On the monodromy conjecture, holomorphy conjecture, and embedded Nash problem for Pfaffian ideals
We resolve the monodromy conjecture, holomorphy conjecture, and embedded Nash problem for Pfaffian ideals.
math.AG↗
arXiv subjects
Yifan Chen
Publications and source records attributed to Yifan Chen.
Split Gibbs Discrete Diffusion Posterior Sampling
We study the problem of posterior sampling in discrete-state spaces using discrete diffusion models. While posterior sampling methods for continuous diffusion models have achieved remarkable progress, analogous methods for discrete diffusion models remain challenging. In this work, we introduce a principled plug-and-play discrete diffusion posterior sampling algorithm based on split Gibbs sampling, which we call SGDD. Our algorithm enables reward-guided generation and solving inverse problems in discrete-state spaces. We demonstrate the convergence of SGDD to the target posterior distribution and verify this through controlled experiments on synthetic benchmarks. Our method enjoys state-of-the-art posterior sampling performance on a range of benchmarks for discrete data, including DNA sequence design, discrete image inverse problems, and music infilling, achieving more than 30% improved performance compared to existing baselines. Our code is available at https://github.com/chuwd19/Split-Gibbs-Discrete-Diffusion-Posterior-Sampling.
cs.LG↗
On the monodromy conjecture for determinantal varieties
This paper presents a proof of the monodromy conjecture for determinantal varieties. Our strategy centers on an in-depth analysis of monodromy zeta functions, leveraging a generalized A'Campo formula, an examination of multiple contact loci, and the exploitation of the intrinsic symmetric structures inherent to these varieties. Furthermore, we prove the holomorphy conjecture for determinantal varieties and the monodromy conjecture for Brill-Noether loci of generic curves. Keywords. monodromy conjecture, determinantal varieties, monodromy zeta function.
math.AG↗
Connecting Domains and Contrasting Samples: A Ladder for Domain Generalization
Distribution shifts between training and testing samples frequently occur in practice and impede model generalization performance. This crucial challenge thereby motivates studies on domain generalization (DG), which aim to predict the label on unseen target domain data by solely using data from source domains. It is intuitive to conceive the class-separated representations learned in contrastive learning (CL) are able to improve DG, while the reality is quite the opposite: users observe directly applying CL deteriorates the performance. We analyze the phenomenon with the insights from CL theory and discover lack of intra-class connectivity in the DG setting causes the deficiency. We thus propose a new paradigm, domain-connecting contrastive learning (DCCL), to enhance the conceptual connectivity across domains and obtain generalizable representations for DG. On the data side, more aggressive data augmentation and cross-domain positive samples are introduced to improve intra-class connectivity. On the model side, to better embed the unseen test domains, we propose model anchoring to exploit the intra-class connectivity in pre-trained representations and complement the anchoring with generative transformation loss. Extensive experiments on five standard DG benchmarks are performed. The results verify that DCCL outperforms state-of-the-art baselines even without domain supervision. The detailed model implementation and the code are provided through https://github.com/weitianxin/DCCL
cs.CV↗
LUMA: Low-Dimension Unified Motion Alignment with Dual-Path Anchoring for Text-to-Motion Diffusion Model
While current diffusion-based models, typically built on U-Net architectures, have shown promising results on the text-to-motion generation task, they still suffer from semantic misalignment and kinematic artifacts. Through analysis, we identify severe gradient attenuation in the deep layers of the network as a key bottleneck, leading to insufficient learning of high-level features. To address this issue, we propose \textbf{LUMA} (\textit{\textbf{L}ow-dimension \textbf{U}nified \textbf{M}otion \textbf{A}lignment}), a text-to-motion diffusion model that incorporates dual-path anchoring to enhance semantic alignment. The first path incorporates a lightweight MoCLIP model trained via contrastive learning without relying on external data, offering semantic supervision in the temporal domain. The second path introduces complementary alignment signals in the frequency domain, extracted from low-frequency DCT components known for their rich semantic content. These two anchors are adaptively fused through a temporal modulation mechanism, allowing the model to progressively transition from coarse alignment to fine-grained semantic refinement throughout the denoising process. Experimental results on HumanML3D and KIT-ML demonstrate that LUMA achieves state-of-the-art performance, with FID scores of 0.035 and 0.123, respectively. Furthermore, LUMA accelerates convergence by 1.4$\times$ compared to the baseline, making it an efficient and scalable solution for high-fidelity text-to-motion generation.
