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Yang, Su; Chen, Shaoxuan; Zhu, Wei; Kevrekidis, P G(
, Frontiers in Photonics)
Introduction
The moment quantities associated with the nonlinear Schrödinger equation offer important insights into the evolution dynamics of such dispersive wave partial differential equation (PDE) models. The effective dynamics of the moment quantities are amenable to both analytical and numerical treatments.
Methods
In this paper, we present a data-driven approach associated with the “Sparse Identification of Nonlinear Dynamics” (SINDy) to capture the evolution behaviors of such moment quantities numerically.
Results and Discussion
Our method is applied first to some well-known closed systems of ordinary differential equations (ODEs) which describe the evolution dynamics of relevant moment quantities. Our examples are, progressively, of increasing complexity and our findings explore different choices within the SINDy library. We also consider the potential discovery of coordinate transformations that lead to moment system closure. Finally, we extend considerations to settings where a closed analytical form of the moment dynamics is not available.
Chen, Ziyu; Zhu, Wei(
, Advances in Neural Information Processing Systems 36 (NeurIPS 2023))
We study the implicit bias of gradient flow on linear equivariant steerable networks in group-invariant binary classification. Our findings reveal that the parameterized predictor converges in direction to the unique group-invariant classifier with a maximum margin defined by the input group action. Under a unitary assumption on the input representation, we establish the equivalence between steerable networks and data augmentation. Furthermore, we demonstrate the improved margin and generalization bound of steerable networks over their non-invariant counterparts.
Devitt, Allison N; Vargas, Abigail L; Zhu, Wei; Des_Soye, Benjamin James; Butun, Fatma Ayaloglu; Alt, Tyler; Kaley, Nicholas; Ferreira, Glaucio M; Moran, Graham R; Kelleher, Neil L; et al(
, ACS Chemical Biology)
He, Chuan
(Ed.)
Human ornithine aminotransferase (hOAT), a pyridoxal 5'-phosphate (PLP)-dependent enzyme, has been shown to play an essential role in the metabolic reprogramming and progression of hepatocellular carcinoma (HCC). HCC accounts for approximately 75% of primary liver cancers and is within the top three causes of cancer death worldwide. As a result of treatment limitations, the overall 5-year survival rate for all patients with HCC is under 20%. The prevalence of HCC necessitates continued development of novel and effective treatment methods. In recent years, the therapeutic potential of selective inactivation of hOAT has been demonstrated for the treatment of HCC. Inspired by previous increased selectivity for hOAT by the expansion of the cyclopentene ring scaffold to a cyclohexene, we designed, synthesized, and evaluated a series of novel fluorinated cyclohexene analogues and identified (R)-3-amino-5,5-difluorocyclohex-1-ene-1-carboxylic acid as a time-dependent inhibitor of hOAT. Structural and mechanistic studies have elucidated the mechanism of inactivation of hOAT by 5, resulting in a PLP-inactivator adduct tightly bound to the active site of the enzyme. Intact protein mass spectrometry, 19F NMR spectroscopy, transient state kinetic studies, and X-ray crystallography were used to determine the structure of the final adduct and elucidate the mechanisms of inactivation. Interestingly, despite the highly electrophilic intermediate species conferred by fluorine and structural evidence of solvent accessibility in the hOAT active site, Lys292 and water did not participate in nucleophilic addition during the inactivation mechanism of hOAT by 5. Instead, rapid aromatization to yield the final adduct was favored.
A recent study by Hon et al. reported that a close-in planet around the red clump star, 8 UMi, should have been engulfed during the expansion phase of its parent star’s evolution. They explained the survival of this exoplanet through a binary-merger channel for 8 UMi. The key to testing this formation scenario is to derive the true age of this star: is it an old “imposter” resulting from a binary merger, or a genuinely young red clump giant? To accomplish this, we derive kinematic and chemical properties for 8 UMi using astrometric data from Gaia DR3 and the element-abundance pattern measured from a high-resolution (R∼ 75,000) spectrum taken by SOPHIE. Our analysis shows that 8 UMi is a normal thin-disk star with orbital rotation speed ofVϕ= 244.96 km s−1, and possesses a solar metallicity ([Fe/H] = −0.05 ± 0.07) andα-element-abundance ratio ([α/Fe] = +0.01 ± 0.03). By adopting well-established relationships between age and space velocities/elemental abundances, we estimate a kinematic age ofGyr, and a chemical age ofGyr from [C/N] and 3.47 ± 1.96 Gyr from [Y/Mg] for 8 UMi, respectively. These estimates are consistent with the isochrone-fitting age (Gyr) of 8 UMi, but are all much younger than the timescale required in a binary-merger scenario. This result challenges the binary-merger model; the existence of such a closely orbiting exoplanet around a giant star remains a mystery yet to be resolved.
Gui, Yuqian; Zang, Weicheng; Zhai, Ruocheng; Ryu, Yoon-Hyun; Udalski, Andrzej; Yang, Hongjing; Han, Cheongho; Mao, Shude; Albrow, Michael D; Chung, Sun-Ju; et al(
, The Astronomical Journal)
Abstract
We report the analysis of four unambiguous planets and one possible planet from the subprime fields (Γ ≤ 1 hr−1) of the 2017 Korea Microlensing Telescope Network (KMTNet) microlensing survey, to complete the KMTNet AnomalyFinder planetary sample for the 2017 subprime fields. They are KMT-2017-BLG-0849, KMT-2017-BLG-1057, OGLE-2017-BLG-0364, and KMT-2017-BLG-2331 (unambiguous), as well as KMT-2017-BLG-0958 (possible). For the four unambiguous planets, the mean planet–host mass ratios,q, are (1.0, 1.2, 4.6, 13) × 10−4, the median planetary masses are (6.4, 24, 76, 171)M⊕, and the median host masses are (0.19, 0.57, 0.49, 0.40)M⊙, respectively, found from a Bayesian analysis. We have completed the Anomaly Finder planetary sample from the first 4 yr of KMTNet data (2016–2019), with 112 unambiguous planets in total, which nearly tripled the microlensing planetary sample. The “sub-Saturn desert” () found in the 2018 and 2019 KMTNet samples is confirmed by the 2016 and 2017 KMTNet samples.
Hu, Zhecheng; Zhu, Wei; Gould, Andrew; Udalski, Andrzej; Sumi, Takahiro; Chen, Ping; Calchi Novati, Sebastiano; Yee, Jennifer C; Beichman, Charles A; Bryden, Geoffery; et al(
, Monthly Notices of the Royal Astronomical Society)
We present the analysis of the microlensing event OGLE-2015-BLG-0845, which was affected by both the microlensing parallax and xallarap effects. The former was detected via the simultaneous observations from the ground and Spitzer, and the latter was caused by the orbital motion of the source star in a relatively close binary. The combination of these two effects led to a mass measurement of the lens object, revealing a low-mass ($0.14 \pm 0.05 \, \mathrm{ M}_{\odot }$) M dwarf at the bulge distance ($7.6 \pm 1.0$ kpc). The source binary consists of a late F-type subgiant and a K-type dwarf of $\sim 1.2$ and $\sim 0.9 \mathrm{ M}_{\odot }$, respectively, and the orbital period is $70 \pm 10$ d. OGLE-2015-BLG-0845 is the first single-lens event in which the lens mass is measured via the binarity of the source. Given the abundance of binary systems as potential microlensing sources, the xallarap effect may not be a rare phenomenon. Our work thus highlights the application of the xallarap effect in the mass determination of microlenses, and the same method can be used to identify isolated dark lenses.
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