selective laser etching (SLE) techniques to manufacture truly three-dimensional (3D) components. To demonstrate the micron-scale accuracy and repeatability of this process from the mm- to the cm-size range, various devices are designed and fabricated: fiber hole arrays with different hole densities, sizes, orientations, and shapes; and fiber V-groove arrays. Additionally, a mechanical flexural fiber mount is presented as an example of how multiple functionalities can be monolithically integrated into a single piece of glass through SLE technology. An example of a passive alignment substrate for optical components is also shown. SLE technique represents a new advancement in the field of microscale manufacturing, enabling the scalable production of custom-designed ULE glass structures with unprecedented precision and complexity, paving the way for the miniaturized integration of highly stable components., Comment: 7 pages, 3 figures, ICALEO conference 2024

Mining information from graph databases is becoming overly important. To approach this problem, current methods focus on identifying subgraphs with specific topologies; as of today, no work has been focused on expressing jointly the syntax and semantics of mining operations over rich property graphs. We define MINE GRAPH RULE, a new operator for mining association rules from graph databases, by extending classical approaches used in relational databases and exploited by recommending systems. We describe the syntax and semantics of the operator, which is based on measuring the support and confidence of each rule, and then we provide several examples of increasing complexity on top of a realistic example; our operator embeds Cypher for expressing the mining conditions. MINE GRAPH RULE is implemented on top of Neo4j, the most successful graph database system; it takes advantage of built-in optimizations of the Neo4j engine, as well as optimizations that are defined in the context of relational association rules. Our implementation is available as a portable Neo4j plugin. At the end of our paper, we show the execution performance in a variety of settings, by varying the operators, the size of the graph, the ratio between node types, the method for creating relationships, and maximum support and confidence.

Cross-talk is a well-known feature of single-photon avalanche detectors. It is especially important to account for this effect in applications involving coincidences of two or more photons registered by the sensor since in this case the cross-talk may mimic the useful signal. In this work, we characterize the cross-talk of the LinoSPAD2 detector, as well as perform joint measurements of the cross-talk and Hanbury Brown - Twiss two-photon interference, comparing and cross-calibrating both effects. With a median dark count rate of 125 cps/pixel, we report the average cross-talk probability of $0.22~\%$ for the nearest neighbor and also observe a long-range cross-talk of the order $2 \cdot 10^{-5}~\%$ for channels separated by up to 20 pixels., Comment: 16 pages, 10 figures. Updated with references

Legislative systems face growing complexity due to the ever-increasing number of laws and intricate interdependencies between them. Traditional methods of storing and analyzing legal systems, mainly based on RDF, struggle with this complexity, hindering efficient knowledge discovery, as required by domain experts. In this paper, we propose to model legislation into a property graph, where edges represent citations, modifications, and abrogations between laws and their articles or attachments, both represented as nodes and edges with properties. As a practical use case, we implement the model in the Italian legislative system. First, we describe our approach to extracting knowledge from legal texts. To this aim, we leverage the recently internationally adopted XML law standard, Akoma Ntoso, to parse and identify entities, relationships and properties. Next, we describe the model and the schema implemented using Neo4j, the market-leading graph database management system. The schema is designed to capture the structure and hierarchy of laws, together with their interdependencies. We show how such a property graph enables an efficient answer to complex and relevant queries previously impractical on raw text. By leveraging other implementations of the Akoma Ntoso standard and the proposed property graph approach, we are confident that this work will facilitate a comprehensive comparison of legislative systems and their complexities.

The Hanbury Brown-Twiss (HBT) effect holds a pivotal place in intensity interferometry and gave a seminal contribution to the development of quantum optics. To observe such an effect, both good spectral and timing resolutions are necessary. Most often, the HBT effect is observed for a single frequency at a time, due to limitations in dealing with multifrequencies simultaneously, halting and limiting some applications. Here, we report a fast and data-driven spectrometer built with a one-dimensional array of single-photon-sensitive avalanche diodes. We report observing the HBT effect for multifrequencies at the same time. Specifically, we observed the HBT for up to 5 lines of the Ne spectrum, but this can be improved even further. Our work represents a major step to make spectral binning and multifrequencies HBT more widely available. The technology we present can benefit both classical and quantum applications.

