arXiv subjects

Yueyang Zhang

Publications and source records attributed to Yueyang Zhang.

At least 37 records · Page 2Linked to original sources

arXiv2024

GenCRF: Generative Clustering and Reformulation Framework for Enhanced Intent-Driven Information Retrieval

Query reformulation is a well-known problem in Information Retrieval (IR) aimed at enhancing single search successful completion rate by automatically modifying user's input query. Recent methods leverage Large Language Models (LLMs) to improve query reformulation, but often generate limited and redundant expansions, potentially constraining their effectiveness in capturing diverse intents. In this paper, we propose GenCRF: a Generative Clustering and Reformulation Framework to capture diverse intentions adaptively based on multiple differentiated, well-generated queries in the retrieval phase for the first time. GenCRF leverages LLMs to generate variable queries from the initial query using customized prompts, then clusters them into groups to distinctly represent diverse intents. Furthermore, the framework explores to combine diverse intents query with innovative weighted aggregation strategies to optimize retrieval performance and crucially integrates a novel Query Evaluation Rewarding Model (QERM) to refine the process through feedback loops. Empirical experiments on the BEIR benchmark demonstrate that GenCRF achieves state-of-the-art performance, surpassing previous query reformulation SOTAs by up to 12% on nDCG@10. These techniques can be adapted to various LLMs, significantly boosting retriever performance and advancing the field of Information Retrieval.

cs.IR↗

arXiv2024

Zero order meromorphic solutions of $q$-difference equations of Malmquist type

We consider the first order $q$-difference equation \begin{equation}\tag† f(qz)^n=R(z,f), \end{equation} where $q\not=0,1$ is a constant and $R(z,f)$ is rational in both arguments. When $|q|\not=1$, we show that, if $(†)$ has a zero order transcendental meromorphic solution, then $(†)$ reduces to a $q$-difference linear or Riccati equation, or to an equation that can be transformed to a $q$-difference Riccati equation. In the autonomous case, explicit meromorphic solutions of $(†)$ are presented. Given that $(†)$ can be transformed into a difference equation, we proceed to discuss the growth of the composite function $f(ω(z))$, where $ω(z)$ is an entire function satisfying $ω(z+1)=qω(z)$, and demonstrate how the proposed difference Painlevé property, as discussed in the literature, applies for $q$-difference equations.

math.CV↗

arXiv2024

Zero distribution of finite order Bank--Laine functions

It is known that a Bank-Laine function $E$ is a product of two normalized solutions of the second order differential equation $f"+Af=0$ $(\dagger)$, where $A=A(z)$ is an entire function. By using Bergweiler and Eremenko's method of constructing transcendental entire function $A(z)$ by gluing certain meromorphic functions with infinitely many times, we show that, for each $λ\in[1,\infty)$ and each $δ\in[0,1]$, there exists a Bank--Laine function $E$ such that $E=f_1f_2$ with $f_1$ and $f_2$ being two entire functions such that $λ(f_1)=δλ$ and $λ(f_2)=λ$, respectively. We actually provide a simpler construction of the special Bank--Laine functions given by Bergweiler and Eremenko.

math.CV↗

arXiv2023

On meromorphic solutions of Malmquist type difference equations

Recently, the present authors used Nevanlinna theory to provide a classification for the Malmquist type difference equations of the form $f(z+1)^n=R(z,f)$ $(†)$ that have transcendental meromorphic solutions, where $R(z,f)$ is rational in both arguments. In this paper, we first complete the classification for the case $°_{f}(R(z,f))=n$ of~$(†)$ by identifying a new equation that was left out in our previous work. We will actually derive all the equations in this case based on some new observations on~$(†)$. Then, we study the relations between $(†)$ and its differential counterpart $(f')^n=R(z,f)$. We show that most autonomous equations, singled out from~$(†)$ with $n=2$, have a natural continuum limit to either the differential Riccati equation $f'=a+f^2$ or the differential equation $(f')^2=a(f^2-τ_1^2)(f^2-τ_2^2)$, where $a\not=0$ and $τ_i$ are constants such that $τ_1^2\not=τ_2^2$. The latter second degree differential equation and the symmetric QRT map are derived from each other using the bilinear method and the continuum limit method.

