On the existence and uniqueness of solutions to stochastic differential equations driven by G-Brownian motion with integral-Lipschitz coefficients

In this paper, we study the existence and uniqueness of solutions to stochastic differential equations driven by G-Brownian motion (GSDEs) with integral-Lipschitz conditions on their coefficients

An Astrometric Approach to Measuring the Color of an Object

The color of a star is a critical feature to reflect its physical property such as the temperature. The color index is usually obtained via absolute photometry, which is demanding for weather conditions and instruments. In this work, we present an astrometric method to measure the catalog-matched color index of an object based on the effect of differential color refraction (DCR). Specifically, we can observe an object using only one filter or alternately using two different filters. Through the difference of the DCR effect compared with reference stars, the catalog-matched color index of an object can be conveniently derived. Hence, we can perform DCR calibration and obtain its accurate and precise positions even if observed with Null filter during a large range of zenith distances, by which the limiting magnitude and observational efficiency of the telescope can be significantly improved. This method takes advantage of the DCR effect and builds a link between astrometry and photometry. In practice, we measure the color indices and positions of Himalia (the sixth satellite of Jupiter) using 857 CCD frames over 8 nights by two telescopes. Totally, the mean color index BP-RP (Gaia photometric system) of Himalia is 0.750 \pm 0.004 magnitude. Through the rotational phased color index analysis, we find two places with their color indices exceeding the mean \pm 3 \sigma.Comment: 10 pages, 5 figures, 4 table

Cryo-EM of full-length α-synuclein reveals fibril polymorphs with a common structural kernel.

α-Synuclein (aSyn) fibrillar polymorphs have distinct in vitro and in vivo seeding activities, contributing differently to synucleinopathies. Despite numerous prior attempts, how polymorphic aSyn fibrils differ in atomic structure remains elusive. Here, we present fibril polymorphs from the full-length recombinant human aSyn and their seeding capacity and cytotoxicity in vitro. By cryo-electron microscopy helical reconstruction, we determine the structures of the two predominant species, a rod and a twister, both at 3.7 Å resolution. Our atomic models reveal that both polymorphs share a kernel structure of a bent β-arch, but differ in their inter-protofilament interfaces. Thus, different packing of the same kernel structure gives rise to distinct fibril polymorphs. Analyses of disease-related familial mutations suggest their potential contribution to the pathogenesis of synucleinopathies by altering population distribution of the fibril polymorphs. Drug design targeting amyloid fibrils in neurodegenerative diseases should consider the formation and distribution of concurrent fibril polymorphs

On the strengthening and embrittlement mechanisms of an additively manufactured Nickel-base superalloy

The γ′ phase strengthened Nickel-base superalloy is one of the most significant dual-phase alloy systems for high-temperature engineering applications. The tensile properties of laser powder-bed-fused IN738LC superalloy in the as-built state have been shown to have both good strength and ductility compared with its post-thermal treated state. A microstructural hierarchy composed of weak texture, sub-micron cellular structures and dislocation cellular walls was promoted in the as-built sample. After post-thermal treatment, the secondary phase γ′ precipitated with various size and fraction depending on heat treatment process. For room-temperature tensile tests, the dominated deformation mechanism is planar slip of dislocations in the as-built sample while dislocations bypassing the precipitates via Orowan looping in the γ′ strengthened samples. The extraordinary strengthening effect due to the dislocation substructure in the as-built sample provides an addition of 372 MPa in yield strength. The results of our calculation are in agreement with experimental yield strength for all the three different conditions investigated. Strikingly, the γ′ strengthened samples have higher work hardening rate than as-built sample but encounter premature failure. Experimental evidence shows that the embrittlement mechanism in the γ′ strengthened samples is caused by the high dislocation hardening of the grain interior region, which reduces the ability to accommodate further plastic strain and leads to premature intergranular cracking. On the basis of these results, the strengthening micromechanism and double-edge effect of strength and ductility of Nickel-base superalloy is discussed in detail

Cross-lingual word embedding refinement by ℓ1 norm optimisation

Cross-Lingual Word Embeddings (CLWEs) encode words from two or more languages in a shared high-dimensional space in which vectors representing words with similar meaning (regardless of language) are closely located. Existing methods for building high-quality CLWEs learn mappings that minimise the L2 norm loss function. However, this optimisation objective has been demonstrated to be sensitive to outliers. Based on the more robust Manhattan norm (aka. â„“1 norm) goodness-of-fit criterion, this paper proposes a simple post-processing step to improve CLWEs. An advantage of this approach is that it is fully agnostic to the training process of the original CLWEs and can therefore be applied widely. Extensive experiments are performed involving ten diverse languages and embeddings trained on different corpora. Evaluation results based on bilingual lexicon induction and cross-lingual transfer for natural language inference tasks show that the L1 refinement substantially outperforms four state-of-the-art baselines in both supervised and unsupervised settings. It is therefore recommended that this strategy be adopted as a standard for CLWE methods