Multi-soliton Solutions of Two-dimensional Matrix Davey-Stewartson Equation

The explicit formulae for m-soliton solutions of (1+2)-dimensional matrix Davey-Stewartson equation are represented. They are found by means of known general solution of the matrix Toda chain with the fixed ends [1]. These solutions are expressed trough m+m independent solutions of a pair of linear Shrodinger equations with Hermitian potentials.Comment: 13 pages, uses article.st

Hopf algebras and Markov chains: Two examples and a theory

The operation of squaring (coproduct followed by product) in a combinatorial Hopf algebra is shown to induce a Markov chain in natural bases. Chains constructed in this way include widely studied methods of card shuffling, a natural "rock-breaking" process, and Markov chains on simplicial complexes. Many of these chains can be explictly diagonalized using the primitive elements of the algebra and the combinatorics of the free Lie algebra. For card shuffling, this gives an explicit description of the eigenvectors. For rock-breaking, an explicit description of the quasi-stationary distribution and sharp rates to absorption follow.Comment: 51 pages, 17 figures. (Typographical errors corrected. Further fixes will only appear on the version on Amy Pang's website, the arXiv version will not be updated.

A review of spatial causal inference methods for environmental and epidemiological applications

The scientific rigor and computational methods of causal inference have had great impacts on many disciplines, but have only recently begun to take hold in spatial applications. Spatial casual inference poses analytic challenges due to complex correlation structures and interference between the treatment at one location and the outcomes at others. In this paper, we review the current literature on spatial causal inference and identify areas of future work. We first discuss methods that exploit spatial structure to account for unmeasured confounding variables. We then discuss causal analysis in the presence of spatial interference including several common assumptions used to reduce the complexity of the interference patterns under consideration. These methods are extended to the spatiotemporal case where we compare and contrast the potential outcomes framework with Granger causality, and to geostatistical analyses involving spatial random fields of treatments and responses. The methods are introduced in the context of observational environmental and epidemiological studies, and are compared using both a simulation study and analysis of the effect of ambient air pollution on COVID-19 mortality rate. Code to implement many of the methods using the popular Bayesian software OpenBUGS is provided

Pulsar Wind Nebulae with Bow Shocks: Non-thermal Radiation and Cosmic Ray Leptons

Pulsars with high spin-down power produce relativistic winds radiating a non-negligible fraction of this power over the whole electromagnetic range from radio to gamma-rays in the pulsar wind nebulae (PWNe). The rest of the power is dissipated in the interactions of the PWNe with the ambient interstellar medium (ISM). Some of the PWNe are moving relative to the ambient ISM with supersonic speeds producing bow shocks. In this case, the ultrarelativistic particles accelerated at the termination surface of the pulsar wind may undergo reacceleration in the converging flow system formed by the plasma outflowing from the wind termination shock and the plasma inflowing from the bow shock. The presence of magnetic perturbations in the flow, produced by instabilities induced by the accelerated particles themselves, is essential for the process to work. A generic outcome of this type of reacceleration is the creation of particle distributions with very hard spectra, such as are indeed required to explain the observed spectra of synchrotron radiation with photon indices Γ≲ 1.5. The presence of this hard spectral component is specific to PWNe with bow shocks (BSPWNe). The accelerated particles, mainly electrons and positrons, may end up containing a substantial fraction of the shock ram pressure. In addition, for typical ISM and pulsar parameters, the e+ released by these systems in the Galaxy are numerous enough to contribute a substantial fraction of the positrons detected as cosmic ray (CR) particles above few tens of GeV and up to several hundred GeV. The escape of ultrarelativistic particles from a BSPWN—and hence, its appearance in the far-UV and X-ray bands—is determined by the relative directions of the interstellar magnetic field, the velocity of the astrosphere and the pulsar rotation axis. In this respect we review the observed appearance and multiwavelength spectra of three different types of BSPWNe: PSR J0437-4715, the Guitar and Lighthouse nebulae, and Vela-like objects. We argue that high resolution imaging of such objects provides unique information both on pulsar winds and on the ISM. We discuss the interpretation of imaging observations in the context of the model outlined above and estimate the BSPWN contribution to the positron flux observed at the Earth