Hidden convex optimization is such a class of nonconvex optimization problems that can be globally solved in polynomial time via equivalent convex programming reformulations. In this paper, we focus on checking local optimality in hidden convex optim
ization. We first introduce a class of hidden convex optimization problems by jointing the classical nonconvex trust-region subproblem (TRS) with convex optimization (CO), and then present a comprehensive study on local optimality conditions. In order to guarantee the existence of a necessary and sufficient condition for local optimality, we need more restrictive assumptions. To our surprise, while (TRS) has at most one local non-global minimizer and (CO) has no local non-global minimizer, their joint problem could have more than one local non-global minimizer.
Identifying super-spreaders in epidemics is important to suppress the spreading of disease especially when the medical resource is limited.In the modern society, the information on epidemics transmits swiftly through various communication channels wh
ich contributes much to the suppression of epidemics. Here we study on the identification of super-spreaders in the information-disease coupled spreading dynamics. Firstly, we find that the centralities in physical contact layer are no longer effective to identify super-spreaders in epidemics, which is due to the suppression effects from the information spreading. Then by considering the structural and dynamical couplings between the communication layer and physical contact layer, we propose a centrality measure called coupling-sensitive centrality to identify super-spreaders in disease spreading. Simulation results on synthesized and real-world multiplex networks show that the proposed measure is not only much more accurate than centralities on the single network, but also outperforms two typical multilayer centralities in identifying super-spreaders. These findings imply that considering the structural and dynamical couplings between layers is very necessary in identifying the key roles in the coupled multilayer systems.
We prove a conjecture of the first-named author ([J14]) on the upper bound Fourier coefficients of automorphic forms in Arthur packets of split classical groups over any number field.
Response properties that are purely intrinsic to physical systems are of paramount importance in physics research, as they probe fundamental properties of band structures and allow quantitative calculation and comparison with experiment. For anomalou
s Hall transport in magnets, an intrinsic effect can appear at the second order to the applied electric field. We show that this intrinsic second-order anomalous Hall effect is associated with an intrinsic band geometric property -- the dipole moment of Berry-connection polarizability (BCP) in momentum space. The effect has scaling relation and symmetry constraints that are distinct from the previously studied extrinsic contributions. Particularly, in antiferromagnets with $mathcal{PT}$ symmetry, the intrinsic effect dominates. Combined with first-principles calculations, we demonstrate the first quantitative evaluation of the effect in the antiferromagnet Mn$_{2}$Au. We show that the BCP dipole and the resulting intrinsic second-order conductivity are pronounced around band near degeneracies. Importantly, the intrinsic response exhibits sensitive dependence on the N{e}el vector orientation with a $2pi$ periodicity, which offers a new route for electric detection of the magnetic order in $mathcal{PT}$-invariant antiferromagnets.
Soft materials can be designed with a functionally graded (FG) property for specific applications. In this paper, we analyze the axisymmetric guided wave propagation in a pressurized FG elastomeric hollow cylinder. The cylinder is subjected to a comb
ined action of axial pre-stretch and pressure difference applied to the inner and outer cylindrical surfaces. We consider both torsional waves and longitudinal waves propagating in the FG cylinder made of incompressible isotropic elastomer, which is characterized by the Mooney-Rivlin strain energy function but with the material parameters varying with the radial coordinate in an affine way. The pressure difference generates an inhomogeneous deformation field in the FG cylinder, which dramatically complicates the superimposed wave problem described by the small-on-large theory. A particularly efficient approach is hence employed which combines the state-space formalism for the incremental wave motion with the approximate laminate or multi-layer technique. Dispersion relations for the two types of axisymmetric guided waves are then derived analytically. The accuracy and convergence of the proposed approach is validated numerically. The effects of the pressure difference, material gradient, and axial pre-stretch on both the torsional and the longitudinal wave propagation characteristics are discussed in detail through numerical examples. It is found that the frequency of axisymmetric waves depends nonlinearly on the pressure difference and the material gradient, and an increase in the material gradient enhances the capability of the pressure difference to adjust the wave behavior in the FG cylinder.
