A method to construct trihamiltonian extensions of a separable system is presented. The procedure is tested for systems, with a natural Hamiltonian, separable in classical sense in one of the four orthogonal separable coordinate systems of the Euclidean plane, and some explicit examples are constructed. Finally a conjecture on possible generalizations to other classes of systems is discussed: i...

Hybrid Monte Carlo (HMC) is a rigorous sampling method that uses molecular dynamics as a global Monte Carlo move. The acceptance rate of HMC decays exponentially with system size. The Shadow Hybrid Monte Carlo (SHMC) was previously introduced to overcome this performance degradation by sampling instead from the shadow Hamiltonian defined for MD when using a symplectic integrator. We show that S...

We present a method for solving linear and nonlinear partial differential equations (PDE) based on the variable projection framework artificial neural networks. For PDEs, enforcing boundary/initial value problem collocation points gives rise to separable least squares about network coefficients. reformulate this by approach eliminate output-layer coefficients, leading reduced hidden-layer coeff...

in this paper, we will give necessary and sufficient conditions for certain hnnextensions of subgroup separable groups with normal associated subgroup to be conjugacyseparable. in fact, we will show that these hnn extensions are conjugacy separable if and onlyif the normalizer of one of its associated subgroup is conjugacy separable.

Despite the wide adoption of spike-and-slab methodology for Bayesian variable selection, its potential for penalized likelihood estimation has largely been overlooked. In this paper, we bridge this gap by cross-fertilizing these two paradigms with the Spike-and-Slab LASSO procedure for variable selection and parameter estimation in linear regression. We introduce a new class of self-adaptive pe...

Gaussian process emulator with separable covariance function has been utilized extensively in modelling large computer model outputs. The assumption of separability imposes constraints on the emulator and may negatively affect its performance in some applications where separability may not hold. We propose a multi-output Gaussian process emulator with a nonseparable autocovariance function to a...