arXiv subjects

Zhiqiang Li

Publications and source records attributed to Zhiqiang Li.

At least 55 records · Page 3Linked to original sources

arXiv2024

Entropy density and large deviation principles without upper semi-continuity of entropy

Expanding Thurston maps were introduced by M. Bonk and D. Meyer with motivation from complex dynamics and Cannon's conjecture from geometric group theory via Sullivan's dictionary. In this paper, we show that the entropy map of an expanding Thurston map is upper semi-continuous if and only if the map has no periodic critical points. For all expanding Thurston maps, even in the presence of periodic critical points, we show that ergodic measures are entropy-dense and establish level-2 large deviation principles for the distribution of Birkhoff averages, periodic points, and iterated preimages. It follows that iterated preimages and periodic points are equidistributed with respect to the unique equilibrium state for an expanding Thurston map and a potential that is Hölder continuous with respect to a visual metric on $S^2$. In particular, our results answer two questions in [Li15]. The main technical tools in this paper are called subsystems of expanding Thurston maps, inspired by a translation of the notion of subgroups via Sullivan's dictionary.

math.DS↗

arXiv2024

OptLLM: Optimal Assignment of Queries to Large Language Models

Large Language Models (LLMs) have garnered considerable attention owing to their remarkable capabilities, leading to an increasing number of companies offering LLMs as services. Different LLMs achieve different performance at different costs. A challenge for users lies in choosing the LLMs that best fit their needs, balancing cost and performance. In this paper, we propose a framework for addressing the cost-effective query allocation problem for LLMs. Given a set of input queries and candidate LLMs, our framework, named OptLLM, provides users with a range of optimal solutions to choose from, aligning with their budget constraints and performance preferences, including options for maximizing accuracy and minimizing cost. OptLLM predicts the performance of candidate LLMs on each query using a multi-label classification model with uncertainty estimation and then iteratively generates a set of non-dominated solutions by destructing and reconstructing the current solution. To evaluate the effectiveness of OptLLM, we conduct extensive experiments on various types of tasks, including text classification, question answering, sentiment analysis, reasoning, and log parsing. Our experimental results demonstrate that OptLLM substantially reduces costs by 2.40% to 49.18% while achieving the same accuracy as the best LLM. Compared to other multi-objective optimization algorithms, OptLLM improves accuracy by 2.94% to 69.05% at the same cost or saves costs by 8.79% and 95.87% while maintaining the highest attainable accuracy.

cs.SE↗

arXiv2024

General harmonic measures for distance-expanding dynamical systems

Partially motivated by the study of I. Binder, N. Makarov, and S. Smirnov [BMS03] on dimension spectra of polynomial Cantor sets, we initiate the investigation on some general harmonic measures, inspired by Sullivan's dictionary, for distance-expanding dynamical systems. Let $f\colon X\to X$ be an open distance-expanding map on a compact metric space $(X,ρ)$. A Gromov hyperbolic tile graph $Γ$ associated to the dynamical system $(X,f)$ is constructed following the ideas from M. Bonk, D. Meyer [BM17] and P. Haïssinsky, K. M. Pilgrim [HP09]. We consider a class of one-sided random walks associated with $(X,f)$ on $Γ$. They induce a Martin boundary of the tile graph, which may be different from the hyperbolic boundary. We show that the Martin boundary of such a random walk admits a surjection to $X$. We provide a class of examples to show that the surjection may not be a homeomorphism. Such random walks also induce measures on $X$ called harmonic measures. When $ρ$ is a visual metric, we establish an equality between the fractal dimension of the harmonic measure and the asymptotic quantities of the random walk.