Bilateral trade models the problem of facilitating trades between a seller and a buyer having private valuations for the item being sold. In the online version of the problem, the learner faces a new seller and buyer at each time step, and has to post a price for each of the two parties without any knowledge of their valuations. We consider a scenario where, at each time step, before posting prices the learner observes a context vector containing information about the features of the item for sale. The valuations of both the seller and the buyer follow an unknown linear function of the context. In this setting, the learner could leverage previous transactions in an attempt to estimate private valuations. We characterize the regret regimes of different settings, taking as a baseline the best context-dependent prices in hindsight. First, in the setting in which the learner has two-bit feedback and strong budget balance constraints, we propose an algorithm with $O(\log T)$ regret. Then, we study the same set-up with noisy valuations, providing a tight $\widetilde O(T^{\frac23})$ regret upper bound. Finally, we show that loosening budget balance constraints allows the learner to operate under more restrictive feedback. Specifically, we show how to address the one-bit, global budget balance setting through a reduction from the two-bit, strong budget balance setup. This established a fundamental trade-off between the quality of the feedback and the strictness of the budget constraints.

We address a generalization of the bandit with knapsacks problem, where a learner aims to maximize rewards while satisfying an arbitrary set of long-term constraints. Our goal is to design best-of-both-worlds algorithms that perform optimally under both stochastic and adversarial constraints. Previous works address this problem via primal-dual methods, and require some stringent assumptions, namely the Slater's condition, and in adversarial settings, they either assume knowledge of a lower bound on the Slater's parameter, or impose strong requirements on the primal and dual regret minimizers such as requiring weak adaptivity. We propose an alternative and more natural approach based on optimistic estimations of the constraints. Surprisingly, we show that estimating the constraints with an UCB-like approach guarantees optimal performances. Our algorithm consists of two main components: (i) a regret minimizer working on \emph{moving strategy sets} and (ii) an estimate of the feasible set as an optimistic weighted empirical mean of previous samples. The key challenge in this approach is designing adaptive weights that meet the different requirements for stochastic and adversarial constraints. Our algorithm is significantly simpler than previous approaches, and has a cleaner analysis. Moreover, ours is the first best-of-both-worlds algorithm providing bounds logarithmic in the number of constraints. Additionally, in stochastic settings, it provides $\widetilde O(\sqrt{T})$ regret \emph{without} Slater's condition.

In the bandits with knapsacks framework (BwK) the learner has $m$ resource-consumption (packing) constraints. We focus on the generalization of BwK in which the learner has a set of general long-term constraints. The goal of the learner is to maximize their cumulative reward, while at the same time achieving small cumulative constraints violations. In this scenario, there exist simple instances where conventional methods for BwK fail to yield sublinear violations of constraints. We show that it is possible to circumvent this issue by requiring the primal and dual algorithm to be weakly adaptive. Indeed, even in absence on any information on the Slater's parameter $\rho$ characterizing the problem, the interplay between weakly adaptive primal and dual regret minimizers yields a "self-bounding" property of dual variables. In particular, their norm remains suitably upper bounded across the entire time horizon even without explicit projection steps. By exploiting this property, we provide best-of-both-worlds guarantees for stochastic and adversarial inputs. In the first case, we show that the algorithm guarantees sublinear regret. In the latter case, we establish a tight competitive ratio of $\rho/(1+\rho)$. In both settings, constraints violations are guaranteed to be sublinear in time. Finally, this results allow us to obtain new result for the problem of contextual bandits with linear constraints, providing the first no-$\alpha$-regret guarantees for adversarial contexts.

