Analysis of a continuous-time adaptive voter model.

In this paper, we study a variant of the voter model on adaptive networks in which nodes can flip their spin, create new connections, or break existing connections. We first perform an analysis based on the mean-field approximation to compute asymptotic values for macroscopic estimates of the system, namely, the total mass of present edges in the system and the average spin. However, numerical results show that this approximation is not very suitable for such a system, for which it does not capture key features such as the network breaking into two disjoint and opposing (in spin) communities. Therefore, we propose another approximation based on an alternate coordinate system to improve accuracy and validate this model through simulations. Finally, we state a conjecture dealing with the qualitative properties of the system, corroborated by numerous numerical simulations.

Analysis of the Tradeoff Between Health and Economic Impacts of the Covid-19 Epidemic.

Various measures have been taken in different countries to mitigate the Covid-19 epidemic. But, throughout the world, many citizens don't understand well how these measures are taken and even question the decisions taken by their government. Should the measures be more (or less) restrictive? Are they taken for a too long (or too short) period of time? To provide some quantitative elements of response to these questions, we consider the well-known SEIR model for the Covid-19 epidemic propagation and propose a pragmatic model of the government decision-making operation. Although simple and obviously improvable, the proposed model allows us to study the tradeoff between health and economic aspects in a pragmatic and insightful way. Assuming a given number of phases for the epidemic (namely, 4 in this paper) and a desired tradeoff between health and economic aspects, it is then possible to determine the optimal duration of each phase and the optimal severity level (i.e., the target transmission rate) for each of them. The numerical analysis is performed for the case of France but the adopted approach can be applied to any country. One of the takeaway messages of this analysis is that being able to implement the optimal 4-phase epidemic management strategy in France would have led to 1.05 million of infected people and a GDP loss of 231 billions € instead of 6.88 millions of infected and a loss of 241 billions €. This indicates that, seen from the proposed model perspective, the effectively implemented epidemic management strategy is good economically, whereas substantial improvements might have been obtained in terms of health impact. Our analysis indicates that the lockdown/severe phase should have been more severe but shorter, and the adjustment phase occurred earlier. Due to the natural tendency of people to deviate from the official rules, updating measures every month over the whole epidemic episode seems to be more appropriate.

Study of Anatomical Variations of 1,2 Intercompartmental Supraretinacular Artery-Based Vascularized Bone Graft in Cadavers.

BACKGROUND: The aim of this study is to describe the anatomy of the 1,2 intercompartmental supraretinacular artery (1,2 ICSRA), including the location of the perforators, number of perforators, and proximal and distal origins of the artery. MATERIALS AND METHODS: The study was done by dissecting both wrists of 11 fresh-frozen cadavers. In each specimen, skin incision and dissections were done in the forearm by the Henry approach. Radial artery was identified and cannulated and dye was injected. The dye consisted of the mixture of polyvinyl chloride and acetone in the ratio of 1:4, to which red-colored resin was added. The artery of interest 1,2 ICSRA was dissected and its anatomical characteristics such as distal origin, proximal origin, number of perforators, and largest perforator were measured. RESULTS: Of the 22 wrists dissected, only in 19 wrists we were able to recognize the perforators. Average number of perforators seen was 3.05 (range 1-5). Average distance of the largest perforator from the radial styloid was 11.79 mm (range 6-19 mm). The average distance of the distal origin of 1,2 ICSRA from the radial styloid was 6.71 mm distal to radial styloid. It ranged from 16 mm distal to styloid process to 6 mm proximal to the styloid process. The average distance of proximal origin of 1,2 ICSRA from the radial styloid was 40.52 mm proximal to the radial styloid (range 25-66 mm). The maximum density of perforators of 2.84 was noticed to be in the region of 6-18 mm from the distal articular margin. CONCLUSION: The distal origin of 1,2 ICSRA in our study was much more distal in comparison to the western population. The detailed anatomy of the 1,2 ICSRA presented in this study may guide in planning and dissection to maximize the vascularity of a pedicled bone graft based on this vessel for the management of scaphoid nonunions and other carpal pathologies.