Layer reinsurance treaty is a common form obtained in the problem of optimal reinsurance design. In this paper, we study allocations of policy limits in layer reinsurance treaties with dependent risks. We investigate the effects of orderings and heterogeneity among policy limits on the expected utility functions of the terminal wealth from the viewpoint of risk-averse insurers faced with right tail weakly stochastic arrangement increasing losses. Orderings on optimal allocations are presented for normal layer reinsurance contracts under certain conditions. Parallel studies are also conducted for randomized layer reinsurance contracts. As a special case, the worst allocations of policy limits are also identified when the exact dependence structure among the losses is unknown. Numerical examples are presented to shed light on the theoretical findings.

A $(p,q)$-colouring of a graph $G$ is an edge-colouring of $G$ which assigns at least $q$ colours to each $p$-clique. The problem of determining the minimum number of colours, $f(n,p,q)$, needed to give a $(p,q)$-colouring of the complete graph $K_n$ is a natural generalization of the well-known problem of identifying the diagonal Ramsey numbers $r_k(p)$. The best-known general upper bound on $f(n,p,q)$ was given by Erdős and Gyárfás in 1997 using a probabilistic argument. Since then, improved bounds in the cases where $p=q$ have been obtained only for $p\in \{4,5\}$, each of which was proved by giving a deterministic construction which combined a $(p,p-1)$-colouring using few colours with an algebraic colouring.

In this paper, we provide a framework for proving new upper bounds on $f(n,p,p)$ in the style of these earlier constructions. We characterize all colourings of $p$-cliques with $p-1$ colours which can appear in our modified version of the $(p,p-1)$-colouring of Conlon, Fox, Lee, and Sudakov. This allows us to greatly reduce the amount of case-checking required in identifying $(p,p)$-colourings, which would otherwise make this problem intractable for large values of $p$. In addition, we generalize our algebraic colouring from the $p=5$ setting and use this to give improved upper bounds on $f(n,6,6)$ and $f(n,8,8)$.

Hyperbolic random graphs (HRGs) and geometric inhomogeneous random graphs (GIRGs) are two similar generative network models that were designed to resemble complex real-world networks. In particular, they have a power-law degree distribution with controllable exponent $\beta$ and high clustering that can be controlled via the temperature $T$.

We present the first implementation of an efficient GIRG generator running in expected linear time. Besides varying temperatures, it also supports underlying geometries of higher dimensions. It is capable of generating graphs with ten million edges in under a second on commodity hardware. The algorithm can be adapted to HRGs. Our resulting implementation is the fastest sequential HRG generator, despite the fact that we support non-zero temperatures. Though non-zero temperatures are crucial for many applications, most existing generators are restricted to $T = 0$. We also support parallelization, although this is not the focus of this paper. Moreover, we note that our generators draw from the correct probability distribution, that is, they involve no approximation.

Besides the generators themselves, we also provide an efficient algorithm to determine the non-trivial dependency between the average degree of the resulting graph and the input parameters of the GIRG model. This makes it possible to specify the desired expected average degree as input.

Moreover, we investigate the differences between HRGs and GIRGs, shedding new light on the nature of the relation between the two models. Although HRGs represent, in a certain sense, a special case of the GIRG model, we find that a straightforward inclusion does not hold in practice. However, the difference is negligible for most use cases.

Digital identity systems are promoted with the promise of great benefit and inclusion. The case of the Ugandan digital identity system demonstrates that the impact of digital identity systems is not only positive but also has negative impacts, significantly affecting human lives for the worse. The impact on the human lives of digital identity systems can be assessed by multiple frameworks. A specific framework that has been mentioned is the capabilities approach (CA). This article demonstrates that the CA is a framework to assess the impact on human lives that can be operationalized for technology and information and communication technology, including digital identity systems. Further research is required to compare the CA with other candidate evaluation frameworks.

This paper provides an examination of inter-organizational collaboration in the UK research system. Data are collected on organizational collaboration on projects funded by four key UK research councils: Arts and Humanities Research Council, Economic and Social Research Council, Engineering and Physical Sciences Research Council, and Biotechnology and Biological Sciences Research Council. The organizational partnerships include both academic and nonacademic institutions. A collaboration network is created for each research council, and an exponential random graph model is applied to inform on the mechanisms underpinning collaborative tie formation on research council-funded projects. We find that in the sciences, collaborative patterns are much more hierarchical and concentrated in a small handful of actors compared to the social sciences and humanities projects. Institutions that are members of the elite Russell Group (a set of 24 high-ranking UK universities) are much more likely to be involved in collaborations across research councils.

