arXiv subjects

Zhiwen Liu

Publications and source records attributed to Zhiwen Liu.

At least 19 recordsLinked to original sources

arXiv2026

Derivations of Generalized Moduli Algebras of Isolated Hypersurface Singularities

Let $(V,0)$ be an isolated complex hypersurface singularity defined by $f\in\mathbb{C}\{x_1,\ldots,x_n\}$. Let $A(V)$ be the moduli(Tjurina) algebra, let $A^*(V)$ be the generalized moduli algebra, and let $$ L(V)=\mathrm{Der}_{\mathbb{C}}(A(V),A(V)),\qquad L^*(V)=\mathrm{Der}_{\mathbb{C}}(A^*(V),A^*(V)) $$ be the Yau algebra and the new Yau algebra of $V$, respectively. Write $λ(V)=\dim_{\mathbb{C}}L(V)$ and $λ^*(V)=\dim_{\mathbb{C}}L^*(V)$. We prove that the difference between these two dimensions is determined by the Hessian corank. In the Morse case, the generalized moduli algebra is zero, and hence both derivation Lie algebras are zero. We have $λ^*(V)=λ(V)-1$ if $\mathrm{corank}(\mathrm{Hess}(f)(0))=1$, and $λ^*(V)=λ(V)$ otherwise. In particular, $λ^*(V)=λ(V)$ when $n\ge2$ and $\mathrm{mult}(f)\ge3$. This proves Conjecture~1.1 proposed in \cite{ChenHussainYauZuo2020}. We construct an exact sequence whose two end terms are copies of the socle of the Milnor algebra. This homological approach reveals the detailed algebraic structure underlying the dimension count. We also give an alternative proof that pushes the original arguments in the proof of \cite[Theorem~C]{ChenHussainYauZuo2020} further. The general case is obtained by combining Saito's criterion for the non-quasi-homogeneous case.

math.AG↗

arXiv2026

The Weighted $\boldsymbol{L}^{\boldsymbol{p}}$ estimates for the fractional Hardy operator and a class of integral operators on the Heisenberg group

In the setting of a Heisenberg group, we first studied the sharp weak estimate for the $n$-dimensional fractional Hardy operator from $L^p$ to $L^{q,\infty}$. Next, we studied the sharp bounds for the $m$-linear $n$-dimensional integral operator with a kernel on weighted Lebesgue spaces. As an application, the sharp bounds for Hardy, Hardy-Littlewood-Pólya, and Hilbert operators on weighted Lebesgue spaces were obtained. Finally, according to the previous steps, we also found the estimate for the Hausdorff operator on weighted $L^p$ spaces.

math.FA↗

arXiv2026

Taming Randomness in Random Lasers: Programmable Disorder for Active Control of Random Lasing via Electric-Field-Directed Assembly of Nanowires

Random lasing exploits multiple scattering to provide optical feedback without conventional resonant cavities, enabling simplified architectures that are readily integrated into compact photonic platforms such as wearable sensors and lab-on-chip devices. However, the same disorder that enables cavity-free lasing also makes it challenging to control and tune the emission properties. Here, an electrically reconfigurable random-lasing platform based on dielectrophoretic assembly of chaining silver nanowires suspended in a dye gain medium is reported. An applied electric field across patterned quadrupole electrodes induces nanowire chaining and programmable alignment, enabling real-time reconfiguration of the disorder landscape. Based on the electrically driven disorder state transitions, tunable random-lasing characteristics, including reduced lasing thresholds, modulation of emission intensity, and control of the polarization state have been demonstrated. Simulations further indicate that chaining enhances scattering relative to absorption, providing more efficient radiative feedback, and the orientation of the nanowire network governs the polarization dependence of the system. These results establish a route to actively modulate random lasing through controllable disorder and point toward adaptive, reconfigurable photonic light sources and sensing systems.