A machine-learned interatomic potential for Ge-rich Ge$_x$Te alloys has been developed aiming at uncovering the kinetics of phase separation and crystallization in these materials. The results are of interest for the operation of embedded phase change memories which exploits Ge-enrichment of GeSbTe alloys to raise the crystallization temperature. The potential is generated by fitting a large database of energies and forces computed within Density Functional Theory with the neural network scheme implemented in the DeePMD-kit package. The potential is highly accurate and suitable to describe the structural and dynamical properties of the liquid, amorphous and crystalline phases of the wide range of compositions from pure Ge and stoichiometric GeTe to the Ge-rich Ge$_2$Te alloy. Large scale molecular dynamics simulations revealed a crystallization mechanism which depends on temperature. At 600 K, segregation of most of Ge in excess occurs on the ns time scale followed by crystallization of nearly stoichiometric GeTe regions. At 500 K, nucleation of crystalline GeTe occurs before phase separation, followed by a slow crystal growth due to the concurrent expulsion of Ge in excess.

We prove the Sarkisov program for projective surfaces over excellent base rings, including the case of non-perfect base fields of characteristic p>0. We classify the Sarkisov links between Mori fibre spaces and their relations for regular surfaces, generalising work of Iskovskikh. As an application, we discuss rationality problems for regular surfaces and the structure of the plane Cremona group., Comment: 71 pages. Expanded the section on existence of Sarkisov links, added theorem that over separably closed fields of characteristic distinct from two, the plane Cremona group is generated by involutions

Machine Learning (ML) has replaced traditional handcrafted methods for perception and prediction in autonomous vehicles. Yet for the equally important planning task, the adoption of ML-based techniques is slow. We present nuPlan, the world's first real-world autonomous driving dataset, and benchmark. The benchmark is designed to test the ability of ML-based planners to handle diverse driving situations and to make safe and efficient decisions. To that end, we introduce a new large-scale dataset that consists of 1282 hours of diverse driving scenarios from 4 cities (Las Vegas, Boston, Pittsburgh, and Singapore) and includes high-quality auto-labeled object tracks and traffic light data. We exhaustively mine and taxonomize common and rare driving scenarios which are used during evaluation to get fine-grained insights into the performance and characteristics of a planner. Beyond the dataset, we provide a simulation and evaluation framework that enables a planner's actions to be simulated in closed-loop to account for interactions with other traffic participants. We present a detailed analysis of numerous baselines and investigate gaps between ML-based and traditional methods. Find the nuPlan dataset and code at nuplan.org., Comment: ICRA 2024 camera ready incl. supplementary material

Quantum computing sets the foundation for new ways of designing algorithms, thanks to the peculiar properties inherited by quantum mechanics. The exploration of this new paradigm faces new challenges concerning which field quantum speedup can be achieved. Towards finding solutions, looking for the design of quantum subroutines that are more efficient than their classical counterpart poses solid pillars to new powerful quantum algorithms. Herewith, we delve into a grounding subroutine, the computation of the variance, whose usefulness spaces across different fields of application, particularly the Artificial Intelligence (AI) one. Indeed, the finding of the quantum counterpart of these building blocks impacts vertically those algorithms that leverage this metric. In this work, we propose QVAR, a quantum subroutine, to compute the variance that exhibits a logarithmic complexity both in the circuit depth and width, excluding the state preparation cost. With the vision of showing the use of QVAR as a subroutine for new quantum algorithms, we tackle two tasks from the AI domain: Feature Selection and Outlier Detection. In particular, we showcase two AI hybrid quantum algorithms that leverage QVAR: the Hybrid Quantum Feature Selection (HQFS) algorithm and the Quantum Outlier Detection Algorithm (QODA). In this manuscript, we describe the implementation of QVAR, HQFS, and QODA, providing their correctness and complexities and showing the effectiveness of these hybrid quantum algorithms with respect to their classical counterpart.

