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Strengthening of two Clarkson-McCarthy inequalities with several operators is established. These not only confirm a conjecture of the author in [Israel J. Math. 2024], but also improve results of Hirazallah-Kittaneh in [Integral Equations Operator Theory 60 (2008)] and Bhatia-Kittaneh in [Bull. London Math. Soc. 36 (2004)]. We also give a generalization of a result for pairs $(A_i,B_i), 1\le i\le n$ and obtain another form of another inequality. The infinite cases of these inequalities are also discussed. The method is an extension of the result obtained by Bourin and Lee in [Linear Algebra Appl. 601 (2020)]. Some related eigenvalue inequalities are also obtained., Comment: 23 pages

In clinical settings, the screening, diagnosis, and monitoring of adolescent idiopathic scoliosis (AIS) typically involve physical or radiographic examinations. However, physical examinations are subjective, while radiographic examinations expose patients to harmful radiation. Consequently, we propose a pipeline that can accurately determine scoliosis severity. This pipeline utilizes posteroanterior (PA) and lateral (LAT) RGB images as input to generate spine curve maps, which are then used to reconstruct the three-dimensional (3D) spine curve for AIS severity grading. To generate the 2D spine curves accurately and efficiently, we further propose an Efficient U-shape transFormer (EUFormer) as the generator. It can efficiently utilize the learned feature across channels, therefore producing consecutive spine curves from both PA and LAT views. Experimental results demonstrate superior performance of EUFormer on spine curve generation against other classical U-shape models. This finding demonstrates that the proposed method for grading the severity of AIS, based on a 3D spine curve, is more accurate when compared to using a 2D spine curve.

This study proposes an approach for error correction in clinical radiology reports, leveraging large language models (LLMs) and retrieval-augmented generation (RAG) techniques. The proposed framework employs internal and external retrieval mechanisms to extract relevant medical entities and relations from the report and external knowledge sources. A three-stage inference process is introduced, decomposing the task into error detection, localization, and correction subtasks, which enhances the explainability and performance of the system. The effectiveness of the approach is evaluated using a benchmark dataset created by corrupting real-world radiology reports with realistic errors, guided by domain experts. Experimental results demonstrate the benefits of the proposed methods, with the combination of internal and external retrieval significantly improving the accuracy of error detection, localization, and correction across various state-of-the-art LLMs. The findings contribute to the development of more robust and reliable error correction systems for clinical documentation.

As a fundamental structural feature, the symmetry of materials determines the exotic quantum properties in transition metal dichalcogenides (TMDs) with charge density wave (CDW). Breaking the inversion symmetry, the Janus structure, an artificially constructed lattice, provides an opportunity to tune the CDW states and the related properties. However, limited by the difficulties in atomic-level fabrication and material stability, the experimental visualization of the CDW states in 2D TMDs with Janus structure is still rare. Here, using surface selenization of VTe2, we fabricated monolayer Janus VTeSe. With scanning tunneling microscopy, an unusual root13-root13 CDW state with threefold rotational symmetry breaking was observed and characterized. Combined with theoretical calculations, we find this CDW state can be attributed to the charge modulation in the Janus VTeSe, beyond the conventional electron-phonon coupling. Our findings provide a promising platform for studying the CDW states and artificially tuning the electronic properties toward the applications.

This paper describes our submission to the MEDIQA-CORR 2024 shared task for automatically detecting and correcting medical errors in clinical notes. We report results for three methods of few-shot In-Context Learning (ICL) augmented with Chain-of-Thought (CoT) and reason prompts using a large language model (LLM). In the first method, we manually analyse a subset of train and validation dataset to infer three CoT prompts by examining error types in the clinical notes. In the second method, we utilise the training dataset to prompt the LLM to deduce reasons about their correctness or incorrectness. The constructed CoTs and reasons are then augmented with ICL examples to solve the tasks of error detection, span identification, and error correction. Finally, we combine the two methods using a rule-based ensemble method. Across the three sub-tasks, our ensemble method achieves a ranking of 3rd for both sub-task 1 and 2, while securing 7th place in sub-task 3 among all submissions., Comment: accepted as NAACL workshop

