arXiv subjects

Kun Meng

Publications and source records attributed to Kun Meng.

At least 19 recordsLinked to original sources

arXiv2026

Gravitational waves of extreme-mass-ratio inspirals in a rotating black hole with Dehnen dark matter halo

Extreme Mass Ratio Inspirals (EMRIs) are among the key targe sources for the space-based gravitational wave (GW) detectors. The waveforms of the EMRIs are highly sensitive to the types of the central supermassive black hole (SBH) and can serve as a novel sensitive tool to probe the background spacetime. In this work, we compute GWs radiated from EMRIs in the backgrounds of Kerr black hole and rotating black hole with Dehnen-type dark matter halo (DMBH). Following the Teukolsky prescription, we obtain the perturbed equations for curvature tensor from the Newman-Penrose (NP) equations, and for the DMBH we obtain the radial and angular equations through separation of variables. To solve the equations with numerical method we apply the Sasaki-Nakamura (SN) transformation to convert the Teykolsky-type equation into the SN equation. We study the radiation reaction of GWs by computing the energy flux and angular momentum flux at infinity and at the horizon. The orbital evolution is then derived from the total fluxes. We extract the two polarizations of GWs by solving the equation numerically. By comparing the waveforms of Kerr and DMBH, it is found that the DM halo induces noticeable changes in both the amplitude and phase of GWs. We compute the strain of GW detector with the response function and evaluate the mismatch between the waveforms of Kerr and DMBH. The results show that the mismatch increases with the mass parameter of DM halo and the spin of the SBH.

gr-qc↗

arXiv2026

Theoretical Foundations of Principal Manifold Estimation with Non-Euclidean Templates

We develop a rigorous theoretical framework for principal manifold estimation that recovers a latent low-dimensional manifold from a point cloud observed in a high-dimensional ambient space. Our framework accommodates manifolds with general, potentially non-Euclidean topology, which can be inferred using tools from topological data analysis. Using the theory of Sobolev spaces on Riemannian manifolds, we establish that the proposed principal manifolds are well defined, prove convergence of the iterative algorithm used to compute them, and show consistency of the finite-sample estimator. Furthermore, we introduce a novel method for selecting the complexity level of a fitted manifold, which addresses the shortcomings of the classical fitting-error criterion. We also provide a detailed geometric interpretation of the penalty term in our framework. In addition to the theoretical developments, we present extensive numerical experiments supporting our results. This article provides theoretical foundations for approaches that have been used in applications such as robotics. More importantly, it extends these approaches to general topological settings with potential applications across a broad range of disciplines, including neuroimaging and shape data analysis.

math.ST↗

arXiv2025

Zero-Shot Learning with Subsequence Reordering Pretraining for Compound-Protein Interaction

Given the vastness of chemical space and the ongoing emergence of previously uncharacterized proteins, zero-shot compound-protein interaction (CPI) prediction better reflects the practical challenges and requirements of real-world drug development. Although existing methods perform adequately during certain CPI tasks, they still face the following challenges: (1) Representation learning from local or complete protein sequences often overlooks the complex interdependencies between subsequences, which are essential for predicting spatial structures and binding properties. (2) Dependence on large-scale or scarce multimodal protein datasets demands significant training data and computational resources, limiting scalability and efficiency. To address these challenges, we propose a novel approach that pretrains protein representations for CPI prediction tasks using subsequence reordering, explicitly capturing the dependencies between protein subsequences. Furthermore, we apply length-variable protein augmentation to ensure excellent pretraining performance on small training datasets. To evaluate the model's effectiveness and zero-shot learning ability, we combine it with various baseline methods. The results demonstrate that our approach can improve the baseline model's performance on the CPI task, especially in the challenging zero-shot scenario. Compared to existing pre-training models, our model demonstrates superior performance, particularly in data-scarce scenarios where training samples are limited. Our implementation is available at https://github.com/Hoch-Zhang/PSRP-CPI.

cs.LG↗

arXiv2025

Phase Transition and Critical Phenomena of Charged Einstein-Maxwell-Scalar Black Holes

