arXiv subjects

Zhigang Li

Publications and source records attributed to Zhigang Li.

At least 19 recordsLinked to original sources

arXiv2026

Metric Correspondences and Low-Rank Deformations for Conformal and $m$-Modified Conformal Vector Fields

We fix a smooth vector field and a positive parameter $m$, and compare the nondegenerate metrics for which the field is conformal or $m$-modified conformal with the same prescribed smooth factor. Metrics of arbitrary signature are allowed. Passing to inverse metrics gives a linear transport equation and an explicit correspondence on the exact nondegeneracy domains. At a regular point, transverse initial data yield a signature-preserving correspondence of metric germs. For a nowhere-zero field and a Killing background in dimension at least three, every metric satisfying the modified conformal equation and differing from the background by a tensor of rank at most one has factor zero; its inverse-metric difference is $rX\otimes X$ for a unique smooth function $r$. Under a complete flow, such global deformations exist precisely when the field is null for the background and admits a smooth function $τ$ with $Xτ=1$. An auxiliary field satisfying $[X,Z]=X$ gives a second correspondence under orthogonality assumptions. Finally, for a nowhere-zero complete field, a Killing metric and a zero-factor modified conformal metric have inverse-metric difference of rank at least two whenever that rank is constant. In the rank-two case, the pair determines a unique auxiliary field. Examples distinguish the roles of dimension, completeness, constant rank, the zero-factor condition, and orthogonality.

math.DG↗

arXiv2026

An Adjoint Criterion for Left-Invariant $m$-Modified Conformal Vector Fields on Even-Dimensional Lie Groups

For a fixed positive real constant $m$, a real Lie algebra of even dimension $2k$ admits a nonzero left-invariant $m$-modified conformal vector field for some nondegenerate metric if and only if an adjoint operator has a nonzero real eigenvalue. In that case, a solution exists with neutral signature $(k,k)$ and zero conformal factor. As an application, we classify the admissible four-dimensional Lie algebras and metric signatures; the only Lorentzian exceptions among the admissible algebras are $\mathfrak{aff}(\mathbb{C})$ and the diamond algebra. On a pseudo-Riemannian manifold of arbitrary indefinite signature, a nonzero $m$-modified conformal vector field forces lightlike geodesic incompleteness, even when its conformal factor is variable.

math.DG↗

arXiv2026

Decentralized Continuous-Time Power Dispatch for Integrated Heat and Power Systems via Bernstein-Galerkin Equivalent Projection

Decentralized power dispatch for integrated heat and power systems (IHPSs) involves coordinating electric power systems (EPSs) and district heating networks (DHNs) while preserving privacy. The existing methods rely mainly on discretetime DHN models and constant-flow operations, limiting the ability to exploit thermal flexibility. Enabling variable-flow and variable-temperature (VF-VT) operations requires thermal-hydraulic coupling to be addressed together with continuous-time thermal dynamics. However, the simultaneous variations in mass flows and temperature lead to a nonconvex IHPS model, for which conventional decomposition methods are difficult to apply. This paper proposes a decentralized continuous-time dispatch framework using Bernstein-Galerkin equivalent projection. For a prescribed mass flow trajectory, DHN thermal dynamics are formulated in the Bernstein space and projected onto boundary variables, yielding an equivalent feasible-region model without disclosing the internal DHN topology or states. The equivalent model and DHN subproblem are derived from a unified Bernstein-Galerkin formulation, ensuring a consistent thermal state representation throughout the EPS-DHN coordination procedure. A safeguarded Anderson prediction scheme further accelerates the alternating coordination process by using historical updates and fixed-point residuals to predict the next input without additional subproblem solving steps. Numerical results show the proposed method preserves thermal state consistency, exploits VF-VT flexibility, and improves economic and computational performance.

eess.SY↗

arXiv2026

Staying on the Attack Path: Structured State for Long-Horizon Automated Penetration Testing

