An autoencoder network uses a set of recognition weights to convert an input vector into a code vector. It then uses a set of generative weights to convert the code vector into an approximate reconstruction of the input vector. We derive an objective function for training autoencoders based on the Minimum Description Length (MDL) principle. The aim is to minimize the information required to des...

We prove first that for the Barycentric refinement G1 of a finite abstract simplicial complexG, the Gauss-Bonnet formula χ(G) = ∑ xK (x) holds, where K(x) = (−1)(1−χ(S(x))) is the curvature of a vertex x with unit sphere S(x) in the graph G1. This curvature is dual toK −(x) = (−1) for which GaussBonnet is the definition of Euler characteristic χ(G). Because the connection Laplacian L′ = 1+A′ of...

We present a new proof, using the log-sum inequality, that the pseudo-Helmholtz free energy function is a Lyapunov function for complex-balanced mass-action systems. This proof is shorter and simpler than previous proofs.

Preferential flow in biological soil structures is of key importance for infiltration and soil water flow at a range of scales. In the present study, we treat soil water flow as a dissipative process in an open non-equilibrium thermodynamic system, to better understand this key process. We define the chemical potential and Helmholtz free energy based on soil physical quantities, parametrize a p...

The investigation and quantification of cardiac motion is important for assessment of cardiac abnormalities and treatment effectiveness. Therefore we consider a new method to track cardiac motion from magnetic resonance (MR) tagged images. Tracking is achieved by following the spatial maxima in scale-space of the MR images over time. Reconstruction of the velocity field is then carried out by m...

The accumulation of damage within a structure due to service loading or environmental conditions is a random phenomenon. Continuum damage mechanics (CDM) enables macroscopic manifestations of damage to be related to microscopic defects and discontinuities present within a material. This permits margins of safety to be assessed prior to the time at which damage becomes visible or detectable. Und...

We study the implications of duality symmetry on the analyticity properties of the partition function as it depends upon the compactification length. In order to obtain non-trivial compactifications, we give a physical prescription to get the Helmholtz free energy for any heterotic string supersymmetric or not. After proving that the free energy is always invariant under the duality transformat...

This paper provides guaranteed upper energy error bounds for a modified lowest-order nonconforming Crouzeix-Raviart finite element method for the Stokes equations. The modification from [A. Linke 2014, On the role of the Helmholtz-decomposition in mixed methods for incompressible flows and a new variational crime] is based on the observation that only the divergence-free part of the right-hand ...