Tail asymptotics of the Brownian signature

The signature of a path \gamma is a sequence whose n-th term is the order-n iterated integrals of \gamma. It arises from solving multidimensional linear differential equations driven by \gamma. We are interested in relating the path properties of \gamma with its signature. If \gamma is C1, then an elegant formula of Hambly and Lyons relates the length of \gamma to the tail asymptotics of the signature. We show an analogous formula for the multidimensional Brownian motion,with the quadratic variation playing a similar role to the length. In the proof, we study the hyperbolic development of Brownian motion and also obtain a new subadditive estimate for the asymptotic of signature, which may be of independent interest. As a corollary, we strengthen the existing uniqueness results for the signatures of Brownian motion

Octet baryon masses in next-to-next-to-next-to-leading order covariant baryon chiral perturbation theory

We study the ground-state octet baryon masses and sigma terms using the covariant baryon chiral perturbation theory (ChPT) with the extended-on-mass-shell (EOMS) renormalization scheme up to next-to-next-to-next-to-leading order (N$^3$LO). By adjusting the available 19 low-energy constants (LECs), a reasonable fit of the $n_f=2+1$ lattice quantum chromodynamics (LQCD) results from the PACS-CS, LHPC, HSC, QCDSF-UKQCD and NPLQCD collaborations is achieved. Finite-volume corrections to the lattice data are calculated self-consistently. Our study shows that N$^3$LO BChPT describes better the light quark mass evolution of the lattice data than the NNLO BChPT does and the various lattice simulations seem to be consistent with each other. We also predict the pion and strangeness sigma terms of the octet baryons using the LECs determined in the fit of their masses. The predicted pion- and strangeness-nucleon sigma terms are $\sigma_{\pi N}=43(1)(6)$ MeV and $\sigma_{s N}=126(24)(54)$ MeV, respectively.Comment: 28 pages, 6 figures, minor revisions, typos corrected, version to appear in JHE

Nickel-catalyzed carbonylative synthesis of dihydrobenzofurans

A nickel-catalyzed carbonylative synthesis of dihydrobenzofurans has been developed. With Mo(CO)6 as the CO source and manganese metal as the reductant, alkyl halides were reacted with aryl iodides to give the desired products in moderate to good yields. © 2020 Elsevier B.V

Investigation of aged aerosols in size-resolved Asian dust storm particles transported from Beijing, China, to Incheon, Korea, using low-<i>Z</i> particle EPMA

This is the first study of Asian dust storm (ADS) particles collected in Beijing, China, and Incheon, Korea, during a spring ADS event. Using a seven-stage May impactor and a quantitative electron probe X-ray microanalysis (ED-EPMA, also known as low-<i>Z</i> particle EPMA), we examined the composition and morphology of 4200 aerosol particles at stages 1–6 (with a size cut-off of 16, 8, 4, 2, 1, and 0.5 μm in equivalent aerodynamic diameter, respectively) collected during an ADS event on 28–29 April 2005. The results showed that there were large differences in the chemical compositions between particles in sample S1 collected in Beijing immediately after the peak time of the ADS and in samples S2 and S3, which were collected in Incheon approximately 5 h and 24 h later, respectively. In sample S1, mineral dust particles accounted for more than 88% in relative number abundance at stages 1–5; and organic carbon (OC) and reacted NaCl-containing particles accounted for 24% and 32%, respectively, at stage 6. On the other hand, in samples S2 and S3, in addition to approximately 60% mineral dust, many sea spray aerosol (SSA) particles reacted with airborne SO₂ and NO_x (accounting for 24% and 14% on average in samples S2 and S3, respectively), often mixed with mineral dust, were encountered at stages 1–5, and (C, N, O, S)-rich particles (likely a mixture of water-soluble organic carbon with (NH₄)₂SO₄ and NH₄NO₃) were abundantly observed at stage 6 (accounting for 68% and 51% in samples S2 and S3, respectively). This suggests that an accumulation of sea-salt components on individual ADS particles larger than 1 μm in diameter occurred and many secondary aerosols smaller than 1 μm in diameter were formed when the ADS particles passed over the Yellow Sea. In the reacted or aged mineral dust and SSA particles, nitrate-containing and both nitrate- and sulfate-containing species vastly outnumbered the sulfate-containing species, implying that ambient NO_x had a greater influence on the atmospheric particles than SO₂ during this ADS episode. In addition to partially- or totally-reacted CaCO₃, reacted or aged Mg-containing aluminosilicates were observed frequently in samples S2 and S3; furthermore, a student's <i>t</i> test showed that both their atomic concentration ratios of [Mg] / [Al] and [Mg] / [Si] were significantly elevated (<i>P</i> < 0.05) compared to those in samples S1 (for [Mg] / [Al], 0.34 ± 0.09 and 0.40 ± 0.03 in samples S2 and S3, respectively, vs. 0.24 ± 0.01 in sample S1; for [Mg] / [Si], 0.21 ± 0.05 and 0.22 ± 0.01 in samples S2 and S3, respectively, vs. 0.12 ± 0.02 in sample S1). The significant increase of [Mg] / [Al] and [Mg] / [Si] ratios in Mg-containing aluminosilicates indicates that a significant evolution or aging must have occurred on the ADS particles in the marine atmosphere during transport from China to Korea