Denoising diffusion probabilistic models (DDPMs) have achieved unprecedented success in computer vision. However, they remain underutilized in medical imaging, a field crucial for disease diagnosis and treatment planning. This is primarily due to the high computational cost associated with (1) the use of large number of time steps (e.g., 1,000) in diffusion processes and (2) the increased dimensionality of medical images, which are often 3D or 4D. Training a diffusion model on medical images typically takes days to weeks, while sampling each image volume takes minutes to hours. To address this challenge, we introduce Fast-DDPM, a simple yet effective approach capable of improving training speed, sampling speed, and generation quality simultaneously. Unlike DDPM, which trains the image denoiser across 1,000 time steps, Fast-DDPM trains and samples using only 10 time steps. The key to our method lies in aligning the training and sampling procedures to optimize time-step utilization. Specifically, we introduced two efficient noise schedulers with 10 time steps: one with uniform time step sampling and another with non-uniform sampling. We evaluated Fast-DDPM across three medical image-to-image generation tasks: multi-image super-resolution, image denoising, and image-to-image translation. Fast-DDPM outperformed DDPM and current state-of-the-art methods based on convolutional networks and generative adversarial networks in all tasks. Additionally, Fast-DDPM reduced the training time to 0.2x and the sampling time to 0.01x compared to DDPM. Our code is publicly available at: https://github.com/mirthAI/Fast-DDPM.

Cervical cancer is one of the leading causes of death in women, and brachytherapy is currently the primary treatment method. However, it is important to precisely define the extent of paracervical tissue invasion to improve cancer diagnosis and treatment options. The fusion of the information characteristics of both computed tomography (CT) and magnetic resonance imaging(MRI) modalities may be useful in achieving a precise outline of the extent of paracervical tissue invasion. Registration is the initial step in information fusion. However, when aligning multimodal images with varying depths, manual alignment is prone to large errors and is time-consuming. Furthermore, the variations in the size of the Region of Interest (ROI) and the shape of multimodal images pose a significant challenge for achieving accurate registration.In this paper, we propose a preliminary spatial alignment algorithm and a weakly supervised multimodal registration network. The spatial position alignment algorithm efficiently utilizes the limited annotation information in the two modal images provided by the doctor to automatically align multimodal images with varying depths. By utilizing aligned multimodal images for weakly supervised registration and incorporating pyramidal features and cost volume to estimate the optical flow, the results indicate that the proposed method outperforms traditional volume rendering alignment methods and registration networks in various evaluation metrics. This demonstrates the effectiveness of our model in multimodal image registration.

The quantum noise in gravitational-wave detectors can be suppressed in a broadband by frequency-dependent squeezing. It usually requires one large scale filter cavity and even two, for example in the low frequency detector of Einstein Telescope, which is a detuned dual recycling Fabry-Perot Michelson interferometer. In this paper, we study the feasibility of replacing two filter cavities with a coupled-cavity, aiming to reduce the optical losses with less number of optics. It turns out this approach is only theoretically valid, however, the required parameters of the optics don't support practical implementation, which is consistent with the results in [Phys. Rev. D {\bf 101}, 082002 (2020)]. Furthermore, we investigate the viability of utilizing EPR squeezing to eliminate either one or two filter cavities in Einstein Telescope. It turns out EPR squeezing would allow to eliminate one filter cavity, and can potentially improve the detector sensitivity with the allowance of higher input squeezing level, benefiting from the longer length of the arm cavity which serves as one of the filter cavities for frequency-dependent squeezing., Comment: 13 pages, 8 figures

