arXiv subjects

Jinsong Liu

Publications and source records attributed to Jinsong Liu.

33 records · Page 2Linked to original sources

arXiv2023

The spectrality of Cantor-Moran measure and Fuglede's Conjecture

Let $\{(p_n, \mathcal{D}_n, L_n)\}$ be a sequence of Hadamard triples on $\mathbb{R}$. Suppose that the associated Cantor-Moran measure $$ μ_{\{p_n,\mathcal{D}_n\}}=δ_{p_1^{-1}\mathcal{D}_1}\astδ_{(p_2p_1)^{-1}\mathcal{D}_2}\ast\cdots, $$ where $\sup_n\{|p_n^{-1}d|:d\in \mathcal{D}_n\}<\infty$ and $\sup\#\mathcal{D}_n<\infty$. It has been observed that the spectrality of $μ_{\{p_n,D_n\}}$ is determined by equi-positivity. A significant problem is what kind of Moran measures can satisfy this property. In this paper, we introduce the conception of \textit{Double Points Condition Set} (\textit{DPCS}) to characterize the equi-positivity equivalently. As applications of our characterization, we show that all singularly continuous Cantor-Moran measures are spectral. For the absolutely continuous case, we study Fuglede's Conjecture on Cantor-Moran set. We show that the equi-positivity of $μ_{\{p_n,D_n\}}$ implies the tiling of its support, and the reverse direction holds under certain conditions.

math.FA↗

arXiv2023

Stochastic Dimension-reduced Second-order Methods for Policy Optimization

In this paper, we propose several new stochastic second-order algorithms for policy optimization that only require gradient and Hessian-vector product in each iteration, making them computationally efficient and comparable to policy gradient methods. Specifically, we propose a dimension-reduced second-order method (DR-SOPO) which repeatedly solves a projected two-dimensional trust region subproblem. We show that DR-SOPO obtains an $\mathcal{O}(ε^{-3.5})$ complexity for reaching approximate first-order stationary condition and certain subspace second-order stationary condition. In addition, we present an enhanced algorithm (DVR-SOPO) which further improves the complexity to $\mathcal{O}(ε^{-3})$ based on the variance reduction technique. Preliminary experiments show that our proposed algorithms perform favorably compared with stochastic and variance-reduced policy gradient methods.

math.OC↗

arXiv2023

Bi-Hölder extensions of quasi-isometries on pseudoconvex domains of finite type in $\mathbb{C}^2$

In this paper, we prove that the identity map for the smoothly bounded pseudoconvex domain of finite type in $\mathbb{C}^2$ extends to a bi-Hölder map between the Euclidean boundary and Gromov boundary. As an application, we show the bi-Hölder boundary extensions for quasi-isometries between these domains. Moreover, we get a more accurate index of the Gehring-Hayman type theorem for the bounded $m$-convex domains with Dini-smooth boundary.

math.CV↗

arXiv2022

A description of $A_{\infty }$-weights for VMO

We present a new characterization of Muckenhoupt $A_{\infty}$-weights whose logarithm is in $\operatorname{VMO}(\mathbb{R})$ in terms of vanishing Carleson measures on $\mathbb{R}_+^2$ and vanishing doubling weights on $\mathbb{R}$. This also gives a novel description of strongly symmetric homeomorphisms on the real line by using a geometric quantity.

math.CV↗

arXiv2022

SOLNP+: A Derivative-Free Solver for Constrained Nonlinear Optimization

SOLNP+ is a derivative-free solver for constrained nonlinear optimization. It starts from SOLNP proposed in 1989 by Ye Ye with the main idea that uses finite difference to approximate the gradient. We incorporate the techniques of implicit filtering, new restart mechanism and modern quadratic programming solver into this new version with an ANSI C implementation. The algorithm exhibits a great advantage in running time and robustness under noise compared with the last version by MATLAB. SOLNP+ is free to download at https://github.com/COPT-Public/SOLNP_plus.

math.OC↗

arXiv2022

Leveraging mid-infrared spectroscopic imaging and deep learning for tissue subtype classification in ovarian cancer

Mid-infrared spectroscopic imaging (MIRSI) is an emerging class of label-free techniques being leveraged for digital histopathology. Modern histopathologic identification of ovarian cancer involves tissue staining followed by morphological pattern recognition. This process is time-consuming, subjective, and requires extensive expertise. This paper presents the first label-free, quantitative, and automated histological recognition of ovarian tissue subtypes using a new MIRSI technique. This technique, called optical photothermal infrared (O-PTIR) imaging, provides a 10X enhancement in spatial resolution relative to prior instruments. It enables sub-cellular spectroscopic investigation of tissue at biochemically important fingerprint wavelengths. We demonstrate that enhanced resolution of sub-cellular features, combined with spectroscopic information, enables reliable classification of ovarian cell subtypes achieving a classification accuracy of 0.98. Moreover, we present statistically robust validation from 74 patient samples with over 60 million data points. We show that sub-cellular resolution from five wavenumbers is sufficient to outperform state-of-the-art diffraction-limited techniques from up to 235 wavenumbers. We also propose two quantitative biomarkers based on the relative quantities of epithelium and stroma that exhibits efficacy in early cancer diagnosis. This paper demonstrates that combining deep learning with intrinsic biochemical MIRSI measurements enables quantitative evaluation of cancerous tissue, improving the rigor and reproducibility of histopathology.

q-bio.TO↗

arXiv2020

Carleson measures on convex domains

Following M.Abate and A.Saracco's work on strongly pseudoconvex domains in $\mathbb{C}^n$, we characterize Carleson measures of $A^2(D)$ in bounded convex domains with smooth boundary of finite type. We also give examples of Carleson measures with uniformly discrete (with respect to the Kobayashi distance) sequences.