In this paper, we identify some conditions to compare the largest order statistics from resilience-scale models with reduced scale parameters in the sense of mean residual life order. As an example of the established result, the exponentiated generalized gamma distribution is examined. Also, for the special case of the scale model, power-generalized Weibull and half-normal distributions are investigated.

This paper is devoted to the study of the asset allocation problem for a DC pension plan with minimum guarantee constraint in a hidden Markov regime-switching economy. Suppose that four types of assets are available in the financial market: a risk-free asset, a zero-coupon bond, an inflation-indexed bond and a stock. The expected return rate of the stock depends on unobservable economic states, and the change of states is described by a hidden Markov chain. In addition, the CIR process is used to describe the evolution of the nominal interest rate. The contribution rate is also assumed to be stochastic. The goal of investment management is to minimize the convex risk measure of the terminal wealth in excess of the minimum guarantee constraint. First, we transform the partially observable optimization problem into the one with complete information using the Wonham filtering technique and deal with the minimum guarantee constraint by constructing auxiliary processes. Furthermore, we derive the optimal investment strategy by the BSDE approach. Finally, some numerical results are presented to illustrate the impacts of some important parameters on investment behaviors.

We study a multivariate system over a finite lifespan represented by a Hermitian-valued random matrix process whose eigenvalues (i) interact in a mean-field way and (ii) converge to their weighted ensemble average at their terminal time. We prove that such a system is guaranteed to converge in time to the identity matrix that is scaled by a Gaussian random variable whose variance is inversely proportional to the dimension of the matrix. As the size of the system grows asymptotically, the eigenvalues tend to mutually independent diffusions that converge to zero at their terminal time, a Brownian bridge being the archetypal example. Unlike commonly studied random matrices that have non-colliding eigenvalues, the proposed eigenvalues of the given system here may collide. We provide the dynamics of the eigenvalue gap matrix, which is a random skew-symmetric matrix that converges in time to the $\textbf{0}$ matrix. Our framework can be applied in producing mean-field interacting counterparts of stochastic quantum reduction models for which the convergence points are determined with respect to the average state of the entire composite system.

Following the report of the first COVID-19 case in Nepal on 23 January 2020, three major waves were documented between 2020 and 2021. By the end of July 2022, 986 596 cases of confirmed COVID-19 and 11 967 deaths had been reported and 70.5% of the population had received at least two doses of a COVID-19 vaccine. Prior to the pandemic, a large dengue virus (DENV) epidemic affected 68 out of 77 districts, with 17 932 cases and six deaths recorded in 2019. In contrast, the country's Epidemiology and Disease Control Division reported 530 and 540 dengue cases in the pandemic period (2020 and 2021), respectively. Furthermore, Kathmandu reported just 63 dengue cases during 2020 and 2021, significantly lower than the 1463 cases reported in 2019. Serological assay showed 3.2% positivity rates for anti-dengue immunoglobulin M antibodies during the pandemic period, contrasting with 26.9–40% prior to it. Real-time polymerase chain reaction for DENV showed a 0.5% positive rate during the COVID-19 pandemic which is far lower than the 57.0% recorded in 2019. Continuing analyses of dengue incidence and further strengthening of surveillance and collaboration at the regional and international levels are required to fully understand whether the reduction in dengue incidence/transmission were caused by movement restrictions during the COVID-19 pandemic.

In this study, a non-linear deterministic model for the transmission dynamics of skin sores (impetigo) disease is developed and analysed by the help of stability of differential equations. Some basic properties of the model including existence and positivity as well as boundedness of the solutions of the model are investigated. The disease-free and endemic equilibrium were investigated, as well as the basic reproduction number, R0, also calculated using the next-generation matrix approach. When R0 < 1, the model's stability analysis reveals that the system is asymptotically stable at disease-free critical point globally as well as locally. If R0 > 1, the system is asymptotically stable at disease-endemic equilibrium both locally and globally. The long-term behaviour of the skin sores model's steady-state solution in a population is investigated using numerical simulations of the model.