Large language model (LLM) based agents are increasingly applied to cybersecurity tasks such as vulnerability discovery and automated penetration testing. On long-horizon security tasks, however, such agents remain limited by context forgetting and intent drift: early critical facts and causal reasoning chains are lost over extended interactions, and the agent falls into aimless, repetitive exploration. This paper proposes Intentest, an intent-graph-guided automated penetration testing agent that externalizes long-horizon state from the LLM's context window onto a persistent fact-intent directed acyclic graph (DAG), thereby substantially reducing invalid transitions. We evaluate Intentest on automated penetration testing of web applications, a representative long-tail task in cybersecurity. In the DAG, verified network states are stored as immutable fact nodes, and exploration directions are constrained as intent edges bounded by predecessor facts. The system adopts a three-layer architecture, in which the fact-intent mapping layer maintains the global state, the task scheduling and allocation layer ensures execution stability through two-phase degradation recovery and multi-dimensional adaptive load balancing, and the intent retrieval and prediction layer provides tactical priors through a top-down five-stage filtering algorithm. On a benchmark of real CTF challenges covering more than ten vulnerability types across three difficulty levels, Intentest achieves an overall success rate of 88.2% and a success rate of 75.0% on hard tasks, improving over the baseline by approximately 44 and 50 percentage points. Ablation experiments further show that the intent retrieval and prediction reduce the average number of rounds on successful medium and hard tasks by about 33% and 48%, respectively, without changing the set of solvable tasks.

cs.CR↗

arXiv2026

Integrated Heat and Power System Scheduling with Continuous-Time Thermal Dynamics via Bernstein-Galerkin Optimization

Coordinated scheduling of district heating networks (DHNs) and electric power systems can improve operational flexibility and reduce costs by exploiting thermal inertia. Most existing formulations rely on simplified discrete-time DHN models, which may inadequately represent continuous spatiotemporal thermal dynamics and can lead to biased flexibility estimation and suboptimal schedules. In this paper, an integrated heat and power system scheduling framework that explicitly incorporates the continuous-time thermal dynamics of DHNs is proposed. A Bernstein-Galerkin transform method is developed to convert the underlying partial-differential thermal-dynamics constraints into a finite set of algebraic constraints, enabling tractable optimization while retaining dynamic fidelity. The resulting model transforms the original infinite-dimensional variational problem into a finite-dimensional coefficient optimization that can be solved using optimization solvers. Compared with conventional discretization approaches, the proposed method provides a more accurate representation of thermal dynamics and yields schedules with improved economic performance and reliability.

eess.SY↗

arXiv2026

Surfsvr: 2D Surface Priors as 3D Geometric Regularizers for Sparse Voxel Reconstruction

Sparse voxel reconstruction offers an efficient representation for high-fidelity 3D modeling, yet its geometry is commonly optimized from local photometric evidence and discrete visibility statistics. This often leads to fragmented surfaces, excessive subdivision, and floating artifacts, particularly in weakly textured or sparsely observed regions. We introduce SurfSVR, a novel sparse voxel reconstruction paradigm that treats 2D surface priors as explicit 3D geometric regularizers. Instead of directly lifting noisy pixel-wise depth predictions, SurfSVR first organizes each image into coherent surface regions by jointly reasoning over appearance, monocular depth, normals and cross-view geometry. Each region is then represented by an adaptively selected planar or quadratic surface model based on fitting reliability and geometric complexity, while cross-model agreement distinguishes reliable geometry from ambiguous predictions. These structured 2D priors are lifted into 3D and integrated throughout the reconstruction pipeline. They guide surface-adaptive voxel subdivision, provide region-level depth and normal supervision during optimization, enhance geometrically reliable sparse-observed surfaces in voxel pruning, and suppress off-surface floaters during post-refinement training. This unified design converts semantic and geometric coherence in image space into persistent structural constraints in 3D. Extensive experiments on 3 public benchmarks demonstrate that SurfSVR consistently improves sparse voxel reconstruction across scenes with substantially different visibility and geometry characteristics, achieving state-of-the-art reconstruction quality. Codes and models will be released soon.

cs.CV↗

arXiv2026

A Necessary and Sufficient Condition for Exact Relaxation of Energy Storage Power Dispatch

Mixed-integer programming (MIP) precludes simultaneous charging and discharging in power dispatch of energy storage system (ESS), but is computationally intensive. Relaxation of this complementarity constraint improves computational efficiency, but may incur an impractical control SCD strategy. To bridge this gap, this letter proposes a necessary and sufficient condition for the exactness of such relaxation. We explicitly derive the relaxation gap and reveal that SCD does not necessarily imply a distinguished optimal value from the MIP model. In such cases, a feasible solution without SCD can be readily recovered without compromising the optimal value. Furthermore, a two-stage relaxation-and-recovery algorithm is proposed to improve the computational efficiency of ESS power dispatch optimization.

eess.SY↗

arXiv2026

Asymptotically Optimal Circuit Depth for Diagonal Unitary Synthesis and Compilation on Two-Dimensional Grids

