Generalized Hilbert Operator Acting on Weighted Bergman Spaces and on Dirichlet Spaces

Let $\mu$ be a positive Borel measure on the interval [0,1). For $\beta > 0$, The generalized Hankel matrix $\mathcal{H}_{\mu,\beta}= (\mu_{n,k,\beta})_{n,k\geq0}$ with entries $\mu_{n,k,\beta}= \int_{[0.1)}\frac{\Gamma(n+\beta)}{n!\Gamma(\beta)} t^{n+k}d\mu(t)$, induces formally the operator $$\mathcal{H}_{\mu,\beta}(f)(z)=\sum_{n=0}^\infty \left(\sum_{k=0}^\infty \mu_{n,k,\beta}a_k\right)z^n$$ on the space of all analytic function $f(z)=\sum_{k=0}^ \infty a_k z^n$ in the unit disc $\mathbb{D}$. In this paper, we characterize those positive Borel measures on $[0,1)$ such that $\mathcal{H}_{\mu,\beta}(f)(z)= \int_{[0,1)} \frac{f(t)}{{(1-tz)^\beta}} d\mu(t)$ for all in weighted Bergman Spaces $A_{\alpha}^p(0-1)$, and among them we describe those for which $\mathcal{H}_{\mu,\beta}(\beta>0)$ is a bounded(resp.,compact) operator on weighted Bergman spaces and Dirichlet spaces.Comment: arXiv admin note: substantial text overlap with arXiv:2206.1202

A Nearly-Linear Time Algorithm for Linear Programs with Small Treewidth: A Multiscale Representation of Robust Central Path

Arising from structural graph theory, treewidth has become a focus of study in fixed-parameter tractable algorithms in various communities including combinatorics, integer-linear programming, and numerical analysis. Many NP-hard problems are known to be solvable in $\widetilde{O}(n \cdot 2^{O(\mathrm{tw})})$ time, where $\mathrm{tw}$ is the treewidth of the input graph. Analogously, many problems in P should be solvable in $\widetilde{O}(n \cdot \mathrm{tw}^{O(1)})$ time; however, due to the lack of appropriate tools, only a few such results are currently known. [Fom+18] conjectured this to hold as broadly as all linear programs; in our paper, we show this is true: Given a linear program of the form $\min_{Ax=b,\ell \leq x\leq u} c^{\top} x$, and a width-$\tau$ tree decomposition of a graph $G_A$ related to $A$, we show how to solve it in time $$\widetilde{O}(n \cdot \tau^2 \log (1/\varepsilon)),$$ where $n$ is the number of variables and $\varepsilon$ is the relative accuracy. Combined with recent techniques in vertex-capacitated flow [BGS21], this leads to an algorithm with $\widetilde{O}(n \cdot \mathrm{tw}^2 \log (1/\varepsilon))$ run-time. Besides being the first of its kind, our algorithm has run-time nearly matching the fastest run-time for solving the sub-problem $Ax=b$ (under the assumption that no fast matrix multiplication is used). We obtain these results by combining recent techniques in interior-point methods (IPMs), sketching, and a novel representation of the solution under a multiscale basis similar to the wavelet basis

Fast Algorithms for Separable Linear Programs

In numerical linear algebra, considerable effort has been devoted to obtaining faster algorithms for linear systems whose underlying matrices exhibit structural properties. A prominent success story is the method of generalized nested dissection~[Lipton-Rose-Tarjan'79] for separable matrices. On the other hand, the majority of recent developments in the design of efficient linear program (LP) solves do not leverage the ideas underlying these faster linear system solvers nor consider the separable structure of the constraint matrix. We give a faster algorithm for separable linear programs. Specifically, we consider LPs of the form $\min_{\mathbf{A}\mathbf{x}=\mathbf{b}, \mathbf{l}\leq\mathbf{x}\leq\mathbf{u}} \mathbf{c}^\top\mathbf{x}$, where the graphical support of the constraint matrix $\mathbf{A} \in \mathbb{R}^{n\times m}$ is $O(n^\alpha)$-separable. These include flow problems on planar graphs and low treewidth matrices among others. We present an $\tilde{O}((m+m^{1/2 + 2\alpha}) \log(1/\epsilon))$ time algorithm for these LPs, where $\epsilon$ is the relative accuracy of the solution. Our new solver has two important implications: for the $k$-multicommodity flow problem on planar graphs, we obtain an algorithm running in $\tilde{O}(k^{5/2} m^{3/2})$ time in the high accuracy regime; and when the support of $\mathbf{A}$ is $O(n^\alpha)$-separable with $\alpha \leq 1/4$, our algorithm runs in $\tilde{O}(m)$ time, which is nearly optimal. The latter significantly improves upon the natural approach of combining interior point methods and nested dissection, whose time complexity is lower bounded by $\Omega(\sqrt{m}(m+m^{\alpha\omega}))=\Omega(m^{3/2})$, where $\omega$ is the matrix multiplication constant. Lastly, in the setting of low-treewidth LPs, we recover the results of [DLY,STOC21] and [GS,22] with significantly simpler data structure machinery.Comment: 55 pages. To appear at SODA 202

