scholarly journals Statistical connections on decomposable Riemann manifold

2020 ◽  
Vol 5 (5) ◽  
pp. 4722-4733
Author(s):  
Cagri Karaman ◽  
Keyword(s):  
Riemann Manifold

Jacobi fields on a Riemann manifold

2006 ◽  
Vol 58 (12) ◽  
pp. 1818-1833
Author(s):  
V. G. Bondarenko
Keyword(s):  
Riemann Manifold ◽  
Jacobi Fields

scholarly journals Markov chain Monte Carlo inference for Markov jump processes via the linear noise approximation

2013 ◽  
Vol 371 (1984) ◽  
pp. 20110541 ◽  
Author(s):  
Vassilios Stathopoulos ◽  
Mark A. Girolami
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Jump Processes ◽  
Mcmc Methods ◽  
Computationally Efficient ◽  
Markov Jump ◽  
Riemann Manifold ◽  
Exact Inference ◽  
Markov Jump Processes

Bayesian analysis for Markov jump processes (MJPs) is a non-trivial and challenging problem. Although exact inference is theoretically possible, it is computationally demanding, thus its applicability is limited to a small class of problems. In this paper, we describe the application of Riemann manifold Markov chain Monte Carlo (MCMC) methods using an approximation to the likelihood of the MJP that is valid when the system modelled is near its thermodynamic limit. The proposed approach is both statistically and computationally efficient whereas the convergence rate and mixing of the chains allow for fast MCMC inference. The methodology is evaluated using numerical simulations on two problems from chemical kinetics and one from systems biology.

scholarly journals Contact Metric Spaces and pseudo-Hermitian Symmetry

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1583
Author(s):  
Jong Taek Cho
Keyword(s):  
Symmetric Space ◽  
Metric Spaces ◽  
Classification Theorem ◽  
Riemann Manifold ◽  
Cr Manifolds ◽  
Pseudo Convex ◽  
Cauchy Riemann

We prove that a contact strongly pseudo-convex CR (Cauchy–Riemann) manifold M2n+1, n≥2, is locally pseudo-Hermitian symmetric and satisfies ∇ξh=μhϕ, μ∈R, if and only if M is either a Sasakian locally ϕ-symmetric space or a non-Sasakian (k,μ)-space. When n=1, we prove a classification theorem of contact strongly pseudo-convex CR manifolds with pseudo-Hermitian symmetry.

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