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 distance-regular Cayley graphs of generalized dicyclic groups

Let G be a generalized dicyclic group with identity 1. An inverse closed subset S of $G?\{1\}$ is called minimal if $〈S〉=G$ and there exists some $s\in S$ such that $〈S?\{s,s^{?1}\}〉\ne G$. In this paper, we characterize distance-regular Cayley graphs $\mathrm{Cay}(G,S)$ of G under the condition that S is minimal.     

Localization and quantification of radical production in cavitating flows with luminol chemiluminescent reactions

Hydrodynamic cavitation experiments in microfluidic systems have been performed with an aqueous solution of luminol as the working fluid. In order to identify where and how much reactive radical species are formed by the violent bubble collapse, the resulting chemiluminescent oxidation reaction of luminol was scrutinized downstream of a constriction in the microchannel. An original method was developed in order to map the intensity of chemiluminescence emitted from the micro-flow, allowing us to localize the region where radicals are produced. Time averaged void fraction measurements performed by laser induced fluorescence experiments were also used to determine the cavitation cloud position. The combination void fraction and chemiluminescence two-dimensional mapping demonstrated that the maximum chemiluminescent intensity area was found just downstream of the cavitation clouds. Furthermore, the radical yield can be obtained with our single photon counting technique. The maximum radical production rates of 1.2*10⁷ OH/s and radical production per processed liquid volume of 2.15*10¹⁰ HO/l were observed. The proposed technique allows for two-dimensional characterisation of radical production in the microfluidic flow and could be a quick, non-intrusive way to optimise hydrodynamic cavitation reactor design and operating parameters, leading to enhancements in wastewater treatments and other process intensifications.     

On Generalized Douglas–Weyl(α, β)-Metrics

In this paper, we study generalized Douglas–Weyl(α, β)-metrics. Suppose that a regular(α, β)-metric F is not of Randers type. We prove that F is a generalized Douglas–Weyl metric with vanishing S-curvature if and only if it is a Berwald metric. Moreover, by ignoring the regularity, if F is not a Berwald metric, then we find a family of almost regular Finsler metrics which is not Douglas nor Weyl. As its application, we show that generalized Douglas–Weyl square metric or Matsumoto metric with isotropic mean Berwald curvature are Berwald metrics.     

Self‐Assembly and Gelation of Poly(aryl ether) Dendrons Containing Hydrazide Units: Factors Controlling the Formation of Helical Structures

Self‐assembly of AB₂ and AB₃ type low molecular weight poly(aryl ether) dendrons that contain hydrazide units were used to investigate mechanistic aspects of helical structure formation during self‐assembly. The results suggest that there are three important aspects that control helical structure formation in such systems with acyl hydrazide/hydrazone linkage: i) J‐type aggregation, ii) the hydrogen‐bond donor/acceptor ability of the solvent, and iii) the dielectric constant of the solvent. The monomer units self‐assemble to form dimer structures through hydrogen‐bonding and further assembly of the hydrogen‐bonded dimers leads to macroscopic chirality in the present case. Dimer formation was confirmed by NMR spectroscopy and by mass spectrometry. The self‐assembly in the system was driven by hydrogen‐bonding and π–π stacking interactions. The morphology of the aggregates formed was examined by scanning electron microscopy, and the analysis suggests that aprotic solvent systems facilitate helical fibre formation, whereas introduction of protic solvents results in the formation of flat ribbons. This detailed mechanistic study suggests that the self‐assembly follows a nucleation–elongation model to form helical structures, rather than the isodesmic model.     

Properties of bounded stochastic processes employed in biophysics

Abstract

Realistic stochastic modeling is increasingly requiring the use of bounded noises. In this work, properties and relationships of commonly employed bounded stochastic processes are investigated within a solid mathematical ground. Four families are object of investigation: the Sine-Wiener (SW), the Doering–Cai–Lin (DCL), the Tsallis–Stariolo–Borland (TSB), and the Kessler–Sørensen (KS) families. We address mathematical questions on existence and uniqueness of the processes defined through Stochastic Differential Equations, which often conceal non-obvious behavior, and we explore the behavior of the solutions near the boundaries of the state space. The expression of the time-dependent probability density of the Sine-Wiener noise is provided in closed form, and a close connection with the Doering–Cai–Lin noise is shown. Further relationships among the different families are explored, pathwise and in distribution. Finally, we illustrate an analogy between the Kessler–Sørensen family and Bessel processes, which allows to relate the respective local times at the boundaries.     

Gravitational wave imprint of new symmetry breaking

It is believed that there are more fundamental gauge symmetries beyond those described by the Standard Model of particle physics. The scales of these new gauge symmetries are usually too high to be reachable by particle colliders. Considering that the phase transition (PT) relating to the spontaneous breaking of new gauge symmetries to the electroweak symmetry might be strongly first order, we propose considering the stochastic gravitational waves (GW) arising from this phase transition as an indirect way of detecting these new fundamental gauge symmetries. As an illustration, we explore the possibility of detecting the stochastic GW generated from the PT of \begin{document}$ {\bf{B}}-{\bf{L}}$\end{document} in the space-based interferometer detectors. Our study demonstrates that the GW energy spectrum is reachable by the LISA, Tianqin, Taiji, BBO, and DECIGO experiments only for the case where the spontaneous breaking of \begin{document}$ {\bf{B}}-{\bf{L}}$\end{document} is triggered by at least two electroweak singlet scalars.     

Inner derivations and norm equality

We characterize when the norm of the sum of two bounded operators on a Hilbert space is equal to the sum of their norms.