The growing concern over cyber risk has become a pivotal issue in the business world. Firms can mitigate this risk through two primary strategies: investing in cybersecurity practices and purchasing cyber insurance. Cybersecurity investments reduce the compromise probability, while cyber insurance transfers potential losses to insurers. This study employs a network model for the spread of infection among interconnected firms and investigates how each firm’s decisions impact each other. We analyze a non-cooperative game in which each firm aims to optimize its objective function through choices of cybersecurity level and insurance coverage ratio. We find that each firm’s cybersecurity investment and insurance purchase are strategic complements. Within this game, we derive sufficient conditions for the existence and uniqueness of Nash equilibrium and demonstrate its inefficiency. These theoretical results form the foundation for our numerical studies, allowing us compute firms’ equilibrium decisions on cybersecurity investments and insurance purchases across various network structures. The numerical results shed light on the impact of network structure on equilibrium decisions and explore how varying insurance premiums influence firms’ cybersecurity investments.

We examine the gravity-driven flow of a thin film of viscous fluid spreading over a rigid plate that is lubricated by another viscous fluid. We model the flow over such a ‘soft’ substrate by applying the principles of lubrication theory, assuming that vertical shear provides the dominant resistance to the flow. We do so in axisymmetric and two-dimensional geometries in settings in which the flow is self-similar. Different flow regimes arise, depending on the values of four key dimensionless parameters. As the viscosity ratio varies, the behaviour of the intruding layer ranges from that of a thin coating film, which exerts negligible traction on the underlying layer, to a very viscous gravity current spreading over a low-viscosity, near-rigid layer. As the density difference between the two layers approaches zero, the nose of the intruding layer steepens, approaching a shock front in the equal-density limit. We characterise a frontal stress singularity, which forms near the nose of the intruding layer, by performing an asymptotic analysis in a small neighbourhood of the front. We find from our asymptotic analysis that unlike single-layer viscous gravity currents, which exhibit a cube-root frontal singularity, the nose of a viscous gravity current propagating over another viscous fluid instead exhibits a square-root singularity, to leading order. We also find that large differences in the densities between the two fluids give rise to flows similar to that of thin films of a single viscous fluid spreading over a rigid, yet mobile, substrate.

During the investigation of parasitic pathogens of Mytilus coruscus, infection of a Perkinsus-like protozoan parasite was detected by alternative Ray's Fluid Thioglycolate Medium (ARFTM). The diameter of hypnospores or prezoosporangia was 8–27 (15.6 ± 4.0, n = 111) μm. The prevalence of the Perkinsus-like species in M. coruscus was 25 and 12.5% using ARFTM and PCR, respectively. The ITS1-5.8S-ITS2 fragments amplified by PCR assay had 100% homology to that of P. beihaiensis, suggesting that the protozoan parasite was P. beihaisensis and M. coruscus was its new host in East China Sea (ECS). Histological analysis showed the presence of trophozoites of P. beihaiensis in gill, mantle and visceral mass, and the schizonts only found in visceral mass. Perkinsus beihaiensis infection led to inflammatory reaction of hemocyte and the destruction of digestive tubules in visceral mass, which had negative effect on health of the farmed M. coruscus and it deserves more attention.

Ridge B is one of the least studied areas in Antarctica but has been considered to be a potential location for the oldest ice on Earth. Among important parameters for calculating where very old ice may exist, geothermal heat flux (GHF) is critical but poorly understood. Here, GHF is determined by quantifying the transitions between dry and wet basal conditions using a radioglaciological method applied to airborne radio-echo sounding data. GHF is then constrained by a thermodynamic model matched to the transitions. The results show that GHF in Ridge B varies locally and ranges from 48.5 to 65.1 mW m−2, with an average value of 58.0 mW m−2, which is consistent with the current known GHF constrained by subglacial lakes and derived from Vostok ice core temperature measurements. Our work highlights the value of considering local GHF when locating the oldest ice in this potential region or other regions.

This study examines the pursuit-evasion game involving unmanned aerial vehicles (UAVs), with a specific focus on the scenario of N-pursuers-one-escapee. The primary objective is to develop an optimal strategy for the escapee when the pursuers possess superior capabilities. To obtain this objective, we conduct the following study. Firstly, to enhance realism, a non-cooperative differential game model is formulated, incorporating multiple motion characteristics, including aerodynamics, overloading, and imposed constraints. Secondly, the end-value performance index is subsequently converted to an integral one, simplifying the solution process of the Hamilton-Jacobi-Bellman (HJB) equation. An iterative method is utilised to determine the covariates using the Cauchy initial value problem, and its convergence and uniqueness are established. The optimal avoidance strategy is subsequently derived from the covariates. Finally, the superiority of the proposed strategy is validated through simulation experiments and compared to three advanced optimal avoidance strategies. A total of 1,000 anti-jamming simulation experiments are conducted to verify the robustness of the proposed strategy.

