WeakIdent: Weak formulation for Identifying Differential Equations using Narrow-fit and Trimming

Data-driven identification of differential equations is an interesting but challenging problem, especially when the given data are corrupted by noise. When the governing differential equation is a linear combination of various differential terms, the identification problem can be formulated as solving a linear system, with the feature matrix consisting of linear and nonlinear terms multiplied by a coefficient vector. This product is equal to the time derivative term, and thus generates dynamical behaviors. The goal is to identify the correct terms that form the equation to capture the dynamics of the given data. We propose a general and robust framework to recover differential equations using a weak formulation, for both ordinary and partial differential equations (ODEs and PDEs). The weak formulation facilitates an efficient and robust way to handle noise. For a robust recovery against noise and the choice of hyper-parameters, we introduce two new mechanisms, narrow-fit and trimming, for the coefficient support and value recovery, respectively. For each sparsity level, Subspace Pursuit is utilized to find an initial set of support from the large dictionary. Then, we focus on highly dynamic regions (rows of the feature matrix), and error normalize the feature matrix in the narrow-fit step. The support is further updated via trimming of the terms that contribute the least. Finally, the support set of features with the smallest Cross-Validation error is chosen as the result. A comprehensive set of numerical experiments are presented for both systems of ODEs and PDEs with various noise levels. The proposed method gives a robust recovery of the coefficients, and a significant denoising effect which can handle up to $100\%$ noise-to-signal ratio for some equations. We compare the proposed method with several state-of-the-art algorithms for the recovery of differential equations

Fourier Features for Identifying Differential Equations (FourierIdent)

We investigate the benefits and challenges of utilizing the frequency information in differential equation identification. Solving differential equations and Fourier analysis are closely related, yet there is limited work in exploring this connection in the identification of differential equations. Given a single realization of the differential equation perturbed by noise, we aim to identify the underlying differential equation governed by a linear combination of linear and nonlinear differential and polynomial terms in the frequency domain. This is challenging due to large magnitudes and sensitivity to noise. We introduce a Fourier feature denoising, and define the meaningful data region and the core regions of features to reduce the effect of noise in the frequency domain. We use Subspace Pursuit on the core region of the time derivative feature, and introduce a group trimming step to refine the support. We further introduce a new energy based on the core regions of features for coefficient identification. Utilizing the core regions of features serves two critical purposes: eliminating the low-response regions dominated by noise, and enhancing the accuracy in coefficient identification. The proposed method is tested on various differential equations with linear, nonlinear, and high-order derivative feature terms. Our results demonstrate the advantages of the proposed method, particularly on complex and highly corrupted datasets

Point Clouds Are Specialized Images: A Knowledge Transfer Approach for 3D Understanding

Self-supervised representation learning (SSRL) has gained increasing attention in point cloud understanding, in addressing the challenges posed by 3D data scarcity and high annotation costs. This paper presents PCExpert, a novel SSRL approach that reinterprets point clouds as "specialized images". This conceptual shift allows PCExpert to leverage knowledge derived from large-scale image modality in a more direct and deeper manner, via extensively sharing the parameters with a pre-trained image encoder in a multi-way Transformer architecture. The parameter sharing strategy, combined with a novel pretext task for pre-training, i.e., transformation estimation, empowers PCExpert to outperform the state of the arts in a variety of tasks, with a remarkable reduction in the number of trainable parameters. Notably, PCExpert's performance under LINEAR fine-tuning (e.g., yielding a 90.02% overall accuracy on ScanObjectNN) has already approached the results obtained with FULL model fine-tuning (92.66%), demonstrating its effective and robust representation capability

Nitrogen transport and assimilation in tea plant (Camellia sinensis): a review

Nitrogen is one of the most important nutrients for tea plants, as it contributes significantly to tea yield and serves as the component of amino acids, which in turn affects the quality of tea produced. To achieve higher yields, excessive amounts of N fertilizers mainly in the form of urea have been applied in tea plantations where N fertilizer is prone to convert to nitrate and be lost by leaching in the acid soils. This usually results in elevated costs and environmental pollution. A comprehensive understanding of N metabolism in tea plants and the underlying mechanisms is necessary to identify the key regulators, characterize the functional phenotypes, and finally improve nitrogen use efficiency (NUE). Tea plants absorb and utilize ammonium as the preferred N source, thus a large amount of nitrate remains activated in soils. The improvement of nitrate utilization by tea plants is going to be an alternative aspect for NUE with great potentiality. In the process of N assimilation, nitrate is reduced to ammonium and subsequently derived to the GS-GOGAT pathway, involving the participation of nitrate reductase (NR), nitrite reductase (NiR), glutamine synthetase (GS), glutamate synthase (GOGAT), and glutamate dehydrogenase (GDH). Additionally, theanine, a unique amino acid responsible for umami taste, is biosynthesized by the catalysis of theanine synthetase (TS). In this review, we summarize what is known about the regulation and functioning of the enzymes and transporters implicated in N acquisition and metabolism in tea plants and the current methods for assessing NUE in this species. The challenges and prospects to expand our knowledge on N metabolism and related molecular mechanisms in tea plants which could be a model for woody perennial plant used for vegetative harvest are also discussed to provide the theoretical basis for future research to assess NUE traits more precisely among the vast germplasm resources, thus achieving NUE improvement

