Hyperparameter on-line learning of stochastic resonance based threshold networks

Aiming at training the feed-forward threshold neural network consisting of nondifferentiable activation functions, the approach of noise injection forms a stochastic resonance based threshold network that can be optimized by various gradient-based optimizers. The introduction of injected noise extends the noise level into the parameter space of the designed threshold network, but leads to a highly non-convex optimization landscape of the loss function. Thus, the hyperparameter on-line learning procedure with respective to network weights and noise levels becomes of challenge. It is shown that the Adam optimizer, as an adaptive variant of stochastic gradient descent, manifests its superior learning ability in training the stochastic resonance based threshold network effectively. Experimental results demonstrate the significant improvement of performance of the designed threshold network trained by the Adam optimizer for function approximation and image classification.     

On tight 6-cycle decompositions of complete 3-uniform hypergraphs

The complete 3-uniform hypergraph of order v has a vertex set V of size v and the set of all 3-element subsets of V as its edge set. A tight 6-cycle is a hypergraph with vertex set $\{a,b,c,d,e,f\}$ and edge set $\{\{a,b,c\},\{b,c,d\},\{c,d,e\},\{d,e,f\},\{e,f,a\},\{f,a,b\}\}$. We show that there exists a decomposition of the complete 3-uniform hypergraph of order v into isomorphic copies of a tight 6-cycle if and only if $v\equiv 1$, 2, 10, 20, 28, or $29(\mathrm{mod}36)$.     

Portable single-sided NMR measurements at variable temperatures: Implementation of a thermo-controlled device and application to the heating of bread dough

A temperature control unit was implemented to vary the temperature of samples studied on a commercial Mobile Universal Surface Explorer nuclear magnetic resonance (MOUSE-NMR) apparatus. The device was miniaturized to fit the maximum MOUSE sampling depth (25 mm). It was constituted by a sample holder sandwiched between two heat exchangers placed below and above the sample. Air was chosen as the fluid to control the temperature at the bottom of the sample, at the interface between the NMR probe and the sample holder, in order to gain space. The upper surface of the sample was regulated by the circulation of water inside a second heat exchanger placed above the sample holder. The feasibility of using such a device was demonstrated first on pure water and then on several samples of bread dough with different water contents. For this, T1 relaxation times were measured at various temperatures and depths and were then compared with those acquired with a conventional compact closed-magnet spectrometer. Discussion of results was based on biochemical transformations in bread dough (starch gelatinization and gluten heat denaturation). It was demonstrated that, within a certain water level range, and because of the low magnetic field strength of the MOUSE, a linear relationship could be established between T1 relaxation times and the local temperature in the dough sample.     

Two solutions for a singular elliptic equation with critical growth at infinity

We look for positive solutions for the singular equation $-\Delta u-\frac{1}{2}\left(x\cdot \nabla u\right)=\mu h\left(x\right)u^{q-1}+\lambda u+u^{(N+2)/(N-2)},\text{in }{\mathbb{R}}^N,$ where $N\ge 3$, $\lambda >0$, $\mu >0$ is a parameter, $0<q<1$ and $h$ has some summability properties. By using a perturbation method and critical point theory, we obtain two solutions when $max\{1,N/4\}<\lambda <N/2$ and the parameter $\mu >0$ is small.