We study the problem faced by a service provider that has to sell services to a user. In our model the service provider proposes various payment options (a menu) to the user which may be based, for example, on the quality of the service. Then, the user chooses one of these options and pays an amount to the service provider, contingent on the observed final outcome. Users are not able to observe directly the action performed by the service provide to reach the final outcome. This might incentivize misconduct. Therefore, we propose a model that enforces trust through economics incentives. The problem has two crucial features: i) the service provider is responsible for both formulating the contract and performing the action for which the user issues payments, and ii) the user is unaware of the true action carried out by the service provider, which is hidden. We study this delegation problem through the lens of contract design, with the overarching goal of enabling the computation of contracts that guarantee that the user can trust the service provider, even if their action is hidden.

We study hidden-action principal-agent problems with multiple agents. Unlike previous work, we consider a general setting in which each agent has an arbitrary number of actions, and the joint action induces outcomes according to an arbitrary distribution. We study two classes of mechanisms: a class of deterministic mechanisms that is the natural extension of single-agent contracts, in which the agents play a Nash equilibrium of the game induced by the contract, and a class of randomized mechanisms that is inspired by single-agent randomized contracts and correlated equilibria.

We study the fundamental problem of designing contracts in principal-agent problems under uncertainty. Previous works mostly addressed Bayesian settings in which principal's uncertainty is modeled as a probability distribution over agent's types. In this paper, we study a setting in which the principal has no distributional information about agent's type. In particular, in our setting, the principal only knows some uncertainty set defining possible agent's action costs. Thus, the principal takes a robust (adversarial) approach by trying to design contracts which minimize the (additive) regret: the maximum difference between what the principal could have obtained had them known agent's costs and what they actually get under the selected contract.

We show that the Frobenius--stable version of the Grauert--Riemenschneider vanishing theorem fails for terminal 3-folds in characteristic $p \in \left\{2, 3, 5\right\}$. To prove this, we introduce the notion of $\mathbb{F}_p$-rationality for singularities in positive characteristic and we show that klt singularities in dimension at most 4 are $\mathbb{F}_p$-rational., Comment: 24 pages, updated version

Over the last decades, many prognostic models based on artificial intelligence techniques have been used to provide detailed predictions in healthcare. Unfortunately, the real-world observational data used to train and validate these models are almost always affected by biases that can strongly impact the outcomes validity: two examples are values missing not-at-random and selection bias. Addressing them is a key element in achieving transportability and in studying the causal relationships that are critical in clinical decision making, going beyond simpler statistical approaches based on probabilistic association. In this context, we propose a novel approach that combines selection diagrams, missingness graphs, causal discovery and prior knowledge into a single graphical model to estimate the cardiovascular risk of adolescent and young females who survived breast cancer. We learn this model from data comprising two different cohorts of patients. The resulting causal network model is validated by expert clinicians in terms of risk assessment, accuracy and explainability, and provides a prognostic model that outperforms competing machine learning methods.

Bilateral trade models the problem of intermediating between two rational agents -- a seller and a buyer -- both characterized by a private valuation for an item they want to trade. We study the online learning version of the problem, in which at each time step a new seller and buyer arrive and the learner has to set prices for them without any knowledge about their (adversarially generated) valuations. In this setting, known impossibility results rule out the existence of no-regret algorithms when budget balanced has to be enforced at each time step. In this paper, we introduce the notion of \emph{global budget balance}, which only requires the learner to fulfill budget balance over the entire time horizon. Under this natural relaxation, we provide the first no-regret algorithms for adversarial bilateral trade under various feedback models. First, we show that in the full-feedback model, the learner can guarantee $\tilde O(\sqrt{T})$ regret against the best fixed prices in hindsight, and that this bound is optimal up to poly-logarithmic terms. Second, we provide a learning algorithm guaranteeing a $\tilde O(T^{3/4})$ regret upper bound with one-bit feedback, which we complement with a $\Omega(T^{5/7})$ lower bound that holds even in the two-bit feedback model. Finally, we introduce and analyze an alternative benchmark that is provably stronger than the best fixed prices in hindsight and is inspired by the literature on bandits with knapsacks., Comment: Accepted at STOC 2024

