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In this paper, we study Lipschitz continuity of the solution mappings of regularized least-squares problems for which the convex regularizers have (Fenchel) conjugates that are $\mathcal{C}^2$-cone reducible. Our approach, by using Robinson's strong regularity on the dual problem, allows us to obtain new characterizations of Lipschitz stability that rely solely on first-order information, thus bypassing the need to explore second-order information (curvature) of the regularizer. We show that these solution mappings are automatically Lipschitz continuous around the points in question whenever they are locally single-valued. We leverage our findings to obtain new characterizations of full stability and tilt stability for a broader class of convex additive-composite problems.

Large language models (LLMs) have demonstrated potential applications in medicine, yet data privacy and computational burden limit their deployment in healthcare institutions. Open-source and lightweight versions of LLMs emerge as potential solutions, but their performance, particularly in pediatric settings remains underexplored. In this cross-sectional study, 250 patient consultation questions were randomly selected from a public online medical forum, with 10 questions from each of 25 pediatric departments, spanning from December 1, 2022, to October 30, 2023. Two lightweight open-source LLMs, ChatGLM3-6B and Vicuna-7B, along with a larger-scale model, Vicuna-13B, and the widely-used proprietary ChatGPT-3.5, independently answered these questions in Chinese between November 1, 2023, and November 7, 2023. To assess reproducibility, each inquiry was replicated once. We found that ChatGLM3-6B demonstrated higher accuracy and completeness than Vicuna-13B and Vicuna-7B (P < .001), but all were outperformed by ChatGPT-3.5. ChatGPT-3.5 received the highest ratings in accuracy (65.2%) compared to ChatGLM3-6B (41.2%), Vicuna-13B (11.2%), and Vicuna-7B (4.4%). Similarly, in completeness, ChatGPT-3.5 led (78.4%), followed by ChatGLM3-6B (76.0%), Vicuna-13B (34.8%), and Vicuna-7B (22.0%) in highest ratings. ChatGLM3-6B matched ChatGPT-3.5 in readability, both outperforming Vicuna models (P < .001). In terms of empathy, ChatGPT-3.5 outperformed the lightweight LLMs (P < .001). In safety, all models performed comparably well (P > .05), with over 98.4% of responses being rated as safe. Repetition of inquiries confirmed these findings. In conclusion, Lightweight LLMs demonstrate promising application in pediatric healthcare. However, the observed gap between lightweight and large-scale proprietary LLMs underscores the need for continued development efforts., Comment: 27 pages in total with 17 pages of main manuscript and 10 pages of supplementary materials; 4 figures in the main manuscript and 2 figures in supplementary material

Monocular camera calibration is a key precondition for numerous 3D vision applications. Despite considerable advancements, existing methods often hinge on specific assumptions and struggle to generalize across varied real-world scenarios, and the performance is limited by insufficient training data. Recently, diffusion models trained on expansive datasets have been confirmed to maintain the capability to generate diverse, high-quality images. This success suggests a strong potential of the models to effectively understand varied visual information. In this work, we leverage the comprehensive visual knowledge embedded in pre-trained diffusion models to enable more robust and accurate monocular camera intrinsic estimation. Specifically, we reformulate the problem of estimating the four degrees of freedom (4-DoF) of camera intrinsic parameters as a dense incident map generation task. The map details the angle of incidence for each pixel in the RGB image, and its format aligns well with the paradigm of diffusion models. The camera intrinsic then can be derived from the incident map with a simple non-learning RANSAC algorithm during inference. Moreover, to further enhance the performance, we jointly estimate a depth map to provide extra geometric information for the incident map estimation. Extensive experiments on multiple testing datasets demonstrate that our model achieves state-of-the-art performance, gaining up to a 40% reduction in prediction errors. Besides, the experiments also show that the precise camera intrinsic and depth maps estimated by our pipeline can greatly benefit practical applications such as 3D reconstruction from a single in-the-wild image.

