Let $n\geq 2$ random lines intersect a planar convex domain D. Consider the probabilities $p_{nk}$, $k=0,1, \ldots, {n(n-1)}/{2}$ that the lines produce exactly k intersection points inside D. The objective is finding $p_{nk}$ through geometric invariants of D. Using Ambartzumian’s combinatorial algorithm, the known results are instantly reestablished for $n=2, 3$. When $n=4$, these probabilities are expressed by new invariants of D. When D is a disc of radius r, the simplest forms of all invariants are found. The exact values of $p_{3k}$ and $p_{4k}$ are established.

This study investigates the asymptotic properties of the Bayesian empirical likelihood (BEL), which uses the empirical likelihood as an alternative to a parametric likelihood for Bayesian inference. We establish two asymptotic equivalence results based on the Bernstein–von Mises (BvM) theorem by introducing a new formulation of the moment restriction model. First, the limiting posterior distribution of the BEL is the same as that of a parametric Bayesian method that uses the likelihood of a least favorable model of the moment restriction model. Second, the limiting posterior distribution is also the same as that of a semiparametric Bayesian method that places priors on both a finite-dimensional parameter of interest and an infinite-dimensional nuisance parameter. Because parametric and semiparametric Bayesian methods are legitimate Bayesian procedures, the equivalence results provide a large sample justification for the BEL as a Bayesian inference method. Moreover, the BvM theorem provides a frequentist justification for BEL posterior inference.

The spread of Severe Acute Respiratory Syndrome Coronavirus 2 new variants increased the number of subjects in home isolation and quarantine. The aim of this study was to assess the compliance with coronavirus disease 2019 home isolation rules for 32 subjects in home care in Marche Region, Italy. The results showed that subjects in home isolation were better informed about isolation rules (P = 0.007) than those who were in quarantine. They had lower educational level (P < 0.001) and none/single income (P < 0.001) and higher rate of clinical manifestation. The education for a safe quarantine should be strengthened widely, especially among disadvantaged subjects.

Antimicrobial-resistant (AMR) bacteria are a threat to public health as they can resist treatment and pass along genetic material that allows other bacteria to become drug-resistant. To assess foodborne AMR risk, the Codex Guidelines for Risk Analysis of Foodborne AMR provide a framework for risk profiles and risk assessments. Several elements of a risk profile may benefit from a scoping review (ScR). To contribute to a larger risk profile structured according to the Codex Guidelines, our objective was to conduct a ScR of the current state of knowledge on the distribution, frequency and concentrations of extended-spectrum β-lactamase (ESBL)-producing Enterobacteriaceae in salmon and shrimp. Articles were identified via a comprehensive search of five bibliographic databases. Two reviewers screened titles and abstracts for relevance and characterised full-text articles with screening forms developed a priori. Sixteen relevant studies were identified. This review found that there is a lack of Canadian data regarding ESBL-producing Enterobacteriaceae in salmon and shrimp. However, ESBL- producing Escherichia coli, Klebsiella pneumoniae and other Enterobacteriaceae have been isolated in multiple regions with a history of exporting seafood to Canada. The literature described herein will support future decision-making on this issue as research/surveillance and subsequent assessments are currently lacking.

Fiduciary agents and trust-based institutions are increasingly proposed and considered in legal, regulatory, and ethical discourse as an alternative or addition to a control-based model of data management. Instead of leaving it up to the citizen to decide what to do with her data and to ensure that her best interests are met, an independent person or organization will act on her behalf, potentially also taking into account the general interest. By ensuring that these interests are protected, the hope is that citizens’ willingness to share data will increase, thereby allowing for more data-driven projects. Thus, trust-based models are presented as a win–win scenario. It is clear, however, that there are also apparent dangers entailed with trust-based approaches. Especially one model, that of data trusts, may have far-reaching consequences.

It is well known that, under suitable regularity conditions, the normalized fractional process with fractional parameter d converges weakly to fractional Brownian motion (fBm) for $d>\frac {1}{2}$. We show that, for any nonnegative integer M, derivatives of order $m=0,1,\dots ,M$ of the normalized fractional process with respect to the fractional parameter d jointly converge weakly to the corresponding derivatives of fBm. As an illustration, we apply the results to the asymptotic distribution of the score vectors in the multifractional vector autoregressive model.