physics.optics↗

arXiv2025

Incoherent Light-Driven Nonlinear Optical Extreme Learner via Data Reverberation

Artificial neural networks have revolutionized fields from computer vision to natural language processing, yet their growing energy and computational demands threaten future progress. Optical neural networks promise greater speed, bandwidth, and energy efficiency, but suffer from weak optical nonlinearities. Here, we demonstrate a low-power, incoherent-light-driven optical extreme learner that leverages 'data nonlinearity' from optical pattern reverberation, eliminating reliance on intrinsic nonlinear materials. By encoding input data in the spatial polarization distribution of a tailored optical cavity and allowing light to pass through it multiple times, we achieve nonlinear transformations at extremely low optical power. Coupled with a simple trainable readout, our optical learner consistently outperforms linear digital networks in standard image classification tasks and XOR benchmarks, delivering accuracy matching fully nonlinear digital models. Our compact, energy-efficient approach significantly reduces complexity, cost, and energy consumption, paving the way for practical, scalable all-optical machine learning platforms.

physics.optics↗

arXiv2025

Quantitative Nonlinear Optical Polarimetry with High Spatial Resolution

Nonlinear optical microscopy such as in the optical second-harmonic generation (SHG) modality has become a popular tool today for probing materials in the physical and biological sciences. While imaging and spectroscopy are widely used in the microscopy mode, nonlinear polarimetry, which can shed light on materials' symmetry and microstructure, is relatively underdeveloped. This is partly because quantitative analytical modeling of the optical SHG response for anisotropic crystals and films largely assumes low-numerical aperture (NA) focusing of light, where the plane-wave approximation is sufficient. Tight focusing provides unique benefits in revealing out-of-plane polarization responses, which cannot be detected by near-plane-wave illumination at normal incidence. Here, we outline a method for quantitatively analyzing SHG polarimetry measurements obtained under high-NA focusing within a microscope geometry. Experiments and simulations of a variety of standard samples, from single crystals to thin films, are in good agreement, including measured and simulated spatial SHG maps of ferroelectric domains. A solution to the inverse problem is demonstrated, where the spatial distribution of an SHG tensor with unknown tensor coefficient magnitudes is determined by experimentally measured polarimetry. The ability to extract the out-of-plane component of the nonlinear polarization in normal incidence is demonstrated, which can be valuable for high-resolution polarimetry of 2D materials, thin films, heterostructures, and uniaxial crystals with a strong out-of-plane response. Copyright 2025 Optica Publishing Group. Users may use, reuse, and build upon the article, or use the article for text or data mining, so long as such uses are for non-commercial purposes and appropriate attribution is maintained. All other rights are reserved. https://doi.org/10.1364/OPTICA.559060

cond-mat.mtrl-sci↗

arXiv2025

Ensemble nonlinear optical learner by electrically tunable linear scattering

Recent progress in effective nonlinearity, achieved by exploiting multiple scatterings within the linear optical regime, has been demonstrated to be a promising approach to enable nonlinear optical processing without relying on actual material nonlinearity. Here we introduce an ensemble nonlinear optical learner, via electrically tunable linear scattering in a liquid-crystal-polymer composite film under low optical power and low applied electrical voltages. We demonstrate, through several image classification tasks, that by combining inference results from an ensemble of nonlinear optical learners realized at different applied voltages, the ensemble optical learning significantly outperforms the classification performance of individual processors. With very low-level optical power and electrical voltage requirements, and ease in reconfiguration simply by varying applied voltages, the ensemble nonlinear optical learning offers a cost-effective and flexible way to improve computing performance and enhance inference accuracy.

