In 2003, Bohman, Frieze, and Martin initiated the study of randomly perturbed graphs and digraphs. For digraphs, they showed that for every $\alpha \gt 0$, there exists a constant $C$ such that for every $n$-vertex digraph of minimum semi-degree at least $\alpha n$, if one adds $Cn$ random edges then asymptotically almost surely the resulting digraph contains a consistently oriented Hamilton cycle. We generalize their result, showing that the hypothesis of this theorem actually asymptotically almost surely ensures the existence of every orientation of a cycle of every possible length, simultaneously. Moreover, we prove that we can relax the minimum semi-degree condition to a minimum total degree condition when considering orientations of a cycle that do not contain a large number of vertices of indegree $1$. Our proofs make use of a variant of an absorbing method of Montgomery.

Since the 1960s Mastermind has been studied for the combinatorial and information-theoretical interest the game has to offer. Many results have been discovered starting with Erdős and Rényi determining the optimal number of queries needed for two colours. For $k$ colours and $n$ positions, Chvátal found asymptotically optimal bounds when $k \le n^{1-\varepsilon }$. Following a sequence of gradual improvements for $k\geq n$ colours, the central open question is to resolve the gap between $\Omega (n)$ and $\mathcal{O}(n\log \log n)$ for $k=n$. In this paper, we resolve this gap by presenting the first algorithm for solving $k=n$ Mastermind with a linear number of queries. As a consequence, we are able to determine the query complexity of Mastermind for any parameters $k$ and $n$.

The switch process alternates independently between 1 and $-1$, with the first switch to 1 occurring at the origin. The expected value function of this process is defined uniquely by the distribution of switching times. The relation between the two is implicitly described through the Laplace transform, which is difficult to use for determining if a given function is the expected value function of some switch process. We derive an explicit relation under the assumption of monotonicity of the expected value function. It is shown that geometric divisible switching time distributions correspond to a non-negative decreasing expected value function. Moreover, an explicit relation between the expected value of a switch process and the autocovariance function of the switch process stationary counterpart is obtained, leading to a new interpretation of the classical Pólya criterion for positive-definiteness.

Choices made by individuals have widespread impacts—for instance, people choose between political candidates to vote for, between social media posts to share, and between brands to purchase—moreover, data on these choices are increasingly abundant. Discrete choice models are a key tool for learning individual preferences from such data. Additionally, social factors like conformity and contagion influence individual choice. Traditional methods for incorporating these factors into choice models do not account for the entire social network and require hand-crafted features. To overcome these limitations, we use graph learning to study choice in networked contexts. We identify three ways in which graph learning techniques can be used for discrete choice: learning chooser representations, regularizing choice model parameters, and directly constructing predictions from a network. We design methods in each category and test them on real-world choice datasets, including county-level 2016 US election results and Android app installation and usage data. We show that incorporating social network structure can improve the predictions of the standard econometric choice model, the multinomial logit. We provide evidence that app installations are influenced by social context, but we find no such effect on app usage among the same participants, which instead is habit-driven. In the election data, we highlight the additional insights a discrete choice framework provides over classification or regression, the typical approaches. On synthetic data, we demonstrate the sample complexity benefit of using social information in choice models.

Skin and Soft Tissue Infections (SSTIs) are common bacterial infections. We hypothesized that due to the COVID-19 pandemic, SSTI rates would significantly decrease due to directives to avoid unneeded care and attenuated SSTIs risk behaviours. We retrospectively examined all patients with an ICD-10 diagnosis code in the Los Angeles County Department of Health Services, the second largest U.S. safety net healthcare system between 16 March 2017 and 15 March 2022. We then compared pre-pandemic with intra-pandemic SSTI rates using an interrupted time series analysis. We found 72,118 SSTIs, 46,206 during the pre-pandemic period and 25,912 during the intra-pandemic period. Pre-pandemic SSTI rate was significantly higher than the intra-pandemic rate (3.27 vs. 2.31 cases per 1,000 empanelled patient-months, P < 0.0001). The monthly SSTI cases decreased by 1.19 SSTIs/1,000 empanelled patient-months between the pre- and intra-pandemic periods (P = 0.0003). SSTI subgroups (inpatient, observation unit, emergency department, and outpatient clinics), all had significant SSTI decreases between the two time periods (P < 0.05) except for observation unit (P = 0.50). Compared to the pre-COVID-19 pandemic period, medically attended SSTI rates in our large U.S. safety net healthcare system significantly decreased by nearly 30%. Whether findings reflect true SSTI decreases or decreased health system utilization for SSTIs requires further examination.