We present the subspace-constrained Tyler's estimator (STE) designed for recovering a low-dimensional subspace within a dataset that may be highly corrupted with outliers. STE is a fusion of the Tyler's M-estimator (TME) and a variant of the fast median subspace. Our theoretical analysis suggests that, under a common inlier-outlier model, STE can effectively recover the underlying subspace, even when it contains a smaller fraction of inliers relative to other methods in the field of robust subspace recovery. We apply STE in the context of Structure from Motion (SfM) in two ways: for robust estimation of the fundamental matrix and for the removal of outlying cameras, enhancing the robustness of the SfM pipeline. Numerical experiments confirm the state-of-the-art performance of our method in these applications. This research makes significant contributions to the field of robust subspace recovery, particularly in the context of computer vision and 3D reconstruction., Comment: 23 pages, accepted by CVPR 24

Byusing equivalence conditions for sectorial matrices obtained by Alakhrass and Sababheh in 2020, we improve a Rotfel'd type inequality for sectorial matrices derived by P. Zhang in 2015 and generalize a result derived by Y. Mao et al. in 2024., Comment: 10pages

This work analyzes the subspace-constrained Tyler's estimator (STE) designed for recovering a low-dimensional subspace within a dataset that may be highly corrupted with outliers. It assumes a weak inlier-outlier model and allows the fraction of inliers to be smaller than a fraction that leads to computational hardness of the robust subspace recovery problem. It shows that in this setting, if the initialization of STE, which is an iterative algorithm, satisfies a certain condition, then STE can effectively recover the underlying subspace. It further shows that under the generalized haystack model, STE initialized by the Tyler's M-estimator (TME), can recover the subspace when the fraction of iniliers is too small for TME to handle.

Most existing methodologies of estimating low-rank matrices rely on Burer-Monteiro factorization, but these approaches can suffer from slow convergence, especially when dealing with solutions characterized by a large condition number, defined by the ratio of the largest to the $r$-th singular values, where $r$ is the search rank. While methods such as Scaled Gradient Descent have been proposed to address this issue, such methods are more complicated and sometimes have weaker theoretical guarantees, for example, in the rank-deficient setting. In contrast, this paper demonstrates the effectiveness of the projected gradient descent algorithm. Firstly, its local convergence rate is independent of the condition number. Secondly, under conditions where the objective function is rank-$2r$ restricted $L$-smooth and $\mu$-strongly convex, with $L/\mu < 3$, projected gradient descent with appropriate step size converges linearly to the solution. Moreover, a perturbed version of this algorithm effectively navigates away from saddle points, converging to an approximate solution or a second-order local minimizer across a wide range of step sizes. Furthermore, we establish that there are no spurious local minimizers in estimating asymmetric low-rank matrices when the objective function satisfies $L/\mu<3.$

We introduce a novel sufficient dimension-reduction (SDR) method which is robust against outliers using $\alpha$-distance covariance (dCov) in dimension-reduction problems. Under very mild conditions on the predictors, the central subspace is effectively estimated and model-free advantage without estimating link function based on the projection on the Stiefel manifold. We establish the convergence property of the proposed estimation under some regularity conditions. We compare the performance of our method with existing SDR methods by simulation and real data analysis and show that our algorithm improves the computational efficiency and effectiveness.

By using the Three-lines theorem for a certain analytic function defined in terms of the trace and a duality argument method, we prove Audenaert-Kittaneh's conjecture related to $p$-Schatten classes. This generalizes the main result obtained by McCarthy in [Israel J. Math. 5 (1967)]., Comment: 11 pages

Ground-based interferometric gravitational wave detectors are highly precise sensors for weak forces, limited in sensitivity across their detection band by quantum fluctuations of light. Current and future instruments address this limitation by injecting frequency-dependent squeezed vacuum into the detection port, utilizing narrow-band, low-loss optical cavities for optimal rotation of the squeezing ellipse at each signal frequency. This study introduces a novel scheme employing the principles of quantum teleportation and entangled states of light. It allows achieving broadband suppression of quantum noise in detuned signal recycled-Fabry-Perot--Michelson interferometers, which is the baseline design of the low-frequency detector within the Einstein Telescope xylophone detector, without requiring additional filter cavities or modifications to the core optics of the main interferometer., Comment: 15 pages, 9 figures, 2 table

