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We connect certain continuous motions of discrete planar curves resulting in semi-discrete potential Korteweg-de Vries (mKdV) equation with Darboux transformations of smooth planar curves. In doing so, we define infinitesimal Darboux transformations that include the aforementioned motions, and also give an alternate geometric interpretation for establishing the semi-discrete potential mKdV equation., Comment: 11 pages

Lithium-ion secondary batteries have been used in a wide variety of purposes, such as for powering mobile devices and electric vehicles, but their performance should be improved. One of the factors that limits their performance is the non-uniformity of the chemical reaction in the process of charging and discharging. Many attempts have been made to elucidate the mechanism behind this reaction non-uniformity. In this paper, to detect non-uniformity in various physical properties from Co K-edge two-dimensional X-ray absorption spectroscopy (2D-XAS) images of lithium ion batteries, we propose a method that consists of one-sided orthogonal non-negative matrix factorization in combination with removal of the reference signal. The difference between X-ray absorption spectra acquired at different positions in the battery is very small. However, even in such a situation, our method can decompose the 2D-XAS data into different spatial domains and their corresponding absorption spectra. From the spectral decomposition of the obtained absorption spectra, we confirmed a transition-energy shift of the main peak as evidence for a change in the state of charge and also found spectral changes due to orbital hybridization in the decomposed spectral components.

In this paper, we present Retargetable AR, a novel AR framework that yields an AR experience that is aware of scene contexts set in various real environments, achieving natural interaction between the virtual and real worlds. To this end, we characterize scene contexts with relationships among objects in 3D space, not with coordinates transformations. A context assumed by an AR content and a context formed by a real environment where users experience AR are represented as abstract graph representations, i.e. scene graphs. From RGB-D streams, our framework generates a volumetric map in which geometric and semantic information of a scene are integrated. Moreover, using the semantic map, we abstract scene objects as oriented bounding boxes and estimate their orientations. With such a scene representation, our framework constructs, in an online fashion, a 3D scene graph characterizing the context of a real environment for AR. The correspondence between the constructed graph and an AR scene graph denoting the context of AR content provides a semantically registered content arrangement, which facilitates natural interaction between the virtual and real worlds. We performed extensive evaluations on our prototype system through quantitative evaluation of the performance of the oriented bounding box estimation, subjective evaluation of the AR content arrangement based on constructed 3D scene graphs, and an online AR demonstration. The results of these evaluations showed the effectiveness of our framework, demonstrating that it can provide a context-aware AR experience in a variety of real scenes., Comment: 11 pages, 15 figures

We study the extremal properties of a stochastic process $x_t$ defined by a Langevin equation $\dot{x}_t=\sqrt{2 D_0 V(B_t)}\,\xi_t$, where $\xi_t$ is a Gaussian white noise with zero mean, $D_0$ is a constant scale factor, and $V(B_t)$ is a stochastic "diffusivity" (noise strength), which itself is a functional of independent Brownian motion $B_t$. We derive exact, compact expressions for the probability density functions (PDFs) of the first passage time (FPT) $t$ from a fixed location $x_0$ to the origin for three different realisations of the stochastic diffusivity: a cut-off case $V(B_t) =\Theta(B_t)$ (Model I), where $\Theta(x)$ is the Heaviside theta function; a Geometric Brownian Motion $V(B_t)=\exp(B_t)$ (Model II); and a case with $V(B_t)=B_t^2$ (Model III). We realise that, rather surprisingly, the FPT PDF has exactly the L\'evy-Smirnov form (specific for standard Brownian motion) for Model II, which concurrently exhibits a strongly anomalous diffusion. For Models I and III either the left or right tails (or both) have a different functional dependence on time as compared to the L\'evy-Smirnov density. In all cases, the PDFs are broad such that already the first moment does not exist. Similar results are obtained in three dimensions for the FPT PDF to an absorbing spherical target., Comment: 8 pages, 3 figures, RevTeX

The passive and active motion of micron-sized tracer particles in crowded liquids and inside living biological cells is ubiquitously characterised by "viscoelastic" anomalous diffusion, in which the increments of the motion feature long-ranged negative and positive correlations. While viscoelastic anomalous diffusion is typically modelled by a Gaussian process with correlated increments, so-called fractional Gaussian noise, an increasing number of systems are reported, in which viscoelastic anomalous diffusion is paired with non-Gaussian displacement distributions. Following recent advances in Brownian yet non-Gaussian diffusion we here introduce and discuss several possible versions of random-diffusivity models with long-ranged correlations. While all these models show a crossover from non-Gaussian to Gaussian distributions beyond some correlation time, their mean squared displacements exhibit strikingly different behaviours: depending on the model crossovers from anomalous to normal diffusion are observed, as well as unexpected dependencies of the effective diffusion coefficient on the correlation exponent. Our observations of the strong non-universality of random-diffusivity viscoelastic anomalous diffusion are important for the analysis of experiments and a better understanding of the physical origins of "viscoelastic yet non-Gaussian" diffusion., Comment: 21 pages, 5 figures, IOP LaTeX