Superquantiles have recently gained significant interest as a risk-aware metric for addressing fairness and distribution shifts in statistical learning and decision making problems. This paper introduces a fast, scalable and robust second-order computational framework to solve large-scale optimization problems with superquantile-based constraints. Unlike empirical risk minimization, superquantile-based optimization requires ranking random functions evaluated across all scenarios to compute the tail conditional expectation. While this tail-based feature might seem computationally unfriendly, it provides an advantageous setting for a semismooth-Newton-based augmented Lagrangian method. The superquantile operator effectively reduces the dimensions of the Newton systems since the tail expectation involves considerably fewer scenarios. Notably, the extra cost of obtaining relevant second-order information and performing matrix inversions is often comparable to, and sometimes even less than, the effort required for gradient computation. Our developed solver is particularly effective when the number of scenarios substantially exceeds the number of decision variables. In synthetic problems with linear and convex diagonal quadratic objectives, numerical experiments demonstrate that our method outperforms existing approaches by a large margin: It achieves speeds more than 750 times faster for linear and quadratic objectives than the alternating direction method of multipliers as implemented by OSQP for computing low-accuracy solutions. Additionally, it is up to 25 times faster for linear objectives and 70 times faster for quadratic objectives than the commercial solver Gurobi, and 20 times faster for linear objectives and 30 times faster for quadratic objectives than the Portfolio Safeguard optimization suite for high-accuracy solution computations., Comment: 34 pages, 2 figures

Neutrino-dominated accretion flows (NDAFs) are one of the important MeV neutrino sources and significantly contribute to the cosmic diffuse neutrino background. In this paper, we investigate the spectrum of diffuse NDAF neutrino background (DNNB) by fully considering the effects of the progenitor properties and initial explosion energies based on core-collapse supernova (CCSN) simulations, and estimate the detectable event rate by Super-Kamiokande detector. We find that the predicted background neutrino flux is mainly determined by the typical CCSN initial explosion energy and progenitor metallicity. For the optimistic cases in which the typical initial explosion energy is low, the diffuse flux of DNNB is comparable to the diffuse supernova neutrino background, which might be detected by the upcoming larger neutrino detectors such as Hyper-Kamiokande, JUNO, and DUNE. Moreover, the strong outflows from NDAFs could dramatically decrease their contribution to the neutrino background., Comment: 12 pages, 7 figures, 1 table, accepted for publication in ApJ

In this work, we propose a novel method for calculating the occupation probability in the Pauli blocking of the quantum molecular dynamics type models. This method refines the description of the Pauli blocking ratio in the nuclear matter and that in the finite nucleus. The influence of the new Pauli blocking method on the heavy ion collisions observables, such as the charge distribution, the free neutron to proton yield ratios, and the extracted physical quantities, such as the in-medium nucleon-nucleon cross sections, are investigated. For the extracted in-medium nucleon-nucleon cross sections, our results show that it will be enhanced 1.1$-$2.5 times than that with the conventional Pauli blocking method at the beam energy less than 150 MeV/u, which highlights the importance of a refined Pauli blocking method for developing an advanced transport model to describe complex heavy ion collisions., Comment: 8 pages, 5 figures, accepted for PRC Letter

Based on an extended Skyrme momentum-dependent interaction (MDI), we derive an isospin asymmetric equation of state, isospin-dependent single-particle potential and the Hamiltonian which can be used in the Boltzmann-Uehling-Uhlenbeck (BUU) model and the quantum molecular dynamics (QMD) model at the beam energy less than 1 GeV/u. As an example of the applications of extended Skyrme MDI, we also present the results obtained with the extended Skyrme momentum-dependent interaction in the improved quantum molecular dynamics model (ImQMD), and the influence of the effective mass splitting on the isospin sensitive observables, i.e., the single and double neutron-to-proton ratios, is discussed again., Comment: 19 pages, 7 figures, accepted by Phys.Rev.C