cs.CV↗
FLAT: Fused Lasso Regression with Adaptive Minimum Spanning Tree with Applications on Thermohaline Circulation
This article introduces a new methodology model both discrete and continuous spatial heterogeneity simultaneously with an application in detection of hyper-plain in thermohaline circulation. To enable the data-driven detection of spatial boundaries with heterogeneity, we constructs an adaptive minimum spanning tree guided by both spatial proximity and coefficient dissimilarity, and combines both a spatial fused regularization and LASSO-type regularization to estimate the spatial coefficients under the framework of spatial regression. Numerical simulations demonstrate the effectiveness of proposed method in both estimation and heterogeneity detection. The usefulness of the approach is further illustrated via an analysis of oceanic data that provides new empirical finds about Atlantic with detected surfaces in temperature-salinity relationship.
stat.ME↗
Convergence of Unadjusted Langevin in High Dimensions: Delocalization of Bias
The unadjusted Langevin algorithm is commonly used to sample probability distributions in extremely high-dimensional settings. However, existing analyses of the algorithm for strongly log-concave distributions suggest that, as the dimension $d$ of the problem increases, the number of iterations required to ensure convergence within a desired error in the $W_2$ metric scales in proportion to $d$ or $\sqrt{d}$. In this paper, we argue that, despite this poor scaling of the $W_2$ error for the full set of variables, the behavior for a small number of variables can be significantly better: a number of iterations proportional to $K$, up to logarithmic terms in $d$, often suffices for the algorithm to converge to within a desired $W_2$ error for all $K$-marginals. We refer to this effect as delocalization of bias. We show that the delocalization effect does not hold universally and prove its validity for Gaussian distributions and strongly log-concave distributions with certain sparse interactions. Our analysis relies on a novel $W_{2,\ell^\infty}$ metric to measure convergence. A key technical challenge we address is the lack of a one-step contraction property in this metric. Finally, we use asymptotic arguments to explore potential generalizations of the delocalization effect beyond the Gaussian and sparse interactions setting.
stat.ML↗
Illuminating Black Hole Shadow with Dark Matter Annihilation
The Event Horizon Telescope (EHT) has significantly advanced our ability to study black holes, achieving unprecedented spatial resolution and revealing horizon-scale structures. Notably, these observations feature a distinctive dark shadow--primarily arising from faint jet emissions--surrounded by a bright photon ring. Anticipated upgrades of the EHT promise substantial improvements in dynamic range, enabling deeper exploration of low-background regions, particularly the inner shadow defined by the lensed equatorial horizon. Our analysis shows that observations of these regions transform supermassive black holes into powerful probes for annihilating dark matter, which is expected to accumulate densely in their vicinity. By analyzing the black hole image morphology and performing electron-positron propagation calculations in realistic plasma backgrounds derived from general relativistic magnetohydrodynamic simulations, we set stringent constraints on dark matter annihilation, requiring contributions below the astrophysical emission. These constraints, derived from both current EHT observations and projections for future upgraded arrays, exclude a substantial region of previously unexplored parameter space and remain robust against astrophysical uncertainties, including black hole spin and plasma temperature variations.
hep-ph↗
MindShot: Multi-Shot Video Reconstruction from fMRI with LLM Decoding
Reconstructing dynamic videos from fMRI is important for understanding visual cognition and enabling vivid brain-computer interfaces. However, current methods are critically limited to single-shot clips, failing to address the multi-shot nature of real-world experiences. Multi-shot reconstruction faces fundamental challenges: fMRI signal mixing across shots, the temporal resolution mismatch between fMRI and video obscuring rapid scene changes, and the lack of dedicated multi-shot fMRI-video datasets. To overcome these limitations, we propose a novel divide-and-decode framework for multi-shot fMRI video reconstruction. Our core innovations are: (1) A shot boundary predictor module explicitly decomposing mixed fMRI signals into shot-specific segments. (2) Generative keyframe captioning using LLMs, which decodes robust textual descriptions from each segment, overcoming temporal blur by leveraging high-level semantics. (3) Novel large-scale data synthesis (20k samples) from existing datasets. Experimental results demonstrate our framework outperforms state-of-the-art methods in multi-shot reconstruction fidelity. Ablation studies confirm the critical role of fMRI decomposition and semantic captioning, with decomposition significantly improving decoded caption CLIP similarity by 71.8%. This work establishes a new paradigm for multi-shot fMRI reconstruction, enabling accurate recovery of complex visual narratives through explicit decomposition and semantic prompting.
