From rr-Spin Intersection Numbers to Hodge Integrals

Generalized Kontsevich Matrix Model (GKMM) with a certain given potential is the partition function of $r$-spin intersection numbers. We represent this GKMM in terms of fermions and expand it in terms of the Schur polynomials by boson-fermion correspondence, and link it with a Hurwitz partition function and a Hodge partition by operators in a $\widehat{GL}(\infty)$ group. Then, from a $W_{1+\infty}$ constraint of the partition function of $r$-spin intersection numbers, we get a $W_{1+\infty}$ constraint for the Hodge partition function. The $W_{1+\infty}$ constraint completely determines the Schur polynomials expansion of the Hodge partition function.Comment: 51 pages, 1 figur

Cache performance of chronological garbage collection

This thesis presents cache performance analysis of the Chronological Garbage Collection Algorithm used in LVM system. LVM is a new Logic Virtual Machine for Prolog. It adopts one stack policy for all dynamic memory requirements and cooperates with an efficient garbage collection algorithm, the Chronological Garbage Collection, to recycle space, not as a deliberate garbage collection operation, but as a natural activity of the LVM engine to gather useful objects. This algorithm combines the advantages of the traditional copying, mark-compact, generational, and incremental garbage collection schemes. In order to determine the improvement of cache performance under our garbage- collection algorithm, we developed a simulator to do trace-driven cache simulation. Direct-mapped cache and set-associative cache with different cache sizes, write policies, block sizes and set associativities are simulated and measured. A comparison of LVM and SICStus 3.1 for the same benchmarks was performed. From the simulation results, we found important factors influencing the performance of the CGC algorithm. Meanwhile, the results from the cache simulator fully support the experimental results gathered from the LVM system: the cost of CGC Is almost paid by the improved cache performance. Further, we found that the memory reference patterns of our benchmarks share the same properties: most writes are for allocation and most reads are to recently written objects. In addition, the results also showed that the write-miss policy can have a dramatic effect on the cache performance of the benchmarks and a write-validate policy gives the best performance. The comparison shows that when the input size of benchmarks is small, SICStus is about 3-8 times faster than LVM. This is an acceptable range of performance ratio for comparing a binary-code engine against a byte-code emulator. When we increase the input sizes, some benchmarks maintain this performance ratio, whereas others greatly narrow the performance gap and at certain breakthrough points perform better than their counterparts under SICStus

Curvature regularization for Non-line-of-sight Imaging from Under-sampled Data

Non-line-of-sight (NLOS) imaging aims to reconstruct the three-dimensional hidden scenes from the data measured in the line-of-sight, which uses photon time-of-flight information encoded in light after multiple diffuse reflections. The under-sampled scanning data can facilitate fast imaging. However, the resulting reconstruction problem becomes a serious ill-posed inverse problem, the solution of which is of high possibility to be degraded due to noises and distortions. In this paper, we propose two novel NLOS reconstruction models based on curvature regularization, i.e., the object-domain curvature regularization model and the dual (i.e., signal and object)-domain curvature regularization model. Fast numerical optimization algorithms are developed relying on the alternating direction method of multipliers (ADMM) with the backtracking stepsize rule, which are further accelerated by GPU implementation. We evaluate the proposed algorithms on both synthetic and real datasets, which achieve state-of-the-art performance, especially in the compressed sensing setting. All our codes and data are available at https://github.com/Duanlab123/CurvNLOS

Quantitative Comparative Analysis of the Bio-Active and Toxic Constituents of Leaves and Spikes of Schizonepeta tenuifolia at Different Harvesting Times

A GC-MS-Selected Ion Monitoring (SIM) detection method was developed for simultaneous determination of four monoterpenes: (−)-menthone, (+)-pulegone, (−)-limonene and (+)-menthofuran as the main bio-active and toxic constituents, and four other main compounds in the volatile oils of Schizonepeta tenuifolia (ST) leaves and spikes at different harvesting times. The results showed that the method was simple, sensitive and reproducible, and that harvesting time was a possible key factor in influencing the quality of ST leaves, but not its spikes. The research might be helpful for determining the harvesting time of ST samples and establishing a validated method for the quality control of ST volatile oil and other relative products

Model Simulation of Cucumber Yield and Microclimate Analysis in a Semi-closed Greenhouse in China

Adequate greenhouse environmental management is very important for improving resource use efficiency and increasing vegetable yield. The objective of this study was to explore suitable climate and cultivation management for cucumber to achieve high yield and build optimal yield models in semi-closed greenhouses. A fruit cucumber cultivar Deltastar was grown over 4 years in greenhouse and weekly data of yields (mean, highest and lowest) and environmental variables, including total radiation, air temperature, relative humidity, and carbon dioxide (CO2) concentration were collected. Regression analyses were applied to develop the relationships and build best regression models of yields with environmental variables using the first 2 years of data. Data collected in years 3 and 4 were used for model validation. Results showed that total radiation, nutrient, temperature, CO2 concentration, and average nighttime relative humidity had significant correlations with cucumber yields. The best regression models fit the mean, lowest, and highest yields very well with R2 values of 0.67, 0.66, and 0.64, respectively. Total radiation and air temperature had the most significant contributions to the variations of the yields. Our results of this study provide useful information for improving greenhouse climate management and yield forecast in semi-closed greenhouses