physics.optics↗

arXiv2023

The Second Monocular Depth Estimation Challenge

This paper discusses the results for the second edition of the Monocular Depth Estimation Challenge (MDEC). This edition was open to methods using any form of supervision, including fully-supervised, self-supervised, multi-task or proxy depth. The challenge was based around the SYNS-Patches dataset, which features a wide diversity of environments with high-quality dense ground-truth. This includes complex natural environments, e.g. forests or fields, which are greatly underrepresented in current benchmarks. The challenge received eight unique submissions that outperformed the provided SotA baseline on any of the pointcloud- or image-based metrics. The top supervised submission improved relative F-Score by 27.62%, while the top self-supervised improved it by 16.61%. Supervised submissions generally leveraged large collections of datasets to improve data diversity. Self-supervised submissions instead updated the network architecture and pretrained backbones. These results represent a significant progress in the field, while highlighting avenues for future research, such as reducing interpolation artifacts at depth boundaries, improving self-supervised indoor performance and overall natural image accuracy.

cs.CV↗

arXiv2023

Positive-unlabeled learning for binary and multi-class cell detection in histopathology images with incomplete annotations

Cell detection in histopathology images is of great interest to clinical practice and research, and convolutional neural networks (CNNs) have achieved remarkable cell detection results. Typically, to train CNN-based cell detection models, every positive instance in the training images needs to be annotated, and instances that are not labeled as positive are considered negative samples. However, manual cell annotation is complicated due to the large number and diversity of cells, and it can be difficult to ensure the annotation of every positive instance. In many cases, only incomplete annotations are available, where some of the positive instances are annotated and the others are not, and the classification loss term for negative samples in typical network training becomes incorrect. In this work, to address this problem of incomplete annotations, we propose to reformulate the training of the detection network as a positive-unlabeled learning problem. Since the instances in unannotated regions can be either positive or negative, they have unknown labels. Using the samples with unknown labels and the positively labeled samples, we first derive an approximation of the classification loss term corresponding to negative samples for binary cell detection, and based on this approximation we further extend the proposed framework to multi-class cell detection. For evaluation, experiments were performed on four publicly available datasets. The experimental results show that our method improves the performance of cell detection in histopathology images given incomplete annotations for network training.

cs.CV↗

arXiv2021

CarveMix: A Simple Data Augmentation Method for Brain Lesion Segmentation

Brain lesion segmentation provides a valuable tool for clinical diagnosis, and convolutional neural networks (CNNs) have achieved unprecedented success in the task. Data augmentation is a widely used strategy that improves the training of CNNs, and the design of the augmentation method for brain lesion segmentation is still an open problem. In this work, we propose a simple data augmentation approach, dubbed as CarveMix, for CNN-based brain lesion segmentation. Like other "mix"-based methods, such as Mixup and CutMix, CarveMix stochastically combines two existing labeled images to generate new labeled samples. Yet, unlike these augmentation strategies based on image combination, CarveMix is lesion-aware, where the combination is performed with an attention on the lesions and a proper annotation is created for the generated image. Specifically, from one labeled image we carve a region of interest (ROI) according to the lesion location and geometry, and the size of the ROI is sampled from a probability distribution. The carved ROI then replaces the corresponding voxels in a second labeled image, and the annotation of the second image is replaced accordingly as well. In this way, we generate new labeled images for network training and the lesion information is preserved. To evaluate the proposed method, experiments were performed on two brain lesion datasets. The results show that our method improves the segmentation accuracy compared with other simple data augmentation approaches.

eess.IV↗

arXiv2021

Positive-unlabeled Learning for Cell Detection in Histopathology Images with Incomplete Annotations

Cell detection in histopathology images is of great value in clinical practice. \textit{Convolutional neural networks} (CNNs) have been applied to cell detection to improve the detection accuracy, where cell annotations are required for network training. However, due to the variety and large number of cells, complete annotations that include every cell of interest in the training images can be challenging. Usually, incomplete annotations can be achieved, where positive labeling results are carefully examined to ensure their reliability but there can be other positive instances, i.e., cells of interest, that are not included in the annotations. This annotation strategy leads to a lack of knowledge about true negative samples. Most existing methods simply treat instances that are not labeled as positive as truly negative during network training, which can adversely affect the network performance. In this work, to address the problem of incomplete annotations, we formulate the training of detection networks as a positive-unlabeled learning problem. Specifically, the classification loss in network training is revised to take into account incomplete annotations, where the terms corresponding to negative samples are approximated with the true positive samples and the other samples of which the labels are unknown. To evaluate the proposed method, experiments were performed on a publicly available dataset for mitosis detection in breast cancer cells, and the experimental results show that our method improves the performance of cell detection given incomplete annotations for training.