Mass gatherings (MG) present a number of challenges to public health authorities and governments across the world with sporting events, tournaments, music festivals, religious gatherings and all other MG having historically posed a risk to the spread and amplification of a range of infectious diseases. Transmission of gastrointestinal, respiratory, waterborne and sexually transmitted infectious diseases pose a particular risk: all have been linked to MG events [1–4]. Infection risk often depends on the nature of the mass gathering, and on the profile and behaviour of its participants. The interaction between environmental, psychological, biological and social factors plays a vital part. The risk of outbreaks particularly as a result of respiratory transmission remains high at MG, with the majority of outbreaks over the last two decades resulting from a variety of respiratory and vaccine preventable pathogens [5–7]. Concerns about the spread of infectious diseases at MG are often focussed on crowding, lack of sanitation and the mixing of population groups from different places. Sporting events, which have in recent decades become more complex and international in nature, pose a challenge to the control of communicable disease transmission [8]. Despite this, large scale outbreaks at sporting events have been rare in recent decades, particularly since the rise of more robust public health planning, prevention, risk assessment and improved health infrastructures in host countries [9].

Bacterial survival on, and interactions with, human skin may explain the epidemiological success of MRSA strains. We evaluated the bacterial counts for 27 epidemic and 31 sporadic MRSA strains on 3D epidermal models based on N/TERT cells (NEMs) after 1, 2 and 8 days. In addition, the expression of antimicrobial peptides (hBD-2, RNase 7), inflammatory cytokines (IL-1β, IL-6) and chemokine IL-8 by NEMs was assessed using immunoassays and the expression of 43 S. aureus virulence factors was determined by a multiplex competitive Luminex assay. To explore donor variation, bacterial counts for five epidemic and seven sporadic MRSA strains were determined on 3D primary keratinocyte models (LEMs) from three human donors. Bacterial survival was comparable on NEMs between the two groups, but on LEMs, sporadic strains showed significantly lower survival numbers compared to epidemic strains. Both groups triggered the expression of immune factors. Upon interaction with NEMs, only the epidemic MRSA strains expressed pore-forming toxins, including alpha-hemolysin (Hla), gamma-hemolysin (HlgB), Panton-Valentine leucocidin (LukS) and LukED. Together, these data indicate that the outcome of the interaction between MRSA and human skin mimics, depends on the unique combination of bacterial strain and host factors.

From 2016–2019, dry bulb onions were the suspected cause of three multistate outbreaks in the United States. We investigated a large multistate outbreak of Salmonella Newport infections that caused illnesses in both the United States and Canada in 2020. Epidemiologic, laboratory and traceback investigations were conducted to determine the source of the infections, and data were shared among U.S. and Canadian public health officials. We identified 1127 U.S. illnesses from 48 states with illness onset dates ranging from 19 June to 11 September 2020. Sixty-six per cent of ill people reported consuming red onions in the week before illness onset. Thirty-five illness sub-clusters were identified during the investigation and seventy-four per cent of sub-clusters served red onions to customers during the exposure period. Traceback for the source of onions in illness sub-clusters identified a common onion grower in Bakersfield, CA as the source of red onions, and onions were recalled at this time. Although other strains of Salmonella Newport were identified in environmental samples collected at the Bakersfield, CA grower, extensive environmental and product testing did not yield the outbreak strain. This was the third largest U.S. foodborne Salmonella outbreak in the last 30 years. It is the first U.S. multistate outbreak with a confirmed link to dry bulb onions, and it was nearly 10-fold larger than prior outbreaks with a suspected link to onions. This outbreak is notable for its size and scope, as well as the international data sharing that led to implication of red onions as the primary cause of the outbreak. Although an environmental assessment at the grower identified several factors that likely contributed to the outbreak, no main reason was identified. The expedient identification of the outbreak vehicle and response of multiple public health agencies allowed for recall and removal of product from the marketplace, and rapid messaging to both the public and industry on actions to protect consumers; these features contributed to a decrease in cases and expeditious conclusion of the outbreak.

The existence of moments of first downward passage times of a spectrally negative Lévy process is governed by the general dynamics of the Lévy process, i.e. whether it is drifting to $+\infty$, $-\infty$, or oscillating. Whenever the Lévy process drifts to $+\infty$, we prove that the $\kappa$th moment of the first passage time (conditioned to be finite) exists if and only if the $(\kappa+1)$th moment of the Lévy jump measure exists. This generalizes a result shown earlier by Delbaen for Cramér–Lundberg risk processes. Whenever the Lévy process drifts to $-\infty$, we prove that all moments of the first passage time exist, while for an oscillating Lévy process we derive conditions for non-existence of the moments, and in particular we show that no integer moments exist.