The task of music-driven dance generation involves creating coherent dance movements that correspond to the given music. While existing methods can produce physically plausible dances, they often struggle to generalize to out-of-set data. The challenge arises from three aspects: 1) the high diversity of dance movements and significant differences in the distribution of music modalities, which make it difficult to generate music-aligned dance movements. 2) the lack of a large-scale music-dance dataset, which hinders the generation of generalized dance movements from music. 3) The protracted nature of dance movements poses a challenge to the maintenance of a consistent dance style. In this work, we introduce the EnchantDance framework, a state-of-the-art method for dance generation. Due to the redundancy of the original dance sequence along the time axis, EnchantDance first constructs a strong dance latent space and then trains a dance diffusion model on the dance latent space. To address the data gap, we construct a large-scale music-dance dataset, ChoreoSpectrum3D Dataset, which includes four dance genres and has a total duration of 70.32 hours, making it the largest reported music-dance dataset to date. To enhance consistency between music genre and dance style, we pre-train a music genre prediction network using transfer learning and incorporate music genre as extra conditional information in the training of the dance diffusion model. Extensive experiments demonstrate that our proposed framework achieves state-of-the-art performance on dance quality, diversity, and consistency.

Model fusion is becoming a crucial component in the context of model-as-a-service scenarios, enabling the delivery of high-quality model services to local users. However, this approach introduces privacy risks and imposes certain limitations on its applications. Ensuring secure model exchange and knowledge fusion among users becomes a significant challenge in this setting. To tackle this issue, we propose PrivFusion, a novel architecture that preserves privacy while facilitating model fusion under the constraints of local differential privacy. PrivFusion leverages a graph-based structure, enabling the fusion of models from multiple parties without necessitating retraining. By employing randomized mechanisms, PrivFusion ensures privacy guarantees throughout the fusion process. To enhance model privacy, our approach incorporates a hybrid local differentially private mechanism and decentralized federated graph matching, effectively protecting both activation values and weights. Additionally, we introduce a perturbation filter adapter to alleviate the impact of randomized noise, thereby preserving the utility of the fused model. Through extensive experiments conducted on diverse image datasets and real-world healthcare applications, we provide empirical evidence showcasing the effectiveness of PrivFusion in maintaining model performance while preserving privacy. Our contributions offer valuable insights and practical solutions for secure and collaborative data analysis within the domain of privacy-preserving model fusion.

This paper studies the commonly utilized windowed Anderson acceleration (AA) algorithm for fixed-point methods, $x^{(k+1)}=q(x^{(k)})$. It provides the first proof that when the operator $q$ is linear and symmetric the windowed AA, which uses a sliding window of prior iterates, improves the root-linear convergence factor over the fixed-point iterations. When $q$ is nonlinear, yet has a symmetric Jacobian at a fixed point, a slightly modified AA algorithm is proved to have an analogous root-linear convergence factor improvement over fixed-point iterations. Simulations verify our observations. Furthermore, experiments with different data models demonstrate AA is significantly superior to the standard fixed-point methods for Tyler's M-estimation., Comment: 32 pages, 14 figures

Single-event burnout and single-event leakage current (SELC) in SiC power devices induced by heavy ions severely limit their space application, and the underlying mechanism is still unclear. One fundamental problem is lack of high-resolution characterization of radiation damage in the irradiated SiC power devices, which is a crucial indicator of the related mechanism. In this letter, high-resolution transmission electron microscopy (TEM) was used to characterize the radiation damage in the 1437.6 MeV 181Ta-irradiated SiC junction barrier Schottky diode under 200 V. The amorphous radiation damage with about 52 nm in diameter and 121 nm in length at the Schottky metal (Ti)-semiconductor (SiC) interface was observed. More importantly, in the damage site the atomic mixing of Ti, Si, and C was identified by electron energy loss spectroscopy and high-angle annular dark-field scanning TEM. It indicates that the melting of the Ti-SiC interface induced by localized Joule heating is responsible for the amorphization and the formation of titanium silicide, titanium carbide, or ternary phases. These modifications at nanoscale in turn cause the localized degradation of the Schottky contact, resulting in the permanent increase in leakage current. This experimental study provides very valuable clues to thorough understanding of the SELC mechanism in SiC diode., Comment: 4 pages,4 figures

