A viscous paint model for interactive applications

We present a viscous paint model for use in an interactive painting system based on the well-known Stokes’ equations for viscous flow. Our method is, to our knowledge, the first unconditionally stable numerical method that treats viscous fluid with a free surface boundary. We have also developed a real-time implementation of the Kubelka-Munk reflectance model for pigment mixing, compositing and rendering entirely on graphics hardware, using programmable fragment shading capabilities. We have integrated our paint model with a prototype painting system, which demonstrates the model’s effectiveness in rendering viscous paint and capturing a thick, impasto-like style of painting. Several users have tested our prototype system and were able to start creating original art work in an intuitive manner not possible with the existing techniques in commercial systems

Computations of Delaunay and Higher Order Triangulations, with Applications to Splines

Digital data that consist of discrete points are frequently captured and processed by scientific and engineering applications. Due to the rapid advance of new data gathering technologies, data set sizes are increasing, and the data distributions are becoming more irregular. These trends call for new computational tools that are both efficient enough to handle large data sets and flexible enough to accommodate irregularity. A mathematical foundation that is well-suited for developing such tools is triangulation, which can be defined for discrete point sets with little assumption about their distribution. The potential benefits from using triangulation are not fully exploited. The challenges fundamentally stem from the complexity of the triangulation structure, which generally takes more space to represent than the input points. This complexity makes developing a triangulation program a delicate task, particularly when it is important that the program runs fast and robustly over large data. This thesis addresses these challenges in two parts. The first part concentrates on techniques designed for efficiently and robustly computing Delaunay triangulations of three kinds of practical data: the terrain data from LIDAR sensors commonly found in GIS, the atom coordinate data used for biological applications, and the time varying volume data generated from from scientific simulations. The second part addresses the problem of defining spline spaces over triangulations in two dimensions. It does so by generalizing Delaunay configurations, defined as follows. For a given point set P in two dimensions, a Delaunay configuration is a pair of subsets (T, I) from P, where T, called the boundary set, is a triplet and I, called the interior set, is the set of points that fall in the circumcircle through T. The size of the interior set is the degree of the configuration. As recently discovered by Neamtu (2004), for a chosen point set, the set of all degree k Delaunay configurations can be associated with a set of degree k plus 1 splines that form the basis of a spline space. In particular, for the trivial case of k equals 0, the spline space coincides with the PL interpolation functions over the Delaunay triangulation. Neamtu’s definition of the spline space relies only on a few structural properties of the Delaunay configurations. This raises the question whether there exist other sets of configurations with identical structural properties. If there are, then these sets of configurations—let us call them generalized configurations from hereon—can be substituted for Delaunay configurations in Neamtu’s definition of spline space thereby yielding a family of splines over the same point set

Investigations on the light hadron decays of Zb(10610)Z_b(10610) and Zb(10650)Z_b(10650)

The light hadron decay processes of $Z_b(10610)/Z_b(10650)$ provide us a way to study their nature and decay mechanism. In this work, we evaluate the branching ratios of $Z_b(10610)/Z_b(10650) \to VP$ ($V$ and $P$ stand for light vector and pseudoscalar mesons, respectively) using an effective Lagrangian approach, in which the contributions of intermediate bottomed meson triangle loops are considered. In our calculations, the $Z_b(10610)$ and $Z_b(10650)$ are regarded as $B\bar{B}^*+c.c.$ and $B^*\bar{B}^*$ molecular states, respectively. The predicted branching ratios of $Z_b(10610)\rightarrow VP$ are about in the order of $10^{-2}$, while the branching ratios of $Z_b(10650)\rightarrow VP$ are in the order of $10^{-3}$. Furthermore, the dependence of these ratios between different decay modes of $Z_b(10610)/Z_b(10650)$ on the mixing $\eta-\eta^\prime$ angle $\theta_P$ is investigated, which may be a good quantity for the experiments. It is hoped that the calculations here could be tested by future experiments.Comment: 7 pages, 8 figures and 1 tabl

COST-EFF: Collaborative Optimization of Spatial and Temporal Efficiency with Slenderized Multi-exit Language Models

Transformer-based pre-trained language models (PLMs) mostly suffer from excessive overhead despite their advanced capacity. For resource-constrained devices, there is an urgent need for a spatially and temporally efficient model which retains the major capacity of PLMs. However, existing statically compressed models are unaware of the diverse complexities between input instances, potentially resulting in redundancy and inadequacy for simple and complex inputs. Also, miniature models with early exiting encounter challenges in the trade-off between making predictions and serving the deeper layers. Motivated by such considerations, we propose a collaborative optimization for PLMs that integrates static model compression and dynamic inference acceleration. Specifically, the PLM is slenderized in width while the depth remains intact, complementing layer-wise early exiting to speed up inference dynamically. To address the trade-off of early exiting, we propose a joint training approach that calibrates slenderization and preserves contributive structures to each exit instead of only the final layer. Experiments are conducted on GLUE benchmark and the results verify the Pareto optimality of our approach at high compression and acceleration rate with 1/8 parameters and 1/19 FLOPs of BERT.Comment: Accepted in EMNLP 2022 main conferenc

Relationship between soil water content and soil particle size on typical slopes of the Loess Plateau during a drought year

In the context of global climate change as well as local climate warming and drying on the Loess Plateau of China, understanding the relationship between soil particle size and soil water distribution during years of atypical precipitation is important. In this study, fractal geometry theory is used to describe the mechanical composition and texture of soils to improve our understanding of hydropedology and ecohydrology in the critical zone on the Loess Plateau. One grassland slope and two shrubland slopes were selected in the hilly and gully region of the Loess Plateau, and soils were sampled along hillslope transects at depths of 0–500 cm. Fractal theory and redundancy analysis (RDA) were used to identify relationships between the fractal dimension of soil particle-size distributions and the corresponding van Genuchten parameters for the soil-water-characteristic curves. The oven-drying method was used to measure soil water content, and the high-speed centrifugation method was used to generate soil-water-characteristic curves. The results show that (1) the soil water that can be used by Caragana korshinskii during a drought year is distributed below 2 m from the surface, whereas the soil water that can be used by grass is below 1.2 m; (2) Caragana korshinskii promotes the conservation of fine soil particles more than does natural restored grass, and the soil particle-size distribution fractal dimension changes with depth and position; and (3) soil hydraulic properties correlate strongly with soil pedological properties such as bulk density and the soil particle-size distribution fractal dimension. These results provide a case study of the relationships among soil distributions, hydrologic and geomorphic processes for vegetation restoration in drylands with a thick vadose zone. More studies on soil property changes are needed to provide case studies and empirical support for ecological restoration in the Loess Plateau of China