This paper proposes a subsampling inference method for extreme conditional quantiles based on a self-normalized version of a local estimator for conditional quantiles, such as the local linear quantile regression estimator. The proposed method circumvents difficulty of estimating nuisance parameters in the limiting distribution of the local estimator. A simulation study and empirical example illustrate usefulness of our subsampling inference to investigate extremal phenomena.

Given a graph $H$, let us denote by $f_\chi (H)$ and $f_\ell (H)$, respectively, the maximum chromatic number and the maximum list chromatic number of $H$-minor-free graphs. Hadwiger’s famous colouring conjecture from 1943 states that $f_\chi (K_t)=t-1$ for every $t \ge 2$. A closely related problem that has received significant attention in the past concerns $f_\ell (K_t)$, for which it is known that $2t-o(t) \le f_\ell (K_t) \le O(t (\!\log \log t)^6)$. Thus, $f_\ell (K_t)$ is bounded away from the conjectured value $t-1$ for $f_\chi (K_t)$ by at least a constant factor. The so-called $H$-Hadwiger’s conjecture, proposed by Seymour, asks to prove that $f_\chi (H)={\textrm{v}}(H)-1$ for a given graph $H$ (which would be implied by Hadwiger’s conjecture).

In this paper, we prove several new lower bounds on $f_\ell (H)$, thus exploring the limits of a list colouring extension of $H$-Hadwiger’s conjecture. Our main results are:

• For every $\varepsilon \gt 0$ and all sufficiently large graphs $H$ we have $f_\ell (H)\ge (1-\varepsilon )({\textrm{v}}(H)+\kappa (H))$, where $\kappa (H)$ denotes the vertex-connectivity of $H$.

• For every $\varepsilon \gt 0$ there exists $C=C(\varepsilon )\gt 0$ such that asymptotically almost every $n$-vertex graph $H$ with $\left \lceil C n\log n\right \rceil$ edges satisfies $f_\ell (H)\ge (2-\varepsilon )n$.

The first result generalizes recent results on complete and complete bipartite graphs and shows that the list chromatic number of $H$-minor-free graphs is separated from the desired value of $({\textrm{v}}(H)-1)$ by a constant factor for all large graphs $H$ of linear connectivity. The second result tells us that for almost all graphs $H$ with superlogarithmic average degree $f_\ell (H)$ is separated from $({\textrm{v}}(H)-1)$ by a constant factor arbitrarily close to $2$. Conceptually these results indicate that the graphs $H$ for which $f_\ell (H)$ is close to the conjectured value $({\textrm{v}}(H)-1)$ for $f_\chi (H)$ are typically rather sparse.

In the present work, neural networks are applied to formulate parametrized hyperelastic constitutive models. The models fulfill all common mechanical conditions of hyperelasticity by construction. In particular, partially input convex neural network (pICNN) architectures are applied based on feed-forward neural networks. Receiving two different sets of input arguments, pICNNs are convex in one of them, while for the other, they represent arbitrary relationships which are not necessarily convex. In this way, the model can fulfill convexity conditions stemming from mechanical considerations without being too restrictive on the functional relationship in additional parameters, which may not necessarily be convex. Two different models are introduced, where one can represent arbitrary functional relationships in the additional parameters, while the other is monotonic in the additional parameters. As a first proof of concept, the model is calibrated to data generated with two differently parametrized analytical potentials, whereby three different pICNN architectures are investigated. In all cases, the proposed model shows excellent performance.