Diagonal unitaries are a fundamental but resource-intensive class of quantum operations, arising as the phase separators of QAOA and the time-evolution blocks of Hamiltonian simulation. Under all-to-all connectivity their optimal depth is established, but on nearest-neighbor hardware general-purpose compilers fall back on heuristic search, which yields no analyzable cost bound and becomes intractable at the very sizes where depth is the bottleneck. We address synthesis and compilation jointly. On the synthesis side, we develop a Gray-Path Framework (GPF) that realizes any $n$-qubit diagonal unitary in asymptotically optimal $R_z$ and CNOT depth $O(2^n/n)$ without ancillas. Our main result is that compiling GPF onto a two-dimensional nearest-neighbor grid preserves this optimality: routing adds depth $Θ(2^n/n)$ and gate count $Θ(2^n)$. Because GPF fixes its entire interaction structure in advance, routing reduces to scheduling a known sequence, with no heuristic search. We give the construction both with and without ancillas: the ancilla-free, cost-optimized layout is a two-row grid, and a $2k$-row layout introduces a space--time tradeoff that cuts depth by $1/k$ while remaining asymptotically optimal for the enlarged register; both are deterministic and analyzed in closed form. The same complexity is also attained on a linear nearest-neighbor chain, so the preservation is topology-independent, holding on any architecture that contains such a chain. All routing bounds are closed-form, giving the concrete resource estimates that heuristic compilers cannot provide at scale.

quant-ph↗

arXiv2026

Si/SiGe multi-channel superlattice structure epitaxial growth with segmented temperature control for Next-Generation Logic Devices

Stacking multiple SiSiGe channels in advanced logic devices faces severe thermal budget accumulation, which degrades interfaces via Ge-Si interdiffusion and strain relaxation.This strategy lowers the Ge diffusion coefficient to 5.6-7% of its value at 650C (Arrhenius estimate), suppressing interdiffusion and preserving pseudomorphic strain. The 4 + 4 channel stack exhibits clear XRD satellite peaks, fully coherent strain state (reciprocal space mapping), sharp interfaces (1.5-2.6 nm transition width) and low RMS roughness (0.08 nm). Quantitative analysis from bottom to top reveals that prolonged high-temperature exposure broadens bottom interfaces and dilutes Ge concentration (from 20% to 18.5%), while the top stack maintains design targets. This work provides a process-physics understanding of thermal budget effects in multi-channel superlattices and establishes a high-quality material foundation for advanced logic devices beyond 2 nm node.

cond-mat.mtrl-sci↗

arXiv2026

A Zero-Inflated Beta Mixture Model for Marginal Mediation Analysis with Compositional Microbiome Mediators

The role of the microbiome in disease pathogenesis is an emerging field with strong evidence suggesting that dysbiosis is associated with precancerous and cancerous states. Microbiome data present substantial challenges for causal mediation analysis due to sparsity, compositional constraints, and latent heterogeneity. To address these issues, we propose a zero-inflated beta mixture (ZIBM) method for mediation analysis with compositional microbiome mediators. The proposed method accommodates excess zeros through a zero-inflation component and captures heterogeneity in non-zero relative abundances using a beta mixture distribution. Within the potential-outcomes framework, the ZIBM provides estimates of marginal microbiome-mediated causal effects, and model parameters are estimated using an expectation-maximization algorithm. Simulation studies demonstrate that the ZIBM yields more accurate estimation and reliable inference under conditions commonly observed in microbiome data, compared with existing approaches. An application to a real microbiome study further illustrates its practical utility. These results indicate that the proposed method provides a more flexible and robust statistical framework for mediation analysis involving compositional microbiome data.

stat.ME↗

arXiv2026

A Quasi-Regression Method for the Mediation Analysis of Zero-Inflated Single-Cell Data

Recent advances in single-cell technologies have advanced our understanding of gene regulation and cellular heterogeneity at single-cell resolution. Single-cell data contain both gene expression levels and the proportion of expressing cells, which makes them structurally different from bulk data. Currently, methodological work on causal mediation analysis for single-cell data remains limited and often requires specific distributional assumptions. To address this challenge, we present QuasiMed, a mediation framework specialized for single-cell data. Our proposed method comprises three steps, including (i) screening mediator candidates through penalized regression and marginal models (similar to sure independence screening), (ii) estimation of indirect effects through the average expression and the proportion of expressing cells, (iii) and hypothesis testing with multiplicity control. The key benefit of QuasiMed is that it specifies only the mean functions of the mediation models through a quasi-regression framework, thereby relaxing strict distributional assumptions. The method performance was evaluated through the real-data-inspired simulations, and demonstrated high power, false discovery rate control, and computational efficiency. Lastly, we applied QuasiMed to ROSMAP single-cell data to illustrate its potential to identify mediating causal pathways. R package is freely available on GitHub repository at https://github.com/sjahnn/QuasiMed.