In this paper, we provide a simple proof of a generalization of the Gauss-Lucas theorem. By using methods of D-companion matrix, we get the majorization relationship between the zeros of convex combinations of incomplete polynomials and an origin polynomial. Moreover, we prove that the set of all zeros of all convex combinations of incomplete polynomials coincides with the closed convex hull of zeros of the original polynomial. The location of zeros of convex combinations of incomplete polynomials is determined., Comment: 13 pages

Sorting is fundamental and ubiquitous in modern computing systems. Hardware sorting systems are built based on comparison operations with Von Neumann architecture, but their performance are limited by the bandwidth between memory and comparison units and the performance of complementary metal-oxide-semiconductor (CMOS) based circuitry. Sort-in-memory (SIM) based on emerging memristors is desired but not yet available due to comparison operations that are challenging to be implemented within memristive memory. Here we report fast and reconfigurable SIM system enabled by digit read (DR) on 1-transistor-1-resistor (1T1R) memristor arrays. We develop DR tree node skipping (TNS) that support variable data quantity and data types, and extend TNS with multi-bank, bit-slice and multi-level strategies to enable cross-array TNS (CA-TNS) for practical adoptions. Experimented on benchmark sorting datasets, our memristor-enabled SIM system presents up to 3.32x~7.70x speedup, 6.23x~183.5x energy efficiency improvement and 2.23x~7.43x area reduction compared with state-of-the-art sorting systems. We apply such SIM system for shortest path search with Dijkstra's algorithm and neural network inference with in-situ pruning, demonstrating the capability in solving practical sorting tasks and the compatibility in integrating with other compute-in-memory (CIM) schemes. The comparison-free TNS/CA-TNS SIM enabled by memristors pushes sorting into a new paradigm of sort-in-memory for next-generation sorting systems., Comment: Submitted to Nature Electronics

In Location-Based Services, Point-Of-Interest(POI) recommendation plays a crucial role in both user experience and business opportunities. Graph neural networks have been proven effective in providing personalized POI recommendation services. However, there are still two critical challenges. First, existing graph models attempt to capture users' diversified interests through a unified graph, which limits their ability to express interests in various spatial-temporal contexts. Second, the efficiency limitations of graph construction and graph sampling in large-scale systems make it difficult to adapt quickly to new real-time interests. To tackle the above challenges, we propose a novel Spatial-Temporal Graph Interaction Network. Specifically, we construct subgraphs of spatial, temporal, spatial-temporal, and global views respectively to precisely characterize the user's interests in various contexts. In addition, we design an industry-friendly framework to track the user's latest interests. Extensive experiments on the real-world dataset show that our method outperforms state-of-the-art models. This work has been successfully deployed in a large e-commerce platform, delivering a 1.1% CTR and 6.3% RPM improvement., Comment: accepted by CIKM 2023

Heterogeneous federated multi-task learning (HFMTL) is a federated learning technique that combines heterogeneous tasks of different clients to achieve more accurate, comprehensive predictions. In real-world applications, visual and natural language tasks typically require large-scale models to extract high-level abstract features. However, large-scale models cannot be directly applied to existing federated multi-task learning methods. Existing HFML methods also disregard the impact of gradient conflicts on multi-task optimization during the federated aggregation process. In this work, we propose an innovative framework called FedBone, which enables the construction of large-scale models with better generalization from the perspective of server-client split learning and gradient projection. We split the entire model into two components: a large-scale general model (referred to as the general model) on the cloud server and multiple task-specific models (referred to as the client model) on edge clients, solving the problem of insufficient computing power on edge clients. The conflicting gradient projection technique is used to enhance the generalization of the large-scale general model between different tasks. The proposed framework is evaluated on two benchmark datasets and a real ophthalmic dataset. Comprehensive results demonstrate that FedBone efficiently adapts to heterogeneous local tasks of each client and outperforms existing federated learning algorithms in most dense prediction and classification tasks with off-the-shelf computational resources on the client side.