Robust PDE Identification from Noisy Data

We propose robust methods to identify underlying Partial Differential Equation (PDE) from a given set of noisy time dependent data. We assume that the governing equation is a linear combination of a few linear and nonlinear differential terms in a prescribed dictionary. Noisy data make such identification particularly challenging. Our objective is to develop methods which are robust against a high level of noise, and to approximate the underlying noise-free dynamics well. We first introduce a Successively Denoised Differentiation (SDD) scheme to stabilize the amplified noise in numerical differentiation. SDD effectively denoises the given data and the corresponding derivatives. Secondly, we present two algorithms for PDE identification: Subspace pursuit Time evolution error (ST) and Subspace pursuit Cross-validation (SC). Our general strategy is to first find a candidate set using the Subspace Pursuit (SP) greedy algorithm, then choose the best one via time evolution or cross validation. ST uses multi-shooting numerical time evolution and selects the PDE which yields the least evolution error. SC evaluates the cross-validation error in the least squares fitting and picks the PDE that gives the smallest validation error. We present a unified notion of PDE identification error to compare the objectives of related approaches. We present various numerical experiments to validate our methods. Both methods are efficient and robust to noise

Correlational Analysis of Sarcopenia and Multimorbidity Among Older Inpatients

BACKGROUND: Sarcopenia and multimorbidity are common in older adults, and most of the available clinical studies have focused on the relationship between specialist disorders and sarcopenia, whereas fewer studies have been conducted on the relationship between sarcopenia and multimorbidity. We therefore wished to explore the relationship between the two. METHODS: The study subjects were older patients (aged ≥ 65 years) who were hospitalized at the Department of Geriatrics of the First Affiliated Hospital of Chongqing Medical University between March 2016 and September 2021. Their medical records were collected. Based on the diagnostic criteria of the Asian Sarcopenia Working Group in 2019, the relationship between sarcopenia and multimorbidity was elucidated. RESULTS: 1.A total of 651 older patients aged 65 years and above with 2 or more chronic diseases were investigated in this study, 46.4% were suffering from sarcopenia. 2. Analysis of the relationship between the number of chronic diseases and sarcopenia yielded that the risk of sarcopenia with 4-5 chronic diseases was 1.80 times higher than the risk of 2-3 chronic diseases (OR 1.80, 95%CI 0.29-2.50), and the risk of sarcopenia with ≥ 6 chronic diseases was 5.11 times higher than the risk of 2-3 chronic diseases (OR 5.11, 95% CI 2.97-9.08), which remained statistically significant, after adjusting for relevant factors. 3. The Charlson comorbidity index was associated with skeletal muscle mass index, handgrip strength, and 6-meter walking speed, with scores reaching 5 and above suggesting the possibility of sarcopenia. 4. After adjusting for some covariates among 14 common chronic diseases in older adults, diabetes (OR 3.20, 95% CI 2.01-5.09), cerebrovascular diseases (OR 2.07, 95% CI 1.33-3.22), bone and joint diseases (OR 2.04, 95% CI 1.32-3.14), and malignant tumors (OR 2.65, 95% CI 1.17-6.55) were among those that still a risk factor for the development of sarcopenia. CONCLUSION: In the hospitalized older adults, the more chronic diseases they have, the higher the prevalence of sarcopenia. When the CCI is 5, attention needs to be paid to the occurrence of sarcopenia in hospitalized older adults

IDMA-Based MAC Protocol for Satellite Networks with Consideration on Channel Quality

In order to overcome the shortcomings of existing medium access control (MAC) protocols based on TDMA or CDMA in satellite networks, interleave division multiple access (IDMA) technique is introduced into satellite communication networks. Therefore, a novel wide-band IDMA MAC protocol based on channel quality is proposed in this paper, consisting of a dynamic power allocation algorithm, a rate adaptation algorithm, and a call admission control (CAC) scheme. Firstly, the power allocation algorithm combining the technique of IDMA SINR-evolution and channel quality prediction is developed to guarantee high power efficiency even in terrible channel conditions. Secondly, the effective rate adaptation algorithm, based on accurate channel information per timeslot and by the means of rate degradation, can be realized. What is more, based on channel quality prediction, the CAC scheme, combining the new power allocation algorithm, rate scheduling, and buffering strategies together, is proposed for the emerging IDMA systems, which can support a variety of traffic types, and offering quality of service (QoS) requirements corresponding to different priority levels. Simulation results show that the new wide-band IDMA MAC protocol can make accurate estimation of available resource considering the effect of multiuser detection (MUD) and QoS requirements of multimedia traffic, leading to low outage probability as well as high overall system throughput

Room-temperature polariton lasing in quantum heterostructure nanocavities

Controlling light-matter interactions in solid-state systems has motivated intense research to produce bosonic quasi-particles known as exciton-polaritons, which requires strong coupling between excitons and cavity photons. Ultra-low threshold coherent light emitters can be achieved through lasing from exciton-polariton condensates, but this generally requires sophisticated device structures and cryogenic temperatures. Polaritonic nanolasers operating at room temperature lie on the crucial path of related research, not only for the exploration of polariton physics at the nanoscale but also for potential applications in quantum information systems, all-optical logic gates, and ultra-low threshold lasers. However, at present, progress toward room-temperature polariton nanolasers has been limited by the thermal instability of excitons and the inherently low quality factors of nanocavities. Here, we demonstrate room-temperature polaritonic nanolasers by designing wide-gap semiconductor heterostructure nanocavities to produce thermally stable excitons coupled with nanocavity photons. The resulting mixed states of exciton-polaritons with Rabi frequencies of approximately 370 meV enable persistent polariton lasing up to room temperature, facilitating the realization of miniaturized and integrated polariton systems