Fake Geometric Brownian Motion And Its Option Pricing

In this thesis, we begin with introducing the notion of a fake geometric Brownian motion in analogy to the fake Brownian motion. Secondly we construct two discontinuous fake geometric Brownian motion processes via the solutions to the Skorokhod embedding problem. Finally we simulate European and path-dependent option pricings for stock prices following these processes, to see how different the results can be compared with the traditional Black & Scholes setting.\ud \ud Key words: fake Brownian motion, fake geometric Brownian motion, Skorokhod embedding problem, Azema-Yor solution, reversed Azema-Yor solution

Continual Driving Policy Optimization with Closed-Loop Individualized Curricula

The safety of autonomous vehicles (AV) has been a long-standing top concern, stemming from the absence of rare and safety-critical scenarios in the long-tail naturalistic driving distribution. To tackle this challenge, a surge of research in scenario-based autonomous driving has emerged, with a focus on generating high-risk driving scenarios and applying them to conduct safety-critical testing of AV models. However, limited work has been explored on the reuse of these extensive scenarios to iteratively improve AV models. Moreover, it remains intractable and challenging to filter through gigantic scenario libraries collected from other AV models with distinct behaviors, attempting to extract transferable information for current AV improvement. Therefore, we develop a continual driving policy optimization framework featuring Closed-Loop Individualized Curricula (CLIC), which we factorize into a set of standardized sub-modules for flexible implementation choices: AV Evaluation, Scenario Selection, and AV Training. CLIC frames AV Evaluation as a collision prediction task, where it estimates the chance of AV failures in these scenarios at each iteration. Subsequently, by re-sampling from historical scenarios based on these failure probabilities, CLIC tailors individualized curricula for downstream training, aligning them with the evaluated capability of AV. Accordingly, CLIC not only maximizes the utilization of the vast pre-collected scenario library for closed-loop driving policy optimization but also facilitates AV improvement by individualizing its training with more challenging cases out of those poorly organized scenarios. Experimental results clearly indicate that CLIC surpasses other curriculum-based training strategies, showing substantial improvement in managing risky scenarios, while still maintaining proficiency in handling simpler cases

Media Exposure and Risk Perception as Predictors of Engagement in COVID-19 Preventive Behaviors: Extending the Theory of Planned Behavior Across Two Cultures

Purpose: This study examined the psychological and social factors that affect the performance of preventive behaviors toward COVID-19, by testing a model based on the theory of planned behavior (TPB). Our model featured media exposure and social networking site (SNS) involvement, and we tested it in two highly contrasted cultures regarding COVID-19 attitudes: U.S. and Japan. Method: An online survey collected 300 samples for each culture. Participation was voluntary, for monetary compensation through crowd-sourcing platforms. Findings: Overall, the results showed a good fit of our TPB model in each culture. Media exposure was a major predictor of risk perception in both cultures, while engagement in SNS predicted intention to perform preventive behavior for the Japanese only, and personal hygiene was found to be a significant predictor of protective behavior once again only for the Japanese. Implications and Value: While there were differences in the variables affecting preventive behaviors, overall, our proposed model proved to be robust across both cultures. Implications were made on differences between tight and loose cultures, as represented by Japan and the US, regarding COVID-19 preventive attitudes

Improving Pre-trained Language Model Fine-tuning with Noise Stability Regularization

The advent of large-scale pre-trained language models has contributed greatly to the recent progress in natural language processing. Many state-of-the-art language models are first trained on a large text corpus and then fine-tuned on downstream tasks. Despite its recent success and wide adoption, fine-tuning a pre-trained language model often suffers from overfitting, which leads to poor generalizability due to the extremely high complexity of the model and the limited training samples from downstream tasks. To address this problem, we propose a novel and effective fine-tuning framework, named Layerwise Noise Stability Regularization (LNSR). Specifically, we propose to inject the standard Gaussian noise or In-manifold noise and regularize hidden representations of the fine-tuned model. We first provide theoretical analyses to support the efficacy of our method. We then demonstrate the advantages of the proposed method over other state-of-the-art algorithms including L2-SP, Mixout and SMART. While these previous works only verify the effectiveness of their methods on relatively simple text classification tasks, we also verify the effectiveness of our method on question answering tasks, where the target problem is much more difficult and more training examples are available. Furthermore, extensive experimental results indicate that the proposed algorithm can not only enhance the in-domain performance of the language models but also improve the domain generalization performance on out-of-domain data.Comment: Accepted by TNNL

Hunting Attributes: Context Prototype-Aware Learning for Weakly Supervised Semantic Segmentation

Recent weakly supervised semantic segmentation (WSSS) methods strive to incorporate contextual knowledge to improve the completeness of class activation maps (CAM). In this work, we argue that the knowledge bias between instances and contexts affects the capability of the prototype to sufficiently understand instance semantics. Inspired by prototype learning theory, we propose leveraging prototype awareness to capture diverse and fine-grained feature attributes of instances. The hypothesis is that contextual prototypes might erroneously activate similar and frequently co-occurring object categories due to this knowledge bias. Therefore, we propose to enhance the prototype representation ability by mitigating the bias to better capture spatial coverage in semantic object regions. With this goal, we present a Context Prototype-Aware Learning (CPAL) strategy, which leverages semantic context to enrich instance comprehension. The core of this method is to accurately capture intra-class variations in object features through context-aware prototypes, facilitating the adaptation to the semantic attributes of various instances. We design feature distribution alignment to optimize prototype awareness, aligning instance feature distributions with dense features. In addition, a unified training framework is proposed to combine label-guided classification supervision and prototypes-guided self-supervision. Experimental results on PASCAL VOC 2012 and MS COCO 2014 show that CPAL significantly improves off-the-shelf methods and achieves state-of-the-art performance. The project is available at https://github.com/Barrett-python/CPAL

Petroleum Hydrocarbon-Degrading Bacteria for the Remediation of Oil Pollution Under Aerobic Conditions: A Perspective Analysis

With the sharp increase in population and modernization of society, environmental pollution resulting from petroleum hydrocarbons has increased, resulting in an urgent need for remediation. Petroleum hydrocarbon-degrading bacteria are ubiquitous in nature and can utilize these compounds as sources of carbon and energy. Bacteria displaying such capabilities are often exploited for the bioremediation of petroleum oil-contaminated environments. Recently, microbial remediation technology has developed rapidly and achieved major gains. However, this technology is not omnipotent. It is affected by many environmental factors that hinder its practical application, limiting the large-scale application of the technology. This paper provides an overview of the recent literature referring to the usage of bacteria as biodegraders, discusses barriers regarding the implementation of this microbial technology, and provides suggestions for further developments