We apply the Painlevé test for integrability of partial differential equations to a system of two coupled Burgers-type equations found by Foursov, which was recently shown by Sergyeyev to possess infinitely many commuting local generalized symmetries without any recursion operator. The Painlevé analysis easily detects that this is a typical C-integrable system in the Calogero sense and rediscov...

Orthogonal approximate message-passing (OAMP) is proposed for signal recovery from right-orthogonally invariant linear measurements with spatial coupling. Conventional state evolution generalized to a unified framework of the coupling and long-memory case. The used formulate so-called Onsager correction in OAMP spatially coupled systems. recursion Bayes-optimal proved converge systems via its e...

We consider a Higgs boson coupled to gluons via the five-dimensional effective operator HtrGμνG μν . We treat H as the real part of a complex field φ that couples to the selfdual gluon field strengths and compute the one-loop corrections to the φ-MHV amplitudes involving φ, two negative helicity gluons and an arbitrary number of positive helicity gluons. Our results generalise earlier work wher...

We study the dependence of the intrinsic conductance of a nanocontact on its shape by using the recursion-transfer-matrix method. Hour-glass, torus, and spherical shapes are defined through analytic potentials, the latter two serving as rough models for ring-like and spherical molecules, respectively. The sensitivity of the conductance to geometric details is analyzed and discussed. Strong reso...

We consider a class of approximated message passing (AMP) algorithms and characterize their high-dimensional behavior in terms of a suitable state evolution recursion. Our proof applies to Gaussian matrices with independent but not necessarily identically distributed entries. It covers – in particular– the analysis of generalized AMP, introduced by Rangan, and of AMP reconstruction in compresse...

Inspired by Quantum Mechanics, we reformulate Hilbert’s tenth problem in the domain of integer arithmetics into problems involving either a set of infinitely-coupled non-linear differential equations or a class of linear Schrödinger equations with some appropriate timedependent Hamiltonians. We then raise the questions whether these two classes of differential equations are computable or not in...

The recursion relations of 2D quantum gravity coupled to the Ising model discussed by the author previously are reexamined. We study the case in which the matter sector satisfies the fusion rules and only the primary operators inside the Kac table contribute. The theory involves unregularized divergences in some of correlators. We obtain the recursion relations which form a closed set among wel...