stat.ME↗

arXiv2026

Physics Guided Exponential Model Design of High Ge Content SiGe Selective Epitaxy for Gate All Around Source/Drain Applications

High germanium content silicon germanium (SiGe) epitaxy is critical for strain engineering in advanced gate all around (GAA) transistors. This paper demonstrates a physics guided exponential function model that quantitatively links selective epitaxial growth (SEG) parameters to Ge incorporation kinetics in nanoscale trenches. By coupling surface diffusion limited transport, gradient strain, and competitive adsorption dynamics, the model predicts optimal conditions for bottom-up filling with maximal Ge content. For trenches with widths of approximately 60 nm, the optimized process achieved a maximum Ge content of 57.93% and demonstrated 100% selectivity against silicon nitride (SiN) and silicon dioxide (SiO). Cross sectional TEM and EDS analyses reveal a graded Ge profile that minimizes interfacial defects and strain energy. Our results show that the established process physics correlation will significantly facilitate the development of GAA devices with 5nm CMOS technology nodes and beyond.

physics.app-ph↗

arXiv2025

A Unified Framework for Optimizing Uniformly Controlled Structures in Quantum Circuits

Quantum unitaries of the form $Σ_{c}\ket{c}\bra{c}\otimes U_{c}$ are ubiquitous in quantum algorithms. This class encompasses not only standard uniformly controlled gates (UCGs) but also a wide range of circuits with uniformly controlled structures. However, their circuit-depth and gate-count complexities have not been systematically analyzed within a unified framework. In this work, we study the general decomposition problem for UCG and UCG-like structure. We then introduce the restricted Uniformly Controlled Gates (rUCGs) as a unified algebraic model, defined by a 2-divisible Abelian group that models the controlled gate set. This model captures uniformly controlled rotations, multi-qubit uniformly controlled gates, and diagonal unitaries. Furthermore, this model also naturally incorporates k-sparse version (k-rUCGs), where only a subset of control qubits participate in each multi-qubit gate. Building on this algebraic model, we develop a general framework. For an n-control rUCG, the framework reduce the gate complexity from ${O(n2^n)}$ to ${O(2^n})$ and the circuit depth from ${O(2^n\log n)}$ to ${O(2^n\log n/n)}$. The framework further provides systematic size and depth bounds for k-rUCGs by exploiting sparsity in the control space, with same optimization coefficient as rUCG, respectively. Empirical evaluations on representative QAOA circuits confirm reductions in depth and size, which highlight that the rUCG model and its associated decomposition framework unify circuits previously considered structurally distinct under a single, asymptotically optimal synthesis paradigm.

quant-ph↗

arXiv2025

A Statistical Framework for Co-Mediators of Zero-Inflated Single-Cell RNA-Seq Data

Single-cell RNA sequencing (scRNA-seq) has revolutionized the study of cellular heterogeneity, enabling detailed molecular profiling at the individual cell level. However, integrating high-dimensional single-cell data into causal mediation analysis remains challenging due to zero inflation and complex mediator structures. We propose a novel mediation framework leveraging zero-inflated negative binomial models to characterize cell-level mediator distributions and beta regression for zero-inflation proportions. The model can identify expression level as well as expressed proportion that could mediate disease-leading causal pathway. Extensive simulation studies demonstrate improved power and controlled false discovery rates. We further illustrate the utility of this approach through application to ROSMAP single-cell transcriptomic data, uncovering biologically meaningful mediation effects that enhance understanding of disease mechanisms.