math.DS↗

arXiv2024

Thermodynamic formalism for subsystems of expanding Thurston maps II

Expanding Thurston maps were introduced by M. Bonk and D. Meyer with motivation from complex dynamics and Cannon's conjecture from geometric group theory via Sullivan's dictionary. In this paper, we study subsystems of expanding Thurston maps motivated via Sullivan's dictionary as analogs of some subgroups of Kleinian groups. We prove the uniqueness and various ergodic properties of the equilibrium states for strongly primitive subsystems and real-valued Hölder continuous potentials, and establish the equidistribution of preimages of subsystems with respect to the equilibrium states. Here, the sphere $S^{2}$ is equipped with a natural metric, called a visual metric, introduced by M. Bonk and D. Meyer. As a result, for strongly primitive subsystems of expanding Thurston maps without periodic critical points, we obtain a level-$2$ large deviation principle for Birkhoff averages and iterated preimages.

math.DS↗

arXiv2024

On the prevalence of the periodicity of maximizing measures

For a continuous map $T: X\rightarrow X$ on a compact metric space $(X,d)$, we say that a function $f: X \rightarrow \mathbb{R}$ has the property $\mathscr{P}_T$ if its time averages along forward orbits of $T$ are maximized at a periodic orbit. In this paper, we prove that for the one-side full shift of two symbols, the property $\mathscr{P}_T$ is prevalent (in the sense of Hunt--Sauer--Yorke) in spaces of Lipschitz functions with respect to metrics with mildly fast decaying rate on the diameters of cylinder sets. This result is a strengthening of \cite[Theorem~A]{BZ16}, confirms the prediction mentioned in the ICM proceeding contribution of J. Bochi (\cite[Seciton 1]{Boc18}) suggested by experimental evidence, and is another step towards the Hunt--Ott conjectures in the area of ergodic optimization.

math.DS↗

arXiv2024

Prime orbit theorems for expanding Thurston maps: Dirichlet series and orbifolds

We obtain an analog of the prime number theorem for a class of branched covering maps on the $2$-sphere $S^2$ called expanding Thurston maps, which are topological models of some non-uniformly expanding rational maps without any smoothness or holomorphicity assumptions. More precisely, we show that the number of primitive periodic orbits, ordered by a weight on each point induced by an (eventually) positive real-valued Hölder continuous function on $S^2$ that is not cohomologous to a constant, is asymptotically the same as the well-known logarithmic integral. In particular, our results apply to postcritically-finite rational maps for which the Julia set is the whole Riemann sphere.

math.DS↗

arXiv2024

Controlled pumping of matter-wave solitons in a one-dimensional optical superlattice

We study the pumping of matter-wave solitons formed in Bose-Einstein condensates (BECs) with attractive atomic interactions that are loaded into optical superlattices in which one of the lattices is moving with respect to the other. We find that solitons exhibit the remarkably similar pumping properties in both shallow and deep lattices, and that for exactly the same soliton initially excited, switching between integer (fractional) pumping and trapping can be achieved by simply adjusting the lattice parameters. In addition, we find that the gap solitons, which bifurcate from the lowest energy band in a semi-infinite band gap, also exhibit this lattice-parameter-dependent pumping and trapping. The treatment of solitons as classical particles with effective centre-of-mass equations of motion provides a good description of this parameter-dependent integer (fractional) pumping and trapping of solitons.

quant-ph↗

arXiv2024

Lookup Table meets Local Laplacian Filter: Pyramid Reconstruction Network for Tone Mapping

Tone mapping aims to convert high dynamic range (HDR) images to low dynamic range (LDR) representations, a critical task in the camera imaging pipeline. In recent years, 3-Dimensional LookUp Table (3D LUT) based methods have gained attention due to their ability to strike a favorable balance between enhancement performance and computational efficiency. However, these methods often fail to deliver satisfactory results in local areas since the look-up table is a global operator for tone mapping, which works based on pixel values and fails to incorporate crucial local information. To this end, this paper aims to address this issue by exploring a novel strategy that integrates global and local operators by utilizing closed-form Laplacian pyramid decomposition and reconstruction. Specifically, we employ image-adaptive 3D LUTs to manipulate the tone in the low-frequency image by leveraging the specific characteristics of the frequency information. Furthermore, we utilize local Laplacian filters to refine the edge details in the high-frequency components in an adaptive manner. Local Laplacian filters are widely used to preserve edge details in photographs, but their conventional usage involves manual tuning and fixed implementation within camera imaging pipelines or photo editing tools. We propose to learn parameter value maps progressively for local Laplacian filters from annotated data using a lightweight network. Our model achieves simultaneous global tone manipulation and local edge detail preservation in an end-to-end manner. Extensive experimental results on two benchmark datasets demonstrate that the proposed method performs favorably against state-of-the-art methods.

