arXiv subjects
Publications and source records attributed to Lu Zheng.
The paper introduce a new type of generalized inverse, called Bott-Duffin drazin inverse (or, in short, BDD-inverse) of a complex square matrix, and give some of its properties, characterizations and representations. Furthermore, We discuss the problem of the minimum P-norm solution of the constraint matrix equation by using the Bott-Duffin drazin inverse, and give Cramer s rule for this minimum P-norm solution.
An induced matching in a graph is a set of edges whose endpoints induce a $1$-regular subgraph. Gupta et al. (2012,\cite{Gupta}) showed that every $n$-vertex graph has at most $10^{\frac{n}{5}}\approx 1.5849^n$ maximal induced matchings, which is attained by the disjoint union of copies of the complete graph $K_5$. In this paper, we show that the maximum number of maximal and maximum induced matchings in a connected graph of order $n$ is \begin{align*} \begin{cases} {n\choose 2} &~ {\rm if}~ 1\leq n\le 8; \\ {{\lfloor \frac{n}{2} \rfloor}\choose 2}\cdot {{\lceil \frac{n}{2} \rceil}\choose 2} -(\lfloor \frac{n}{2} \rfloor-1)\cdot (\lceil \frac{n}{2} \rceil-1)+1 &~ {\rm if}~ 9\leq n\le 13; \\ 10^{\frac{n-1}{5}}+\frac{n+144}{30}\cdot 6^{\frac{n-6}{5}} &~ {\rm if}~ 14\leq n\le 30;\\ 10^{\frac{n-1}{5}}+\frac{n-1}{5}\cdot 6^{\frac{n-6}{5}} & ~ {\rm if}~ n\geq 31, \\ \end{cases} \end{align*} and also show that this bound is tight. This result implies that we can enumerate all maximal induced matchings of an $n$-vertex connected graph in time $O(1.5849^n)$. Moreover, our result provides an estimate on the number of maximal dissociation sets of an $n$-vertex connected graph.
This paper introduces LiNR, LinkedIn's large-scale, GPU-based retrieval system. LiNR supports a billion-sized index on GPU models. We discuss our experiences and challenges in creating scalable, differentiable search indexes using TensorFlow and PyTorch at production scale. In LiNR, both items and model weights are integrated into the model binary. Viewing index construction as a form of model training, we describe scaling our system for large indexes, incorporating full scans and efficient filtering. A key focus is on enabling attribute-based pre-filtering for exhaustive GPU searches, addressing the common challenge of post-filtering in KNN searches that often reduces system quality. We further provide multi-embedding retrieval algorithms and strategies for tackling cold start issues in retrieval. Our advancements in supporting larger indexes through quantization are also discussed. We believe LiNR represents one of the industry's first Live-updated model-based retrieval indexes. Applied to out-of-network post recommendations on LinkedIn Feed, LiNR has contributed to a 3% relative increase in professional daily active users. We envisage LiNR as a step towards integrating retrieval and ranking into a single GPU model, simplifying complex infrastructures and enabling end-to-end optimization of the entire differentiable infrastructure through gradient descent.
The current design of space-based gravitational wave detectors utilizes heterodyne laser interferometry in inter-satellite science measurements. Frequency variations of the heterodyne beatnotes are predominantly caused by the Doppler effect from relative satellite motion along lines of sight. Generally considered to be outside the measurement band, this Doppler frequency shift appears to have been overlooked in numerical simulations of time-delay interferometry (TDI). However, the potential impact on the implementation of TDI should be assessed. The issue is particularly relevant to TianQin that features geocentric orbits, because of strong gravity disturbances from the Earth-Moon system at frequencies $<1\times 10^{-4}$ Hz. In this proof-of-principle study, based on high-precision orbital data obtained from detailed gravity field modeling, we incorporate the Doppler shift in the generation of TianQin's beatnote phase signals. To remove the large-scale Doppler phase drift at frequencies $<1\times 10^{-4}$ Hz, we develop a high-performance high-pass filter and consider two possible processing sequences, i.e., applying the filter before or after TDI combinations. Our simulation results favor the former and demonstrate successful removal of the low-frequency gravity disturbances for TianQin without degrading the TDI performance, assuming 10 m pseudo-ranging uncertainty. The filtering scheme can be used in developing the initial noise-reduction pipeline for TianQin.
