We study a variant of the classical Markovian logistic SIS epidemic model on a complete graph, which has the additional feature that healthy individuals can become infected without contacting an infected member of the population. This additional ‘self-infection’ is used to model situations where there is an unknown source of infection or an external disease reservoir, such as an animal carrier population. In contrast to the classical logistic SIS epidemic model, the version with self-infection has a non-degenerate stationary distribution, and we derive precise asymptotics for the time to converge to stationarity (mixing time) as the population size becomes large. It turns out that the chain exhibits the cutoff phenomenon, which is a sharp transition in time from one to zero of the total variation distance to stationarity. We obtain the exact leading constant for the cutoff time and show that the window size is of constant (optimal) order. While this result is interesting in its own right, an additional contribution of this work is that the proof illustrates a recently formalised methodology of Barbour, Brightwell and Luczak (2022), ‘Long-term concentration of measure and cut-off’, Stochastic Processes and their Applications 152, 378–423, which can be used to show cutoff via a combination of concentration-of-measure inequalities for the trajectory of the chain and coupling techniques.

In this paper we derive cumulant bounds for subgraph counts and power-weighted edge lengths in a class of spatial random networks known as weight-dependent random connection models. These bounds give rise to different probabilistic results, from which we mainly focus on moderate deviations of the respective statistics, but also show a concentration inequality and a normal approximation result. This involves dealing with long-range spatial correlations induced by the profile function and the weight distribution. We start by deriving the bounds for the classical case of a Poisson vertex set, and then provide extensions to α-determinantal processes.

We define a random graph obtained by connecting each point of $\mathbb{Z}^d$ independently and uniformly to a fixed number $1 \leq k \leq 2d$ of its nearest neighbors via a directed edge. We call this graph the directed k-neighbor graph. Two natural associated undirected graphs are the undirected and the bidirectional k-neighbor graph, where we connect two vertices by an undirected edge whenever there is a directed edge in the directed k-neighbor graph between the vertices in at least one, respectively precisely two, directions. For these graphs we study the question of percolation, i.e. the existence of an infinite self-avoiding path. Using different kinds of proof techniques for different classes of cases, we show that for $k=1$ even the undirected k-neighbor graph never percolates, while the directed k-neighbor graph percolates whenever $k \geq d+1$, $k \geq 3$, and $d \geq 5$, or $k \geq 4$ and $d=4$. We also show that the undirected 2-neighbor graph percolates for $d=2$, the undirected 3-neighbor graph percolates for $d=3$, and we provide some positive and negative percolation results regarding the bidirectional graph as well. A heuristic argument for high dimensions indicates that this class of models is a natural discrete analogue of the k-nearest-neighbor graphs studied in continuum percolation, and our results support this interpretation.

Participation is a prevalent topic in many areas, and data-driven projects are no exception. While the term generally has positive connotations, ambiguities in participatory approaches between facilitators and participants are often noted. However, how facilitators can handle these ambiguities has been less studied. In this paper, we conduct a systematic literature review of participatory data-driven projects. We analyse 27 cases regarding their openness for participation and where participation most often occurs in the data life cycle. From our analysis, we describe three typical project structures of participatory data-driven projects, combining a focus on labour and resource participation and/or rule- and decision-making participation with the general set-up of the project as participatory-informed or participatory-at-core. From these combinations, different ambiguities arise. We discuss mitigations for these ambiguities through project policies and procedures for each type of project. Mitigating and clarifying ambiguities can support a more transparent and problem-oriented application of participatory processes in data-driven projects.

Spoken term discovery (STD) is challenging when a large volume of spoken content is generated without annotations. Unsupervised approaches resolve this challenge by directly computing pattern matches from the acoustic feature representation of the speech signal. However, this approach produces a lot of false alarms due to inherent speech variabilities, leading to performance degradation in the STD task. To overcome these challenges and improve performance, we propose a two-stage approach. First, we identify an acoustic feature representation that emphasizes spoken content irrespective of the variability challenge. Second, we employ the proposed diagonal pattern search to capture spoken term matches in an unsupervised way without any transcriptions. The proposed approach validated using Microsoft Speech Corpus for Low-Resource languages reveals that an 18% gain in hit ratio and 37% reduction in the false alarm ratio was achieved compared with the state-of-the-art methods.

