Higher regularity and finite time blow-up to nonlocal pseudo-parabolic equation with conical degeneration

This paper deals with the initial-boundary value problem to a nonlocal semilinear pseudo-parabolic equation with conical degeneration. Firstly, we improve the regularity of weak solution and amend some proofs in [Global well-posedness for a nonlocal semilinear pseudo-parabolic equation with conical degeneration, J. Differential Equations, 2020, 269(5): 4566--4597]. Secondly, we study finite time blow-up of the weak solution, our initial condition only depends on Nehari functional and conservative integral and then improves the result in original paper under high initial energy.Comment: 18 page

An Algebro-Geometric Approach to Twisted Indices of Supersymmetric Gauge Theories

This thesis studies the algebro-geometric aspects of supersymmetric abelian gauge theories in three dimensions. The supersymmetric vacua are demonstrated to exhibit a window phenomenon in Chern-Simons levels, which is analogous to the window phenomenon in quantum K-theory with level structures. This correspondence between three-dimensional gauge theories and quantum K-theory is investigated from the perspectives of semi-classical vacua, twisted chiral rings, and twisted indices. In particular, the twisted index admits an algebro-geometric interpretation as the supersymmetric index of an effective quantum mechanics. Via supersymmetric localisation, the contributions from both topological and vortex saddle points are shown to agree with the Jeffrey-Kirwan contour integral formula. The algebro-geometric construction of Chern-Simons contributions to the twisted index from determinant line bundles provides a natural connection with quantum K-theory

Emergence of lager densities in chemotaxis system with generalized logistic growth and indirect signal production

This paper deals with the classical solution of following chemotaxis system with indirect signal production \begin{eqnarray*} \left\{ \begin{array}{llll} u_t=\epsilon\Delta u-\chi\nabla\cdot(u\nabla v)+ru-\mu u^\theta, &x\in \Omega,\ t>0,\\ \tau_1v_t=d_1\Delta v-\alpha v+\beta w, &x\in \Omega,\ t>0,\\ \tau_2w_t = d_2\Delta w-\gamma w+\lambda u, &x\in \Omega,\ t>0, \end{array} \right. \end{eqnarray*} in arbitrary bounded domain $\Omega\subset\mathbb{R}^n$, $n\geq1$, where $\chi, r, \mu, d_1, \alpha, \beta, \gamma, \lambda>0$ and $\theta>1$. Let $M$ be an arbitrary positive constant, (i) for $\epsilon\in(0, 1), d_2>0$ and $\tau_1=\tau_2=0$, if the initial data is suitably large, or $\mu$ is appropriately small such that $\|u_0\|_{L^\theta(\Omega)}^{\frac{\theta+1}{\theta}}>C_0(1+\mu)$, where $C_0$ is a positive constant which depends on the parameters and $n, \Omega, M$ but not on $\mu$, then for the associated solution of system and any positive constant $M$, one can find some points such that \begin{equation} u(\tilde{x}, \tilde{t})>M. \qquad\qquad (0.1) \end{equation} (ii) for $\epsilon, \tau_1, \tau_2>0, d_2\geq0$ and $\theta\in(1, \theta_0)$, here $\theta_0$ is a constant. If $\mu$ is appropriately small or $u_0$ and $v_0$ are suitable lager such that $\mathcal {F}(u_0, v_0)\leq-K(\mu\theta+1)$, where $K$ is a positive constant which depends on the parameters and $n, \Omega, M$ but not on $\mu$ and $\theta$, $\mathcal {F}$ is the Lyapunov functional to the system without damping source $ru-\mu u^\theta$, then (0.1) still holds. Our results extend greatly the existing knowledge for relevant model, therein the classical Keller-Segel growth systems were considered and the radially symmetric assumptions on $\Omega$ and initial data were necessary

Circulation, hydrography, and transport over the summit of Axial Seamount, a deep volcano in the Northeast Pacific

