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Through the action of an anti-holomorphic involution $\sigma$ (a real structure) on a Riemann surface $X$, we consider the induced actions on ${\rm SL}(r,\mathbb{C})$-opers and study the real slices fixed by such actions. By constructing this involution for different descriptions of the space of ${\rm SL}(r,\mathbb{C})$-opers, we are able to give a natural parametrization of the fixed point locus via differentials on the Riemann surface, which in turn allows us to study their geometric properties.

 

A dramatic increase in the number of outbreaks of dengue has recently been reported, and climate change is likely to extend the geographical spread of the disease. In this context, this paper shows how a neural network approach can incorporate dengue and COVID-19 data as well as external factors (such as social behaviour or climate variables), to develop predictive models that could improve our knowledge and provide useful tools for health policy makers. Through the use of neural networks with different social and natural parameters, in this paper we define aCorrelation Modelthrough which we show that the number of cases of COVID-19 and dengue have very similar trends. We then illustrate the relevance of our model by extending it to a Long short-term memory model (LSTM) that incorporates both diseases, and using this to estimate dengue infections via COVID-19 data in countries that lack sufficient dengue data.

 

This paper presents a novel biologically-inspired explore-and-fuse approach to solving a large array of problems. The inspiration comes from Physarum, a unicellular slime mold capable of solving the traveling salesman and Steiner tree problems. Besides exhibiting individual intelligence,Physarumcan also share information with otherPhysarumorganisms through fusion. These characteristics of Physarum imply that spawning many such organisms we can explore the problem space in parallel, each individual gathering information and forming partial solutions pertaining to a local region of the problem space. When the organisms meet, they fuse and share information, eventually forming one organism which has a global view of the problem and can apply its intelligence to find an overall solution to the problem. This approach can be seen as a “softer” method of divide and conquer. We demonstrate this novel approach, developing thePhysarum Steiner Algorithmwhich is capable of finding feasible solutions to the Euclidean Steiner tree problem. This algorithm is of particular interest due to its resemblance toPhysarum polycephalum, ability to leverage parallel processing, avoid obstacles, and operate on various shapes and topological surfaces including the rectilinear grid.

 

Physarum polycephalum is a unicellular slime mould that has been intensely studied owing to its ability to solve mazes, find shortest paths, generate Steiner trees, share knowledge and remember past events and the implied applications to unconventional computing. The CELL model is a cellular automaton introduced in Gunji et al . (Gunji et al. 2008 J. Theor. Biol. 253 , 659–667 ( doi:10.1016/j.jtbi.2008.04.017 )) that models Physarum ’s amoeboid motion, tentacle formation, maze solving and network creation. In the present paper, we extend the CELL model by spawning multiple CELLs, allowing us to understand the interactions between multiple cells and, in particular, their mobility, merge speed and cytoplasm mixing. We conclude the paper with some notes about applications of our work to modelling the rise of present-day civilization from the early nomadic humans and the spread of trends and information around the world. Our study of the interactions of this unicellular organism should further the understanding of how P. polycephalum communicates and shares information. 

Abstract We present a modified age-structured SIR model based on known patterns of social contact and distancing measures within Washington, USA. We find that population age-distribution has a significant effect on disease spread and mortality rate, and contribute to the efficacy of age-specific contact and treatment measures. We consider the effect of relaxing restrictions across less vulnerable age-brackets, comparing results across selected groups of varying population parameters. Moreover, we analyze the mitigating effects of vaccinations and examine the effectiveness of age-targeted distributions. Lastly, we explore how our model can applied to other states to reflect social-distancing policy based on different parameters and metrics. 

Through the triality of SO(8,C), we study three interrelated homogeneous basis of the ring of invariant polynomials of Lie algebras, which give the basis of three Hitchin fibrations, and identify the explicit automorphisms that relate them.