cs.CV↗

arXiv2023

Fast Sampling generative model for Ultrasound image reconstruction

Image reconstruction from radio-frequency data is pivotal in ultrafast plane wave ultrasound imaging. Unlike the conventional delay-and-sum (DAS) technique, which relies on somewhat imprecise assumptions, deep learning-based methods perform image reconstruction by training on paired data, leading to a notable enhancement in image quality. Nevertheless, these strategies often exhibit limited generalization capabilities. Recently, denoising diffusion models have become the preferred paradigm for image reconstruction tasks. However, their reliance on an iterative sampling procedure results in prolonged generation time. In this paper, we propose a novel sampling framework that concurrently enforces data consistency of ultrasound signals and data-driven priors. By leveraging the advanced diffusion model, the generation of high-quality images is substantially expedited. Experimental evaluations on an in-vivo dataset indicate that our approach with a single plane wave surpasses DAS with spatial coherent compounding of 75 plane waves.

cs.CV↗

arXiv2023

Single PW takes a shortcut to compound PW in US imaging

Reconstruction of ultrasound (US) images from radio-frequency data can be conceptualized as a linear inverse problem. Traditional deep learning approaches, which aim to improve the quality of US images by directly learning priors, often encounter challenges in generalization. Recently, diffusion-based generative models have received significant attention within the research community due to their robust performance in image reconstruction tasks. However, a limitation of these models is their inherent low speed in generating image samples from pure Gaussian noise progressively. In this study, we exploit the inherent similarity between the US images reconstructed from a single plane wave (PW) and PW compounding PWC). We hypothesize that a single PW can take a shortcut to reach the diffusion trajectory of PWC, removing the need to begin with Gaussian noise. By employing an advanced diffusion model, we demonstrate its effectiveness in US image reconstruction, achieving a substantial reduction in sampling steps. In-vivo experimental results indicate that our approach can reduce sampling steps by 60%, while preserving comparable performance metrics with the conventional diffusion model.

cs.CV↗

arXiv2023

Active Encoding of Flexural Wave with Non-Diffractive Talbot Effect

This study employs the theory of conformal transformation to devise a Mikaelian lens for flexural waves manipulation. We investigate the propagation patterns of flexural waves in the lens under scenarios of plane wave and point source incidence. Additionally, the study explores the Talbot effect generated by interference patterns of multiple sources. Within the Mikaelian lens, the Talbot effect displays non diffractive characteristics, facilitating propagation over considerable distances. Leveraging the non-diffractive attributes of the Talbot effect in the Mikaelian lens, the paper discusses the feasibility of encoding flexural waves based on active interference sources. Simulation and experimental validation attest to the lens's effective active encoding. This research introduces novel perspectives on flexural wave encoding, showcasing potential applications in flexural wave communication, detection, and related fields.

physics.app-ph↗

arXiv2023

HyperLips: Hyper Control Lips with High Resolution Decoder for Talking Face Generation

