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This study explores reduced-order modeling for analyzing the time-dependent diffusion-deformation of hydrogels. The full-order model describing hydrogel transient behavior consists of a coupled system of partial differential equations in which chemical potential and displacements are coupled. This system is formulated in a monolithic fashion and solved using the finite element method. We employ proper orthogonal decomposition as a model order reduction approach. The reduced-order model performance is tested through a benchmark problem on hydrogel swelling and a case study simulating co-axial printing. Then, we embed the reduced-order model into an optimization loop to efficiently identify the coupled problem's material parameters using full-field data. Finally, a study is conducted on the uncertainty propagation of the material parameter.

In the analysis of spatially resolved transcriptomics data, detecting spatially variable genes (SVGs) is crucial. Numerous computational methods exist, but varying SVG definitions and methodologies lead to incomparable results. We review 31 state-of-the-art methods, categorizing SVGs into three types: overall, cell-type-specific, and spatial-domain-marker SVGs. Our review explains the intuitions underlying these methods, summarizes their applications, and categorizes the hypothesis tests they use in the trade-off between generality and specificity for SVG detection. We discuss challenges in SVG detection and propose future directions for improvement. Our review offers insights for method developers and users, advocating for category-specific benchmarking.

We provide a novel dimension-free uniform concentration bound for the empirical risk function of constrained logistic regression. Our bound yields a milder sufficient condition for a uniform law of large numbers than conditions derived by the Rademacher complexity argument and McDiarmid's inequality. The derivation is based on the PAC-Bayes approach with second-order expansion and Rademacher-complexity-based bounds for the residual term of the expansion.

Sequential recommendation systems that model dynamic preferences based on a use's past behavior are crucial to e-commerce. Recent studies on these systems have considered various types of information such as images and texts. However, multimodal data have not yet been utilized directly to recommend products to users. In this study, we propose an attention-based sequential recommendation method that employs multimodal data of items such as images, texts, and categories. First, we extract image and text features from pre-trained VGG and BERT and convert categories into multi-labeled forms. Subsequently, attention operations are performed independent of the item sequence and multimodal representations. Finally, the individual attention information is integrated through an attention fusion function. In addition, we apply multitask learning loss for each modality to improve the generalization performance. The experimental results obtained from the Amazon datasets show that the proposed method outperforms those of conventional sequential recommendation systems.

We propose a coefficient that measures dependence in paired samples of functions. It has properties similar to the Pearson correlation, but differs in significant ways: 1) it is designed to measure dependence between curves, 2) it focuses only on extreme curves. The new coefficient is derived within the framework of regular variation in Banach spaces. A consistent estimator is proposed and justified by an asymptotic analysis and a simulation study. The usefulness of the new coefficient is illustrated on financial and and climate functional data.

This work is concerned with the construction and analysis of structure-preserving Galerkin methods for computing the dynamics of rotating Bose-Einstein condensate (BEC) based on the Gross-Pitaevskii equation with angular momentum rotation. Due to the presence of the rotation term, constructing finite element methods (FEMs) that preserve both mass and energy remains an unresolved issue, particularly in the context of nonconforming FEMs. Furthermore, in comparison to existing works, we provide a comprehensive convergence analysis, offering a thorough demonstration of the methods' optimal and high-order convergence properties. Finally, extensive numerical results are presented to check the theoretical analysis of the structure-preserving numerical method for rotating BEC, and the quantized vortex lattice's behavior is scrutinized through a series of numerical tests.

Detecting differences in gene expression is an important part of single-cell RNA sequencing experiments, and many statistical methods have been developed for this aim. Most differential expression analyses focus on comparing expression between two groups (e.g., treatment vs. control). But there is increasing interest in multi-condition differential expression analyses in which expression is measured in many conditions, and the aim is to accurately detect and estimate expression differences in all conditions. We show that directly modeling single-cell RNA-seq counts in all conditions simultaneously, while also inferring how expression differences are shared across conditions, leads to greatly improved performance for detecting and estimating expression differences compared to existing methods. We illustrate the potential of this new approach by analyzing data from a single-cell experiment studying the effects of cytokine stimulation on gene expression. We call our new method "Poisson multivariate adaptive shrinkage", and it is implemented in an R package available online at //github.com/stephenslab/poisson.mash.alpha.