We study nonconvex homogeneous quadratically constrained quadratic optimization with one or two constraints, denoted by (QQ1) and (QQ2), respectively. (QQ2) contains (QQ1), trust region subproblem (TRS) and ellipsoid regularized total least squares p
roblem as special cases. It is known that there is a necessary and sufficient optimality condition for the global minimizer of (QQ2). In this paper, we first show that any local minimizer of (QQ1) is globally optimal. Unlike its special case (TRS) with at most one local non-global minimizer, (QQ2) may have infinitely many local non-global minimizers. At any local non-global minimizer of (QQ2), both linearly independent constraint qualification and strict complementary condition hold, and the Hessian of the Lagrangian has exactly one negative eigenvalue. As a main contribution, we prove that the standard second-order sufficient optimality condition for any strict local non-global minimizer of (QQ2) remains necessary. Applications and the impossibility of further extension are discussed.
One big achievement in modern condensed matter physics is the recognition of the importance of various band geometric quantities in physical effects. As prominent examples, Berry curvature and Berry curvature dipole are connected to the linear and th
e second-order Hall effects, respectively. Here, we show that the Berry connection polarizability (BCP) tensor, as another intrinsic band geometric quantity, plays a key role in the third-order Hall effect. Based on the extended semiclassical formalism, we develop a theory for the third-order charge transport and derive explicit formulas for the third-order conductivity. Our theory is applied to the two-dimensional (2D) Dirac model to investigate the essential features of BCP and the third-order Hall response. We further demonstrate the combination of our theory with the first-principles calculations to study a concrete material system, the monolayer FeSe. Our work establishes a foundation for the study of third-order transport effects, and reveals the third-order Hall effect as a tool for characterizing a large class of materials and for probing the BCP in band structure.
Low-dose CT has been a key diagnostic imaging modality to reduce the potential risk of radiation overdose to patient health. Despite recent advances, CNN-based approaches typically apply filters in a spatially invariant way and adopt similar pixel-le
vel losses, which treat all regions of the CT image equally and can be inefficient when fine-grained structures coexist with non-uniformly distributed noises. To address this issue, we propose a Structure-preserving Kernel Prediction Network (StructKPN) that combines the kernel prediction network with a structure-aware loss function that utilizes the pixel gradient statistics and guides the model towards spatially-variant filters that enhance noise removal, prevent over-smoothing and preserve detailed structures for different regions in CT imaging. Extensive experiments demonstrated that our approach achieved superior performance on both synthetic and non-synthetic datasets, and better preserves structures that are highly desired in clinical screening and low-dose protocol optimization.
A two-dimensional (2D) topological semimetal is characterized by the nodal points in its low-energy band structure. While the linear nodal points have been extensively studied, especially in the context of graphene, the realm beyond linear nodal poin
ts remains largely unexplored. Here, we explore the possibility of higher-order nodal points, i.e., points with higher-order energy dispersions, in 2D systems. We perform an exhaustive search over all 80 layer groups both with and without spin-orbit coupling (SOC), and reveal all possible higher-order nodal points. We show that they can be classified into two categories: the quadratic nodal point (QNP) and the cubic nodal point (CNP). All the 2D higher-order nodal points have twofold degeneracy, and the order of dispersion cannot be higher than three. QNPs only exist in the absence of SOC, whereas CNPs only exist in the presence of SOC. Particularly, the CNPs represent a new topological state not known before. We show that they feature nontrivial topological charges, leading to extensive topological edge bands. Our work completely settles the problem of higher-order nodal points, discovers novel topological states in 2D, and provides detailed guidance to realize these states. Possible material candidates and experimental signatures are discussed.
Food image segmentation is a critical and indispensible task for developing health-related applications such as estimating food calories and nutrients. Existing food image segmentation models are underperforming due to two reasons: (1) there is a lac
k of high quality food image datasets with fine-grained ingredient labels and pixel-wise location masks -- the existing datasets either carry coarse ingredient labels or are small in size; and (2) the complex appearance of food makes it difficult to localize and recognize ingredients in food images, e.g., the ingredients may overlap one another in the same image, and the identical ingredient may appear distinctly in different food images. In this work, we build a new food image dataset FoodSeg103 (and its extension FoodSeg154) containing 9,490 images. We annotate these images with 154 ingredient classes and each image has an average of 6 ingredient labels and pixel-wise masks. In addition, we propose a multi-modality pre-training approach called ReLeM that explicitly equips a segmentation model with rich and semantic food knowledge. In experiments, we use three popular semantic segmentation methods (i.e., Dilated Convolution based, Feature Pyramid based, and Vision Transformer based) as baselines, and evaluate them as well as ReLeM on our new datasets. We believe that the FoodSeg103 (and its extension FoodSeg154) and the pre-trained models using ReLeM can serve as a benchmark to facilitate future works on fine-grained food image understanding. We make all these datasets and methods public at url{https://xiongweiwu.github.io/foodseg103.html}.