Vaccination against hepatitis B virus (HBV) is effective at preventing vertical transmission. Sierra Leone, Liberia, and Guinea are hyperendemic West African countries; yet, childhood vaccination coverage is suboptimal, and the determinants of incomplete vaccination are poorly understood. We analyzed national survey data (2018–2020) of children aged 4–35 months to assess complete HBV vaccination (receiving 3 doses of the pentavalent vaccine) and incomplete vaccination (receiving <3 doses). Statistical analysis was conducted using the complex sample command in SPSS (version 28). Multivariate logistic regression was used to identify determinants of incomplete immunization. Overall, 11,181 mothers were analyzed (4,846 from Sierra Leone, 2,788 from Liberia, and 3,547 from Guinea). Sierra Leone had the highest HBV childhood vaccination coverage (70.3%), followed by Liberia (64.6%) and Guinea (39.3%). Within countries, HBV vaccination coverage varied by socioeconomic characteristics and healthcare access. In multivariate regression analysis, factors that were significantly associated with incomplete vaccination in at least one country included sex of the child, Muslim mothers, lower household wealth index, <4 antenatal visits, home delivery, and distance to health facility vaccination (all p < 0.05). Understanding and addressing modifiable determinants of incomplete vaccination will be essential to help achieve the 2030 viral hepatitis elimination goals.

There have been consistent calls for more research on managing teams and embedding processes in data science innovations. Widely used frameworks (e.g., the cross-industry standard process for data mining) provide a standardized approach to data science but are limited in features such as role clarity, skills, and cross-team collaboration that are essential for developing organizational capabilities in data science. In this study, we introduce a data workflow method (DWM) as a new approach to break organizational silos and create a multi-disciplinary team to develop, implement and embed data science. Different from current data science process workflows, the DWM is managed at the system level that shapes business operating model for continuous improvement, rather than as a function of a particular project, one single business unit, or isolated individuals. To further operationalize the DWM approach, we investigated an embedded data workflow at a mining operation that has been using geological data in a machine-learning model to stabilize daily mill production for the last 2 years. Based on the findings in this study, we propose that the DWM approach derives its capability from three aspects: (a) a systemic data workflow; (b) multi-disciplinary networks of collaboration and responsibility; and (c) clearly identified data roles and the associated skills and expertise. This study suggests a whole-of-organization approach and pathway to develop data science capability.

Modeling complex dynamical systems with only partial knowledge of their physical mechanisms is a crucial problem across all scientific and engineering disciplines. Purely data-driven approaches, which only make use of an artificial neural network and data, often fail to accurately simulate the evolution of the system dynamics over a sufficiently long time and in a physically consistent manner. Therefore, we propose a hybrid approach that uses a neural network model in combination with an incomplete partial differential equations (PDEs) solver that provides known, but incomplete physical information. In this study, we demonstrate that the results obtained from the incomplete PDEs can be efficiently corrected at every time step by the proposed hybrid neural network—PDE solver model, so that the effect of the unknown physics present in the system is correctly accounted for. For validation purposes, the obtained simulations of the hybrid model are successfully compared against results coming from the complete set of PDEs describing the full physics of the considered system. We demonstrate the validity of the proposed approach on a reactive flow, an archetypal multi-physics system that combines fluid mechanics and chemistry, the latter being the physics considered unknown. Experiments are made on planar and Bunsen-type flames at various operating conditions. The hybrid neural network—PDE approach correctly models the flame evolution of the cases under study for significantly long time windows, yields improved generalization and allows for larger simulation time steps.

Processes of random tessellations of the Euclidean space $\mathbb{R}^d$, $d\geq 1$, are considered that are generated by subsequent division of their cells. Such processes are characterized by the laws of the life times of the cells until their division and by the laws for the random hyperplanes that divide the cells at the end of their life times. The STIT (STable with respect to ITerations) tessellation processes are a reference model. In the present paper a generalization concerning the life time distributions is introduced, a sufficient condition for the existence of such cell division tessellation processes is provided, and a construction is described. In particular, for the case that the random dividing hyperplanes have a Mondrian distribution—which means that all cells of the tessellations are cuboids—it is shown that the intrinsic volumes, except the Euler characteristic, can be used as the parameter for the exponential life time distribution of the cells.