Bipartite graphs are a prevalent modeling tool for real-world networks, capturing interactions between vertices of two different types. Within this framework, bicliques emerge as crucial structures when studying dense subgraphs: they are sets of vertices such that all vertices of the first type interact with all vertices of the second type. Therefore, they allow identifying groups of closely related vertices of the network, such as individuals with similar interests or webpages with similar contents. This article introduces a new algorithm designed for the exhaustive enumeration of maximal bicliques within a bipartite graph. This algorithm, called BBK for Bipartite Bron-Kerbosch, is a new extension to the bipartite case of the Bron-Kerbosch algorithm, which enumerates the maximal cliques in standard (non-bipartite) graphs. It is faster than the state-of-the-art algorithms and allows the enumeration on massive bipartite graphs that are not manageable with existing implementations. We analyze it theoretically to establish two complexity formulas: one as a function of the input and one as a function of the output characteristics of the algorithm. We also provide an open-access implementation of BBK in C++, which we use to experiment and validate its efficiency on massive real-world datasets and show that its execution time is shorter in practice than state-of-the art algorithms. These experiments also show that the order in which the vertices are processed, as well as the choice of one of the two types of vertices on which to initiate the enumeration have an impact on the computation time.

Lattice structures have been widely used in applications due to their superior mechanical properties. To fabricate such structures, a geometric processing step called triangulation is often employed to transform them into the STL format before sending them to 3D printers. Because lattice structures tend to have high geometric complexity, this step usually generates a large amount of triangles, a memory and compute-intensive task. This problem manifests itself clearly through large-scale lattice structures that have millions or billions of struts. To address this problem, this paper proposes to transform a lattice structure into an intermediate model called meta-mesh before undergoing real triangulation. Compared to triangular meshes, meta-meshes are very lightweight and much less compute-demanding. The meta-mesh can also work as a base mesh reusable for conveniently and efficiently triangulating lattice structures with arbitrary resolutions. A CPU+GPU asynchronous meta-meshing pipeline has been developed to efficiently generate meta-meshes from lattice structures. It shifts from the thread-centric GPU algorithm design paradigm commonly used in CAD to the recent warp-centric design paradigm to achieve high performance. This is achieved by a new data compression method, a GPU cache-aware data structure, and a workload-balanced scheduling method that can significantly reduce memory divergence and branch divergence. Experimenting with various billion-scale lattice structures, the proposed method is seen to be two orders of magnitude faster than previously achievable.

Inference for functional linear models in the presence of heteroscedastic errors has received insufficient attention given its practical importance; in fact, even a central limit theorem has not been studied in this case. At issue, conditional mean estimates have complicated sampling distributions due to the infinite dimensional regressors, where truncation bias and scaling issues are compounded by non-constant variance under heteroscedasticity. As a foundation for distributional inference, we establish a central limit theorem for the estimated conditional mean under general dependent errors, and subsequently we develop a paired bootstrap method to provide better approximations of sampling distributions. The proposed paired bootstrap does not follow the standard bootstrap algorithm for finite dimensional regressors, as this version fails outside of a narrow window for implementation with functional regressors. The reason owes to a bias with functional regressors in a naive bootstrap construction. Our bootstrap proposal incorporates debiasing and thereby attains much broader validity and flexibility with truncation parameters for inference under heteroscedasticity; even when the naive approach may be valid, the proposed bootstrap method performs better numerically. The bootstrap is applied to construct confidence intervals for centered projections and for conducting hypothesis tests for the multiple conditional means. Our theoretical results on bootstrap consistency are demonstrated through simulation studies and also illustrated with a real data example.