We study the phase transition and critical phenomenon of charged black holes in Einstein-Maxwell-scalar (EMs) theory. Through comprehensive analysis of thermodynamic behaviors manifested in P-V diagrams, G(T,P) surfaces, and C_P curves, we establish that these black holes exhibit van der Waals-type phase transition behavior. The derived critical exponents governing the phase transition show precise correspondence with both van der Waals gas-liquid systems, reinforcing the connection between black hole thermodynamics and mean field theory statistics. The findings reveal a crucial dependence of phase transition properties on the scalar charge parameter. A critical threshold emerges where phase transitions become prohibited when scalar charge exceeds a specific magnitude. However, the transition persists asymptotically as scalar charge approaches zero. The analysis further demonstrates nonlinear relationships between scalar charge and critical parameters: while small scalar charges induce increasing critical volume with charge magnitude, larger values produce an inverse trend. Critical temperature displays complementary behavior, maintaining monotonic variation under certain conditions while exhibiting inverse correlation with critical volume in others. Significantly, the transition points governing critical volume and temperature trends occur at distinct scalar charge values for different black holes, indicating a non-trivial parameter dependence. These results highlight the scalar charge's dual role as both an enabler and suppressor of phase transitions in EMs black holes, providing new insights into the interplay between geometric configurations and thermodynamic properties in modified gravity theories.

gr-qc↗

arXiv2025

Optically detected and radio wave-controlled spin chemistry in flavoproteins

Optically addressable spin systems, such as nitrogen-vacancy centers in diamond, have been widely studied for quantum sensing applications. In this work, we demonstrate that certain flavoproteins, specifically cryptochrome and iLOV, which generate spin correlated radical pairs upon optical excitation, also exhibit optically detected magnetic resonance (ODMR). Remarkably, the iLOV protein, commonly used in cellular imaging, displays ODMR contrast approaching 50%. We present initial applications including widefield magnetic field sensing and spatial modulation of photoluminescence using radiofrequency pulses and magnetic field gradients. Our results establish radical pairs in proteins as a novel platform for optically addressable spin systems, offering the key advantages of molecular designability and genetic encodability. Moreover, due to the spin-selective nature of radical pair chemistry, the results lay the groundwork for future radiofrequency-based manipulation of biological systems.

quant-ph↗

arXiv2024

Longitudinal Principal Manifold Estimation

Longitudinal magnetic resonance imaging data is used to model trajectories of change in brain regions of interest to identify areas susceptible to atrophy in those with neurodegenerative conditions like Alzheimer's disease. Most methods for extracting brain regions are applied to scans from study participants independently, resulting in wide variability in shape and volume estimates of these regions over time in longitudinal studies. To address this problem, we propose a longitudinal principal manifold estimation method, which seeks to recover smooth, longitudinally meaningful manifold estimates of shapes over time. The proposed approach uses a smoothing spline to smooth over the coefficients of principal manifold embedding functions estimated at each time point. This mitigates the effects of random disturbances to the manifold between time points. Additionally, we propose a novel data augmentation approach to enable principal manifold estimation on self-intersecting manifolds. Simulation studies demonstrate performance improvements over naive applications of principal manifold estimation and principal curve/surface methods. The proposed method improves the estimation of surfaces of hippocampuses and thalamuses using data from participants of the Alzheimer's Disease Neuroimaging Initiative. An analysis of magnetic resonance imaging data from 236 individuals shows the advantages of our proposed methods that leverage regional longitudinal trends for segmentation.

stat.AP↗

arXiv2024

Observability of gravitational waves excited by binary stars orbiting around a supermassive black hole by space-based gravitational wave observatory

We produce the gravitational waveforms for the extreme mass ratio inspiral systems (EMRIs) of binary stars moving around central supermassive black hole (SBH), or called B-EMRIs. We calculate the external orbits of the binary stars via the commonly used Hamilton-Jacobi (HJ) approach, and calculate the internal orbits of the binary stars via Lagrangian approach. To improve accuracy we adopt the quadrupole-octupole expression of gravitational wave (GW) and study the contribution of radiation reaction. Compared to the waveforms of EMRIs, there are higher frequency oscillations superposed on the waveforms of B-EMRIs. We perform frequency spectrum analysis of the GW waveforms, and find that higher frequency signals give their prominency in the waveforms of B-EMRIs. To obtain high precise result for future observation of GWs from space-based detector, we take into account gravito-electromagnetic (GEM) force, and compare the waveforms of B-EMRIs with GEM effects against those of B-EMRIs without GEM effects and against those of EMRIs. The result of mismatch shows that the waveforms of B-EMRIs are credibly distinguishable by the space-based GW detectors when GEM force is considered.

gr-qc↗

arXiv2023

Euler Characteristics and Homotopy Types of Definable Sublevel Sets, with Applications to Topological Data Analysis

