Spectral triples and quantum statistical mechanical systems are two important constructions in noncommutative geometry. In particular, both lead to interesting reconstruction theorems for a broad range of geometric objects, including number fields, spin manifolds, graphs. There are similarities between the two structures, and we show that the notion of type III σspectral triple, introduced rece...

Noncommutative geometric gauge theory is reconstructed based on the superconnection concept. The bosonic action of the Connes-Lott model including the symmetry breaking Higgs sector is obtained by using a new generalized derivative, which consists of the usual 1-form exterior derivative plus an extra element called the matrix derivative, for the curvatures. We first derive the matrix derivative...

Differential structure of a d-dimensional lattice, which is essentially a noncommutative exterior algebra, is defined using reductions in first order and second order of universal differential calculus in the context of noncommutative geometry(NCG) developed by Dimakis et al. This differential structure can be realized adopting a Dirac-Connes operator proposed by us recently within Connes’ NCG....

Abstract In this work, the surrogate model of collapse load in terms structural morphology is established based on radial basis function (RBF) network, and form-finding optimization fabricated single-layer grid shell aiming at improvement collapse-resistance capacity realized. To improve accuracy optimal solution, density used to determine sparse region design domain add new sample points regio...

Statisticians often use Monte Carlo methods to approximate probability distributions, primarily with Markov chain and importance sampling. Sequential samplers are a class of algorithms that combine both techniques distributions interest their normalizing constants. These originate from particle filtering for state space models have become general scalable sampling techniques. This article descr...