Large language models such as ChatGPT are increasingly explored in medical domains. However, the absence of standard guidelines for performance evaluation has led to methodological inconsistencies. This study aims to summarize the available evidence on evaluating ChatGPT's performance in medicine and provide direction for future research. We searched ten medical literature databases on June 15, 2023, using the keyword "ChatGPT". A total of 3520 articles were identified, of which 60 were reviewed and summarized in this paper and 17 were included in the meta-analysis. The analysis showed that ChatGPT displayed an overall integrated accuracy of 56% (95% CI: 51%-60%, I2 = 87%) in addressing medical queries. However, the studies varied in question resource, question-asking process, and evaluation metrics. Moreover, many studies failed to report methodological details, including the version of ChatGPT and whether each question was used independently or repeatedly. Our findings revealed that although ChatGPT demonstrated considerable potential for application in healthcare, the heterogeneity of the studies and insufficient reporting may affect the reliability of these results. Further well-designed studies with comprehensive and transparent reporting are needed to evaluate ChatGPT's performance in medicine.

The \emph{top-$k$-sum} operator computes the sum of the largest $k$ components of a given vector. The Euclidean projection onto the top-$k$-sum sublevel set serves as a crucial subroutine in iterative methods to solve composite superquantile optimization problems. In this paper, we introduce a solver that implements two finite-termination algorithms to compute this projection. Both algorithms have $O(n)$ complexity of floating point operations when applied to a sorted $n$-dimensional input vector, where the absorbed constant is \emph{independent of $k$}. This stands in contrast to an existing grid-search-inspired method that has $O(k(n-k))$ complexity, a partition-based method with $O(n+D\log D)$ complexity, where $D\leq n$ is the number of distinct elements in the input vector, and a semismooth Newon method with a finite termination property but unspecified floating point complexity. The improvement of our methods over the first method is significant when $k$ is linearly dependent on $n$, which is frequently encountered in practical superquantile optimization applications. In instances where the input vector is unsorted, an additional cost is incurred to (partially) sort the vector, whereas a full sort of the input vector seems unavoidable for the other two methods. To reduce this cost, we further derive a rigorous procedure that leverages approximate sorting to compute the projection, which is particularly useful when solving a sequence of similar projection problems. Numerical results show that our methods solve problems of scale $n=10^7$ and $k=10^4$ within $0.05$ seconds, whereas the most competitive alternative, the semismooth Newton-based method, takes about $1$ second. The existing grid-search method and Gurobi's QP solver can take from minutes to hours., Comment: 32 pages

This paper tackles the challenging problem of finding global optimal solutions for two-stage stochastic programs with continuous decision variables and nonconvex recourse functions. We introduce a two-phase approach. The first phase involves the construction of a polynomial lower bound for the recourse function through a linear optimization problem over a nonnegative polynomial cone. Given the complex structure of this cone, we employ semidefinite relaxations with quadratic modules to facilitate our computations. In the second phase, we solve a surrogate first-stage problem by substituting the original recourse function with the polynomial lower approximation obtained in the first phase. Our method is particularly advantageous for two reasons: it not only generates global lower bounds for the nonconvex stochastic program, aiding in the certificate of global optimality for prospective solutions like stationary solutions computed from other methods, but it also yields an explicit polynomial approximation for the recourse function through the solution of a linear conic optimization problem, where the number of variables is independent of the support of the underlying random vector. Therefore, our approach is particularly suitable for the case where the random vector follows a continuous distribution or when dealing with a large number of scenarios. Numerical experiments are conducted to demonstrate the effectiveness of our proposed approach., Comment: 27 pages

We investigate a class of composite nonconvex functions, where the outer function is the sum of univariate extended-real-valued convex functions and the inner function is the limit of difference-of-convex functions. A notable feature of this class is that the inner function can be merely lower semicontinuous instead of continuously differentiable. It covers a range of important yet challenging applications, including the composite value functions of nonlinear programs and the value-at-risk constraints. We propose an asymptotic decomposition of the composite function that guarantees epi-convergence to the original function, leading to necessary optimality conditions for the corresponding minimization problem. The proposed decomposition also enables us to design a numerical algorithm such that any accumulation point of the generated sequence, if exists, satisfies the newly introduced optimality conditions. These results expand on the study of so-called amenable functions introduced by Poliquin and Rockafellar in 1992, which are compositions of convex functions with smooth maps, and the prox-linear methods for their minimization.