视觉工作记忆中数量和精度的权衡关系是否受个体自发控制

There is a negative correlation between the quality and quantity of memory representations in visual working memory, and this negative correlation is seen as a trade-off between quantity and quality. However, it is unclear whether this trade-off is entirely stimulus-driven or can be controlled voluntarily by individuals according to task demands, which has led to a debate on the mechanism of memory resource allocation. This paper systematically reviews the development of research on whether the trade-off between quantity and quality is subject to individual voluntary control, and point out this voluntary control is influenced by the exposure duration and working memory capacity, and some suggestions for future research are proposed.peerReviewe

内部注意在维度层面对视觉工作记忆的影响

Visual working memory is a memory system with limited capacity, thus internal attention plays a crucial role in selecting, controlling, and maintaining its stored content. Retro-cues are an important tool to study the influence of internal attention on visual working memory. Retro-cues are an important paradigm for studying the influence of internal attention on visual working memory. Depending on the different content of the cue, it can be divided into object-based retro-cue and dimension-based retro-cue and there are significant differences between them. The emergence of dimension-based retro-cue in recent years has become one of the hot topics of research. There are articles summarizing the research contents of object-based retro-cue, but the contents and progress of research on dimension-based retro-cue have not been sorted out and summarized. In this paper, we find that compared with object-based retro-cue, dimension-based retro-cue is more global, fragile; the effect of dimension-based retro-cue is influenced by visual dimensions, the number of memory sequences, individual differences and other factors; and the intrinsic mechanism of retro-cue benefits may be based on the reasons of preventing memory from time-based decay or taking non-target objects as the cost. Finally, we make suggestions for future directions and research.peerReviewe

A Highway In-Transit Vehicle Position Estimation Method Considering Road Characteristics and Short-Term Driving Style

Existing vehicle position estimation methods are mostly based on Global Positioning System (GPS) or a fusion of GPS and machine learning methods to realize vehicle position estimation. While highway tunnels are many, GPS signals are easy to be interfered, and the vehicle loading rate of GPS devices is limited, this kind of method can not be realized in a wide range of applications. In this context, taking into account the ETC equipment that has been deployed and applied in large scale in China, the vehicle equipment loading rate is over 90%, but the ETC gantry interval is large, and it is not possible to effectively perceive the vehicle driving status inside the segment. Therefore, this paper is based on the ETC transaction data to build the basic driving characteristics and short-term driving style of the vehicle history segment, using GPS positioning data to build the internal characteristics of the segment, including the characteristics of the road structure within the segment, the pattern of change of the vehicle position, so as to put forward the highway in-transit vehicle position estimation method that considers the road characteristics and short-term driving style. Firstly, the SC-Kmeans-Bilstm vehicle segment speed prediction model based on PCA optimization is constructed by fusing vehicle short-term driving styles; secondly, the road model within the segment is constructed by using moving average and wavelet smoothing methods; lastly, the vehicle position data is temporally stabilized using linear interpolation and first-order inverse difference, and vehicle position estimation within the highway segment is realized by using DLCNN-LSTM-ATTENTION fusion model based on L1 regularization by combining vehicle segment speeds, road characteristics, and vehicle base driving characteristics. Among them, the short-term driving style helps us to obtain the vehicle segment speed more accurately, and the addition of the road model makes this method better explain the variability of the data. The experimental results show that the present method can achieve on- travel vehicle position estimation within 2km with an error of less than 50m in a full-sample highway environment, and can provide over-the-horizon sensing for intelligent vehicles

