We study the bilateral preference graphs $\mathit{LK}(n, k)$ of La and Kabkab, obtained as follows. Put independent and uniform [0, 1] weights on the edges of the complete graph $K_n$. Then, each edge (i, j) is included in $\mathit{LK}(n,k)$ if it is bilaterally preferred, in the sense that it is among the k edges of lowest weight incident to vertex i, and among the k edges of lowest weight incident to vertex j. We show that $k = \log(n)$ is the connectivity threshold, solving a conjecture of La and Kabkab, and obtaining finer results about the window. We also investigate the asymptotic behavior of the average degree of vertices in $\mathit{LK}(n, k)$ as $n\rightarrow\infty$.

In the 1980s, Erdős and Sós initiated the study of Turán problems with a uniformity condition on the distribution of edges: the uniform Turán density of a hypergraph $H$ is the infimum over all $d$ for which any sufficiently large hypergraph with the property that all its linear-size subhypergraphs have density at least $d$ contains $H$. In particular, they asked to determine the uniform Turán densities of $K_4^{(3)-}$ and $K_4^{(3)}$. After more than 30 years, the former was solved in [Israel J. Math. 211 (2016), 349 – 366] and [J. Eur. Math. Soc. 20 (2018), 1139 – 1159], while the latter still remains open. Till today, there are known constructions of $3$-uniform hypergraphs with uniform Turán density equal to $0$, $1/27$, $4/27$, and $1/4$ only. We extend this list by a fifth value: we prove an easy to verify sufficient condition for the uniform Turán density to be equal to $8/27$ and identify hypergraphs satisfying this condition.

Blockchain technology has attracted attention from public sector agencies, mainly for its perceived potential to improve transparency, data integrity, and administrative processes. However, its concrete value and applicability within government settings remain contested, and real-world adoption has been limited and uneven. This raises questions regarding the conditions that promote or impede adoption at the institutional level. Fuzzy-set qualitative comparative analysis is employed in this research to explore how the combined effects of national-level regulatory clarity, financial provision, digital readiness, and ecosystem engagement shape patterns of blockchain adoption in the European public sector. Rather than identifying any single factor as decisive, our findings reveal a plurality of institutional paths leading to high adoption intensity, with regulatory certainty and European Union funding appearing most frequently on high-consistency paths. In contrast, digital readiness indicators and national research and development budgets are substitutable, challenging resource-based perceptions of technology adoption and supporting a configurational understanding that accounts for institutional interdependence and contextuality. We argue that policy strategies cannot look for overall readiness but should place key institutional strengths relative to local conditions and public value objectives.

This paper considers option valuation under finite mixture models in a discrete-time economy. Specifically, the Esscher transform is employed to select a pricing kernel. Novel finite mixture models with negative-shifted Gamma and negative-shifted inverse Gaussian distributions are developed. A hybrid finite mixture model that allows different parametric forms for component distributions is introduced to incorporate model uncertainty. An empirical characteristic function estimation method is employed to estimate the finite mixture models. Closed-form pricing formulas for a European call option are obtained for some finite mixture models. Empirical examples using data on the Bitcoin-USD prices are provided to illustrate an application of the proposed models to value Bitcoin options.

Credibility theory provides a fundamental framework in actuarial science for estimating policyholder premiums by blending individual claims experience with overall portfolio data. Bühlmann and Bühlmann–Straub credibility models are widely used because, in the Bayesian hierarchical setting, they are the best linear Bayes estimators, minimizing the Bayes risk (expected squared error loss) within the class of linear estimators given the experience data for a particular risk class. To improve estimation accuracy, quadratic credibility models incorporate higher-order terms, capturing more information about the underlying risk structure. This study develops a robust quadratic credibility (RQC) framework that integrates second-order polynomial adjustments of robustly transformed ground-up loss data, such as winsorized moments, to improve stability in the presence of extreme claims or heavy-tailed distributions. Extending semi-linear credibility, RQC maintains interpretability while enhancing statistical efficiency. We establish its asymptotic properties, derive closed-form expressions for the RQC premium, and demonstrate its superior performance in reducing mean square error (MSE). We additionally derive semi-linear credibility structural parameters using winsorized data, further strengthening the robustness of credibility estimation. Analytical comparisons and empirical applications highlight RQC’s ability to capture claim heterogeneity, offering a more reliable and equitable approach to premium estimation. This research advances credibility theory by introducing a refined methodology that balances efficiency, robustness, and practical applicability across diverse insurance settings.

