Stability Estimate for an Inverse Stochastic Parabolic Problem of Determining Unknown Time-varying Boundary

Stochastic parabolic equations are widely used to model many random phenomena in natural sciences, such as the temperature distribution in a noisy medium, the dynamics of a chemical reaction in a noisy environment, or the evolution of the density of bacteria population. In many cases, the equation may involve an unknown moving boundary which could represent a change of phase, a reaction front, or an unknown population. In this paper, we focus on an inverse problem where the goal is to determine an unknown moving boundary based on data observed in a specific interior subdomain for the stochastic parabolic equation and prove that the unknown boundary depends logarithmically on the interior measurement. This allows us, theoretically, to track and to monitor the behavior of unknown boundary from observation in an arbitrary interior domain. The stability estimate is based on a new Carleman estimate for stochastic parabolic equations. As a byproduct, we obtain a quantitative unique continuation property for stochastic parabolic equations

Exact controllability for a refined Stochastic Wave Equation

In this paper, we obtain the exact controllability for a refined stochastic wave equation with three controls by establishing a novel Carleman estimate for a backward hyperbolic-like operator. Compared with the known result, the novelty of this paper is twofold: (1) Our model contains the effects in the drift terms when we put controls directly in the diffusion terms, which is more sensible for practical applications; (2) We provide an explicit description of the waiting time which is sharp in the case of dimension one and is independent of the coefficients of lower terms

Use of coronary CT angiography in the diagnosis of patients with suspected coronary artery disease: findings and clinical indications

Objective: To investigate the clinical applications of coronary CT angiography in patients with suspected coronary artery disease and identify factors that affect CT findings. Methods: Medical records of patients suspected of coronary artery disease over a period of 12 months from a tertiary teaching hospital were retrospectively reviewed. Patient age, sex (male/female), duration of symptoms and abnormal rates of coronary CT angiography scans were analysed to investigate the relationship among these parameters. The patients by age were characterized into five groups: under 36 years, 36–45 years, 46–55 years, 56–65 years and more than 66 years, respectively; while the duration of symptoms was also classified into five groups: less than one week, one week to one month, one to three months, three to six months and more than six months. Results: Of the 880 patient records reviewed, 800 met the above study criteria. Five hundred and forty nine patients demonstrated abnormal CT findings (68.6%). There was no significant difference in the percentage of abnormal CT findings based on patient sex and the duration of symptoms (P = 0.14). The abnormal rates of coronary CT angiography, however, increased significantly with increasing age (P < 0.001); with patients over 65 years of age 2.5 times more likely to have an abnormal CT scan relative to a patient under 45 years. A significant difference was found between abnormal coronary CT angiography and the duration of symptoms (P = 0.012). Conclusions: Our results indicate coronary CT angiography findings are significantly related to the patient age group and duration of symptoms. Clinical referral for coronary CT angiography of patients with suspected coronary artery disease needs to be justified with regard to the judicious use of this imaging modality

FocusFlow: Boosting Key-Points Optical Flow Estimation for Autonomous Driving

Key-point-based scene understanding is fundamental for autonomous driving applications. At the same time, optical flow plays an important role in many vision tasks. However, due to the implicit bias of equal attention on all points, classic data-driven optical flow estimation methods yield less satisfactory performance on key points, limiting their implementations in key-point-critical safety-relevant scenarios. To address these issues, we introduce a points-based modeling method that requires the model to learn key-point-related priors explicitly. Based on the modeling method, we present FocusFlow, a framework consisting of 1) a mix loss function combined with a classic photometric loss function and our proposed Conditional Point Control Loss (CPCL) function for diverse point-wise supervision; 2) a conditioned controlling model which substitutes the conventional feature encoder by our proposed Condition Control Encoder (CCE). CCE incorporates a Frame Feature Encoder (FFE) that extracts features from frames, a Condition Feature Encoder (CFE) that learns to control the feature extraction behavior of FFE from input masks containing information of key points, and fusion modules that transfer the controlling information between FFE and CFE. Our FocusFlow framework shows outstanding performance with up to +44.5% precision improvement on various key points such as ORB, SIFT, and even learning-based SiLK, along with exceptional scalability for most existing data-driven optical flow methods like PWC-Net, RAFT, and FlowFormer. Notably, FocusFlow yields competitive or superior performances rivaling the original models on the whole frame. The source code will be available at https://github.com/ZhonghuaYi/FocusFlow_official.Comment: The source code of FocusFlow will be available at https://github.com/ZhonghuaYi/FocusFlow_officia