This paper proposes a new test for a class of conditional moment restrictions (CMRs) whose parameterization involves unknown, unrestricted conditional expectation functions. Motivating examples of such CMRs arise from models of discrete choice under uncertainty including certain static games of incomplete information. The proposed test may be viewed as a semi-/nonparametric extension of the Bierens (1982, Journal of Econometrics 20, 105–134) goodness-of-fit test of a parametric model for the conditional mean. Estimating conditional expectations using series methods and employing a Gaussian multiplier bootstrap to obtain critical values, the test is shown to be asymptotically correctly sized and consistent. Simulation studies indicate good finite-sample properties. In an empirical application, the test is used to study the validity of a game-theoretical model for discount store market entry, treating equilibrium beliefs as nonparametric conditional expectations. The test indicates that Walmart and Kmart entry decisions do not result from a static discrete game of incomplete information with linearly specified profits.

In this perspective, I give my answer to the question of how quantum computing will impact on data-intensive applications in engineering and science. I focus on quantum Monte Carlo integration as a likely source of (relatively) near-term quantum advantage, but also discuss some other ideas that have garnered widespread interest.

We prove existence and uniqueness for the solution of a class of mixed fractional stochastic differential equations with discontinuous drift driven by both standard and fractional Brownian motion. Additionally, we establish a generalized Itô rule valid for functions with an absolutely continuous derivative and applicable to solutions of mixed fractional stochastic differential equations with Lipschitz coefficients, which plays a key role in our proof of existence and uniqueness. The proof of such a formula is new and relies on showing the existence of a density of the law under mild assumptions on the diffusion coefficient.

We establish exponential ergodicity for a class of Markov processes with interactions, including two-factor type processes and Gruschin type processes. The proof is elementary and direct via the Markov coupling technique.

We study the time-consistent investment and contribution policies in a defined benefit stochastic pension fund where the manager discounts the instantaneous utility over a finite planning horizon and the final function at constant but different instantaneous rates of time preference. This difference, which can be motivated for some uncertainties affecting payoffs at the end of the planning horizon, will induce a variable bias between the relative valuation of the final function and the previous payoffs and will lead the manager to show time-inconsistent preferences. Both the benefits and the contribution rate are proportional to the total wage of the workers that we suppose is stochastic. The aim is to maximize a CRRA utility function of the net benefit relative to salary in a bounded horizon and to maximize a CRRA final utility of the fund level relative to the salary. The problem is solved by means of dynamic programming techniques, and main results are illustrated numerically.

The dimension of models derived on the basis of data is commonly restricted by the number of observations, or in the context of monitored systems, sensing nodes. This is particularly true for structural systems, which are typically high-dimensional in nature. In the scope of physics-informed machine learning, this article proposes a framework—termed neural modal ordinary differential equations (Neural Modal ODEs)—to integrate physics-based modeling with deep learning for modeling the dynamics of monitored and high-dimensional engineered systems. In this initiating exploration, we restrict ourselves to linear or mildly nonlinear systems. We propose an architecture that couples a dynamic version of variational autoencoders with physics-informed neural ODEs (Pi-Neural ODEs). An encoder, as a part of the autoencoder, learns the mappings from the first few items of observational data to the initial values of the latent variables, which drive the learning of embedded dynamics via Pi-Neural ODEs, imposing a modal model structure on that latent space. The decoder of the proposed model adopts the eigenmodes derived from an eigenanalysis applied to the linearized portion of a physics-based model: a process implicitly carrying the spatial relationship between degrees-of-freedom (DOFs). The framework is validated on a numerical example, and an experimental dataset of a scaled cable-stayed bridge, where the learned hybrid model is shown to out perform a purely physics-based approach to modeling. We further show the functionality of the proposed scheme within the context of virtual sensing, that is, the recovery of generalized response quantities in unmeasured DOFs from spatially sparse data.

Motivated by Ahmadi-Javid (Journal of Optimization Theory Applications, 155(3), 2012, 1105–1123) and Ahmadi-Javid and Pichler (Mathematics and Financial Economics, 11, 2017, 527–550), the concept of Tsallis Value-at-Risk (TsVaR) based on Tsallis entropy is introduced in this paper. TsVaR corresponds to the tightest possible upper bound obtained from the Chernoff inequality for the Value-at-Risk. The main properties and analogous dual representation of TsVaR are investigated. These results partially generalize the Entropic Value-at-Risk by involving Tsallis entropies. Three spaces, called the primal, dual, and bidual Tsallis spaces, corresponding to TsVaR are fully studied. It is shown that these spaces equipped with the norm induced by TsVaR are Banach spaces. The Tsallis spaces are related to the $L^p$ spaces, as well as specific Orlicz hearts and Orlicz spaces. Finally, we derive explicit formula for the dual TsVaR norm.