The optimal implementation of federated learning (FL) in practical edge computing systems has been an outstanding problem. In this paper, we propose an optimization-based quantized FL algorithm, which can appropriately fit a general edge computing system with uniform or nonuniform computing and communication resources at the workers. Specifically, we first present a new random quantization scheme and analyze its properties. Then, we propose a general quantized FL algorithm, namely GQFedWAvg. Specifically, GQFedWAvg applies the proposed quantization scheme to quantize wisely chosen model update-related vectors and adopts a generalized mini-batch stochastic gradient descent (SGD) method with the weighted average local model updates in global model aggregation. Besides, GQFedWAvg has several adjustable algorithm parameters to flexibly adapt to the computing and communication resources at the server and workers. We also analyze the convergence of GQFedWAvg. Next, we optimize the algorithm parameters of GQFedWAvg to minimize the convergence error under the time and energy constraints. We successfully tackle the challenging non-convex problem using general inner approximation (GIA) and multiple delicate tricks. Finally, we interpret GQFedWAvg's function principle and show its considerable gains over existing FL algorithms using numerical results., Comment: to appear in IEEE Transactions on Wireless Communications

Most existing studies on massive grant-free access, proposed to support massive machine-type communications (mMTC) for the Internet of things (IoT), assume Rayleigh fading and perfect synchronization for simplicity. However, in practice, line-of-sight (LoS) components generally exist, and time and frequency synchronization are usually imperfect. This paper systematically investigates maximum likelihood estimation (MLE)-based device activity detection under Rician fading for massive grant-free access with perfect and imperfect synchronization. We assume that the large-scale fading powers, Rician factors, and normalized LoS components can be estimated offline. We formulate device activity detection in the synchronous case and joint device activity and offset detection in three asynchronous cases (i.e., time, frequency, and time and frequency asynchronous cases) as MLE problems. In the synchronous case, we propose an iterative algorithm to obtain a stationary point of the MLE problem. In each asynchronous case, we propose two iterative algorithms with identical detection performance but different computational complexities. In particular, one is computationally efficient for small ranges of offsets, whereas the other one, relying on fast Fourier transform (FFT) and inverse FFT, is computationally efficient for large ranges of offsets. The proposed algorithms generalize the existing MLE-based methods for Rayleigh fading and perfect synchronization. Numerical results show that the proposed algorithm for the synchronous case can reduce the detection error probability by up to 50.4% at a 78.6% computation time increase, compared to the MLEbased state-of-the-art, and the proposed algorithms for the three asynchronous cases can reduce the detection error probabilities and computation times by up to 65.8% and 92.0%, respectively, compared to the MLE-based state-of-the-arts.

There are many significant applied contexts that require the solution of discontinuous optimization problems in finite dimensions. Yet these problems are very difficult, both computationally and analytically. With the functions being discontinuous and a minimizer (local or global) of the problems, even if it exists, being impossible to verifiably compute, a foremost question is what kind of ''stationary solutions'' one can expect to obtain; these solutions provide promising candidates for minimizers; i.e., their defining conditions are necessary for optimality. Motivated by recent results on sparse optimization, we introduce in this paper such a kind of solution, termed ''pseudo B- (for Bouligand) stationary solution'', for a broad class of discontinuous piecewise continuous optimization problems with objective and constraint defined by indicator functions of the positive real axis composite with functions that are possibly nonsmooth. We present two approaches for computing such a solution. One approach is based on lifting the problem to a higher dimension via the epigraphical formulation of the indicator functions; this requires the addition of some auxiliary variables. The other approach is based on certain continuous (albeit not necessarily differentiable) piecewise approximations of the indicator functions and the convergence to a pseudo B-stationary solution of the original problem is established. The conditions for convergence are discussed and illustrated by an example.