Given a definable function $f: S \to \mathbb{R}$ on a definable set $S$, we study sublevel sets of the form $S^f_t \coloneqq \{x \in S: f(x) \leq t\}$ for all $t \in \mathbb{R}$. Using o-minimal structures, we prove that the Euler characteristic of $S^f_t$ is right-continuous with respect to $t$. Furthermore, when $S$ is compact, we show that $S^f_{t+\delta}$ deformation retracts to $S^f_t$ for all sufficiently small $\delta > 0$. Applying these results, we also characterize the connections between the following concepts in topological data analysis: the Euler characteristic transform (ECT), smooth ECT, Euler-Radon transform (ERT), and smooth ERT.

math.AT↗

arXiv2023

Statistical Inference on Grayscale Images via the Euler-Radon Transform

Tools from topological data analysis have been widely used to represent binary images in many scientific applications. Methods that aim to represent grayscale images (i.e., where pixel intensities instead take on continuous values) have been relatively underdeveloped. In this paper, we introduce the Euler-Radon transform, which generalizes the Euler characteristic transform to grayscale images by using o-minimal structures and Euler integration over definable functions. Coupling the Karhunen-Loeve expansion with our proposed topological representation, we offer hypothesis-testing algorithms based on the chi-squared distribution for detecting significant differences between two groups of grayscale images. We illustrate our framework via extensive numerical experiments and simulations.

stat.ME↗

arXiv2023

Hypothesis testing for medical imaging analysis via the smooth Euler characteristic transform

Shape-valued data are of interest in applied sciences, particularly in medical imaging. In this paper, inspired by a specific medical imaging example, we introduce a hypothesis testing method via the smooth Euler characteristic transform to detect significant differences among collections of shapes. Our proposed method has a solid mathematical foundation and is computationally efficient. Through simulation studies, we illustrate the performance of our proposed method. We apply our method to images of lung cancer tumors from the National Lung Screening Trial database, comparing its performance to a state-of-the-art machine learning model.

stat.ME↗

arXiv2023

Dynamics of null particles and shadow for general rotating black hole

The Johannsen black hole (BH) is a generic rotating BH admitting three constants of motions (energy, angular momentum, and Carter constant) and is characterized by four deviation parameters besides mass and spin, which could be a model-independent probe of the no-hair theorem. We systematically study the dynamics of null particles around Johannsen BH, revealing the effects of the deviation parameters on the BH shadow as well as the effects of spin. By using the shadow boundaries of M87* and SgrA*, for the first time, the deviation parameters of those BHs are constrained. The detailed results depend on the spin $a$ and inclination angle $ \theta_0$. Assuming $a=0.2$ and $\theta_0=15^{\circ}$, the deviation parameter $\alpha_{13}$ are constained within $\sim $ [-3.5, 6] for M87* observation and [-3, 0.5] for SgrA* observation. We also show the images of a Johannsen BH surrounded by a Page-Thorne thin accretion disk observed by a remote observer with a ray-tracing method and discuss the effects of the deviation parameters on deforming the accretion disk image, which could be tested by observations with higher sensitivities in the future.

gr-qc↗

arXiv2022

Gravito-Electromagnetic Perturbations and QNMs of Regular Black Holes

In the framework of Einstein's gravity coupled to nonlinear electromagnetic fields, we study gravito-electromagnetic perturbations of magnetic regular black holes. The master equations of perturbations are obtained through Chandrasekhar's procedure, in which gravitational perturbations with odd-parity are coupled to the electromagnetic perturbations with even-parity. As an application, we apply the master equations to obtain quasinormal modes (QNMs) for three types of regular black holes by using numerical method. Results show that QNMs of regular black holes depends significantly on the parameters of the theory and the magnetic charge of the black holes and are very different from that of the Reissner-Nordstr\"om black hole. Indications of these results on the stability of these regular black holes are discussed in detail.

gr-qc↗

arXiv2022

Efficient free-space to chip coupling of ultrafast sub-ps THz pulse for biomolecule fingerprint sensing