cs.CV↗

arXiv2020

Electric field induced metallic behavior in thin crystals of ferroelectric α-In2Se3

Ferroelectric semiconductor field effect transistors (FeSmFETs), which employ ferroelectric semiconducting thin crystals of α-In2Se3 as the channel material as opposed to the gate dielectric in conventional ferroelectric FETs (FeFETs) were prepared and measured from room to the liquid-helium temperatures. These FeSmFETs were found to yield evidence for the reorientation of the electrical polarization and an electric field induced metallic state in α-In2Se3. Our findings suggest that FeSmFETs can serve as a platform for the fundamental study of ferroelectric metals as well as the exploration of the integration of data storage and logic operations in the same device.

cond-mat.mtrl-sci↗

arXiv2020

Non-line-of-sight imaging off a Phong surface through deep learning

A deep learning based non-line-of-sight (NLOS) imaging system is developed to image an occluded object off a scattering surface. The neural net is trained using only handwritten digits, and yet exhibits capability to reconstruct patterns distinct from the training set, including physical objects. It can also reconstruct a cartoon video from its scattering patterns in real time, demonstrating the robustness and generalization capability of the deep learning based approach. Several scattering surfaces with varying degree of Lambertian and specular contributions were examined experimentally; it is found that for a Lambertian surface the structural similarity index (SSIM) of reconstructed images is about 0.63, while the SSIM obtained from a scattering surface possessing a specular component can be as high as 0.93. A forward model of light transport was developed based on the Phong scattering model. Scattering patterns from Phong surfaces with different degrees of specular contribution were numerically simulated. It is found that a specular contribution of as small as 5% can enhance the SSIM from 0.83 to 0.93, consistent with the results from experimental data. Singular value spectra of the underlying transfer matrix were calculated for various Phong surfaces. As the weight and the shininess factor increase, i.e., the specular contribution increases, the singular value spectrum broadens and the 50-dB bandwidth is increased by more than 4X with a 10% specular contribution, which indicates that at the presence of even a small amount of specular contribution the NLOS measurement can retain significantly more singular value components, leading to higher reconstruction fidelity. With an ordinary camera and incoherent light source, this work enables a low-cost, real-time NLOS imaging system without the need of an explicit physical model of the underlying light transport process.

eess.IV↗

arXiv2019

Knowledge Transfer between Datasets for Learning-based Tissue Microstructure Estimation

Learning-based approaches, especially those based on deep networks, have enabled high-quality estimation of tissue microstructure from low-quality diffusion magnetic resonance imaging (dMRI) scans, which are acquired with a limited number of diffusion gradients and a relatively poor spatial resolution. These learning-based approaches to tissue microstructure estimation require acquisitions of training dMRI scans with high-quality diffusion signals, which are densely sampled in the q-space and have a high spatial resolution. However, the acquisition of training scans may not be available for all datasets. Therefore, we explore knowledge transfer between different dMRI datasets so that learning-based tissue microstructure estimation can be applied for datasets where training scans are not acquired. Specifically, for a target dataset of interest, where only low-quality diffusion signals are acquired without training scans, we exploit the information in a source dMRI dataset acquired with high-quality diffusion signals. We interpolate the diffusion signals in the source dataset in the q-space using a dictionary-based signal representation, so that the interpolated signals match the acquisition scheme of the target dataset. Then, the interpolated signals are used together with the high-quality tissue microstructure computed from the source dataset to train deep networks that perform tissue microstructure estimation for the target dataset. Experiments were performed on brain dMRI scans with low-quality diffusion signals, where the benefit of the proposed strategy is demonstrated.