Multi-phase liver contrast-enhanced computed tomography (CECT) images convey the complementary multi-phase information for liver tumor segmentation (LiTS), which are crucial to assist the diagnosis of liver cancer clinically. However, the performances of existing multi-phase liver tumor segmentation (MPLiTS)-based methods suffer from redundancy and weak interpretability, % of the fused result, resulting in the implicit unreliability of clinical applications. In this paper, we propose a novel trustworthy multi-phase liver tumor segmentation (TMPLiTS), which is a unified framework jointly conducting segmentation and uncertainty estimation. The trustworthy results could assist the clinicians to make a reliable diagnosis. Specifically, Dempster-Shafer Evidence Theory (DST) is introduced to parameterize the segmentation and uncertainty as evidence following Dirichlet distribution. The reliability of segmentation results among multi-phase CECT images is quantified explicitly. Meanwhile, a multi-expert mixture scheme (MEMS) is proposed to fuse the multi-phase evidences, which can guarantee the effect of fusion procedure based on theoretical analysis. Experimental results demonstrate the superiority of TMPLiTS compared with the state-of-the-art methods. Meanwhile, the robustness of TMPLiTS is verified, where the reliable performance can be guaranteed against the perturbations.

To improve the constraints of symmetry energy at subsaturation density, measuring and accumulating more neutron skin data for neutron rich unstable nuclei is naturally required. Aiming to probe the neutron skin of unstable nuclei by using low-intermediate energy heavy ion collisions, we develop a new version of improved quantum molecular dynamics model, in which the neutron skin of the initial nucleus and the mean field potential in nucleon propagation are consistently treated. Our calculations show that the three observables, such as the cross sections of the primary projectile-like residues with $A>100$ ($\sigma_{A>100}$), the difference of $\sigma_{A>100}$ between $^{132}$Sn+$^{124}$Sn and $^{124}$Sn+$^{124}$Sn systems ($\delta \sigma_{A>100}$), and the neutron to proton yield ratio ($R(n/p)$) in the transverse direction, could be used to measure the neutron skin of the unstable nuclei and to constrain the slope of the symmetry energy in the future., Comment: 9 pages, 4 figures

In this work, we first analyze the correlations among different nuclear matter parameters which are obtained by the 119 effective Skyrme interaction sets. The values of the correlation coefficients illustrate that the magnitude of the effective mass splitting is crucial for the tight constraints of the symmetry energy via HICs. Thus, the main object of this work is to investigate the impacts of the effective mass splitting on the heavy ion collisions observables. The $^{86}$Kr+$^{208}$Pb system at the beam energy ranging from 25A MeV to 200A MeV are simulated within the framework of the improved quantum molecular dynamics model (ImQMD-Sky) for this goal. Our calculations show that the slopes of the spectra of $\ln$[Y(n)/Y(p)] and $\ln$[Y(t)/Y($^3$He)], which are the logarithms of the neutron to proton yield ratios and triton to Helium-3 yield ratios, are directly related to the effective mass splitting and can be used to probe the effective mass splitting., Comment: 9 pages, 4 figures

Massive access has been challenging for the fifth generation (5G) and beyond since the abundance of devices causes communication overload to skyrocket. In an uplink massive access scenario, device traffic is sporadic in any given coherence time. Thus, channels across the antennas of each device exhibit correlation, which can be characterized by the row sparse channel matrix structure. In this work, we develop a bilinear generalized approximate message passing (BiGAMP) algorithm based on the row sparse channel matrix structure. This algorithm can jointly detect device activities, estimate channels, and detect signals in massive multiple-input multiple-output (MIMO) systems by alternating updates between channel matrices and signal matrices. The signal observation provides additional information for performance improvement compared to the existing algorithms. We further analyze state evolution (SE) to measure the performance of the proposed algorithm and characterize the convergence condition for SE. Moreover, we perform theoretical analysis on the error probability of device activity detection, the mean square error of channel estimation, and the symbol error rate of signal detection. The numerical results demonstrate the superiority of the proposed algorithm over the state-of-the-art methods in DADCE-SD, and the numerical results are relatively close to the theoretical analysis results., Comment: 15 pages, 8 figures, IEEE TSP