Essays on strong and weak approximations of stochastic differential equations

The thesis is composed of two projects on approximations of stochastic differential equations. In the first project, we present a method to construct positivity-preserving strong approximation schemes for jump-extended CEV and CIR processes where the jumps are governed by a compensated spectrally positive alpha-stable process with alpha in (1, 2). To the best of our knowledge, the proposed scheme is the first of its kind, i.e. a positivity preserving scheme for alpha-stable-extended CEV processes, and it has the advantage that at each discretisation step, an explicit form of the scheme is available and it's given by the positive solution of a quadratic equation. We show that the proposed scheme converges and theoretically achieves a strong convergence rate that we believe is very close to the optimal rate. The second project is on the weak approximation and density estimates for a skew diffusion with coefficients depending on its local time at zero. In the existing literature, the parametrix method has been applied to obtain density estimates for skew diffusion processes, and more recently, for Ito diffusion processes with coefficients depending on local time. The goal of the second project is to extend the class of processes for which one can apply the parametrix method. As our main contribution, We obtain an explicit representation and Gaussian estimates of the joint transition density, which can lead to an exact simulation method for the skew diffusion process and it's local time at zero

Unchain the Search Space with Hierarchical Differentiable Architecture Search

Differentiable architecture search (DAS) has made great progress in searching for high-performance architectures with reduced computational cost. However, DAS-based methods mainly focus on searching for a repeatable cell structure, which is then stacked sequentially in multiple stages to form the networks. This configuration significantly reduces the search space, and ignores the importance of connections between the cells. To overcome this limitation, in this paper, we propose a Hierarchical Differentiable Architecture Search (H-DAS) that performs architecture search both at the cell level and at the stage level. Specifically, the cell-level search space is relaxed so that the networks can learn stage-specific cell structures. For the stage-level search, we systematically study the architectures of stages, including the number of cells in each stage and the connections between the cells. Based on insightful observations, we design several search rules and losses, and mange to search for better stage-level architectures. Such hierarchical search space greatly improves the performance of the networks without introducing expensive search cost. Extensive experiments on CIFAR10 and ImageNet demonstrate the effectiveness of the proposed H-DAS. Moreover, the searched stage-level architectures can be combined with the cell structures searched by existing DAS methods to further boost the performance. Code is available at: https://github.com/MalongTech/research-HDASComment: To appear in AAAI2021. Code is availabl

Optical ReLU-like Activation Function Based on a Semiconductor Laser with Optical Injection

Artificial neural networks usually consist of successive linear multiply-accumulate operations and nonlinear activation functions. However, most optical neural networks only achieve the linear operation in the optical domain, while the optical implementation of activation function remains challenging. Here we present an optical ReLU-like activation function based on a semiconductor laser subject to the optical injection in experiment. The ReLU-like function is achieved in a broad regime above the Hopf bifurcation of the injection-locking diagram. In particular, the slope of the activation function is reconfigurable by tuning the frequency difference between the master laser and the slave laser

OccuQuest: Mitigating Occupational Bias for Inclusive Large Language Models

The emergence of large language models (LLMs) has revolutionized natural language processing tasks. However, existing instruction-tuning datasets suffer from occupational bias: the majority of data relates to only a few occupations, which hampers the instruction-tuned LLMs to generate helpful responses to professional queries from practitioners in specific fields. To mitigate this issue and promote occupation-inclusive LLMs, we create an instruction-tuning dataset named \emph{OccuQuest}, which contains 110,000+ prompt-completion pairs and 30,000+ dialogues covering over 1,000 occupations in 26 occupational categories. We systematically request ChatGPT, organizing queries hierarchically based on Occupation, Responsibility, Topic, and Question, to ensure a comprehensive coverage of occupational specialty inquiries. By comparing with three commonly used datasets (Dolly, ShareGPT, and WizardLM), we observe that OccuQuest exhibits a more balanced distribution across occupations. Furthermore, we assemble three test sets for comprehensive evaluation, an occu-test set covering 25 occupational categories, an estate set focusing on real estate, and an occu-quora set containing real-world questions from Quora. We then fine-tune LLaMA on OccuQuest to obtain OccuLLaMA, which significantly outperforms state-of-the-art LLaMA variants (Vicuna, Tulu, and WizardLM) on professional questions in GPT-4 and human evaluations. Notably, on the occu-quora set, OccuLLaMA reaches a high win rate of 86.4\% against WizardLM

Prognostic and therapeutic significance of microbial cell-free DNA in plasma of people with acutely decompensated cirrhosis