As evidenced by recent survey results, majority of asteroids are slow rotators (P>12 h), but lack spin and shape models due to selection bias. This bias is skewing our overall understanding of the spins, shapes, and sizes of asteroids, as well as of their other properties. Also, diameter determinations for large (>60km) and medium-sized asteroids (between 30 and 60 km) often vary by over 30% for multiple reasons. Our long-term project is focused on a few tens of slow rotators with periods of up to 60 hours. We aim to obtain their full light curves and reconstruct their spins and shapes. We also precisely scale the models, typically with an accuracy of a few percent. We used wide sets of dense light curves for spin and shape reconstructions via light-curve inversion. Precisely scaling them with thermal data was not possible here because of poor infrared data: large bodies are too bright for WISE mission. Therefore, we recently launched a campaign among stellar occultation observers, to scale these models and to verify the shape solutions, often allowing us to break the mirror pole ambiguity. The presented scheme resulted in shape models for 16 slow rotators, most of them for the first time. Fitting them to stellar occultations resolved previous inconsistencies in size determinations. For around half of the targets, this fitting also allowed us to identify a clearly preferred pole solution, thus removing the ambiguity inherent to light-curve inversion. We also address the influence of the uncertainty of the shape models on the derived diameters. Overall, our project has already provided reliable models for around 50 slow rotators. Such well-determined and scaled asteroid shapes will, e.g. constitute a solid basis for density determinations when coupled with mass information. Spin and shape models continue to fill the gaps caused by various biases., Comment: Accepted to Astronomy & Astrophysics. 12 pages + appendices

Superconducting quantum processors have made significant progress in size and computing potential. As a result, the practical cryogenic limitations of operating large numbers of superconducting qubits are becoming a bottleneck for further scaling. Due to the low thermal conductivity and the dense optical multiplexing capacity of telecommunications fiber, converting qubit signal processing to the optical domain using microwave-to-optics transduction would significantly relax the strain on cryogenic space and thermal budgets. Here, we demonstrate optical readout through an optical fiber of a superconducting transmon qubit connected via a coaxial cable to a fully integrated piezo-optomechanical transducer. Using a demolition readout technique, we achieve a single shot readout fidelity of 81%. Due to the small footprint (<0.15mm$^2$) and the modular fiber-based architecture, this device platform has the potential to scale towards use with thousands of qubits. Our results illustrate the potential of piezo-optomechanical transduction for low-dissipation operation of large quantum processors.

Objective: This study aims to consider small graphs of concepts and exploit them for expressing graph searches over existing COVID-19-related literature, leveraging the increasing use of graphs to represent and query scientific knowledge and providing a user-friendly search and exploration experience. Methods: We considered the COVID-19 Open Research Dataset corpus and summarized its content by annotating the publications' abstracts using terms selected from the UMLS and the Ontology of Coronavirus Infectious Disease. Then, we built a co-occurrence network that includes all relevant concepts mentioned in the corpus, establishing connections when their mutual information is relevant. A sophisticated graph query engine was built to allow the identification of the best matches of graph queries on the network. It also supports partial matches and suggests potential query completions using shortest paths. Results: We built a large co-occurrence network, consisting of 128,249 entities and 47,198,965 relationships; the GRAPH-SEARCH interface allows users to explore the network by formulating or adapting graph queries; it produces a bibliography of publications, which are globally ranked; and each publication is further associated with the specific parts of the query that it explains, thereby allowing the user to understand each aspect of the matching. Conclusions: Our approach supports the process of query formulation and evidence search upon a large text corpus; it can be reapplied to any scientific domain where documents corpora and curated ontologies are made available., Comment: 18 pages, 11 figures

