Hilbert Scheme of skew lines on Cubic threefolds and Locus of primitive vanishing cycles

On a smooth cubic threefold $Y$, the set of pairs of skew lines determines an irreducible component of the Hilbert scheme of $Y$. We prove that such component is smooth and is isomorphic to the blowup of symmetric product of the Fano surface of lines along the diagonal. The local system of integral vanishing cohomology $\mathcal{H}^2_{van}$ over the universal locus of hyperplane sections $U$ of $Y$ determines a covering space $T\to U$. It has a distinguished component $T'$ containing a vanishing cycle associated to a nodal degeneration. $T'$ admits a canonical normal completion $\bar{T}'$ by Stein. We show that $\bar{T}'$ is achieved by contracting finitely many curves on $Bl_0\Theta$ corresponding to Eckardt points on $Y$, where $Bl_0\Theta$ is the blowup of the theta divisor of the intermediate Jacobian of $Y$ at the isolated singularity. We provide interpretions of boundary points of the completion space $\bar{T}'$ via minimal resolution of hyperplane sections with ADE singularities and the related theory on root systems. We also explore the relation to some Bridgland stable moduli spaces on $Y$.Comment: 50 pages. 2 Figures. Most of the sections are completely new. Original theorem was proved using Hilbert schemes instead. (Lemma 3 in the previous version is wrong as stated, which is corrected in the current version.) Comments are welcome

A maximal clique based multiobjective evolutionary algorithm for overlapping community detection

Detecting community structure has become one im-portant technique for studying complex networks. Although many community detection algorithms have been proposed, most of them focus on separated communities, where each node can be-long to only one community. However, in many real-world net-works, communities are often overlapped with each other. De-veloping overlapping community detection algorithms thus be-comes necessary. Along this avenue, this paper proposes a maxi-mal clique based multiobjective evolutionary algorithm for over-lapping community detection. In this algorithm, a new represen-tation scheme based on the introduced maximal-clique graph is presented. Since the maximal-clique graph is defined by using a set of maximal cliques of original graph as nodes and two maximal cliques are allowed to share the same nodes of the original graph, overlap is an intrinsic property of the maximal-clique graph. Attributing to this property, the new representation scheme al-lows multiobjective evolutionary algorithms to handle the over-lapping community detection problem in a way similar to that of the separated community detection, such that the optimization problems are simplified. As a result, the proposed algorithm could detect overlapping community structure with higher partition accuracy and lower computational cost when compared with the existing ones. The experiments on both synthetic and real-world networks validate the effectiveness and efficiency of the proposed algorithm

Number of Repetitions in Re-randomization Tests

In covariate-adaptive or response-adaptive randomization, the treatment assignment and outcome can be correlated. Under this situation, re-randomization tests are a straightforward and attractive method to provide valid statistical inference. In this paper, we investigate the number of repetitions in the re-randomization tests. This is motivated by the group sequential design in clinical trials, where the nominal significance bound can be very small at an interim analysis. Accordingly, re-randomization tests lead to a very large number of required repetitions, which may be computationally intractable. To reduce the number of repetitions, we propose an adaptive procedure and compare it with multiple approaches under pre-defined criteria. Monte Carlo simulations are conducted to show the performance of different approaches in a limited sample size. We also suggest strategies to reduce total computation time and provide practical guidance in preparing, executing and reporting before and after data are unblinded at an interim analysis, so one can complete the computation within a reasonable time frame