In tensor eigenvalue problems, one is likely to be more interested in H-eigenvalues of tensors. The largest H-eigenvalue of a nonnegative tensor or of a uniform hypergraph is the spectral radius of the tensor or of the uniform hypergraph. We find upper bounds and lower bounds (interlacing inequalities) for the largest H-eigenvalue of a principal subtensor of a symmetric zero diagonal tensor that is of even order or nonnegative, as well as lower bounds for the largest H-eigenvalue of a uniform hypergraph with some vertices or edges removed. We also investigate similar problems for the least H-eigenvalues. We give examples to verify the sharpness of the bounds or in some cases for uniform hypergraphs, we characterize the equality. Particularly, for a connected linear $k$-uniform hypergraph $G$ with $v\in V(G)$, we give a sharp lower bound for the spectral radius of $G-v$ in terms of the spectral radius of $G$ and the degree of $v$ and characterize the extremal hypergraphs, and show that the maximum spectral radius of the subhypergraphs with one vertex removed is greater than or equal to the spectral radius of the hypergraph minus one, which is attained if and only if it is a Steiner system $S(2,k,n)$.
TianQin is a proposed geocentric space-based gravitational wave observatory mission, which requires time-delay interferometry (TDI) to cancel laser frequency noise. With high demands for precision, solar-wind plasma environment at $\sim 10^5$ km above the Earth may constitute a non-negligible noise source to laser interferometric measurements between satellites, as charged particles perturb the refractivity along light paths. In this paper, we first assess the plasma noises along single links from space-weather models and numerical orbits, and analyze the time and frequency domain characteristics. Particularly, to capture the plasma noise in the entire measurement band of $10^{-4} - 1$ Hz, we have performed additional space-weather magnetohydrodynamic simulations in finer spatial and temporal resolutions and utilized Kolmogorov spectra in high-frequency data generation. Then we evaluate the residual plasma noises of the first- and second-generation TDI combinations. Both analytical and numerical estimations have shown that under normal solar conditions the plasma noise after TDI is less than the secondary noise requirement. Moreover, TDI is shown to exhibit moderate suppression on the plasma noise below $\sim 10^{-2}$ Hz due to noise correlation between different arms, when compared with the secondary noise before and after TDI.
Integrating multimodal knowledge for abstractive summarization task is a work-in-progress research area, with present techniques inheriting fusion-then-generation paradigm. Due to semantic gaps between computer vision and natural language processing, current methods often treat multiple data points as separate objects and rely on attention mechanisms to search for connection in order to fuse together. In addition, missing awareness of cross-modal matching from many frameworks leads to performance reduction. To solve these two drawbacks, we propose an Iterative Contrastive Alignment Framework (ICAF) that uses recurrent alignment and contrast to capture the coherences between images and texts. Specifically, we design a recurrent alignment (RA) layer to gradually investigate fine-grained semantical relationships between image patches and text tokens. At each step during the encoding process, cross-modal contrastive losses are applied to directly optimize the embedding space. According to ROUGE, relevance scores, and human evaluation, our model outperforms the state-of-the-art baselines on MSMO dataset. Experiments on the applicability of our proposed framework and hyperparameters settings have been also conducted.
Topological phononics offers numerous opportunities in manipulating elastic waves that can propagate in solids without being backscattered. Due to the lack of nanoscale imaging tools that aid the system design, however, acoustic topological metamaterials have been mostly demonstrated in macroscale systems operating at low (kilohertz to megahertz) frequencies. Here, we report the realization of gigahertz topological valley Hall effect in nanoelectromechanical AlN membranes. Propagation of elastic wave through phononic crystals is directly visualized by microwave microscopy with unprecedented sensitivity and spatial resolution. The valley Hall edge states, protected by band topology, are vividly seen in both real- and momentum-space. The robust valley-polarized transport is evident from the wave transmission across local disorder and around sharp corners, as well as the power distribution into multiple edge channels. Our work paves the way to exploit topological physics in integrated acousto-electronic systems for classical and quantum information processing in the microwave regime.
