Partial islands and subregion complexity in geometric secret-sharing model

We compute the holographic subregion complexity of a radiation subsystem in a geometric secret-sharing model of Hawking radiation in the “complexity = volume” proposal. The model is constructed using multiboundary wormhole geometries in AdS3. The entanglement curve for secret-sharing captures a crossover between two minimal curves in the geometry apart from the usual eternal Page curve present for the complete radiation entanglement. We compute the complexity dual to the secret-sharing minimal surfaces and study their “time” evolution. When we have access to a small part of the radiation, the complexity shows a jump at the secret-sharing time larger than the Page time. Moreover, the minimal surfaces do not have access to the entire island region for this particular case. They can only access it partially. We describe this inaccessibility in the context of “classical” Markov recovery.

Variational model of scoliosis

Scoliosis, being one of the most widespread spinal diseases among children, has been studied extensively throughout the history of medicine, yet there is no clear understanding of its initiating factors and the mechanogenesis of the monomorphic three-dimensional deformation due to its polyetiological nature. We present a novel mathematical model of the process of emergence of the three-dimensional deformation of the human spine based on variational principles. Typical scoliosis geometry is assumed to be described as minimal curves of a particular energy functional, which are shown to closely resemble actual scoliosis. We investigate the numerical properties of the first stage of scoliosis, which is shown to have the highest influence on the development of the disease.