Nanostructure Analysis of In-flame Soot Particles in a Diesel Engine

Soot particles emitted from modern diesel engines, despite significantly lower total mass, show higher reactivity and toxicity than black-smoking old engines, which cause serious health and environmental issues. Soot nanostructure, i.e. the internal structure of soot particles composed of nanoscale carbon fringes, can provide useful information to the investigation of the particle reactivity and its oxidation status. This thesis presents the nanostructure details of soot particles sampled directly from diesel flames in a working diesel engine as well as from exhaust gases to compare the internal structure of soot particles in the high formation stage and after in-cylinder oxidation. Thermophoretic soot sampling was conducted using an in-house-designed probe with a lacy transmission electron microscope (TEM) grid stored at the tip. The soot particles deposited on the grid were imaged using a high-resolution TEM to obtain key nanostructure parameters such as carbon fringe length, tortuosity and fringe-to-fringe separation. The TEM images show that in-flame soot particles are consisted of multiple amorphous cores with many defective carbon fringes, which are surrounded by a more oriented and graphitised outer shell. The same core-shell structures are found in the exhaust soot particles, suggesting the overall shape developed within the diesel flame does not change during soot oxidation. However, the exhaust soot particles exhibit more oxidised and less reactive nanostructures as evidenced by the increased fringe length, reduced fringe tortuosity, and lower fringe separation distance. In investigating the in-cylinder particles, the effect of jet-jet interaction on soot nanostructure was considered as one of the major factors. This is because a wall-jet head merging with a neighbouring jet head, which always occurs in diesel engines, is well known to cause high soot formation due to locally rich mixtures. This topic was investigated by performing nanostructure analysis and corresponding morphology analysis of soot particles together with the assistance of planar laser-induced fluorescence of fuel and hydroxyl (fuel- and OH-PLIF) and incandescence of soot (soot-PLII). Since a conventional diesel flame produces a large amount of soot leading to significant beam attenuation to laser diagnostics, methyl decanoate was selected as a surrogate fuel due to its low-sooting propensity. Prior to investigate the effect of jet-jet interaction on soot particles, a direct comparison in soot nanostructure and corresponding morphology is conducted between methyl decanoate and conventional diesel in single jet configuration. The results show that methyl decanoate generates smaller soot primary particles and aggregates with lower fractal dimension, which could be explained either by the earlier stage of soot formation or more oxidised soot status. From the fringe separation results showing a smaller gap for methyl decanoate, it is concluded that the sampled in-flame soot particles were more oxidised likely due to the presence of oxidisers in fuel. As for studying the impact of jet-jet interaction, two different nozzle configurations of one hole and two holes were used to simulate isolated single-jet and double-jet conditions, respectively. These soot particles impacted by the jet-jet interaction have larger aggregates composed of larger primaries, and the nanoscale internal structures are very consistent previous observations to soot particles sampled from conventional diesel flame show higher carbon fringe-to-fringe separations, both of which indicate higher particle reactivity and the formation stage of soot. In the later stage of the PhD study, the existing in-flame soot sampling system that collects only the particles close to the cylinder liner wall, and thus has limitations in clarifying the particle evolution during the development of diesel flames was upgraded by successfully designing and implementing the innovative in-bowl sampling technique. Using the new method, the soot formation processes occurring inside the piston-bowl of a small-bore diesel engine were investigated by conducting the thermophoresis-based soot sampling experiments at various locations along the flame development path. Based on soot-PLII and OH-PLIF imaging performed in the same optical engine previously, it was understood that the sooting flame impinges on and then flows along the bowl wall, suggesting a soot growth and persistence near the fuel-rich wall region. For this study, soot sampling technique was further developed to place the sampling probe in five different locations including the flame-wall impingement point and four further downstream regions: two 60 degree and two 120 degree from the jet axis with two different distances from the bowl wall in each angle. The TEM images of the sampled soot particle aggregates and their statistical analysis of sizes and fractal dimensions show that precursor-like, small soot particles form in the flame-wall impingement region, which grow in size and become large soot aggregates as travelling along the bowl wall. During this particle growth, its internal pattern also changes such that an amorphous carbon layer structure becomes a typical core-shell structure. The detailed analysis clearly indicates that the soot precursors underwent the surface growth, aggregation and coagulation to produce large, long-stretched soot aggregates during which the amorphous soot carbon layers transformed into a typical core-shell structure. At further downstream locations, the continued surface growth increases the size of soot primary particles in the core region of the soot aggregates while the oxidation of the soot primary particles located in the outer region tends to reduce the aggregate size, resulting in more compact structures. In the outer region of the flame, the intensive soot oxidation induced by the hydroxyl attack further reduces the size of large soot aggregates and at the same time, eliminates the small soot aggregates. Throughout these soot formation/oxidation processes, the soot carbon layer gaps continue to decrease, indicating more mature soot primary particles

FFT: Towards Harmlessness Evaluation and Analysis for LLMs with Factuality, Fairness, Toxicity

The widespread of generative artificial intelligence has heightened concerns about the potential harms posed by AI-generated texts, primarily stemming from factoid, unfair, and toxic content. Previous researchers have invested much effort in assessing the harmlessness of generative language models. However, existing benchmarks are struggling in the era of large language models (LLMs), due to the stronger language generation and instruction following capabilities, as well as wider applications. In this paper, we propose FFT, a new benchmark with 2116 elaborated-designed instances, for LLM harmlessness evaluation with factuality, fairness, and toxicity. To investigate the potential harms of LLMs, we evaluate 9 representative LLMs covering various parameter scales, training stages, and creators. Experiments show that the harmlessness of LLMs is still under-satisfactory, and extensive analysis derives some insightful findings that could inspire future research for harmless LLM research.Comment: Work in progres