cs.CV↗
Enhancing Spectroscopy and Microscopy with Emerging Methods in Photon-Correlation and Quantum Illumination
Quantum optics has driven major advances in our ability to generate and detect correlations between individual photons. Its principles are now increasingly translated into nanoscale characterization techniques, enhancing spectroscopy, microscopy, and metrology. In this Review, we highlight rapid progress in the field driven by advances in single-photon detectors and quantum light sources, including time-resolved single-photon counting cameras, superconducting nanowire detectors, and increasingly bright sources of entangled photons. We emphasize emerging applications in super-resolution microscopy, measurements below classical noise limits, and photon-number-resolved spectroscopy-a powerful paradigm for probing nanoscale electronic materials and molecular dynamics. We conclude by outlining key technological challenges and future opportunities across materials science and bio-nanophotonics.
physics.optics↗
Identifying the Quadrupolar Nature of Gravitational Wave Background through Space-based Missions
The stochastic gravitational wave background (SGWB) consists of an incoherent collection of waves from both astrophysical and cosmological sources. To distinguish the SGWB from noise, it is essential to verify its quadrupolar nature, exemplified by the cross-correlations among pairs of pulsars within a pulsar timing array, commonly referred to as the Hellings-Downs curve. We study how this quadrupolar signature manifests in correlations between general GW detector pairs, characterized by their antenna responses. Focusing on space-based missions including laser interferometers (LISA, Taiji, TianQin) and atom interferometers (AEDGE/MAGIS), we demonstrate how orbital motion dynamically modulates detector correlations through time-dependent separations and relative orientation shifts. These modulations encode unique statistical features that serve as definitive markers of the SGWB's quadrupolar nature. Our findings identify optimal configurations for these missions, offer forecasts for the time needed to identify the quadrupolar nature of the SGWB, and are applicable to both space-space and space-terrestrial correlations.
gr-qc↗
On jet closures of singularities
The jet closure and jet support closure were first introduced by de Fernex, Ein and Ishii to solve the local isomorphism problem. In this paper, we introduce two local algebras associated to jet closure and jet support closure respectively. We show that these two algebras are invariants of the singularities. We compute and investigate these invariants for some interesting cases, such as the cases of monomial ideals and homogeneous ideals. We also introduce a new filtration and jet index to jet closures. The jet index describes which jet scheme recover the information of base scheme. Moreover, we obtain some properties of the jet index. Keywords:jet closure, jet support closure and filtration.
math.AC↗
Enhancement of quantum coherence in solid-state qubits via interface engineering
Shallow nitrogen-vacancy (NV) centers in diamond are promising quantum sensors but suffer from noise-induced short coherence times due to bulk and surface impurities. We present interfacial engineering via oxygen termination and graphene patching, extending shallow NV coherence to over 1 ms, approaching the T1 limit. Raman spectroscopy and density-functional theory reveal surface termination-driven graphene charge transfer reduces spin noise by pairing surface electrons, supported by double electron-electron resonance spectroscopy showing fewer unpaired spins. Enhanced sensitivity enables detection of single weakly coupled 13C nuclear spins and external 11B spins from a hexagonal boron nitride (h-BN) layer, achieving nanoscale nuclear magnetic resonance. A protective h-BN top layer stabilizes the platform, ensuring robustness against harsh treatments and compatibility with target materials. This integrated approach advances practical quantum sensing by combining extended coherence, improved sensitivity, and device durability.
cond-mat.mes-hall↗
Smooth minimal surfaces of general type with $p_g=0, K^2=7$ and involutions
Lee and the second named author studied involutions on smooth minimal surfaces $S$ of general type with $p_g(S)=0$ and $K_S^2=7$. They gave the possibilities of the birational models $W$ of the quotients and the branch divisors $B_0$ induced by involutions $σ$ on the surfaces $S$. In this paper we improve and refine the results of Lee and the second named author. We exclude the case of the Kodaira dimension $κ(W)=1$ when the number $k$ of isolated fixed points of an involution $σ$ on $S$ is nine. The possibilities of branch divisors $B_0$ are reduced for the case $k=9$, and are newly given for the case $k=11$. Moreover, we show that if the branch divisor $B_0$ has three irreducible components, then $S$ is an Inoue surface.