Syphilis remains a serious public health problem in mainland China that requires attention, modelling to describe and predict its prevalence patterns can help the government to develop more scientific interventions. The seasonal autoregressive integrated moving average (SARIMA) model, long short-term memory network (LSTM) model, hybrid SARIMA-LSTM model, and hybrid SARIMA-nonlinear auto-regressive models with exogenous inputs (SARIMA-NARX) model were used to simulate the time series data of the syphilis incidence from January 2004 to November 2023 respectively. Compared to the SARIMA, LSTM, and SARIMA-LSTM models, the median absolute deviation (MAD) value of the SARIMA-NARX model decreases by 352.69%, 4.98%, and 3.73%, respectively. The mean absolute percentage error (MAPE) value decreases by 73.7%, 23.46%, and 13.06%, respectively. The root mean square error (RMSE) value decreases by 68.02%, 26.68%, and 23.78%, respectively. The mean absolute error (MAE) value decreases by 70.90%, 23.00%, and 21.80%, respectively. The hybrid SARIMA-NARX and SARIMA-LSTM methods predict syphilis cases more accurately than the basic SARIMA and LSTM methods, so that can be used for governments to develop long-term syphilis prevention and control programs. In addition, the predicted cases still maintain a fairly high level of incidence, so there is an urgent need to develop more comprehensive prevention strategies.

Background: The formation of pial-pial collateral network aneurysms due to carotid occlusion is a rare neurological phenomenon. This case details a 69-year-old male who developed a pial-pial collateral network aneurysm secondary to left internal carotid artery occlusion, leading to intracranial hemorrhage. Methods: The patient presented with altered consciousness due to left temporal intracerebral hemorrhage, subdural hematoma, and intraventricular hemorrhage. Cerebral angiography revealed an occluded left internal carotid artery, with superficial temporal artery (STA) and superior orbital artery anastomosis, and extensive pial-pial collaterals from the posterior temporal artery. A 4 mm aneurysm arising from this collateral network was identified. Surgical intervention involved a left temporal craniectomy and excision of the aneurysm, prioritizing the preservation of the STA. N.B., Informed patient consent was obtained in this study. Results: Successful aneurysm removal and preservation of collateral pathways were confirmed by postoperative imaging. The patient exhibited rapid neurological improvement; by postoperative day (POD) one, the patient showed limited response to stimuli. He was extubated by POD4 and discharged on POD27, where he conversed well, was independently ambulatory, and needed minimal to no assistance in activities of daily living. Conclusions: This case highlights the need for careful preoperative planning and intraoperative precision, especially in preserving vital collateral vascular pathways.

Background: The diagnosis of leptomeningeal metastatic disease has major prognostic implications. We report 13 patients with a radiologically distinct, focal, enhancing leptomeningeal lesion on brain MRI mimicking leptomeningeal metastatic disease. Methods: These patients were assessed at University Health Network between January 2001 and December 2023. Results: Median age was 68 years and 10 patients were women. All patients had brain MRI including contrast-enhanced T2-weighted FLAIR and T1-weighted spin echo sequences. MRI in all patients showed a focal enhancing lesion along the leptomeningeal surface of the brain. The MRI exams were reported as possible metastatic disease for the majority (9/13) of patients. Each lesion was curvilinear rather than sheet-like, and some consisted of multiple connected/branching curvilinear structures with the appearance of abnormal vessels. Some lesions had visible connection with a nearby cortical vein. The lesions were distinct from normal blood vessels. Follow-up contrast-enhanced brain MRI for 8/13 patients at a median of 3.9 years showed all lesions were unchanged over time. Conclusions: We describe a distinct kind of focal, enhancing leptomeningeal lesion on brain MRI that mimics metastatic disease. These lesions are likely a type of low-flow vascular anomaly. Their curvilinear/branching shape and intense enhancement particularly on T2-weighted FLAIR images distinguishes these lesions from tumor.

Background: Prolonged length of stay (LOS) after elective spine surgery increases patients’ risk for in-hospital complications and contributes significantly to healthcare costs. Here we explored the role of pain control and other perioperative factors on LOS. Methods: Consecutive adult patients undergoing elective spine surgery were enrolled. The primary outcome was in-hospital LOS following surgery. The primary independent variable was poor pain control on postoperative day 1 (POD1). Univariable analyses followed by multivariable regression analysis were used to investigate the relationship between poor pain control and LOS. Results: 1305 patients were enrolled. Mean LOS was 4.38 days. Incidence of poor pain control was 56.9%. Multivariable analysis revealed poor POD1 pain control was significantly associated with increased LOS (p=0.03), after adjusting for other significant predictors of increased LOS including perioperative hemodynamic instability (p=0.001), perioperative blood transfusion (p=0.000), delirium (p=0.000), POD1 morphine equivalent dose (p=0.000), urinary tract infection (p=0.000), urinary retention (p=0.003), surgical site infection (p=0.000), wound complication (p=0.000), neurologic deterioration (p=0.000), surgical levels (p=0.016), operative time (p=0.007), ASA score (p=0.000), preoperative disability score (p=0.001). Conclusions: Poor pain control on POD1 was an independent predictor of increased LOS after elective spine surgery, highlighting the importance of a proactive approach to addressing pain in the immediate postoperative period.