We analyse the convergence to stationarity of a simple non-reversible Markov chain that serves as a model for several non-reversible Markov chain sampling methods that are used in practice. Our theoretical and numerical results show that non-reversibility can indeed lead to improvements over the diiusive behavior of simple Markov chain sampling schemes. The analysis uses both probabilistic tech...

An analytical solution is provided to the problem of minimising a convex quadratic under a general quadratic (inequality) constraint, additional affine constraints being easily accommodated. Such problems occur widely. The explicit, analytical solution provided offers insight into the diverse nature both of special cases of this problem and of their solution sets. This sheds light on algorithm ...

In principle, it is straightforward to compute the vibrational spectrum of a molecule without neglecting coupling and anharmonicity: one must calculate eigenvalues and eigenvectors of a matrix representing the Hamiltonian in an appropriate basis. In practice, this is difficult because the matrix is very large. To obviate the N memory and N CPU costs of standard diagonalisation methods, it is no...

Constructor rewriting systems are said to be cons-free if any constructor term occurring in the rhs of a rule must be a subterm of the lhs of the rule. Roughly, such systems cannot build new data structures during their evaluation. In earlier work by several authors, (typed) cons-free systems have been used to characterise complexity classes such as polynomial or exponential time or space by va...

We study the asymptotic scaling of the entanglement of a block of spins for the ground state of the one-dimensional quantum Ising model with transverse field. When the field is sufficiently strong, the entanglement grows at most logarithmically in the number of spins. The proof utilises a transformation to a model of classical probability called the continuum random-cluster model, and is based ...

We study the asymptotic scaling of the entanglement of a block of spins for the ground state of the one-dimensional quantum Ising model with transverse field. When the field is sufficiently strong, the entanglement grows at most logarithmically in the number of spins. The proof utilises a transformation to a model of classical probability called the continuum random-cluster model, and is based ...

Sparse coding remains a core building block in many data analysis and machine learning pipelines. Typically it is solved by relying on generic optimization techniques, that are optimal in the class of first-order methods for non-smooth, convex functions, such as the Iterative Soft Thresholding Algorithm and its accelerated version (ISTA, FISTA). However, these methods don’t exploit the particul...