Sparse Bilinear Logistic Regression

In this paper, we introduce the concept of sparse bilinear logistic regression for decision problems involving explanatory variables that are two-dimensional matrices. Such problems are common in computer vision, brain-computer interfaces, style/content factorization, and parallel factor analysis. The underlying optimization problem is bi-convex; we study its solution and develop an efficient algorithm based on block coordinate descent. We provide a theoretical guarantee for global convergence and estimate the asymptotical convergence rate using the Kurdyka-{\L}ojasiewicz inequality. A range of experiments with simulated and real data demonstrate that sparse bilinear logistic regression outperforms current techniques in several important applications.Comment: 27 pages, 5 figure

Primordial Black Hole Formation in Starobinsky's Linear Potential Model

We study the power spectrum of the comoving curvature perturbation $\cal R$ in the model that glues two linear potentials of different slopes, originally proposed by Starobinsky. We find that the enhanced power spectrum reaches its maximum at the wavenumber which is $\pi$ times the junction scale. The peak is $\sim2.61$ times larger than the ultraviolet plateau. We also show that its near-peak behavior can be well approximated by a constant-roll model, once we define the effective ultra-slow-roll $e$-folding number appropriately by considering the contribution from non-single-clock phase only. Such an abrupt transition to non-attractor phase can leave some interesting characteristic features in the energy spectrum of the scalar-induced gravitational waves, which are detectable in the space-borne interferometers if the primordial black holes generated at such a high peak are all the dark matter.Comment: 45 pages, 8 figure

Video Compressive Sensing for Dynamic MRI

We present a video compressive sensing framework, termed kt-CSLDS, to accelerate the image acquisition process of dynamic magnetic resonance imaging (MRI). We are inspired by a state-of-the-art model for video compressive sensing that utilizes a linear dynamical system (LDS) to model the motion manifold. Given compressive measurements, the state sequence of an LDS can be first estimated using system identification techniques. We then reconstruct the observation matrix using a joint structured sparsity assumption. In particular, we minimize an objective function with a mixture of wavelet sparsity and joint sparsity within the observation matrix. We derive an efficient convex optimization algorithm through alternating direction method of multipliers (ADMM), and provide a theoretical guarantee for global convergence. We demonstrate the performance of our approach for video compressive sensing, in terms of reconstruction accuracy. We also investigate the impact of various sampling strategies. We apply this framework to accelerate the acquisition process of dynamic MRI and show it achieves the best reconstruction accuracy with the least computational time compared with existing algorithms in the literature.Comment: 30 pages, 9 figure

Rapidity scan approach for net-baryon cumulants with a statistical thermal model

Utilizing rapidity-dependent measurements to map the QCD phase diagram provides a complementary approach to traditional beam-energy-dependent measurements around midrapidity. The changing nature of thermodynamic properties of QCD matter along the beam axis in heavy-ion collisions at low collision energies both motivates and poses challenges for this method. In this study, we derive the analytical cumulant-generating function for subsystems within distinct rapidity windows, while accounting for global net-baryon charge conservation of the full system. Rapidity-dependent net-baryon cumulants are then calculated for a system exhibiting inhomogeneity along the beam axis, and their sensitivity to finite acceptances through changing rapidity bin widths is explored. We highlight the nontrivial behaviors exhibited by these cumulants, underscoring their importance in establishing a noncritical baseline for interpreting net-proton cumulants in the search for the QCD critical point. Finally, we discuss the implications of the rapidity scan for mapping the QCD phase diagram within the current context.Comment: 16 pages, 9 figures. Content, figures, and references are updated to the publication versio

Optimal treatment allocation for efficient policy evaluation in sequential decision making

A/B testing is critical for modern technological companies to evaluate the effectiveness of newly developed products against standard baselines. This paper studies optimal designs that aim to maximize the amount of information obtained from online experiments to estimate treatment effects accurately. We propose three optimal allocation strategies in a dynamic setting where treatments are sequentially assigned over time. These strategies are designed to minimize the variance of the treatment effect estimator when data follow a non-Markov decision process or a (time-varying) Markov decision process. We further develop estimation procedures based on existing off-policy evaluation (OPE) methods and conduct extensive experiments in various environments to demonstrate the effectiveness of the proposed methodologies. In theory, we prove the optimality of the proposed treatment allocation design and establish upper bounds for the mean squared errors of the resulting treatment effect estimator