Talking face generation has a wide range of potential applications in the field of virtual digital humans. However, rendering high-fidelity facial video while ensuring lip synchronization is still a challenge for existing audio-driven talking face generation approaches. To address this issue, we propose HyperLips, a two-stage framework consisting of a hypernetwork for controlling lips and a high-resolution decoder for rendering high-fidelity faces. In the first stage, we construct a base face generation network that uses the hypernetwork to control the encoding latent code of the visual face information over audio. First, FaceEncoder is used to obtain latent code by extracting features from the visual face information taken from the video source containing the face frame.Then, HyperConv, which weighting parameters are updated by HyperNet with the audio features as input, will modify the latent code to synchronize the lip movement with the audio. Finally, FaceDecoder will decode the modified and synchronized latent code into visual face content. In the second stage, we obtain higher quality face videos through a high-resolution decoder. To further improve the quality of face generation, we trained a high-resolution decoder, HRDecoder, using face images and detected sketches generated from the first stage as input.Extensive quantitative and qualitative experiments show that our method outperforms state-of-the-art work with more realistic, high-fidelity, and lip synchronization. Project page: https://semchan.github.io/HyperLips Project/

cs.CV↗

arXiv2023

Cross-domain Self-supervised Framework for Photoacoustic Computed Tomography Image Reconstruction

Accurate image reconstruction is crucial for photoacoustic (PA) computed tomography (PACT). Recently, deep learning has been used to reconstruct the PA image with a supervised scheme, which requires high-quality images as ground truth labels. In practice, there are inevitable trade-offs between cost and performance since the use of more channels is an expensive strategy to access more measurements. Here, we propose a cross-domain unsupervised reconstruction (CDUR) strategy with a pure transformer model, which overcomes the lack of ground truth labels from limited PA measurements. The proposed approach exploits the equivariance of PACT to achieve high performance with a smaller number of channels. We implement a self-supervised reconstruction in a model-based form. Meanwhile, we also leverage the self-supervision to enforce the measurement and image consistency on three partitions of measured PA data, by randomly masking different channels. We find that dynamically masking a high proportion of the channels, e.g., 80%, yields nontrivial self-supervisors in both image and signal domains, which decrease the multiplicity of the pseudo solution to efficiently reconstruct the image from fewer PA measurements with minimum error of the image. Experimental results on in-vivo PACT dataset of mice demonstrate the potential of our unsupervised framework. In addition, our method shows a high performance (0.83 structural similarity index (SSIM) in the extreme sparse case with 13 channels), which is close to that of supervised scheme (0.77 SSIM with 16 channels). On top of all the advantages, our method may be deployed on different trainable models in an end-to-end manner.

eess.IV↗

arXiv2023

Chaos signatures of current phase transition in a toroidal trap

In this work we demonstrate how the directed motion of atomic Bose-Einstein condensates in a toroidal trap can be controlled by applying a zero-mean oscillatory driving field. We show that due to the self-trapping effect in momentum space, the oscillatory amplitude of the current can be significantly suppressed and a nearly constant directed current can be obtained preserving the initial current values, by decreasing the driving amplitude, even when the atomic interactions are relatively small. We also reveal numerically the mean-field chaos can serve as an indicator of a quantum phase transition between the vanishing current regime and nonvanishing current regime. Our results are corroborated by an effective three-mode model, which provides an excellent account of the ratchet dynamics of the system.

quant-ph↗

arXiv2023

Towards General Low-Light Raw Noise Synthesis and Modeling

Modeling and synthesizing low-light raw noise is a fundamental problem for computational photography and image processing applications. Although most recent works have adopted physics-based models to synthesize noise, the signal-independent noise in low-light conditions is far more complicated and varies dramatically across camera sensors, which is beyond the description of these models. To address this issue, we introduce a new perspective to synthesize the signal-independent noise by a generative model. Specifically, we synthesize the signal-dependent and signal-independent noise in a physics- and learning-based manner, respectively. In this way, our method can be considered as a general model, that is, it can simultaneously learn different noise characteristics for different ISO levels and generalize to various sensors. Subsequently, we present an effective multi-scale discriminator termed Fourier transformer discriminator (FTD) to distinguish the noise distribution accurately. Additionally, we collect a new low-light raw denoising (LRD) dataset for training and benchmarking. Qualitative validation shows that the noise generated by our proposed noise model can be highly similar to the real noise in terms of distribution. Furthermore, extensive denoising experiments demonstrate that our method performs favorably against state-of-the-art methods on different sensors.

