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Haidong Li

Publications and source records attributed to Haidong Li.

At least 19 recordsLinked to original sources

A $p$-part Birch and Swinnerton-Dyer Formula over Totally Imaginary Quadratic Extension of Totally Real Fields

This article studies a modular semistable elliptic curve $E$ over a totally real number field $F$ such that, upon base change to a totally imaginary quadratic extension $K$, it has analytic rank one. Assuming the Iwasawa main conjecture, along with a substantial number of assumptions, we prove a variant of the $p$-part of the Birch and Swinnerton-Dyer formula over $K$, where $p$ is an odd prime. More precisely, up to a $p$-adic unit, we have $$ \frac{L'(E/K,1)}{\Omega^{\mathrm{cong}}_{\mathbf{f}} \operatorname{Reg}(E/K)} = \# Sha(E/K)[p^\infty]\prod_{u} c_u(E/K), $$ where $\Omega^{\mathrm{cong}}_{\mathbf{f}}$ is the congruence period of the Hilbert modular form $\mathbf{f}$ associated to $E$ via the modularity conjecture.

math.NT

Near-Oracle Robustification of Finite-Difference Stochastic Gradient Estimators via Cheap Pilot Calibration

We study stochastic gradient estimation in black-box environments where only noisy simulation observations of function values are available. Finite-difference (FD) methods are among the most widely used zeroth-order gradient estimators in such settings, by measuring the change in function values against a perturbation size. While the optimal order in choosing this perturbation size with respect to the simulation budget is well understood, the optimal constant factor relies on model characteristics that are typically unknown and viewed to be as difficult to estimate as the gradient itself. Consequently, FD estimators are often based on ad hoc tuning of the perturbation size, which may exhibit highly unstable performance across problem instances. In this paper, we challenge this conventional wisdom from both theoretical and practical perspectives. We show that, by pilot-estimating these model quantities using a negligible fraction of the simulation budget, substantial robustness is attained in the resulting FD estimators. Theoretically, we show that using a perturbation size governed by this pilot estimation can already achieve an MSE that is first-order identical to the ``oracle" MSE as if the optimal perturbation size is known in advance. Moreover, we show how such an approach is competitive against any choices of prescribed perturbation size, even if they are designed to be minimax-optimal over reasonable classes of target functions and FD schemes. Our proposed pilot estimation is practically easy to run, and a variety of numerical experiments demonstrate both the robustness and near-oracle optimality of our estimator relative to conventional FD schemes based on ad hoc tuning.

stat.ME

Torsion groups of rational elliptic curves over $\mathbb{Z}_p$-extensions of quadratic fields: the $p\le 5$ case

Let $E$ be a rational elliptic curve. We generalize a theorem due to Avc{\i}\cite{AVCI2026153}, which asserts that for any quadratic field \(K\) and prime \(p>5\), the equality \(E(K)_{\mathrm{tors}} = E(L)_{\mathrm{tors}}\) holds for every \(\mathbb{Z}_p\)-extension \(L/K\). In this paper, we consider the setting where the \(\mathbb{Z}_p\)-extension \(L\) is replaced by the compositum \(K_{\infty}\) of all \(\mathbb{Z}_p\)-extensions of \(K\). Under this new setting, we prove the analogous statement for \(p=5\), and further provide partial results for the remaining primes \(p=3\) and \(p=2\).

math.NT

Large values of logarithmic derivatives of quadratic Dirichlet $L$-functions

In this article, we apply the resonance method to derive conditional Omega results for logarithmic derivatives of quadratic Dirichlet $L$-functions. We improve a previous result of Mortada and Murty \cite{MM13}, as well as generalize some results of Yang \cite{yang2023omegatheoremslogarithmicderivatives}.

math.NT

Time-independent theoretical framework for stroboscopic nonlinear dynamics based on time-nonlocal response

Recent experiments have demonstrated the ability to manipulate nonlinear interactions via time modulation, giving rise to the so-called stroboscopic nonlinearity. To date, however, this phenomenon has not been subjected to a rigorous theoretical analysis. In this work, we clarify the physical mechanism underlying stroboscopic nonlinear dynamics based on time-nonlocal response and establish an effective time-independent model under suitable modulation conditions. The proposed model almost exactly reproduces the full time-dependent dynamics in the quasi-steady state and significantly outperforms empirical descriptions used previously. Our results provide a clear physical picture of stroboscopic nonlinear dynamics, and can be extended to other systems with time-nonlocal response, establishing a general framework for engineering nonlinear interactions through temporal modulation.