Leptospirosis in NZ has historically been associated with male workers in livestock industries; however, the disease epidemiology is changing. This study identified risk factors amid these shifts. Participants (95 cases:300 controls) were recruited nationwide between 22 July 2019 and 31 January 2022, and controls were frequency-matched by sex (90% male) and rurality (65% rural). Multivariable logistic regression models, adjusted for sex, rurality, age, and season—with one model additionally including occupational sector—identified risk factors including contact with dairy cattle (aOR 2.5; CI: 1.0–6.0), activities with beef cattle (aOR 3.0; 95% CI: 1.1–8.2), cleaning urine/faeces from yard surfaces (aOR 3.9; 95% CI: 1.5–10.3), uncovered cuts/scratches (aOR 4.6; 95% CI: 1.9–11.7), evidence of rodents (aOR 2.2; 95% CI: 1.0–5.0), and work water supply from multiple sources—especially creeks/streams (aOR 7.8; 95% CI: 1.5–45.1) or roof-collected rainwater (aOR 6.6; 95% CI: 1.4–33.7). When adjusted for occupational sector, risk factors remained significant except for contact with dairy cattle, and slaughter without gloves emerged as a risk (aOR 3.3; 95% CI: 0.9–12.9). This study highlights novel behavioural factors, such as uncovered cuts and inconsistent glove use, alongside environmental risks from rodents and natural water sources.

In this paper, we study discrepancy questions for spanning subgraphs of $k$-uniform hypergraphs. Our main result is that, for any integers $k \ge 3$ and $r \ge 2$, any $r$-colouring of the edges of a $k$-uniform $n$-vertex hypergraph $G$ with minimum $(k-1)$-degree $\delta (G) \ge (1/2+o(1))n$ contains a tight Hamilton cycle with high discrepancy, that is, with at least $n/r+\Omega (n)$ edges of one colour. The minimum degree condition is asymptotically best possible and our theorem also implies a corresponding result for perfect matchings. Our tools combine various structural techniques such as Turán-type problems and hypergraph shadows with probabilistic techniques such as random walks and the nibble method. We also propose several intriguing problems for future research.

We describe an outbreak of Legionnaires’ disease linked to an exclusive cold-water source in a private residential setting in Yorkshire. The cold-water source was identified following microbiological testing of clinical and environmental samples. Legionella pneumophila was only detected in the cold-water system. Three cases were identified over the course of the outbreak: two confirmed and one probable. Conditions favourable to bacterial growth included system ‘dead legs’ and significant heat transfer to the cold-water system. We describe challenges in implementing control measures at the venue and highlight the importance of using enforcement powers, where necessary, to reduce risk.

For a spectrally negative Lévy process X, consider $g_t$ and its infinitesimal generator. Moreover, with $t\geq 0$, the last time X is below the level zero before time $\{(g_t,t, X_t), t\geq 0 \}$ the length of a current positive excursion, we derive a general formula that allows us to calculate a functional of the whole path of $U_t\,:\!=\,t-g_t$. We use a perturbation method for Lévy processes to derive an Itô formula for the three-dimensional process $ (U, X)=\{(U_t, X_t),t\geq 0\}$ in terms of the positive and negative excursions of the process X. As a corollary, we find the joint Laplace transform of $(U_{\mathbf{e}_q}, X_{\mathbf{e}_q})$, where $\mathbf{e}_q$ is an independent exponential time, and the q-potential measure of the process (U, X). Furthermore, using the results mentioned above, we find a solution to a general optimal stopping problem depending on (U, X) with an application in corporate bankruptcy. Lastly, we establish a link between the optimal prediction of $g_{\infty}$ and optimal stopping problems in terms of (U, X) as per Baurdoux, E. J. and Pedraza, J. M., $L_p$ optimal prediction of the last zero of a spectrally negative Lévy process, Annals of Applied Probability, 34 (2024), 1350–1402.