eess.IV↗

arXiv2017

Iteratively seeded mode-locking

Ultrashort pulsed mode-locked lasers enable research at new time-scales and revolutionary technologies from bioimaging to materials processing. In general, the performance of these lasers is determined by the degree to which the pulses of a particular resonator can be scaled in energy and pulse duration before destabilizing. To date, milestones have come from the application of more tolerant pulse solutions, drawing on nonlinear concepts like soliton formation and self-similarity. Despite these advances, lasers have not reached the predicted performance limits anticipated by these new solutions. In this letter, towards resolving this discrepancy, we demonstrate that the route by which the laser arrives at the solution presents a limit to performance which, moreover, is reached before the solution itself becomes unstable. In contrast to known self-starting limitations stemming from suboptimal saturable absorption, we show that this limit persists even with an ideal saturable absorber. Furthermore, we demonstrate that this limit can be completely surmounted with an iteratively seeded technique for mode-locking. Iteratively seeded mode-locking is numerically explored and compared to traditional static seeding, initially achieving a five-fold increase in energy. This approach is broadly applicable to mode-locked lasers and can be readily implemented into existing experimental architectures.

physics.optics↗

arXiv2016

High-resolution Collinear Chiral Sum Frequency Generation Microscopy by Using Vectorial Beam

In chiral sum frequency generation (C-SFG), the chiral nature of $χ^{(2)}$ requires the three involved electric fields to be pairwise non-parallel, leading to the traditional non-collinear configuration which is a hindrance for achieving diffraction limited resolution while utilizing it as a label-free imaging contrast mechanism . Here we propose a collinear C-SFG (CC-SFG) microscopy modality by using longitudinal z-polarized vectorial field. Label-free chiral imaging with enhanced spatial resolution (~1.4 times improvement in one lateral and the longitudinal directions over the traditional non-collinear scheme) is demonstrated, providing a new path for SFG microscopy with diffraction-limited resolution for mapping chirality.

physics.optics↗

arXiv2016

High-Q silk fibroin whispering gallery microresonator

We have experimentally demonstrated an on-chip all-silk fibroin whispering gallery mode microresonator by using a simple molding and solution-casting technique. The quality factors of the fabricated silk protein microresonators are up to 10^5. A high-sensitivity thermal sensor was realized in this silk fibroin microtoroid with sensitivity of 1.17 nm/K, 8 times higher than previous WGM resonator based thermal sensors. This opens the way to fabricate biodegradable and biocompatible protein based microresonators on a flexible chip for biophotonics applications.

physics.optics↗

arXiv2016

Quaternion-Valued Single-Phase Model for Three-Phase Power Systems

In this work, a quaternion-valued model is proposed in lieu of the Clarke's α, βtransformation to convert three-phase quantities to a hypercomplex single-phase signal. The concatenated signal can be used for harmonic distortion detection in three-phase power systems. In particular, the proposed model maps all the harmonic frequencies into frequencies in the quaternion domain, while the Clarke's transformation-based methods will fail to detect the zero sequence voltages. Based on the quaternion-valued model, the Fourier transform, the minimum variance distortionless response (MVDR) algorithm and the multiple signal classification (MUSIC) algorithm are presented as examples to detect harmonic distortion. Simulations are provided to demonstrate the potentials of this new modeling method.

stat.AP↗

arXiv2015

Three-Dimensional Wind Profile Prediction with Trinion-Valued Adaptive Algorithms

The problem of three-dimensional (3-D) wind profile prediction is addressed based a trinion wind model, which inherently reckons the coupling of the three perpendicular components of a wind field. The augmented trinion statistics are developed and employed to enhance the prediction performance due to its full exploitation of the second-order statistics. The proposed trinion domain processing can be regarded as a more compact version of the existing quaternion-valued approach, with a lower computational complexity. Simulations based on recorded wind data are provided to demonstrate the effectiveness of the proposed methods.

math.OC↗