Non-isospectral extension of the Volterra lattice hierarchy, and Hankel determinants

For the first two equations of the Volterra lattice hierarchy and the first two equations of its non-autonomous (non-isospectral) extension, we present Riccati systems for functions c_j(t), j=0,1,..., such that an expression in terms of Hankel determinants built from them solves these equations on the right half of the lattice. This actually achieves a complete linearization of these equations of the extended Volterra lattice hierarchy.Comment: 31 pages, 3rd version: introduction extended, part of Section 2 moved there, Appendix D added, additional references, to appear in Nonlinearit

Parameter-tuning Networks: Experiments and Active Walk Model

The tuning process of a large apparatus of many components could be represented and quantified by constructing parameter-tuning networks. The experimental tuning of the ion source of the neutral beam injector of HT-7 Tokamak is presented as an example. Stretched-exponential cumulative degree distributions are found in the parameter-tuning networks. An active walk model with eight walkers is constructed. Each active walker is a particle moving with friction in an energy landscape; the landscape is modified by the collective action of all the walkers. Numerical simulations show that the parameter-tuning networks generated by the model also give stretched exponential functions, in good agreement with experiments. Our methods provide a new way and a new insight to understand the action of humans in the parameter-tuning of experimental processes, is helpful for experimental research and other optimization problems.Comment: 4 pages, 5 figure

Optimal Vaccine Distribution Strategy for Different Age Groups of Population: A Differential Evolution Algorithm Approach

Vaccination is one of the effective ways for protecting susceptible individuals from infectious diseases. Different age groups of population have different vulnerability to the disease and different contact frequencies. In order to achieve the maximum effects, the distribution of vaccine doses to the groups of individuals needs to be optimized. In this paper, a differential evolution (DE) algorithm is proposed to address the problem. The performance of the proposed algorithm has been tested by a classical infectious disease transmission model and a series of simulations have been made. The results show that the proposed algorithm can always obtain the best vaccine distribution strategy which can minimize the number of infectious individuals during the epidemic outbreak. Furthermore, the effects of vaccination on different days and the vaccine coverage percentages have also been discussed

Bis[μ-1-(2-pyridylmeth­yl)-1H-benzo­triazole]disilver(I) bis­(perchlorate)

In the title centrosymmetric binuclear AgI complex, [Ag2(C12H10N4)2](ClO4)2, each AgI center is two-coordinated by one pyridine and one benzotriazole N-donor atom of two inversion-related 1-(2-pyridylmeth­yl)-1H-benzotriazole (L) ligands. This forms a unique box-like cyclic dimer with an intra­molecular Ag⋯Ag separation of 4.479 (2) Å. Inter­molecular C—H⋯O hydrogen-bonding inter­actions, involving uncoordinated ClO4 − ions, link the binuclear units, forming a two-dimensional network parallel to (10)