physics.optics

On the Mordell-Weil rank of certain CM abelian varieties over anticyclotomic towers

Let $K/\mathbb{Q}$ be an imaginary quadratic extension, and let $p$ be an odd prime. In this paper, we investigate the growth of Mordell-Weil ranks of CM abelian varieties associated with Hecke characters over $K$ of infinite type $(1, 0)$ along the $\mathbb{Z}_p$-anticyclotomic tower of $K$. Our results cover all decomposition types of $p$ in $K$. The analytic aspect of our proof is based on our computations of the local and global root numbers of Hecke characters, together with a recent generalization by H. Jia of D. Rohrlich's result concerning the relation between the vanishing orders of Hecke $L$-functions and their root numbers. The arithmetic conclusions then follow from the Gross-Zagier formula and the Kolyvagin machinery.

math.NT

Enhanced Masked Image Modeling to Avoid Model Collapse on Multi-modal MRI Datasets

Multi-modal magnetic resonance imaging (MRI) provides information of lesions for computer-aided diagnosis from different views. Deep learning algorithms are suitable for identifying specific anatomical structures, segmenting lesions, and classifying diseases. Manual labels are limited due to the high expense, which hinders further improvement of accuracy. Self-supervised learning, particularly masked image modeling (MIM), has shown promise in utilizing unlabeled data. However, we spot model collapse when applying MIM to multi-modal MRI datasets. The performance of downstream tasks does not see any improvement following the collapsed model. To solve model collapse, we analyze and address it in two types: complete collapse and dimensional collapse. We find complete collapse occurs because the collapsed loss value in multi-modal MRI datasets falls below the normally converged loss value. Based on this, the hybrid mask pattern (HMP) masking strategy is introduced to elevate the collapsed loss above the normally converged loss value and avoid complete collapse. Additionally, we reveal that dimensional collapse stems from insufficient feature uniformity in MIM. We mitigate dimensional collapse by introducing the pyramid barlow twins (PBT) module as an explicit regularization method. Overall, we construct the enhanced MIM (E-MIM) with HMP and PBT module to avoid model collapse multi-modal MRI. Experiments are conducted on three multi-modal MRI datasets to validate the effectiveness of our approach in preventing both types of model collapse. By preventing model collapse, the training of the model becomes more stable, resulting in a decent improvement in performance for segmentation and classification tasks. The code is available at https://github.com/LinxuanHan/E-MIM.

eess.IV

Encoding Enhanced Complex CNN for Accurate and Highly Accelerated MRI

Magnetic resonance imaging (MRI) using hyperpolarized noble gases provides a way to visualize the structure and function of human lung, but the long imaging time limits its broad research and clinical applications. Deep learning has demonstrated great potential for accelerating MRI by reconstructing images from undersampled data. However, most existing deep conventional neural networks (CNN) directly apply square convolution to k-space data without considering the inherent properties of k-space sampling, limiting k-space learning efficiency and image reconstruction quality. In this work, we propose an encoding enhanced (EN2) complex CNN for highly undersampled pulmonary MRI reconstruction. EN2 employs convolution along either the frequency or phase-encoding direction, resembling the mechanisms of k-space sampling, to maximize the utilization of the encoding correlation and integrity within a row or column of k-space. We also employ complex convolution to learn rich representations from the complex k-space data. In addition, we develop a feature-strengthened modularized unit to further boost the reconstruction performance. Experiments demonstrate that our approach can accurately reconstruct hyperpolarized 129Xe and 1H lung MRI from 6-fold undersampled k-space data and provide lung function measurements with minimal biases compared with fully-sampled image. These results demonstrate the effectiveness of the proposed algorithmic components and indicate that the proposed approach could be used for accelerated pulmonary MRI in research and clinical lung disease patient care.

eess.IV

Efficient Distributed Learning in Stochastic Non-cooperative Games without Information Exchange

In this work, we study stochastic non-cooperative games, where only noisy black-box function evaluations are available to estimate the cost function for each player. Since each player's cost function depends on both its own decision variables and its rivals' decision variables, local information needs to be exchanged through a center/network in most existing work for seeking the Nash equilibrium. We propose a new stochastic distributed learning algorithm that does not require communications among players. The proposed algorithm uses simultaneous perturbation method to estimate the gradient of each cost function, and uses mirror descent method to search for the Nash equilibrium. We provide asymptotic analysis for the bias and variance of gradient estimates, and show the proposed algorithm converges to the Nash equilibrium in mean square for the class of strictly monotone games at a rate faster than the existing algorithms. The effectiveness of the proposed method is buttressed in a numerical experiment.