The COVID-19 pandemic has changed the research agendas of most scientific communities, resulting in an overwhelming production of research articles in a variety of domains, including medicine, virology, epidemiology, economy, psychology, and so on. Several open-access corpora and literature hubs were established; among them, the COVID-19 Open Research Dataset (CORD-19) has systematically gathered scientific contributions for 2.5 years, by collecting and indexing over one million articles. Here, we present the CORD-19 Topic Visualizer (CORToViz), a method and associated visualization tool for inspecting the CORD-19 textual corpus of scientific abstracts. Our method is based upon a careful selection of up-to-date technologies (including large language models), resulting in an architecture for clustering articles along orthogonal dimensions and extraction techniques for temporal topic mining. Topic inspection is supported by an interactive dashboard, providing fast, one-click visualization of topic contents as word clouds and topic trends as time series, equipped with easy-to-drive statistical testing for analyzing the significance of topic emergence along arbitrarily selected time windows. The processes of data preparation and results visualization are completely general and virtually applicable to any corpus of textual documents - thus suited for effective adaptation to other contexts., Comment: 16 pages, 6 figures, 1 table

The European Spallation Source, currently under construction in Lund, Sweden, is a multidisciplinary international laboratory. Once completed to full specifications, it will operate the world's most powerful pulsed neutron source. Supported by a 3 million Euro Research and Innovation Action within the EU Horizon 2020 program, a design study (HighNESS) has been completed to develop a second neutron source located below the spallation target. Compared to the first source, designed for high cold and thermal brightness, the new source has been optimized to deliver higher intensity, and a shift to longer wavelengths in the spectral regions of cold (CN, 2--20\,\AA), very cold (VCN, 10--120\,\AA), and ultracold (UCN, ${>}\,{500}$\,\AA) neutrons. The second source comprises a large liquid deuterium moderator designed to produce CN and support secondary VCN and UCN sources. Various options have been explored in the proposed designs, aiming for world-leading performance in neutronics. These designs will enable the development of several new instrument concepts and facilitate the implementation of a high-sensitivity neutron-antineutron oscillation experiment (NNBAR). This document serves as the Conceptual Design Report for the HighNESS project, representing its final deliverable., Comment: 269 pages, 255 figures. Volume I of the final deliverable of the HighNESS Project (HORIZON 2020 grant agreement ID: 951782)

We show that many statements of the Minimal Model Program, including the cone theorem, the base point free theorem and the existence of Mori fibre spaces, fail for 1-foliated surface pairs $(X,\mathcal{F})$ with canonical singularities in characteristic $p>0$., Comment: 9 pages, minor corrections. To appear in the Edge volume at Ann. Univ. Ferrara

We prove that a geometrically integral smooth 3-fold $X$ with nef anti-canonical class and negative Kodaira dimension over a finite field $\mathbb{F}_q$ of characteristic $p>5$ and cardinality $q=p^e > 19$ has a rational point. Additionally, under the same assumptions on $p$ and $q$, we show that a 3-fold $X$ with trivial canonical class and non-zero first Betti number $b_1(X) \neq 0$ has a rational point. Our techniques rely on the Minimal Model Program to establish several structure results for generalized log Calabi--Yau 3-fold pairs over perfect fields., Comment: 27 pages, comments are welcome

Digital media have enabled the access to unprecedented literary knowledge. Authors, readers, and scholars are now able to discover and share an increasing amount of information about books and their authors. However, these sources of knowledge are fragmented and do not adequately represent non-Western writers and their works. In this paper we present The World Literature Knowledge Graph, a semantic resource containing 194,346 writers and 965,210 works, specifically designed for exploring facts about literary works and authors from different parts of the world. The knowledge graph integrates information about the reception of literary works gathered from 3 different communities of readers, aligned according to a single semantic model. The resource is accessible through an online visualization platform, which can be found at the following URL: https://literaturegraph.di.unito.it/. This platform has been rigorously tested and validated by $3$ distinct categories of experts who have found it to be highly beneficial for their respective work domains. These categories include teachers, researchers in the humanities, and professionals in the publishing industry. The feedback received from these experts confirms that they can effectively utilize the platform to enhance their work processes and achieve valuable outcomes.