math.AG↗
A Recipe for Causal Graph Regression: Confounding Effects Revisited
Through recognizing causal subgraphs, causal graph learning (CGL) has risen to be a promising approach for improving the generalizability of graph neural networks under out-of-distribution (OOD) scenarios. However, the empirical successes of CGL techniques are mostly exemplified in classification settings, while regression tasks, a more challenging setting in graph learning, are overlooked. We thus devote this work to tackling causal graph regression (CGR); to this end we reshape the processing of confounding effects in existing CGL studies, which mainly deal with classification. Specifically, we reflect on the predictive power of confounders in graph-level regression, and generalize classification-specific causal intervention techniques to regression through a lens of contrastive learning. Extensive experiments on graph OOD benchmarks validate the efficacy of our proposals for CGR. The model implementation and the code are provided on https://github.com/causal-graph/CGR.
cs.LG↗
Hilbert series of second order jets of determinantal varieties
In this paper, we will investigate the jet schemes of determinantal varieties. It is quite often the case that the geometric information concerning the jet schemes of an algebraic variety can be described, but the more refined algebraic information is quite mysterious. For example, it is known that computing the Hilbert function associated to a natural grading on these jet schemes is a very hard problem. The present paper handles a few such computations. It succeeds in computing the Hilbert functions of the second order jet schemes in the case of maximal minors of a $2\times n$ matrix.
math.AG↗
On jet schemes of determinantal varieties
Determinantal varieties are important objects of study in algebraic geometry. In this paper, we will investigate them using the jet scheme approach. We have found a new connection for the Hilbert series between a determinantal variety and its jet schemes. We denote the $k$-th order jet scheme of the determinantal variety defined by $r$-minors in an $m \times n$ matrix as $\mathscr{L}^{m,n}_{r,k}$. For the special case where $m$, $n$, and $r$ are equal, and $m$ and $r$ are 3 while $k$ is 1, we establish a correspondence between the defining ideals of $\mathscr{L}^{m,n}_{r,k}$ and abstract simplicial complexes, proving their shellability and obtaining the Hilbert series of $\mathscr{L}^{m,n}_{r,k}$ accordingly. Moreover, for general $\mathscr{L}^{m,n}_{r,k}$, \cite{12} provides its irreducible decomposition. We further provide a specific polynomial family defining its irreducible components. Keywords. Determinantal varieties, jet schemes, shellability, Hilbert series.
math.AG↗
In-flight calibration of the Lobster Eye Imager for Astronomy
The Lobster Eye Imager for Astronomy (LEIA), as a pathfinder of the Wide-field X-ray Telescope (WXT) onboard the Einstein Probe (EP) satellite, is the first lobster-eye focusing X-ray telescope with a considerably large field-of-view (FoV) ever flown. During the two and half years of operations, a series of calibration observations were performed, to fully characterize its performance and calibrate the instrumental properties. In this paper, we present the results of the in-flight calibration campaign of LEIA, focusing on the properties of the PSF, source positional accuracy, effective area, energy response and the instrumental background. The calibration sources used are the Crab nebula, Sco X-1 and Cassiopeia A supernova remnant. Specifically, it is found that the spatial resolution remains almost unchanged compared to the pre-launch values, ranging from 3.6'-9.3' with a median of 5.9'. The post-calibration source positional accuracy is found to be ~2' (at the 90% C.L.). The Crab spectra can be well reproduced by the absorbed power-law model with the best-fit parameters in large agreement with the literature values, indicating that the in-orbit effective area is overall consistent with the model predictions and ground measurements. The effective area exhibits a systematic of $\lesssim10\%$ (at the 68% C.L.), and a mild deterioration of ~15% at the lower energy end after one year of operation. The Cas A spectral analysis shows that the energy scale and spectral resolution of the detectors are generally consistent with ground values. The instrumental background is found to be largely consistent among the four detectors, with strong modulations by the geomagnetic activity and the spectrum qualitatively consistent with our previous simulations. These instrumental performances well meet the design requirements. This work paves the way for the in-orbit calibration of the EP-WXT.
astro-ph.IM↗