Two harmonic Jacobi--Davidson methods for computing a partial generalized singular value decomposition of a large matrix pair

Two harmonic extraction based Jacobi--Davidson (JD) type algorithms are proposed to compute a partial generalized singular value decomposition (GSVD) of a large regular matrix pair. They are called cross product-free (CPF) and inverse-free (IF) harmonic JDGSVD algorithms, abbreviated as CPF-HJDGSVD and IF-HJDGSVD, respectively. Compared with the standard extraction based JDGSVD algorithm, the harmonic extraction based algorithms converge more regularly and suit better for computing GSVD components corresponding to interior generalized singular values. Thick-restart CPF-HJDGSVD and IF-HJDGSVD algorithms with some deflation and purgation techniques are developed to compute more than one GSVD components. Numerical experiments confirm the superiority of CPF-HJDGSVD and IF-HJDGSVD to the standard extraction based JDGSVD algorithm.Comment: 24 pages, 5 figure

Preconditioning correction equations in Jacobi--Davidson type methods for computing partial singular value decompositions of large matrices

In a Jacobi--Davidson (JD) type method for singular value decomposition (SVD) problems, called JDSVD, a large symmetric and generally indefinite correction equation is approximately solved iteratively at each outer iteration, which constitutes the inner iterations and dominates the overall efficiency of JDSVD. In this paper, a convergence analysis is made on the minimal residual (MINRES) method for the correction equation. Motivated by the results obtained, a preconditioned correction equation is derived that extracts useful information from current searching subspaces to construct effective preconditioners for the correction equation and is proved to retain the same convergence of outer iterations of JDSVD. The resulting method is called inner preconditioned JDSVD (IPJDSVD) method. Convergence results show that MINRES for the preconditioned correction equation can converge much faster when there is a cluster of singular values closest to a given target, so that IPJDSVD is more efficient than JDSVD. A new thick-restart IPJDSVD algorithm with deflation and purgation is proposed that simultaneously accelerates the outer and inner convergence of the standard thick-restart JDSVD and computes several singular triplets of a large matrix. Numerical experiments justify the theory and illustrate the considerable superiority of IPJDSVD to JDSVD.Comment: 26 pages, 2 figure

Dynamics of cell-type transition mediated by epigenetic modifications

Maintaining tissue homeostasis requires appropriate regulation of stem cell differentiation. The Waddington landscape posits that gene circuits in a cell form a potential landscape of different cell types, wherein cells follow attractors of the probability landscape to develop into distinct cell types. However, how adult stem cells achieve a delicate balance between self-renewal and differentiation remains unclear. We propose that random inheritance of epigenetic states plays a pivotal role in stem cell differentiation and present a hybrid model of stem cell differentiation induced by epigenetic modifications. Our comprehensive model integrates gene regulation networks, epigenetic state inheritance, and cell regeneration, encompassing multi-scale dynamics ranging from transcription regulation to cell population. Through model simulations, we demonstrate that random inheritance of epigenetic states during cell divisions can spontaneously induce cell differentiation, dedifferentiation, and transdifferentiation. Furthermore, we investigate the influences of interfering with epigenetic modifications and introducing additional transcription factors on the probabilities of dedifferentiation and transdifferentiation, revealing the underlying mechanism of cell reprogramming. This \textit{in silico} model provides valuable insights into the intricate mechanism governing stem cell differentiation and cell reprogramming and offers a promising path to enhance the field of regenerative medicine.Comment: 34 pages, 12 figure

Modelling infectious disease transmission dynamics in conference environments: An individual-based approach

The global public health landscape is perpetually challenged by the looming threat of infectious diseases. Central to addressing this concern is the imperative to prevent and manage disease transmission during pandemics, particularly in unique settings. This study addresses the transmission dynamics of infectious diseases within conference venues, presenting a computational model designed to simulate transmission processes within a condensed timeframe (one day), beginning with sporadic cases. Our model intricately captures the activities of individual attendees within the conference venue, encompassing meetings, rest intervals, and meal breaks. While meetings entail proximity seating, rest and lunch periods allow attendees to interact with diverse individuals. Moreover, the restroom environment poses an additional avenue for potential infection transmission. Employing an individual-based model, we meticulously replicated the transmission dynamics of infectious diseases, with a specific emphasis on close-contact interactions between infected and susceptible individuals. Through comprehensive analysis of model simulations, we elucidated the intricacies of disease transmission dynamics within conference settings and assessed the efficacy of control strategies to curb disease dissemination. Ultimately, our study proffers a numerical framework for assessing the risk of infectious disease transmission during short-duration conferences, furnishing conference organizers with valuable insights to inform the implementation of targeted prevention and control measures.Comment: 25 pages; 8 figure

1965 Volume 14 No. 2

https://engagedscholarship.csuohio.edu/lawpublications_gavel1960s/1032/thumbnail.jp

OmniSeg3D: Omniversal 3D Segmentation via Hierarchical Contrastive Learning

Towards holistic understanding of 3D scenes, a general 3D segmentation method is needed that can segment diverse objects without restrictions on object quantity or categories, while also reflecting the inherent hierarchical structure. To achieve this, we propose OmniSeg3D, an omniversal segmentation method aims for segmenting anything in 3D all at once. The key insight is to lift multi-view inconsistent 2D segmentations into a consistent 3D feature field through a hierarchical contrastive learning framework, which is accomplished by two steps. Firstly, we design a novel hierarchical representation based on category-agnostic 2D segmentations to model the multi-level relationship among pixels. Secondly, image features rendered from the 3D feature field are clustered at different levels, which can be further drawn closer or pushed apart according to the hierarchical relationship between different levels. In tackling the challenges posed by inconsistent 2D segmentations, this framework yields a global consistent 3D feature field, which further enables hierarchical segmentation, multi-object selection, and global discretization. Extensive experiments demonstrate the effectiveness of our method on high-quality 3D segmentation and accurate hierarchical structure understanding. A graphical user interface further facilitates flexible interaction for omniversal 3D segmentation