Minimalist and High-Quality Panoramic Imaging with PSF-aware Transformers

High-quality panoramic images with a Field of View (FoV) of 360-degree are essential for contemporary panoramic computer vision tasks. However, conventional imaging systems come with sophisticated lens designs and heavy optical components. This disqualifies their usage in many mobile and wearable applications where thin and portable, minimalist imaging systems are desired. In this paper, we propose a Panoramic Computational Imaging Engine (PCIE) to address minimalist and high-quality panoramic imaging. With less than three spherical lenses, a Minimalist Panoramic Imaging Prototype (MPIP) is constructed based on the design of the Panoramic Annular Lens (PAL), but with low-quality imaging results due to aberrations and small image plane size. We propose two pipelines, i.e. Aberration Correction (AC) and Super-Resolution and Aberration Correction (SR&AC), to solve the image quality problems of MPIP, with imaging sensors of small and large pixel size, respectively. To provide a universal network for the two pipelines, we leverage the information from the Point Spread Function (PSF) of the optical system and design a PSF-aware Aberration-image Recovery Transformer (PART), in which the self-attention calculation and feature extraction are guided via PSF-aware mechanisms. We train PART on synthetic image pairs from simulation and put forward the PALHQ dataset to fill the gap of real-world high-quality PAL images for low-level vision. A comprehensive variety of experiments on synthetic and real-world benchmarks demonstrates the impressive imaging results of PCIE and the effectiveness of plug-and-play PSF-aware mechanisms. We further deliver heuristic experimental findings for minimalist and high-quality panoramic imaging. Our dataset and code will be available at https://github.com/zju-jiangqi/PCIE-PART.Comment: The dataset and code will be available at https://github.com/zju-jiangqi/PCIE-PAR

Molecular evolution of calcium signaling and transport in plant adaptation to abiotic stress

Adaptation to unfavorable abiotic stresses is one of the key processes in the evolution of plants. Calcium (Ca2+) signaling is characterized by the spatiotemporal pattern of Ca2+ distribution and the activities of multi-domain proteins in integrating environmental stimuli and cellular responses, which are crucial early events in abiotic stress responses in plants. However, a comprehensive summary and explanation for evolutionary and functional synergies in Ca2+ signaling remains elusive in green plants. We review mechanisms of Ca2+ membrane transporters and intracellular Ca2+ sensors with evolutionary imprinting and structural clues. These may provide molecular and bioinformatics insights for the functional analysis of some non-model species in the evolutionarily important green plant lineages. We summarize the chronological order, spatial location, and characteristics of Ca2+ functional proteins. Furthermore, we highlight the integral functions of calcium-signaling components in various nodes of the Ca2+ signaling pathway through conserved or variant evolutionary processes. These ultimately bridge the Ca2+ cascade reactions into regulatory networks, particularly in the hormonal signaling pathways. In summary, this review provides new perspectives towards a better understanding of the evolution, interaction and integration of Ca2+ signaling components in green plants, which is likely to benefit future research in agriculture, evolutionary biology, ecology and the environment

Highly conserved evolution of aquaporin PIPs and TIPs confers their crucial contribution to flowering process in plants

Flowering is the key process for the sexual reproduction in seed plants. In gramineous crops, the process of flowering, which includes the actions of both glume opening and glume closing, is directly driven by the swelling and withering of lodicules due to the water flow into and out of lodicule cells. All these processes are considered to be controlled by aquaporins, which are the essential transmembrane proteins that facilitate the transport of water and other small molecules across the biological membranes. In the present study, the evolution of aquaporins and their contribution to flowering process in plants were investigated via an integration of genome-wide analysis and gene expression profiling. Across the barley genome, we found that HvTIP1;1, HvTIP1;2, HvTIP2;3, and HvPIP2;1 were the predominant aquaporin genes in lodicules and significantly upregulated in responding to glume opening and closing, suggesting the importance of them in the flowering process of barley. Likewise, the putative homologs of the above four aquaporin genes were also abundantly expressed in lodicules of the other monocots like rice and maize and in petals of eudicots like cotton, tobacco, and tomato. Furthermore, all of them were mostly upregulated in responding to the process of floret opening, indicating a conserved function of these aquaporin proteins in plant flowering. The phylogenetic analysis based on the OneKP database revealed that the homologs of TIP1;1, TIP1;2, TIP2;3, and PIP2;1 were highly conserved during the evolution, especially in the angiosperm species, in line with their conserved function in controlling the flowering process. Taken together, it could be concluded that the highly evolutionary conservation of TIP1;1, TIP1;2, TIP2;3 and PIP2;1 plays important roles in the flowering process for both monocots and eudicots

Network during light-induced cotyledons opening and greening in Astragalus membranaceus

Opening and greening are main characteristics of morphogenesis of cotyledons. For revealing interrelationship between metabolism and morphogenesis, metabolic shifts were analyzed in cotyledon of A. membranaceus seedlings with different stages in light and in darkness. Light induced 69 metabolites (MA), related to cotyledon greening; additional 89 metabolites (MB), related to cotyledon opening, were identified by WGCNA. The screening of metabolites shared in both MA and MB obtained 37 specific metabolites (MC) related to both opening and greening. In this context, main changes in MC occurred during A3, the stage in which cotyledons fully opened and greened. Within MC, few sugars, including L-(-)-sorbose, mannose, glucose and its derivatives, markedly decreased, while other sugars, amino acids, and unsaturated fatty acids increased. Most isoflavones and flavonols including ononin, caycosin-7-glucosides, quercetin, genistein, and catechin increased 5.3, 5.5, 13.4, 6.4 and 1.8 times, respectively. Thus, accumulated flavonoids play an important role during this developmental stage. © 2020 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group