cs.GT

Direct Observation of A Large-scale CME Flux Rope Event Arising from an Unwinding Coronal Jet

Coronal mass ejections (CMEs) and coronal jets are two types of common solar eruptive phenomena, which often independently happen at different spatial scales. In this work, we present a stereoscopic observation of a large-scale CME flux rope arising from an unwinding blowout jet in a multipolar complex magnetic system. Based on a multi-band observational analysis, we find that this whole event starts with a small filament whose eruption occurs at a coronal geyser site after a series of homologous jets. Aided by magnetic field extrapolations, it reveals that the coronal geyser site forms above an elongate opposite-polarity interface, where the emergence-driven photospheric flux cancellation and repetitive reconnection are responsible for those preceding recurrent jets and also contribute to the ultimate filament destabilization. By interacting with overlying fields, the erupting filament breaks one of its legs and results in an unwinding blowout jet. Our estimation suggests that around 1.4$-$2.0 turns of twist release in its jet spire. This prominent twist transport in jet spire rapidly creates a newborn larger-scale flux rope from the jet base to a remote site. Soon after its formation, this large-scale flux rope erupts towards the outer coronae causing an Earth-directed CME. In its source region, two sets of distinct post-flare loops form in succession, indicating this eruption involves two-stage of flare magnetic reconnection. This work not only reveals a real magnetic coupling process between different eruptive activities but provides a new hint for understanding the creation of large-scale CME flux ropes during the solar eruption.

astro-ph.SR

Context-dependent Ranking and Selection under a Bayesian Framework

We consider a context-dependent ranking and selection problem. The best design is not universal but depends on the contexts. Under a Bayesian framework, we develop a dynamic sampling scheme for context-dependent optimization (DSCO) to efficiently learn and select the best designs in all contexts. The proposed sampling scheme is proved to be consistent. Numerical experiments show that the proposed sampling scheme significantly improves the efficiency in context-dependent ranking and selection.

stat.ME

Efficient Learning for Clustering and Optimizing Context-Dependent Designs

We consider a simulation optimization problem for a context-dependent decision-making. A Gaussian mixture model is proposed to capture the performance clustering phenomena of context-dependent designs. Under a Bayesian framework, we develop a dynamic sampling policy to efficiently learn both the global information of each cluster and local information of each design for selecting the best designs in all contexts. The proposed sampling policy is proved to be consistent and achieve the asymptotically optimal sampling ratio. Numerical experiments show that the proposed sampling policy significantly improves the efficiency in context-dependent simulation optimization.

stat.ME

Minimax Efficient Finite-Difference Stochastic Gradient Estimators Using Black-Box Function Evaluations

Standard approaches to stochastic gradient estimation, with only noisy black-box function evaluations, use the finite-difference method or its variants. While natural, it is open to our knowledge whether their statistical accuracy is the best possible. This paper argues so by showing that central finite-difference is a nearly minimax optimal zeroth-order gradient estimator for a suitable class of objective functions and mean squared risk, among both the class of linear estimators and the much larger class of all (nonlinear) estimators.

math.ST

Recurrent Two-Sided Loop Jets Caused by Magnetic Reconnection between Erupting Minifilaments and Nearby Large Filament

Using high spatial and temporal data from the New Vacuum Solar Telescope (NVST) and the Solar Dynamics Observatory (SDO), we present unambiguous observations of recurrent two-sided loop jets caused by magnetic reconnection between erupting minifilaments and nearby large filament. The observations demonstrate that three two-sided loop jets, which ejected along the large filament in opposite directions, had similar appearance and originated from the same region. We find that a minifilament erupted and drove the first jet. It reformed at the same neutral line later, and then underwent partial and total eruptions, drove the second and third jets, respectively. In the course of the jets, cool plasma was injected into the large filament. Furthermore, persistent magnetic flux cancelation occurred at the neutral line under the minifilament before its eruption and continued until the end of the observation. We infer that magnetic flux cancellation may account for building and then triggering the minifilament to erupt to produce the two-sided loop jets. This observation not only indicates that two-sided loop jets can be driven by minifilament eruptions, but also sheds new light on our understanding of the recurrent mechanism of two-sided loop jets.