math.CV↗

arXiv2020

Large quotients of group actions with a contracting element

For any proper action of a non-elementary group $G$ on a proper geodesic metric space, we show that if $G$ contains a contracting element, then there exists a sequence of proper quotient groups whose growth rate tends to the growth rate of $G$. Similar statements are obtained for a product of proper actions with contracting elements. The tools involved in this paper include the extension lemma for the construction of large tree, the theory of rotating families developed by F. Dahmani, V. Guirardel and D. Osin, and the construction of a quasi-tree of metric spaces introduced by M. Bestvina, K. Bromberg and K. Fujiwara. Several applications are given to CAT(0) groups and mapping class groups.

math.GR↗

arXiv2020

The Gehring-Hayman type theorems on complex domains

In this paper we establish Gehring-Hayman type theorems for some complex domains. Suppose that $Ω\subset \mathbb{C}^n$ is a bounded $m$-convex domain with Dini-smooth boundary, or a bounded strongly pseudoconvex domain with $C^2$-smooth boundary. Then we prove that the Euclidean length of Kobayashi geodesic $[x,y]$ in $Ω$ is less than $c_1|x-y|^{c_2}$. Furthermore, if $Ω$ endowed with the Kobayashi metric is Gromov hyperbolic, then we can generalize this result to quasi-geodesics with respect to Bergman metric, Carathéodory metric or Kähler-Einstein metric. As applications, we prove the bi-Hölder equivalence between the Euclidean boundary and the Gromov boundary. Moreover, by using this boundary correspondence, we can show some extension results for biholomorphisms, and more general rough quasi-isometries with respect to the Kobayashi metrics between the domains.

math.CV↗

arXiv2020

Localization of the Kobayashi metric and applications

In this paper we introduce a new class of domains -- log-type convex domains, which have no boundary regularity assumptions. Then we will localize the Kobayashi metric in log-type convex subdomains. As an application, we prove a local version of continuous extension of rough isometric maps between two bounded domains with log-type convex Dini-smooth boundary points. Moreover we prove that the Teichmüller space $\mathcal T_{g,n}$ is not biholomorphic to any bounded pseudoconvex domain in $\mathbb C^{3g-3+n}$ which is locally log-type convex near some boundary point.

math.CV↗

arXiv2019

The CAT(0) geometry of convex domains with the Kobayashi metrics

Let $(Ω,K_Ω)$ be a convex domain in $\mathbb C^d$ with the Kobayashi metric $K_Ω$. In this paper we prove that $m$-convexity is a necessary condition for $(Ω, K_Ω)$ to be CAT(0) if $d=2$. Moreover, when $Ω\subset \mathbb{C}^d, \: d\geq3$, we obtain a similar result with the further smoothness assumption on its boundary.

math.CV↗

arXiv2018

Patch-based Fake Fingerprint Detection Using a Fully Convolutional Neural Network with a Small Number of Parameters and an Optimal Threshold

Fingerprint authentication is widely used in biometrics due to its simple process, but it is vulnerable to fake fingerprints. This study proposes a patch-based fake fingerprint detection method using a fully convolutional neural network with a small number of parameters and an optimal threshold to solve the above-mentioned problem. Unlike the existing methods that classify a fingerprint as live or fake, the proposed method classifies fingerprints as fake, live, or background, so preprocessing methods such as segmentation are not needed. The proposed convolutional neural network (CNN) structure applies the Fire module of SqueezeNet, and the fewer parameters used require only 2.0 MB of memory. The network that has completed training is applied to the training data in a fully convolutional way, and the optimal threshold to distinguish fake fingerprints is determined, which is used in the final test. As a result of this study experiment, the proposed method showed an average classification error of 1.35%, demonstrating a fake fingerprint detection method using a high-performance CNN with a small number of parameters.

cs.CV↗

arXiv2015

Intersection number and the stability of some inscribable graphs

A planar graph is inscribable if it is combinatorial equivalent to the skeleton of a polyhedra which is inscribed in a sphere. For an inscribable graph, in its combinatorial equivalent class, if we could always find polyhedra inscribed in any given convex surface which is sufficiently close to the sphere, then we call such an inscribable graph a stable one. By combining the Teichmüller theory of packings with differential topology method, in this paper there is investigation on the stability of some inscribable graphs.

math.MG↗

arXiv2014

How many cages midscribe an egg?

The Midscribability Theorem, which was first proved by O. Schramm, states that: given a strictly convex body $K\subset\mathbb{R}^{3}$ with smooth boundary and a convex polyhedron $P$, there exists a polyhedron $Q \subset \mathbb{RP}^3$ combinatorially equivalent to $P$ which midscribes $K$. Here the word "midscribe" means that all it's edges are tangent to the boundary surface of $K$. By using of the intersection number technique, together with the Teichmüller theory of packings, this paper provides an alternative approach to this theorem. Furthermore, combining Schramm's method with the above ones, the authors prove a rigidity result concerning this theorem as well. Namely, such a polyhedron is unique under certain normalization conditions.

math.MG↗

arXiv2014

Thermal Fluctuation-Induced Electricity Generation across a Non-Ideal Diode

We report experimentally that the electricity is generated from ambient thermal fluctuations across a non-ideal diode consisted of a silicon tip and an aluminum surface. The output is tuned by the contact force which modulates Schottky barrier heights as well as rectifying ratios of the diodes. The interaction regime between the silicon and the aluminum locates at the quantum-classical boundary where thermal fluctuations are appreciable, and the rectification of thermal fluctuations leads to the electricity generation. This finding offers an innovative approach to environmental energy harvesting.

cond-mat.mes-hall↗