Ultrafast sub-ps THz pulse conveys rich distinctive spectral fingerprints related to the vibrational or rotational modes of biomolecules and can be used to resolve the time-dependent dynamics of the motions. Thus, an efficient platform for enhancing the THz light-matter interaction is strongly demanded. Waveguides, owing to their tightly spatial confinement of the electromagnetic fields and the longer interaction distance, are promising platforms. However, the efficient feeding of the sub-ps THz pulse to the waveguides remains challenging due to the ultra-wide bandwidth property of the ultrafast signal. We propose a sensing chip comprised of a pair of back-to-back Vivaldi antennas and a 90{\deg} bent slotline waveguide to overcome the challenge. The effective operating bandwidth of the sensing chip ranges from 0.2 to 1.15 THz, with the free-space to chip coupling efficiency up to 50%. Over the entire band, the THz signal is 42.44 dB above the noise level with a peak of 73.40 dB. To take advantages of the efficient sensing chip, we have measured the characteristic fingerprint of {\alpha}-lactose monohydrate, and a sharp absorption dip at near 0.53 THz has been successfully observed demonstrating the accuracy of the proposed solution. The proposed sensing chip has the advantages of efficient in-plane coupling, ultra-wide bandwidth, easy integration and fabrication, large-scale manufacturing capability, and cost-effective, and can be a strong candidate for THz light-matter interaction platform.

physics.optics↗

arXiv2022

Randomness of Shapes and Statistical Inference on Shapes via the Smooth Euler Characteristic Transform

In this article, we establish the mathematical foundations for modeling the randomness of shapes and conducting statistical inference on shapes using the smooth Euler characteristic transform. Based on these foundations, we propose two chi-squared statistic-based algorithms for testing hypotheses on random shapes. Simulation studies are presented to validate our mathematical derivations and to compare our algorithms with state-of-the-art methods to demonstrate the utility of our proposed framework. As real applications, we analyze a data set of mandibular molars from four genera of primates and show that our algorithms have the power to detect significant shape differences that recapitulate known morphological variation across suborders. Altogether, our discussions bridge the following fields: algebraic and computational topology, probability theory and stochastic processes, Sobolev spaces and functional analysis, analysis of variance for functional data, and geometric morphometrics.

stat.ME↗

arXiv2021

Circuit complexity in proca theory

In this paper, we study circuit complexity in Proca theory with Nielsen's approach and Fubini-Study (FS) metric approach. We place the fields on a lattice to gain a regularized theory, and obtain the ground state by adopting proper coordinates. We calculate complexities of the ground and thermofield double (TFD) states with Nielsen's approach, complexity of the TFD state is found to grows like a logarithmic function. We quantize the Proca fields and give the approximate ground state and TFD state by acting unitary circuit operators on the associated reference states. The circuit lengths are calculated with FS metric, the minimal lengths are given according to the associated geometric spaces. The complexity of TFD state is found to grows linearly with time.

hep-th↗

arXiv2021

Principal manifold estimation via model complexity selection

We propose a framework of principal manifolds to model high-dimensional data. This framework is based on Sobolev spaces and designed to model data of any intrinsic dimension. It includes principal component analysis and principal curve algorithm as special cases. We propose a novel method for model complexity selection to avoid overfitting, eliminate the effects of outliers, and improve the computation speed. Additionally, we propose a method for identifying the interiors of circle-like curves and cylinder/ball-like surfaces. The proposed approach is compared to existing methods by simulations and applied to estimate tumor surfaces and interiors in a lung cancer study.

stat.ME↗

arXiv2021

Population-level Task-evoked Functional Connectivity via Fourier Analysis

Functional magnetic resonance imaging (fMRI) is a non-invasive and in-vivo imaging technique essential for measuring brain activity. Functional connectivity is used to study associations between brain regions, either while study subjects perform tasks or during periods of rest. In this paper, we propose a rigorous definition of task-evoked functional connectivity at the population level (ptFC). Importantly, our proposed ptFC is interpretable in the context of task-fMRI studies. An algorithm for estimating the ptFC is provided. We present the performance of the proposed algorithm compared to existing functional connectivity frameworks using simulations. Lastly, we apply the proposed algorithm to estimate the ptFC in a motor-task study from the Human Connectome Project.

stat.AP↗

arXiv2021

Dyonic Born-Infeld black hole in four-dimensional Horndeski gravity

The action of four-dimensional Horndeski gravity coupled to Born-Infeld electromagnetic fields is given via the Kaluza-Klein process. Dyonic black hole solution of the theory is constructed. The metric is devoid of singularity at the origin independent of the parameter selections, this property is different from the one of Einstein-Born-Infeld black holes. Thermodynamics of the black hole is studied, thermodynamic quantities are calculated and the first law is checked to be satisfied. Thermodynamic phase transitions of the black holes are studied in extended phase space.

gr-qc↗