astro-ph.SR

Efficient Sampling for Selecting Important Nodes in Random Network

We consider the problem of selecting important nodes in a random network, where the nodes connect to each other randomly with certain transition probabilities. The node importance is characterized by the stationary probabilities of the corresponding nodes in a Markov chain defined over the network, as in Google's PageRank. Unlike deterministic network, the transition probabilities in random network are unknown but can be estimated by sampling. Under a Bayesian learning framework, we apply the first-order Taylor expansion and normal approximation to provide a computationally efficient posterior approximation of the stationary probabilities. In order to maximize the probability of correct selection, we propose a dynamic sampling procedure which uses not only posterior means and variances of certain interaction parameters between different nodes, but also the sensitivities of the stationary probabilities with respect to each interaction parameter. Numerical experiment results demonstrate the superiority of the proposed sampling procedure.

stat.ME

Observational Evidence of Magnetic Reconnection Associated with Magnetic Flux Cancellation

Using high spatial and temporal data from the \emph{Solar Dynamics Observatory} (\emph{SDO}) and the \emph{Interface Region Imaging Spectrograph} (\emph{IRIS}), several observational signatures of magnetic reconnection in the course of magnetic flux cancellation are presented, including two loop-loop interaction processes, multiple plasma blob ejections, and a sheet-like structure that appeared above the flux cancellation sites with a Y-shaped and an inverted Y-shaped ends. The \emph{IRIS} 1400 Å observations show that the plasma blobs were ejected from the tip of the Y-shaped ends of the sheet-like structure. Obvious photospheric magnetic flux cancellation occurred after the first loop-loop interaction and continued until the end of the observation. Complemented by the nonlinear force-free field extrapolation, we found that two sets of magnetic field lines, which reveal an X-shaped configuration, align well with the interacted coronal loops. Moreover, a magnetic null point is found to be situated at about $0.9$ Mm height right above the flux cancellation sites and located between the two sets of magnetic field lines. These results suggest that the flux cancellation might be a result of submergence of magnetic field lines following magnetic reconnection that occurs in the lower atmosphere of the Sun, and the ejected plasma blobs should be plasmoids created in the sheet-like structure due to the tearing-mode instability. This observation reveals detailed magnetic field structure and dynamic process above the flux cancellation sites and will help us to understand magnetic reconnection in the lower atmosphere of the Sun.

astro-ph.SR

Generalized transfer matrix theory on electronic transport through graphene waveguide

In the effective mass approximation, electronic property in graphene can be characterized by the relativistic Dirac equation. Within such a continuum model we investigate the electronic transport through graphene waveguides formed by connecting multiple segments of armchair-edged graphene nanoribbons of different widths. By using appropriate wavefunction connection conditions at the junction interfaces, we generalize the conventional transfer matrix approach to formulate the linear conductance of the graphene waveguide in terms of the structure parameters and the incident electron energy. In comparison with the tight-binding calculation, we find that the generalized transfer matrix method works well in calculating the conductance spectrum of a graphene waveguide even with a complicated structure and relatively large size. The calculated conductance spectrum indicates that the graphene waveguide exhibits a well-defined insulating band around the Dirac point, even though all the constituent ribbon segments are gapless. We attribute the occurrence of the insulating band to the antiresonance effect which is intimately associated with the edge states localized at the shoulder regions of the junctions. Furthermore, such an insulating band can be sensitively shifted by a gate voltage, which suggests a device application of the graphene waveguide as an electric nanoswitch.

cond-mat.str-el

Contact conductance between graphene and quantum wires

The contact conductance between graphene and two quantum wires which serve as the leads to connect graphene and electron reservoirs is theoretically studied. Our investigation indicates that the contact conductance depends sensitively on the graphene-lead coupling configuration. When each quantum wire couples solely to one carbon atom, the contact conductance vanishes at the Dirac point if the two carbon atoms coupling to the two leads belong to the same sublattice of graphene. We find that such a feature arises from the chirality of the Dirac electron in graphene. Such a chirality associated with conductance zero disappears when a quantum wire couples to multiple carbon atoms. The general result irrelevant to the coupling configuration is that the contact conductance decays rapidly with the increase of the distance between the two leads. In addition, in the weak graphene-lead coupling limit, when the distance between the two leads is much larger than the size of the graphene-lead contact areas and the incident electron energy is close to the Dirac point, the contact conductance is proportional to the square of the product of the two graphene-lead contact areas, and inversely proportional to the square of the distance between the two leads.

cond-mat.mes-hall