Dynamic Identification Method for Potential Threat Vehicles beyond Line of Sight in Expressway Scenarios

Due to the challenge of limited line of sight in the perception system of intelligent driving vehicles (cameras, radar, body sensors, etc.), which can only perceive threats within a limited range, potential threats outside the line of sight cannot be fed back to the driver. Therefore, this article proposes a safety perception detection method for beyond the line of sight for intelligent driving. This method can improve driving safety, enabling drivers to perceive potential threats to vehicles in the rear areas beyond the line of sight earlier and make decisions in advance. Firstly, the electronic toll collection (ETC) transaction data are preprocessed to construct the vehicle trajectory speed dataset; then, wavelet transform (WT) is used to decompose and reconstruct the speed dataset, and lightweight gradient noosting machine learning (LightGBM) is adopted to train and learn the features of the vehicle section speed. On this basis, we also consider the features of vehicle type, traffic flow, and other characteristics, and construct a quantitative method to identify potential threat vehicles (PTVs) based on a fuzzy set to realize the dynamic safety assessment of vehicles, so as to effectively detect PTVs within the over-the-horizon range behind the driver. We simulated an expressway scenario using an ETC simulation platform to evaluate the detection of over-the-horizon PTVs. The simulation results indicate that the method can accurately detect PTVs of different types and under different road scenarios with an identification accuracy of 97.66%, which verifies the effectiveness of the method in this study. This result provides important theoretical and practical support for intelligent driving safety assistance in vehicle–road collaboration scenarios

Nested Dissection Meets IPMs: Planar Min-Cost Flow in Nearly-Linear Time

We present a nearly-linear time algorithm for finding a minimum-cost flow in planar graphs with polynomially bounded integer costs and capacities. The previous fastest algorithm for this problem was based on interior point methods (IPMs) and worked for general sparse graphs in O(n1.5 poly(log n)) time [Daitch-Spielman, STOC'08]. Intuitively, Ω(n1.5) is a natural runtime barrier for IPM based methods, since they require iterations, each routing a possibly-dense electrical flow. To break this barrier, we develop a new implicit representation for flows based on generalized nested-dissection [Lipton-Rose-Tarjan, JSTOR'79] and approximate Schur complements [Kyng-Sachdeva, FOCS'16]. This implicit representation permits us to design a data structure to route an electrical flow with sparse demands in roughly update time, resulting in a total running time of O(n · poly(log n)). Our results immediately extend to all families of separable graphs

SURGE: uncovering context-specific genetic-regulation of gene expression from single-cell RNA sequencing using latent-factor models

Abstract Genetic regulation of gene expression is a complex process, with genetic effects known to vary across cellular contexts such as cell types and environmental conditions. We developed SURGE, a method for unsupervised discovery of context-specific expression quantitative trait loci (eQTLs) from single-cell transcriptomic data. This allows discovery of the contexts or cell types modulating genetic regulation without prior knowledge. Applied to peripheral blood single-cell eQTL data, SURGE contexts capture continuous representations of distinct cell types and groupings of biologically related cell types. We demonstrate the disease-relevance of SURGE context-specific eQTLs using colocalization analysis and stratified LD-score regression

Hybrid Carbon Nanospheres with Encapsulated (Bi)Metallic Nanocrystals as Lubricant Additives for Antiwear and Friction Reduction

Herein, the novel core–shell organo-inorganic hybrid carbon nanospheres with encapsulated ultrafine bimetal nanocrystals were successfully prepared by a one-pot domino drive synthesis combined with postcarbonization. The excellent properties of the metals such as high strength and thermal conductivity are retained, and the poor dispersion of the metal in the oil could be improved by encapsulating the metal in organic–inorganic hybrid carbon nanospheres. The vanadium and wolframium nanocrystals embedded in nitrogen-doped carbon nanospheres (V/W@NCNs) manifested remarkable oil dispersity on account of the lipophilic organic phase of the carbon shell. It is worth noting that the as-obtained V/W@NCNs display better tribological properties compared with the base oil, such as a higher extreme pressure of 1250 N, a lower friction coefficient of about 0.09, and a significant reduction in wear volume of 91.5%, which are attributed to the robust protective film that was formed on the surface of the friction pair through mechanical deposition and physical and tribochemical reaction during the friction process