stat.ME↗

arXiv2025

From Equipartition to Curvature: The Spectral Evolution of 4FGL Blazars

We investigate the evolution of spectral energy distribution (SED) and underlying electron energy distribution (EED) by modeling the nearly simultaneous broadband spectra of selected bright 4FGL blazars, in the context of a combined cooling and stochastic acceleration scenario. We find that one-zone leptonic model with log-parabolic (LP) EED can successfully fit the GeV-TeV emission of blazars. The synchrotron frequency $ν_s$ of blazars mainly evolves due to variation of electron peak energy $γ_{3p}$. The BL Lac objects (BL Lacs) show a negative trend in the $ν_s- ν_s L_s$ SED plane, known as blazar sequence, that does not seem to be an artifact of Doppler boosting, but driven by the equipartition constraints. A positive correlation is found between the derived magnetic field $B$ and electron density $n_e$, whereas $n_e$ and $γ_{3p}$ negatively relate, as expected in an equipartition scenario. The flat spectrum radio quasars (FSRQs) deviate significantly from such a scenario, indicating their jet parameters should be varying independently. The synchrotron peak frequency $ν_s$ and its spectral curvature $b_s$ negatively correlate for all blazars, confirming the stochastic particle acceleration in blazar jets. However, blazars do not show the signature of hard-sphere acceleration, indicating that magnetic turbulence in the jets might be soft and physical conditions might be near to steady state, consistent with equipartition. Furthermore, for BL Lacs, the SED curvature $b_s$ and the EED curvature $r$ and nearly meet the theoretical relationship $r=5b_s$, whereas the FSRQs show large deviation due to poor constrain on $b_s$ due to presence of thermal component.

astro-ph.HE↗

arXiv2025

Causal Mediation Analysis for Zero-inflated Mixture Mediators

Causal mediation analysis is an important statistical tool to quantify effects transmitted by intermediate variables from a cause to an outcome. There is a gap in mediation analysis methods to handle mixture mediator data that are zero-inflated with multi-modality and atypical behaviors. We propose an innovative way to model zero-inflated mixture mediators from the perspective of finite mixture distributions to flexibly capture such mediator data. Multiple data types are considered for modeling such mediators including the zero-inflated log-normal mixture, zero-inflated Poisson mixture and zero-inflated negative binomial mixture. A two-part mediation effect is derived to better understand effects on outcomes attributable to the numerical change as well as binary change from 0 to 1 in mediators. The maximum likelihood estimates are obtained by an expectation maximization algorithm to account for unobserved mixture membership and whether an observed zero is a true or false zero. The optimal number of mixture components are chosen by a model selection criterion. The performance of the proposed method is demonstrated in a simulation study and an application to a neuroscience study in comparison with standard mediation analysis methods.

stat.ME↗

arXiv2025

An RRAM compute-in-memory architecture for high energy-efficient processing of binary matrix-vector multiplication in cryptography

Binary matrix-vector multiplication (BMVM) is a key operation in post-quantum cryptography schemes like the Classic McEliece cryptosystem. Conventional computing architectures incur significant energy efficiency loss due to data movement of large matrices when handling such tasks. Resistive memory (RRAM) non-volatile compute-in-memory (nvCIM) is an ideal technology for high energy-efficient BMVM processing but faces challenges, including signal margin degradation in high input-parallelism arrays due to device non-idealities and high hardware overhead from current readout and XOR operations. This work presents a RRAM nvCIM architecture featuring: 1) 1T1R cells with high-resistive-state compensation modules; and 2) pulsed current-sensing parity checkers. Based on the 180nm process and test results from RRAM devices, the computing accuracy and efficiency of the architecture are verified by simulation. The proposed architecture performs high-precision current accumulation with a maximum MAC value of 10 and achieves an energy efficiency of 1.51TOPS/W, offering approximately 1.62 times improvement compared to an advanced 28nm FPGA platform.

cs.ET↗

arXiv2025

A Language Anchor-Guided Method for Robust Noisy Domain Generalization

Real-world machine learning applications often struggle with two major challenges: distribution shift and label noise. Models tend to overfit by focusing on redundant and uninformative features in the training data, which makes it hard for them to generalize to the target domain. Noisy data worsens this problem by causing further overfitting to the noise, meaning that existing methods often fail to tell the difference between true, invariant features and misleading, spurious ones. To tackle these issues, we introduce Anchor Alignment and Adaptive Weighting (A3W). This new algorithm uses sample reweighting guided by natural language processing (NLP) anchors to extract more representative features. In simple terms, A3W leverages semantic representations from natural language models as a source of domain-invariant prior knowledge. Additionally, it employs a weighted loss function that adjusts each sample's contribution based on its similarity to the corresponding NLP anchor. This adjustment makes the model more robust to noisy labels. Extensive experiments on standard benchmark datasets show that A3W consistently outperforms state-of-the-art domain generalization methods, offering significant improvements in both accuracy and robustness across different datasets and noise levels.

cs.CL↗