This article provides a general asymptotic theory for mildly explosive autoregression. We confirm that Cauchy limit theory remains invariant across a broad range of error processes, including general linear processes with martingale difference innovations, stationary causal processes, and nonlinear autoregressive time series, such as threshold autoregressive and bilinear models. Our results unify the Cauchy limit theory for long memory, short memory, and anti-persistent innovations within a single framework. Notably, we demonstrate that in the presence of anti-persistent innovations, the Cauchy limit theory may be violated when the regression coefficient approaches the local-to-unity range. Additionally, we explore extensions to models with varying drift, which is of significant interest in its own right.

Designing efficient and rigorous numerical methods for sequential decision-making under uncertainty is a difficult problem that arises in many applications frameworks. In this paper we focus on the numerical solution of a subclass of impulse control problems for the piecewise deterministic Markov process (PDMP) when the jump times are hidden. We first state the problem as a partially observed Markov decision process (POMDP) on a continuous state space and with controlled transition kernels corresponding to some specific skeleton chains of the PDMP. We then proceed to build a numerically tractable approximation of the POMDP by tailor-made discretizations of the state spaces. The main difficulty in evaluating the discretization error comes from the possible random jumps of the PDMP between consecutive epochs of the POMDP and requires special care. Finally, we discuss the practical construction of discretization grids and illustrate our method on simulations.

In recent years, the manufacturing sector has seen an influx of artificial intelligence applications, seeking to harness its capabilities to improve productivity. However, manufacturing organizations have limited understanding of risks that are posed by the usage of artificial intelligence, especially those related to trust, responsibility, and ethics. While significant effort has been put into developing various general frameworks and definitions to capture these risks, manufacturing and supply chain practitioners face difficulties in implementing these and understanding their impact. These issues can have a significant effect on manufacturing companies, not only at an organization level but also on their employees, clients, and suppliers. This paper aims to increase understanding of trustworthy, responsible, and ethical Artificial Intelligence challenges as they apply to manufacturing and supply chains. We first conduct a systematic mapping study on concepts relevant to trust, responsibility and ethics and their interrelationships. We then use a broadened view of a machine learning lifecycle as a basis to understand how risks and challenges related to these concepts emanate from each phase in the lifecycle. We follow a case study driven approach, providing several illustrative examples that focus on how these challenges manifest themselves in actual manufacturing practice. Finally, we propose a series of research questions as a roadmap for future research in trustworthy, responsible and ethical artificial intelligence applications in manufacturing, to ensure that the envisioned economic and societal benefits are delivered safely and responsibly.

In many contexts, an individual’s beliefs and behavior are affected by the choices of their social or geographic neighbors. This influence results in local correlation in people’s actions, which in turn affects how information and behaviors spread. Previously developed frameworks capture local social influence using network games, but discard local correlation in players’ strategies. This paper develops a network games framework that allows for local correlation in players’ strategies by incorporating a richer partial information structure than previous models. Using this framework we also examine the dependence of equilibrium outcomes on network clustering—the probability that two individuals with a mutual neighbor are connected to each other. We find that clustering reduces the number of players needed to provide a public good and allows for market sharing in technology standards competitions.

When overdispersion and correlation co-occur in longitudinal count data, as is often the case, an analysis method that can handle both phenomena simultaneously is needed. The correlated Poisson distribution (CPD) proposed by Drezner and Farnum (Communications in Statistics-Theory and Methods, 22(11), 3051–3063, 1994) is a generalization of the classical Poisson distribution with the incorporation of an additional parameter that allows dependence between successive observations of the phenomenon under study. This parameter both measures the correlation and reflects the degree of dispersion. The classical Poisson distribution is obtained as a special case when the correlation is zero. We present an in-depth review of this CPD and discuss some methods to estimate the distribution parameters. The inclusion of regression components in this distribution is enabled by allowing one of the parameters to include available information concerning, in this case, automobile insurance policyholders. The proposed distribution can be viewed as an alternative to the Poisson, negative binomial, and Poisson-inverse Gaussian approaches. We then describe applications of the distribution, suggest it is appropriate for modeling the number of claims in an automobile insurance portfolio, and establish some new distribution properties.

The practice of actuarial science has always been rooted in computation. From the early days of hand-constructed tables and commutation functions to today’s large-scale stochastic simulations and machine learning models, actuaries have continuously adapted their analytical tools to the technology of their time. The rapid growth of high-performance computing, open-source software, and data-driven methodologies now offers new possibilities for actuarial modeling – transforming not only how we calculate, but also how we think about risk, uncertainty, and decision-making. This editorial introduces a thematic collection on Actuarial Software, which showcases recent advances at the intersection of actuarial modeling and computational science.