Integrating multi-type aberrations from DNA and RNA through dynamic mapping gene space for subtype-specific breast cancer driver discovery

Driver event discovery is a crucial demand for breast cancer diagnosis and therapy. Especially, discovering subtype-specificity of drivers can prompt the personalized biomarker discovery and precision treatment of cancer patients. still, most of the existing computational driver discovery studies mainly exploit the information from DNA aberrations and gene interactions. Notably, cancer driver events would occur due to not only DNA aberrations but also RNA alternations, but integrating multi-type aberrations from both DNA and RNA is still a challenging task for breast cancer drivers. On the one hand, the data formats of different aberration types also differ from each other, known as data format incompatibility. One the other hand, different types of aberrations demonstrate distinct patterns across samples, known as aberration type heterogeneity. To promote the integrated analysis of subtype-specific breast cancer drivers, we design a "splicing-and-fusing" framework to address the issues of data format incompatibility and aberration type heterogeneity respectively. To overcome the data format incompatibility, the "splicing-step" employs a knowledge graph structure to connect multi-type aberrations from the DNA and RNA data into a unified formation. To tackle the aberration type heterogeneity, the "fusing-step" adopts a dynamic mapping gene space integration approach to represent the multi-type information by vectorized profiles. The experiments also demonstrate the advantages of our approach in both the integration of multi-type aberrations from DNA and RNA and the discovery of subtype-specific breast cancer drivers. In summary, our "splicing-and-fusing" framework with knowledge graph connection and dynamic mapping gene space fusion of multi-type aberrations data from DNA and RNA can successfully discover potential breast cancer drivers with subtype-specificity indication.Comment: 14 pages, 5 figures, 1 tabl

Generalist Vision Foundation Models for Medical Imaging: A Case Study of Segment Anything Model on Zero-Shot Medical Segmentation

In this paper, we examine the recent Segment Anything Model (SAM) on medical images, and report both quantitative and qualitative zero-shot segmentation results on nine medical image segmentation benchmarks, covering various imaging modalities, such as optical coherence tomography (OCT), magnetic resonance imaging (MRI), and computed tomography (CT), as well as different applications including dermatology, ophthalmology, and radiology. Those benchmarks are representative and commonly used in model development. Our experimental results indicate that while SAM presents remarkable segmentation performance on images from the general domain, its zero-shot segmentation ability remains restricted for out-of-distribution images, e.g., medical images. In addition, SAM exhibits inconsistent zero-shot segmentation performance across different unseen medical domains. For certain structured targets, e.g., blood vessels, the zero-shot segmentation of SAM completely failed. In contrast, a simple fine-tuning of it with a small amount of data could lead to remarkable improvement of the segmentation quality, showing the great potential and feasibility of using fine-tuned SAM to achieve accurate medical image segmentation for a precision diagnostics. Our study indicates the versatility of generalist vision foundation models on medical imaging, and their great potential to achieve desired performance through fine-turning and eventually address the challenges associated with accessing large and diverse medical datasets in support of clinical diagnostics.Comment: Published in Diagnostic

Dynamic characteristics and drivers of the regional household energy-carbon-water nexus in China

Being a node of the energy-water consumer and carbon dioxide (CO2) emitter, the household is one key sector to pilot integrated energy-carbon-water (ECW) management. This study developed an integrated framework to explore China’s provincial household ECW nexus as well as their drivers from the years 2000 through 2016. The absolute amount and growth rate of household energy use (HEU), household CO2 emissions (HCE), and household water use (HWU) were abstracted to reveal the dynamic characteristics of the household ECW nexus. Efficiency advance, income growth, urbanization, family size, and household number were defined to explain the changes in the household ECW nexus. This study revealed that there is a huge regional heterogeneity in China’s household ECW nexus. Developed regions such as Zhejiang, Jiangsu, Guangdong, and Shanghai are the most important household ECW nexus nodes with larger amounts and growth rates of household ECW. Income growth overwhelmingly increases ECW, while efficiency advance effectively curbs its growth. Comparatively, household number, family size, and urbanization have small effects. Therefore, implementing differentiated management and focusing on the synergy of socioeconomic factors are the keys to achieving integrated household ECW management. And the analytical framework can be used to analyze ECW nexus from a sector, city, or country perspective