Author Posting. © American Geophysical Union, 2017. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research: Oceans 122 (2017): 5404–5422, doi:10.1002/2016JC012464.A numerical model of ocean flow, hydrography, and transport is used to extrapolate observations of currents and hydrography and infer patterns of material flux in the deep ocean around Axial Seamount, a destination node of NSF's Ocean Observatories Initiative's Cabled Array. Using an inverse method, the model is made to approximate measured deep ocean flow around this site during a 35 day time period in the year 2002. The model is then used to extract month-long mean patterns and examine smaller-scale spatial and temporal variability around Axial. Like prior observations, model month-long mean currents flow anticyclonically around the seamount's summit in toroidal form with maximum speeds at 1500 m depth of 10–11 cm/s. As a time mean, the temperature (salinity) anomaly distribution takes the form of a cold (briny) dome above the summit. Passive tracer material continually released at the location of the ASHES vent field exits the caldera primarily through its southern open end before filling the caldera. Once outside the caldera, the tracer circles the summit in clockwise fashion, fractionally reentering the caldera over lower walls at its north end, while gradually bleeding southwestward during the modeled time period into the ambient ocean. A second tracer release experiment using a source of only 2 day duration inside and near the CASM vent field at the northern end of the caldera suggests a residence time of the fluid at that locale of 8–9 days.WHOI as a postdoctoral scholar2018-01-0

Benchmarking Small-Dataset Structure-Activity-Relationship Models for Prediction of Wnt Signaling Inhibition

Quantitative structure-activity relationship (QSAR) models based on machine learning algorithms are powerful tools to expedite drug discovery processes and therapeutics development. Given the cost in acquiring large-sized training datasets, it is useful to examine if QSAR analysis can reasonably predict drug activity with only a small-sized dataset (size \u3c; 100) and benchmark these small-dataset QSAR models in application-specific studies. To this end, here we present a systematic benchmarking study on small-dataset QSAR models built for prediction of effective Wnt signaling inhibitors, which are essential to therapeutics development in prevalent human diseases (e.g., cancer). Specifically, we examined a total of 72 two-dimensional (2D) QSAR models based on 4 best-performing algorithms, 6 commonly used molecular fingerprints, and 3 typical fingerprint lengths. We trained these models using a training dataset (56 compounds), benchmarked their performance on 4 figures-of-merit (FOMs), and examined their prediction accuracy using an external validation dataset (14 compounds). Our data show that the model performance is maximized when: 1) molecular fingerprints are selected to provide sufficient, unique, and not overly detailed representations of the chemical structures of drug compounds; 2) algorithms are selected to reduce the number of false predictions due to class imbalance in the dataset; and 3) models are selected to reach balanced performance on all 4 FOMs. These results may provide general guidelines in developing high-performance small-dataset QSAR models for drug activity prediction

The relative effect of particles and turbulence on acoustic scattering from deep sea hydrothermal vent plumes revisited

Author Posting. © Acoustical Society of America, 2017. This article is posted here by permission of Acoustical Society of America for personal use, not for redistribution. The definitive version was published in Journal of the Acoustical Society of America 141 (2017): 1446–1458, doi:10.1121/1.4974828.The relative importance of suspended particles and turbulence as backscattering mechanisms within a hydrothermal plume located on the Endeavour Segment of the Juan de Fuca Ridge is determined by comparing acoustic backscatter measured by the Cabled Observatory Vent Imaging Sonar (COVIS) with model calculations based on in situ samples of particles suspended within the plume. Analysis of plume samples yields estimates of the mass concentration and size distribution of particles, which are used to quantify their contribution to acoustic backscatter. The result shows negligible effects of plume particles on acoustic backscatter within the initial 10-m rise of the plume. This suggests turbulence-induced temperature fluctuations are the dominant backscattering mechanism within lower levels of the plume. Furthermore, inversion of the observed acoustic backscatter for the standard deviation of temperature within the plume yields a reasonable match with the in situ temperature measurements made by a conductivity-temperature-depth instrument. This finding shows that turbulence-induced temperature fluctuations are the dominant backscattering mechanism and demonstrates the potential of using acoustic backscatter as a remote-sensing tool to measure the temperature variability within a hydrothermal plume.We thank the National Science Foundation for support (NSF Award Nos. OCE-0824612 and OCE-1234163 to APL-UW; NSF Award Nos. OCE-0825088 and OCE-1234141 to Rutgers)

4,5,7-Trimeth­oxy-2-methyl-3-(2,4,5-trimethoxy­phen­yl)-1-[3-(2,4,5-tri­methoxy­phen­yl)pentan-2-yl]indane acetone 0.858-solvate

In the title compound, C36H48O9.0.858C3H6O, the five-membered ring adopts an envelope conformation. The acetone solvent mol­ecule was disordered and was refined over two positions with equal occupancies, giving an overall occupancy of 0.858 (4). There are weak intra­molecular C—H⋯O hydrogen bonds and intermolecular C—H⋯π inter­actions in the structure