Background: The current clinical workflow for esophageal gross tumor volume (GTV) contouring relies on manual delineation of high labor-costs and interuser variability. Purpose: To validate the clinical applicability of a deep learning (DL) multi-modality esophageal GTV contouring model, developed at 1 institution whereas tested at multiple ones. Methods and Materials: We collected 606 esophageal cancer patients from four institutions. 252 institution-1 patients had a treatment planning-CT (pCT) and a pair of diagnostic FDG-PETCT; 354 patients from other 3 institutions had only pCT. A two-streamed DL model for GTV segmentation was developed using pCT and PETCT scans of a 148 patient institution-1 subset. This built model had the flexibility of segmenting GTVs via only pCT or pCT+PETCT combined. For independent evaluation, the rest 104 institution-1 patients behaved as unseen internal testing, and 354 institutions 2-4 patients were used for external testing. We evaluated manual revision degrees by human experts to assess the contour-editing effort. The performance of the deep model was compared against 4 radiation oncologists in a multiuser study with 20 random external patients. Contouring accuracy and time were recorded for the pre-and post-DL assisted delineation process. Results: Our model achieved high segmentation accuracy in internal testing (mean Dice score: 0.81 using pCT and 0.83 using pCT+PET) and generalized well to external evaluation (mean DSC: 0.80). Expert assessment showed that the predicted contours of 88% patients need only minor or no revision. In multi-user evaluation, with the assistance of a deep model, inter-observer variation and required contouring time were reduced by 37.6% and 48.0%, respectively. Conclusions: Deep learning predicted GTV contours were in close agreement with the ground truth and could be adopted clinically with mostly minor or no changes.
We report direct visualization of gigahertz-frequency Lamb waves propagation in aluminum nitride phononic circuits by transmission-mode microwave impedance microscopy (TMIM). Consistent with the finite-element modeling, the acoustic eigenmodes in both a horn-shaped coupler and a sub-wavelength waveguide are revealed in the TMIM images. Using fast Fourier transform filtering, we quantitatively analyze the acoustic loss of individual Lamb modes along the waveguide and the power coupling coefficient between the waveguide and the parabolic couplers. Our work provides insightful information on the propagation, mode conversion, and attenuation of acoustic waves in piezoelectric nanostructures, which is highly desirable for designing and optimizing phononic devices for microwave signal processing and quantum information transduction.
Nanoelectronic devices based on ferroelectric domain walls (DWs), such as memories, transistors, and rectifiers, have been demonstrated in recent years. Practical high-speed electronics, on the other hand, usually demand operation frequencies in the giga-Hertz (GHz) regime, where the effect of dipolar oscillation is important. In this work, an unexpected giant GHz conductivity on the order of 103 S/m is observed in certain BiFeO3 DWs, which is about 100,000 times greater than the carrier-induced dc conductivity of the same walls. Surprisingly, the nominal configuration of the DWs precludes the ac conduction under an excitation electric field perpendicular to the surface. Theoretical analysis shows that the inclined DWs are stressed asymmetrically near the film surface, whereas the vertical walls in a control sample are not. The resultant imbalanced polarization profile can then couple to the out-of-plane microwave fields and induce power dissipation, which is confirmed by the phase-field modeling. Since the contributions from mobile-carrier conduction and bound-charge oscillation to the ac conductivity are equivalent in a microwave circuit, the research on local structural dynamics may open a new avenue to implement DW nano-devices for RF applications.
Phonons are considered to be universal quantum transducers due to their ability to couple to a wide variety of quantum systems. Among these systems, solid-state point defect spins are known for being long-lived optically accessible quantum memories. Recently, it has been shown that inversion-symmetric defects in diamond, such as the negatively charged silicon vacancy center (SiV), feature spin qubits that are highly susceptible to strain. Here, we leverage this strain response to achieve coherent and low-power acoustic control of a single SiV spin, and perform acoustically driven Ramsey interferometry of a single spin. Our results demonstrate a novel and efficient method of spin control for these systems, offering a path towards strong spin-phonon coupling and phonon-mediated hybrid quantum systems.
Reducing the lateral scale of two-dimensional (2D) materials to one-dimensional (1D) has attracted substantial research interest not only to achieve competitive electronic device applications but also for the exploration of fundamental physical properties. Controllable synthesis of high-quality 1D nanoribbons (NRs) is thus highly desirable and essential for the further study. Traditional exploration of the optimal synthesis conditions of novel materials is based on the trial-and-error approach, which is time consuming, costly and laborious. Recently, machine learning (ML) has demonstrated promising capability in guiding material synthesis through effectively learning from the past data and then making recommendations. Here, we report the implementation of supervised ML for the chemical vapor deposition (CVD) synthesis of high-quality 1D few-layered WTe2 nanoribbons (NRs). The synthesis parameters of the WTe2 NRs are optimized by the trained ML model. On top of that, the growth mechanism of as-synthesized 1T' few-layered WTe2 NRs is further proposed, which may inspire the growth strategies for other 1D nanostructures. Our findings suggest that ML is a powerful and efficient approach to aid the synthesis of 1D nanostructures, opening up new opportunities for intelligent material development.
