1,007 research outputs found
Highly accurate operator factorization methods for the integral fractional Laplacian and its generalization
In this paper, we propose a new class of operator factorization methods to
discretize the integral fractional Laplacian for
. The main advantage of our method is to easily increase
numerical accuracy by using high-degree Lagrange basis functions, but remain
the scheme structure and computer implementation unchanged. Moreover, our
discretization of the fractional Laplacian results in a symmetric (multilevel)
Toeplitz differentiation matrix, which not only saves memory cost in
simulations but enables efficient computations via the fast Fourier transforms.
The performance of our method in both approximating the fractional Laplacian
and solving the fractional Poisson problems was detailedly examined. It shows
that our method has an optimal accuracy of for constant or
linear basis functions, while if quadratic basis functions
are used, with a small mesh size. Note that this accuracy holds for any
and can be further increased if higher-degree basis
functions are used. If the solution of fractional Poisson problem satisfies for and , then our
method has an accuracy of for
constant and linear basis functions, while for quadratic basis functions. Additionally, our method can be
readily applied to study generalized fractional Laplacians with a symmetric
kernel function, and numerical study on the tempered fractional Poisson problem
demonstrates its efficiency.Comment: 21 pages, 7 figure
Understanding Patient Journeys with Telehealth: A Poisson-Factor-Marked Hawkes Process
The emerging telehealth platforms connect patients with physicians using telecommunication technologies and are transforming the traditional healthcare delivery process. Meanwhile, patient care journeys spreading across online and offline health service channels call for new research methodologies. Using a dataset from a telehealth platform, we develop a novel Poisson-factor-marked Hawkes process to model such a journey and quantify the mutual-modulating effects of various patient activities. Our estimation results demonstrate the disparate impacts of the patient’s health conditions and physician characteristics on choosing care channels. Taking advantage of the self-generation property of our model, we simulate policy and strategic interventions, which highlights the practical value of the proposed model and offers implications for better patient routing and service design for telehealth platforms
Bias Mitigation in Fine-tuning Pre-trained Models for Enhanced Fairness and Efficiency
Fine-tuning pre-trained models is a widely employed technique in numerous
real-world applications. However, fine-tuning these models on new tasks can
lead to unfair outcomes. This is due to the absence of generalization
guarantees for fairness properties, regardless of whether the original
pre-trained model was developed with fairness considerations. To tackle this
issue, we introduce an efficient and robust fine-tuning framework specifically
designed to mitigate biases in new tasks. Our empirical analysis shows that the
parameters in the pre-trained model that affect predictions for different
demographic groups are different, so based on this observation, we employ a
transfer learning strategy that neutralizes the importance of these influential
weights, determined using Fisher information across demographic groups.
Additionally, we integrate this weight importance neutralization strategy with
a matrix factorization technique, which provides a low-rank approximation of
the weight matrix using fewer parameters, reducing the computational demands.
Experiments on multiple pre-trained models and new tasks demonstrate the
effectiveness of our method
Eat4Thought: A Design of Food Journaling
Food journaling is an effective method to help people identify their eating
patterns and encourage healthy eating habits as it requires self-reflection on
eating behaviors. Current tools have predominately focused on tracking food
intake, such as carbohydrates, proteins, fats, and calories. Other factors,
such as contextual information and momentary thoughts and feelings that are
internal to an individual, are also essential to help people reflect upon and
change attitudes about eating behaviors. However, current dietary tracking
tools rarely support capturing these elements as a way to foster deep
reflection. In this work, we present Eat4Thought -- a food journaling
application that allows users to track their emotional, sensory, and
spatio-temporal elements of meals as a means of supporting self-reflection. The
application enables vivid documentation of experiences and self-reflection on
the past through video recording. We describe our design process and an initial
evaluation of the application. We also provide design recommendations for
future work on food journaling.Comment: 8 page
A Comprehensive Study and Comparison of the Robustness of 3D Object Detectors Against Adversarial Attacks
Recent years have witnessed significant advancements in deep learning-based
3D object detection, leading to its widespread adoption in numerous
applications. As 3D object detectors become increasingly crucial for
security-critical tasks, it is imperative to understand their robustness
against adversarial attacks. This paper presents the first comprehensive
evaluation and analysis of the robustness of LiDAR-based 3D detectors under
adversarial attacks. Specifically, we extend three distinct adversarial attacks
to the 3D object detection task, benchmarking the robustness of
state-of-the-art LiDAR-based 3D object detectors against attacks on the KITTI
and Waymo datasets. We further analyze the relationship between robustness and
detector properties. Additionally, we explore the transferability of
cross-model, cross-task, and cross-data attacks. Thorough experiments on
defensive strategies for 3D detectors are conducted, demonstrating that simple
transformations like flipping provide little help in improving robustness when
the applied transformation strategy is exposed to attackers. Finally, we
propose balanced adversarial focal training, based on conventional adversarial
training, to strike a balance between accuracy and robustness. Our findings
will facilitate investigations into understanding and defending against
adversarial attacks on LiDAR-based 3D object detectors, thus advancing the
field. The source code is publicly available at
\url{https://github.com/Eaphan/Robust3DOD}.Comment: 30 pages, 14 figure
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