BACKGROUND AND AIMS: Although the effect of bacterial infection on cirrhosis has been well-described, the effect of non-hepatotropic virus (NHV) infection is unknown. This study evaluated the genome fragments of circulating microorganisms using metagenomic next-generation sequencing (mNGS) in cirrhosis patients with acute decompensation (AD), focusing on NHVs and related the findings to clinical outcomes. METHODS: Plasma mNGS was performed in 129 cirrhosis patients with AD in study cohort. Ten healthy volunteers and 20, 39, and 81 patients with stable cirrhosis, severe sepsis and hematological malignancies, respectively, were enrolled as controls. Validation assays for human cytomegalovirus (CMV) reactivation in a validation cohort (n = 58) were performed and exploratory treatment instituted. RESULTS: In study cohort, 188 microorganisms were detected in 74.4% (96/129) patients, including viruses (58.0%), bacteria (34.1%), fungi (7.4%) and chlamydia (0.5%). Patients with AD had an NHV signature, and CMV was the most frequent NHV, which correlated with the clinical effect of empirical antibiotic treatment, progression to acute-on-chronic liver failure (ACLF), and 90-day mortality. The NHV signature in ACLF patients was similar to patients with sepsis and hematological malignancies. The treatable NHV, CMV was detected in 24.1% (14/58) patients in the validation cohort. Of the 14 cases with detectable CMV by mNGS, 9 were further validated by DNA RT-PCR or pp65 antigenemia testing. Three patients with CMV reactivation received ganciclovir therapy in exploratory manner with clinical resolutions. CONCLUSIONS: The results of this study suggests that NHVs may have a pathogenic role in complicating the course of AD. Further validation is needed to define whether this should be incorporated in the routine management of AD patients. IMPACT AND IMPLICATIONS: ●Cirrhosis patients with acute decompensation have a non-hepatotropic virus (NHV) signature, which is similar to that in sepsis and hematological malignancies patients. ●The detected viral signature had clinical correlates, including clinical efficacy of empirical antibiotic treatment, progression to acute-on-chronic liver failure and short-term mortality. ●The treatable NHV, CMV reactivation may be involved in the clinical outcomes of decompensated cirrhosis. ●Routine screening for NHVs, especially CMV, may be useful for the management of patients with acutely decompensated cirrhosis

P2P LENDING MARKET: DETERMINANTS OF INTEREST RATE AND DEFAULT RISK

The peer to peer (p2p) lending industry has grown fast in recent years. This study put an eye on the credit evaluation system of one of the p2p platform named lending club. The author used the empirical method and discussed the determinants of the interest rate and the default risk in the p2p lending market. The author concluded that the evaluation system founded by lending club could predict the risk of loans. Collecting more information about borrowers’ credit history may increase the accuracy of the model

Antiplane Fracture Problem of Three Nanocracks Emanating from an Electrically Permeable Hexagonal Nanohole in One-Dimensional Hexagonal Piezoelectric Quasicrystals

Based on the Gurtin-Murdoch surface/interface model and complex potential theory, by constructing a new conformal mapping, the electrically permeable boundary condition with surface effect is established, and the antiplane fracture problem of three nanocracks emanating from a hexagonal nanohole in one-dimensional hexagonal piezoelectric quasicrystals with surface effect is studied. The exact solutions of the stress intensity factor of the phonon field and the phason field, the electric displacement intensity factor, and the energy release rate are obtained under the two electrically permeable and the electrically impermeable boundary conditions. The numerical examples show the influence of surface effect on the stress intensity factors of the phonon field and the phason field, the electric displacement intensity factor, and the energy release rate under the two boundary conditions. It can be seen that the surface effect leads to the coupling of the phonon field, phason field, and electric field, and with the decrease of cavity size, the influence of surface effect is more obvious

Vital node searcher: find out critical node measure with deep reinforcement learning

How to find the critical nodes in the network structure quickly and accurately is a topic of network science. Various algorithms for critical nodes already exist, of which, however, some are with high time complexity and the rest are limited in application range. To solve this problem, an algorithm, referred to as Vital Node Searcher (VNS), is proposed, which discovers critical nodes from a network based on deep reinforcement learning. The VNS method first takes advantage of the Graph Embedding to downscale the feature information of the target network, and then uses the deep Q network method to extract the critical node sequence. A Long-Short Term network module is designed and applied to fully exploit historical information that is contained in the sequence data. Moreover, a duelling Q network module is developed to enhance the precision of prediction. Both in terms of time complexity and performance, the VNS method is superior compared with other methods, which are validated by experiments of real world datasets. Moreover, VNS method has strong generalisation performance and can be applied to different types of critical node problems. The VNS method performed experiments on four datasets and obtained ANC scores that outperformed the other models respectively. The experiment results demonstrated that the VNS method had a stable and effective performance on finding out the critical node sequence

Worldspace Heatmaps

Many games are set in 3D worlds and have shifting camera viewpoints. In this study, we attempt to create and evaluate a Proof-of-Concept Worldspace Heatmap System that accounts for the shifting camera views in 3D game worlds, in an attempt to improve user testing processes. We test the system by conducting a stimulated recall user study, in which we examine the areas in a game that drew the attention of the participants, with the help of heatmaps placed in the game world. Our results include observations of several behavior patterns and participant evaluations of the Worldspace Heatmap System. We observed multiple indications in the data we gathered, that such a system can be useful for obtaining player behavior insights and for enhancing user testing processes, especially if some of the limitations are overcome