We demonstrate conversion of up to 4.5 GHz-frequency microwaves to 1500 nm-wavelength light using optomechanical interactions on suspended thin-film lithium niobate. Our method utilizes an interdigital transducer that drives a free-standing 100 $μ$m-long thin-film acoustic resonator to modulate light travelling in a Mach-Zehnder interferometer or racetrack cavity. Owing to the strong microwave-to-acoustic coupling offered by the transducer in conjunction with the strong photoelastic, piezoelectric, and electro-optic effects of lithium niobate, we achieve a half-wave voltage of $V_π$ = 4.6 V and $V_π$ = 0.77 V for the Mach-Zehnder interferometer and racetrack resonator, respectively. The acousto-optic racetrack cavity exhibits an optomechancial single-photon coupling strength of 1.1 kHz. Our integrated nanophotonic platform coherently leverages the compelling properties of lithium niobate to achieve microwave-to-optical transduction. To highlight the versatility of our system, we also demonstrate a lossless microwave photonic link, which refers to a 0 dB microwave power transmission over an optical channel.
Phonons at gigahertz frequencies interact with electrons, photons, and atomic systems in solids, and therefore have extensive applications in signal processing, sensing, and quantum technologies. Surface acoustic wave (SAW) resonators that confine surface phonons can play a crucial role in such integrated phononic systems due to small mode size, low dissipation, and efficient electrical transduction. To date, it has been challenging to achieve high quality (Q) factor and small phonon mode size for SAW resonators at gigahertz frequencies. Here, we present a methodology to design compact high-Q SAW resonators on lithium niobate operating at gigahertz frequencies. We experimentally verify out designs and demonstrate Q factors in excess of $2\times10^4$ at room temperature ($6\times10^4$ at 4 Kelvin) and mode area as low as $1.87 λ^2$. This is achieved by phononic band structure engineering, which provides high confinement with low mechanical loss. The frequency-Q products (fQ) of our SAW resonators are greater than $10^{13}$. These high-fQ and small mode size SAW resonators could enable applications in quantum phononics and integrated hybrid systems with phonons, photons, and solid-state qubits.
We review recent experimental progresses on layered topological materials, mainly focusing on transitional metal dichalcogenides with various lattice types including 1T, Td and 1T' structural phases. Their electronic quantum states are interestingly rich, and many appear to be topological nontrivial, such as Dirac/Weyl semimetallic phase in multilayers and quantum spin hall insulator phase in monolayers. The content covers recent major advances from material synthesis, basic characterizations, angle-resolved photoemission spectroscopy measurements, transport and optical responses. Following those, we outlook the exciting future possibilities enabled by the marriage of topological physics and two dimensional van der Waals layered heterostructures.
The generalized distance spectral radius of a connected graph $G$ is the spectral radius of the generalized distance matrix of $G$, defined by $$D_α(G)=αTr(G)+(1-α)D(G), \;\;0\leα\le 1,$$ where $D(G)$ and $Tr(G)$ denote the distance matrix and diagonal matrix of the vertex transmissions of $G$, respectively. This paper characterizes the unique graph with minimum generalized distance spectral radius among the connected graphs with fixed chromatic number, which answers a question about the generalized distance spectral radius in spectral extremal theories. In addition, we also determine graphs with minimum generalized distance spectral radius among the $n$-vertex trees and unicyclic graphs, respectively. These results generalize some known results about distance spectral radius and distance signless Laplacian spectral radius of graphs.
We report the nanoscale electrical imaging results in hexagonal $Lu_{0.6}Sc_{0.4}FeO_3$ single crystals using conductive atomic force microscopy (C-AFM) and scanning microwave impedance microscopy (MIM). While the dc and ac response of the ferroelectric domains can be explained by the surface band bending, the drastic enhancement of domain wall (DW) ac conductivity is clearly dominated by the dielectric loss due to DW vibration rather than mobile-carrier conduction. Our work provides a unified physical picture to describe the local conductivity of ferroelectric domains and domain walls, which will be important for future incorporation of electrical conduction, structural dynamics, and multiferroicity into high-frequency nano-devices.