Graph databases are emerging as the leading data management technology for storing large knowledge graphs; significant efforts are ongoing to produce new standards (such as the Graph Query Language, GQL), as well as enrich them with properties, types, schemas, and keys. In this article, we introduce PG-Triggers, a complete proposal for adding triggers to Property Graphs, along the direction marked by the SQL3 Standard. We define the syntax and semantics of PG-Triggers and then illustrate how they can be implemented on top of Neo4j, one of the most popular graph databases. In particular, we introduce a syntax-directed translation from PG-Triggers into Neo4j, which makes use of the so-called {\it APOC triggers}; APOC is a community-contributed library for augmenting the Cypher query language supported by Neo4j. We also cover Memgraph, and show that our approach applies to this system in a similar way. We illustrate the use of PG-Triggers through a life science application inspired by the COVID-19 pandemic. The main objective of this article is to introduce an active database standard for graph databases as a first-class citizen at a time when reactive graph management is in its infancy, so as to minimize the conversion efforts towards a full-fledged standard proposal., Comment: 13 pages, 5 figures, 4 tables

Bayesian persuasion studies the problem faced by an informed sender who strategically discloses information to influence the behavior of an uninformed receiver. Recently, a growing attention has been devoted to settings where the sender and the receiver interact sequentially, in which the receiver's decision-making problem is usually modeled as a Markov decision process (MDP). However, previous works focused on computing optimal information-revelation policies (a.k.a. signaling schemes) under the restrictive assumption that the receiver acts myopically, selecting actions to maximize the one-step utility and disregarding future rewards. This is justified by the fact that, when the receiver is farsighted and thus considers future rewards, finding an optimal Markovian signaling scheme is NP-hard. In this paper, we show that Markovian signaling schemes do not constitute the "right" class of policies. Indeed, differently from most of the MDPs settings, we prove that Markovian signaling schemes are not optimal, and general history-dependent signaling schemes should be considered. Moreover, we also show that history-dependent signaling schemes circumvent the negative complexity results affecting Markovian signaling schemes. Formally, we design an algorithm that computes an optimal and {\epsilon}-persuasive history-dependent signaling scheme in time polynomial in 1/{\epsilon} and in the instance size. The crucial challenge is that general history-dependent signaling schemes cannot be represented in polynomial space. Nevertheless, we introduce a convenient subclass of history-dependent signaling schemes, called promise-form, which are as powerful as general history-dependent ones and efficiently representable. Intuitively, promise-form signaling schemes compactly encode histories in the form of honest promises on future receiver's rewards.

The bandits with knapsack (BwK) framework models online decision-making problems in which an agent makes a sequence of decisions subject to resource consumption constraints. The traditional model assumes that each action consumes a non-negative amount of resources and the process ends when the initial budgets are fully depleted. We study a natural generalization of the BwK framework which allows non-monotonic resource utilization, i.e., resources can be replenished by a positive amount. We propose a best-of-both-worlds primal-dual template that can handle any online learning problem with replenishment for which a suitable primal regret minimizer exists. In particular, we provide the first positive results for the case of adversarial inputs by showing that our framework guarantees a constant competitive ratio $\alpha$ when $B=\Omega(T)$ or when the possible per-round replenishment is a positive constant. Moreover, under a stochastic input model, our algorithm yields an instance-independent $\tilde{O}(T^{1/2})$ regret bound which complements existing instance-dependent bounds for the same setting. Finally, we provide applications of our framework to some economic problems of practical relevance.

We prove several boundedness statements for geometrically integral normal del Pezzo surfaces $X$ over arbitrary fields. We give an explicit sharp bound on the irregularity if $X$ is canonical or regular. In particular, we show that wild canonical del Pezzo surfaces exist only in characteristic 2. As an application, we deduce that canonical del Pezzo surfaces form a bounded family over $\mathbb{Z}$, generalising work of Tanaka. More generally, we prove the BAB conjecture on the boundedness of $\varepsilon$-klt del Pezzo surfaces over arbitrary fields of characteristic different from 2, 3, and 5., Comment: 26 pages, v2: minor changes. To appear in Forum Math Sigma