cs.CV↗

arXiv2023

Ratchet current in a $\mathcal{PT}$-symmetric Floquet quantum system with symmetric sinusoidal driving

We consider the ratchet dynamics in a $\mathcal{PT}$-symmetric Floquet quantum system with symmetric temporal (harmonic) driving. In the exact $\mathcal{PT}$ phase, for a finite number of resonant frequencies, we show that the long-lasting resonant currents can be generated with the symmetric time-continuous driving, which would otherwise forbid the generation of directed currents in the Hermitian limit. Such a non-Hermitian resonant current can be enhanced by increasing the non-Hermitian level, and in particular, the resonant current peaks (reaches the largest negative value) under the condition that the imaginary part of the potential depth is equal to the real part, at which the stable asymptotic current occurs owing to exceptional points (EPs) mechanism. Moreover, the directed currents originating from the symmetry breaking are reported, which increase linearly with the driving frequency, the mechanism behind which is that the cutoff of the momentum eigenstates for the Floquet state with maximum imaginary quasienergy increases as the driving frequency is continuously increased. We also present a non-Hermitian three-level model that can account for the resonant currents and gives surprisingly good agreement with direct numerical results for weak driving, even in the $\mathcal{PT}$-broken regime for the first-order resonance. Our results provide a new means of realizing the non-Hermiticity-controlled ratchet current by means of a smooth continuous driving, previously used only to generate currents in Hermitian systems.

quant-ph↗

arXiv2023

Scattering of one-dimensional quantum droplets by a reflectionless potential well

We investigate, both analytically and numerically, the scattering of one-dimensional quantum droplets by a Pöschl-Teller reflectionless potential well, confirming that there is a sharp transition between full reflection and full transmission at a certain critical incident speed for both small droplets and large flat-top droplets. We observe sharp differences between small quantum droplet scattering and large quantum droplet scattering. The scattering of small quantum droplets is similar to that of solitons, where a spatially symmetric trapped mode is formed at the critical speed, whereas for large quantum droplets a spatially asymmetric trapped mode is formed. Additionally, a nonmonotonous dependence of the critical speed on the atom number is identified$:$ on the small-droplet side, the critical speed increases with the atom number, while in the flat-top regime, the critical speed decreases with increasing the atom number. Strikingly, the scattering excites internal modes below the particle-emission threshold, preventing the quantum droplets from emitting radiation upon interaction with the potential. Analysis of the small-amplitude excitation spectrum shows that as the number of particles increases, it becomes increasingly difficult to emit particles outside the droplet during scattering, while radiation from solitons cannot be completely avoided. Finally, we study the collision of two quantum droplets at the reflectionless potential, revealing the role of the $π$-phase difference ``generator'' played by the reflectionless potential.

quant-ph↗

arXiv2023

Magnetic poles enabled kirigami meta-structure for stable mechanical memory storage with high information density

Some bi or multi-stable Mechanical meta-structures have been implemented as mechanical memory devices which however are with limits such as complex structural forms, low information storage capability and/or fragile structural stability to maintain the stored information bits robustly under external interferences. To address these issues, we refer to the structural intelligence by constructing a simple 3D-printable multi-layered cylindrical kirigami module with gradient structural parameters and propose a mechanical memory device that can robustly store information bits exponentially larger than previous designs. We demonstrate the promising enhancement of information storage capability of our proposed mechanical memory device relies on two mechanisms 1 the deformation sequences of the kirigami module enabled by the gradient structural parameter, which brings the extra dimensional degree of freedom to break the traditional mechanical memory unit with only planar form and merits information bits with spatially combinatorical programmability, and 2 the combinatorics of the deformation independences among the cylindrical kiriagmi unit arrays in the constructed mechanical memory device. Particularly, we achieve both the structural stabilities and the desired structural robustness in the mechanical memory devices by additively introducing magnetic N-S poles in units, which can protect the stored information from interferences like mechanical crushing, impacting and or shaking.

cond-mat.mtrl-sci↗