Fine-grained mortality forecasting has gained momentum in actuarial research due to its ability to capture localized, short-term fluctuations in death rates. This paper introduces MortFCNet, a deep-learning method that predicts weekly death rates using region-specific weather inputs. Unlike traditional Serfling-based methods and gradient-boosting models that rely on predefined fixed Fourier terms and manual feature engineering, MortFCNet automatically learns patterns from raw time-series data without needing explicitly defined Fourier terms or manual feature engineering. Extensive experiments across over 200 NUTS-3 regions in France, Italy, and Switzerland demonstrate that MortFCNet consistently outperforms both a standard Serfling-type baseline and XGBoost in terms of predictive accuracy. Our ablation studies further confirm its ability to uncover complex relationships in the data without feature engineering. Moreover, this work underscores a new perspective on exploring deep learning for advancing fine-grained mortality forecasting.

We study a continuous-time mutually catalytic branching model on the $\mathbb{Z}^{d}$. The model describes the behavior of two different populations of particles, performing random walk on the lattice in the presence of branching, that is, each particle dies at a certain rate and is replaced by a random number of offspring. The branching rate of a particle in one population is proportional to the number of particles of another population at the same site. We study the long time behavior for this model, in particular, coexistence and noncoexistence of two populations in the long run. Finally, we construct a sequence of renormalized processes and use duality techniques to investigate its limiting behavior.

This article examines the governance challenges of human genomic data sharing. The analysis builds upon the unique characteristics that distinguish genomic data from other forms of personal data, particularly its dual nature as both uniquely identifiable to individuals and inherently collective, reflecting familial and ethnic group characteristics. This duality informs a tripartite risk taxonomy: individual privacy violations, group-level harms, and bioterrorism threats. Examining regulatory frameworks in the European Union (EU) and China, the article demonstrates how current data protection mechanisms—primarily anonymisation and informed consent—prove inadequate for genomic data governance due to the impossibility of true anonymisation and the limitations of consent-based models in addressing the risks of such sharing. Drawing on the concept of “genomic contextualism,” the article proposes a nuanced framework that incorporates interest balancing, comprehensive data lifecycle management, and tailored technical safeguards. The objective is to protect individuals and underrepresented groups while maximising the scientific and clinical value of genomic data.

We introduce a family of parsimonious network models that are intended to generalize the configuration model to temporal settings. We present consistent estimators for the model parameters and perform numerical simulations to illustrate the properties of the estimators on finite samples. We also derive analytical solutions for the basic and effective reproduction numbers for the early stage of the discrete-time SIR spreading process for our temporal configuration model (TCM). We apply three distinct TCMs to empirical student proximity networks and compare their performance.

We study how COVID-19 affected the ownership co-location network of French multinationals over 2012–2022. Using INSEE’s LiFi, we build annual country-industry co-location networks and assess robustness via topology (density, centralization, assortativity, and clustering) and edge survival (Weighted Jaccard). We then test for post-shock shifts in the determinants of dyadic co-location with multiple regression quadratic assignment procedure. Three results emerge. First, the network’s core is robust: topology shows no discontinuity and centrality persists. Second, adaptation is continuous at the margin: around one-third of edges rewire, concentrated in the periphery while core ties endure. Third, after 2020 the determinants of tie weights change, with a reduced role for gravity-like factors and greater cross-sector rebalancing. Thus the system is structurally robust with active peripheral adjustment. Rather than strict resilience in the sense of a return to the pre-COVID configuration, we observe durable strategic reweighting.

Many empirical systems contain complex interactions of arbitrary size, representing, for example, chemical reactions, social groups, co-authorship relationships, and ecological dependencies. These interactions are known as higher-order interactions, and the collection of these interactions comprise a higher-order network, or hypergraph. Hypergraphs have established themselves as a popular and versatile mathematical representation of such systems, and a number of software packages written in various programming languages have been designed to analyze these networks. However, the ecosystem of higher-order network analysis software is fragmented due to specialization of each software’s programming interface and compatible data representations. To enable seamless data exchange between higher-order network analysis software packages, we introduce the Hypergraph Interchange Format (HIF), a standardized format for storing higher-order network data. HIF supports multiple types of higher-order networks, including undirected hypergraphs, directed hypergraphs, and abstract simplicial complexes, while actively exploring extensions to represent multiplex hypergraphs, temporal hypergraphs, and ordered hypergraphs. To accommodate the wide variety of metadata used in different contexts, HIF also includes support for attributes associated with nodes, edges, and incidences. This initiative is a collaborative effort involving authors, maintainers, and contributors from prominent hypergraph software packages. This project introduces a JSON schema with corresponding documentation and unit tests, example HIF-compliant datasets, and tutorials demonstrating the use of HIF with several popular higher-order network analysis software packages.