Algebro-Geometric Solutions to a New Hierarchy of Soliton Equations

With the help of the Lenard recursion equations, we derive a new hierarchy of soliton equations associated with a 3×3 matrix spectral problem and establish Dubrovin type equations in terms of the introduced trigonal curve Km-1 of arithmetic genus m - 1. Basing on the theory of algebraic curve, we construct the corresponding Baker-Akhiezer functions and meromorphic functions on Km-1. The known zeros and poles for the Baker-Akhiezer function and meromorphic functions allow us to find their theta function representations, from which algebro-geometric constructions and theta function representations of the entire hierarchy of soliton equations are obtained.С помощью рекуррентных уравнений Ленарда получена новая иерархия солитонных уравнений, связанных с 3×3 матричной спектральной задачей, и установлены уравнения типа Дубровина в терминах представленной тригональной кривой Km-1 арифметического рода m - 1. Основываясь на теории алгебраических кривых, построены соответствующие функции Бейкера- Ахиезера и мероморфные функции на Km-1. Известные нули и полюсы для функций Бейкера-Ахиезера и мероморфных функций позволяют найти их представления в тета-функциях, из которых получены алгебро-геометрические конструкции и представления в тета-функциях решений всей иерархии солитонных уравнений

Hybrid expansions for local structural relaxations

A model is constructed in which pair potentials are combined with the cluster expansion method in order to better describe the energetics of structurally relaxed substitutional alloys. The effect of structural relaxations away from the ideal crystal positions, and the effect of ordering is described by interatomic-distance dependent pair potentials, while more subtle configurational aspects associated with correlations of three- and more sites are described purely within the cluster expansion formalism. Implementation of such a hybrid expansion in the context of the cluster variation method or Monte Carlo method gives improved ability to model phase stability in alloys from first-principles.Comment: 8 pages, 1 figur

Association Between Inflammatory Bowel Disease and Dementia: A Longitudinal Cohort Study

BACKGROUND: The association between inflammatory bowel disease (IBD) and dementia remains uncertain. We aim to investigate whether IBD is associated with higher dementia risk. METHODS: Using multivariable Cox regression models, we analyzed the onset of all-cause dementia among 497,775 participants, including 5778 IBD patients in the UK Biobank as primary analysis. In secondary analysis, we further examined the difference in brain structure and cognitive function changes between IBD and non-IBD individuals. The diagnosis of IBD and dementia was confirmed with combination of primary care data, hospital inpatient data, death registry, and self-report data. Brain structure was measured by brain MRI as anatomic and tissue-specific volumes; cognitive function was tested in terms of reaction, visual episodic memory, verbal-numerical reasoning, and prospective memory. RESULTS: During a mean follow-up of 11.58 years, 100 and 6709 incident all-cause dementia with or without IBD were documented, respectively. In multivariable Cox regression model, hazard ratio for incident dementia among IBD patients was 1.14 (95% confidence interval [CI], 0.94-1.39; P=.182) comparing with non-IBD participants; no statistically significant difference was observed in their brain MRI measures of anatomic and tissue-specific volumes, whereas IBD patients had a significantly increased reaction time (β=12.32; 95% CI, 1.97, 22.67; P = .020). Results of subgroup and sensitivity analyses were consistent with the main analysis. CONCLUSIONS: Our study does not support a significant association between IBD and dementia. Further studies with better design and longer follow-up are needed to elucidate the association