Since the emergence of Omicron variant of SARS-CoV-2 in late 2021, a number of sub-lineages have arisen and circulated internationally. Little is known about the relative severity of Omicron sub-lineages BA.2.75, BA.4.6, and BQ.1. We undertook a case–control analysis to determine the clinical severity of these lineages relative to BA.5, using whole genome sequenced, PCR-confirmed infections, between 1 August 2022 and 27 November 2022, among those who presented to emergency care in England 14 days after and up to one day prior to the positive specimen. A total of 10,375 episodes were included in the analysis; of which, 5,207 (50.2%) were admitted to the hospital or died. Multivariable conditional regression analyses found no evidence of greater odds of hospital admission or death among those with BA.2.75 (odds ratio (OR) = 0.96, 95% confidence interval (CI): 0.84–1.09) and BA.4.6 (OR = 1.02, 95% CI: 0.88– 1.17) or BQ.1 (OR = 1.03, 95% CI: 0.94–1.13) compared to BA.5. Future lineages may not follow the same trend and there remains a need for continued surveillance of COVID-19 variants and their clinical outcomes to inform the public health response.

In this paper we study the drift parameter estimation for reflected stochastic linear differential equations of a large signal. We discuss the consistency and asymptotic distributions of trajectory fitting estimator (TFE).

For some time now, Solvency II requires that insurance companies calculate minimum capital requirements to face the risk of insolvency, either in accordance with the Standard Formula or using a full or partial Internal Model. An Internal Model must be based on a market-consistent valuation of assets and liabilities at a 1-year time span, where a real-world probabilistic structure is used for the first year of projection. In this paper, we describe the major risks of a non-life insurance company, i.e. the non-life underwriting risk and market risk, and their interactions, focusing on the non-life premium risk, equity risk, and interest rate risk. This analysis is made using some well-known stochastic models in the financial-actuarial literature and practical insurance business, i.e. the Collective Risk Model for non-life premium risk, the Geometric Brownian Motion for equity risk, and a real-world version of the G2++ Model for interest rate risk, where parameters are calibrated on current and real market data. Finally, we illustrate a case study on a single-line and a multi-line insurance company in order to see how the risk drivers behave in both a stand-alone and an aggregate framework.

Birth–death processes form a natural class where ideas and results on large deviations can be tested. We derive a large-deviation principle under an assumption that the rate of jump down (death) grows asymptotically linearly with the population size, while the rate of jump up (birth) grows sublinearly. We establish a large-deviation principle under various forms of scaling of the underlying process and the corresponding normalization of the logarithm of the large-deviation probabilities. The results show interesting features of dependence of the rate functional upon the parameters of the process and the forms of scaling and normalization.

We used primary care data to retrospectively describe the entry, spread, and impact of COVID-19 in a remote rural community and the associated risk factors and challenges faced by the healthcare team. Generalized linear models were fitted to assess the relationship between age, sex, period, risk group status, symptom duration, post-COVID illness, and disease severity. Social network and cluster analyses were also used. The first six cases, including travel events and a social event in town, contributed to early infection spread. About 351 positive cases were recorded and 6% of patients experienced two COVID-19 episodes in the 2.5-year study period. Five space–time case clusters were identified. One case, linked with the social event, was particularly central in its contact network. The duration of disease symptoms was driven by gender, age, and risk factors. The probability of suffering severe disease increased with symptom duration and decreased over time. About 27% and 23% of individuals presented with residual symptoms and post-COVID illness, respectively. The probability of developing a post-COVID illness increased with age and the duration of COVID-associated symptoms. Carefully registered primary care data may help optimize infection prevention and control efforts and upscale local healthcare capacities in vulnerable rural communities.