Dynamical topology and statistical properties of spatiotemporal chaos

For spatiotemporal chaos described by partial differential equations, there are generally locations where the dynamical variable achieves its local extremum or where the time partial derivative of the variable vanishes instantaneously. To a large extent, the location and movement of these topologically special points determine the qualitative structure of the disordered states. We analyze numerically statistical properties of the topologically special points in one-dimensional spatiotemporal chaos. The probability distribution functions for the number of point, the lifespan, and the distance covered during their lifetime are obtained from numerical simulations. Mathematically, we establish a probabilistic model to describe the dynamics of these topologically special points. In despite of the different definitions in different spatiotemporal chaos, the dynamics of these special points can be described in a uniform approach.Comment: 6 pages, 5 figure

Electron-phonon coupling and superconductivity in LiB1+x_{1+x}C1−x_{1-x}

By means of the first-principles density-functional theory calculation and Wannier interpolation, electron-phonon coupling and superconductivity are systematically explored for boron-doped LiBC (i.e. LiB$_{1+x}$C$_{1-x}$), with $x$ between 0.1 and 0.9. Hole doping introduced by boron atoms is treated through virtual-crystal approximation. For the investigated doping concentrations, our calculations show the optimal doping concentration corresponds to 0.8. By solving the anisotropic Eliashberg equations, we find that LiB$_{1.8}$C$_{0.2}$ is a two-gap superconductor, whose superconducting transition temperature, T$_c$, may exceed the experimentally observed value of MgB$_2$. Similar to MgB$_2$, the two-dimensional bond-stretching $E_{2g}$ phonon modes along $\Gamma$-$A$ line have the largest contribution to electron-phonon coupling. More importantly, we find that the first two acoustic phonon modes $B_1$ and $A_1$ around the midpoint of $K$-$\Gamma$ line play a vital role for the rise of T$_c$ in LiB$_{1.8}$C$_{0.2}$. The origin of strong couplings in $B_1$ and $A_1$ modes can be attributed to enhanced electron-phonon coupling matrix elements and softened phonons. It is revealed that all these phonon modes couple strongly with $\sigma$-bonding electronic states.Comment: 7 pages, 10 figures, accepted for publication in EP

On meromorphic functions that share three values of finite weights

AbstractA uniqueness theorem for two distinct non-constant meromorphic functions that share three values of finite weights is proved, which generalizes two previous results by H.X. Yi, and X.M. Li and H.X. Yi. As applications of it, many known results by H.X. Yi and P. Li, etc. could be improved. Furthermore, with the concept of finite-weight sharing, extensions on Osgood–Yang's conjecture and Mues' conjecture, and a generalization of some prevenient results by M. Ozawa and H. Ueda, ect. could be obtained

NMR analysis of the dynamic exchange of the NS2B cofactor between open and closed conformations of the West Nile Virus NS2B-NS3 protease

BACKGROUND The two-component NS2B-NS3 proteases of West Nile and dengue viruses are essential for viral replication and established targets for drug development. In all crystal structures of the proteases to date, the NS2B cofactor is located far from the substrate binding site (open conformation) in the absence of inhibitor and lining the substrate binding site (closed conformation) in the presence of an inhibitor. METHODS In this work, nuclear magnetic resonance (NMR) spectroscopy of isotope and spin-labeled samples of the West Nile virus protease was used to investigate the occurrence of equilibria between open and closed conformations in solution. FINDINGS In solution, the closed form of the West Nile virus protease is the predominant conformation irrespective of the presence or absence of inhibitors. Nonetheless, dissociation of the C-terminal part of the NS2B cofactor from the NS3 protease (open conformation) occurs in both the presence and the absence of inhibitors. Low-molecular-weight inhibitors can shift the conformational exchange equilibria so that over 90% of the West Nile virus protease molecules assume the closed conformation. The West Nile virus protease differs from the dengue virus protease, where the open conformation is the predominant form in the absence of inhibitors. CONCLUSION Partial dissociation of NS2B from NS3 has implications for the way in which the NS3 protease can be positioned with respect to the host cell membrane when NS2B is membrane associated via N- and C-terminal segments present in the polyprotein. In the case of the West Nile virus protease, discovery of low-molecular-weight inhibitors that act by breaking the association of the NS2B cofactor with the NS3 protease is impeded by the natural affinity of the cofactor to the NS3 protease. The same strategy can be more successful in the case of the dengue virus NS2B-NS3 protease.The project was funded by the Australian Research Council (http://www.arc.gov.au), grant DP0877540

RHINO: Regularizing the Hash-based Implicit Neural Representation

The use of Implicit Neural Representation (INR) through a hash-table has demonstrated impressive effectiveness and efficiency in characterizing intricate signals. However, current state-of-the-art methods exhibit insufficient regularization, often yielding unreliable and noisy results during interpolations. We find that this issue stems from broken gradient flow between input coordinates and indexed hash-keys, where the chain rule attempts to model discrete hash-keys, rather than the continuous coordinates. To tackle this concern, we introduce RHINO, in which a continuous analytical function is incorporated to facilitate regularization by connecting the input coordinate and the network additionally without modifying the architecture of current hash-based INRs. This connection ensures a seamless backpropagation of gradients from the network's output back to the input coordinates, thereby enhancing regularization. Our experimental results not only showcase the broadened regularization capability across different hash-based INRs like DINER and Instant NGP, but also across a variety of tasks such as image fitting, representation of signed distance functions, and optimization of 5D static / 6D dynamic neural radiance fields. Notably, RHINO outperforms current state-of-the-art techniques in both quality and speed, affirming its superiority.Comment: 17 pages, 11 figure