Multifidelity approximate Bayesian computation (MF-ABC) is a likelihood-free technique for parameter inference that exploits model approximations to significantly increase the speed of ABC algorithms [T. P. Prescott and R. E. Baker, SIAM/ASA J. Uncertain. Quantif., 8 (2020), pp. 114--138]. Previous work has considered MF-ABC only in context rejection sampling, which does not explore space parti...

Suppose A, B, C, D, E, F are points and L is a line other than the line at infinity. This work examines cases in which a translation D′E′F ′ of DEF in the direction of L is perspective to ABC, in the sense that the lines AD′, BE′, CF ′ concur.

Let K,L,M be orthogonal projections of a point P onto the sides of a triangle ABC. Then the locus of P such that K,L,M are collinear, is the circumcircle of ABC. This theorem has several generalizations [4], [5], [10],[6], [7], [9]. A generalization of the Simson–Wallace theorem which is by [2] ascribed to J. D. Gergonne is as follows: Let K,L,M be orthogonal projections of a point P onto the s...

Among topological descriptors connectivity topological indices are very important and they have a prominent role in chemistry. One of them is atom-bond connectivity (ABC) index defined as ABC(G)= [formula:see text], in which degree of vertex v denoted by dv . Recently, a new version of atom-bond connectivity (ABC4) index was introduced by M. Ghorbani et.al in 2010 and is defined as ABC4(G)= [fo...

Abstract Likelihood-free inference provides a rigorous approach to performing Bayesian analysis using forward simulations only. The main advantage of likelihood-free methods is their ability account for complex physical processes and observational effects in simulations. Here we explore the potential modeling cosmological redshift evolution cluster abundance combined with weak-lensing mass cali...