math.CV↗

arXiv2023

A Malmquist--Steinmetz theorem for difference equations

It is shown that if the equation \begin{equation*} f(z+1)^n=R(z,f), \end{equation*} where $R(z,f)$ is rational in both arguments and $°_f(R(z,f))\not=n$, has a transcendental meromorphic solution, then the equation above reduces into one out of several types of difference equations where the rational term $R(z,f)$ takes particular forms. Solutions of these equations are presented in terms of Weierstrass or Jacobian elliptic functions, exponential type functions or functions which are solutions to a certain autonomous first-order difference equation having meromorphic solutions with preassigned asymptotic behavior. These results complement our previous work on the case $°_f(R(z,f))=n$ of the equation above and thus provide a complete difference analogue of Steinmetz' generalization of Malmquist's theorem.

math.CV↗

arXiv2022

On the oscillation of certain second-order linear differential equations

This paper consists of three parts: First, letting $b_1(z)$, $b_2(z)$, $p_1(z)$ and $p_2(z)$ be nonzero polynomials such that $p_1(z)$ and $p_2(z)$ have the same degree $k\geq 1$ and distinct leading coefficients $1$ and $α$, respectively, we solve entire solutions of the Tumura--Clunie type differential equation $f^{n}+P(z,f)=b_1(z)e^{p_1(z)}+b_2(z)e^{p_2(z)}$, where $n\geq 2$ is an integer, $P(z,f)$ is a differential polynomial in $f$ of degree $\leq n-1$ with coefficients having polynomial growth. Second, we study the oscillation of the second-order differential equation $f''-[b_1(z)e^{p_1(z)}+b_2(z)e^{p_2(z)}]f=0$ and prove that $α=[2(m+1)-1]/[2(m+1)]$ for some integer $m\geq 0$ if this equation admits a nontrivial solution such that $λ(f)<\infty$. This partially answers a question of Ishizaki. Finally, letting $b_2\not=0$ and $b_3$ be constants and $l$ and $s$ be relatively prime integers such that $l> s\geq 1$, we prove that $l=2$ if the equation $f''-(e^{lz}+b_2e^{sz}+b_3)f=0$ admits two linearly independent solutions $f_1$ and $f_2$ such that $\max\{λ(f_1),λ(f_2)\}<\infty$. In particular, we precisely characterize all solutions such that $λ(f)<\infty$ when $l=2$ and $l=4$.

math.CV↗

arXiv2021

On entire function $e^{p(z)}\int_0^{z}β(t)e^{-p(t)}dt$ with applications to Tumura--Clunie equations and complex dynamics

Let $p(z)$ be a nonconstant polynomial and $β(z)$ be a small entire function of $e^{p(z)}$ in the sense of Nevanlinna. We first describe the growth behavior of the entire function $H(z):=e^{p(z)}\int_0^{z}β(t)e^{-p(t)}dt$ on the complex plane $\mathbb{C}$. As an application, we solve entire solutions of Tumura--Clunie type differential equation $f(z)^n+P(z,f)=b_1(z)e^{p_1(z)}+b_2(z)e^{p_2(z)}$, where $b_1(z)$ and $b_2(z)$ are nonzero polynomials, $p_1(z)$ and $p_2(z)$ are two polynomials of the same degree~$k\geq 1$ and $P(z,f)$ is a differential polynomial in $f$ of degree $\leq n-1$ with meromorphic functions of order~$<k$ as coefficients. These results allow us to determine all solutions with relatively few zeros of the second-order differential equation $f''-[b_1(z)e^{p_1(z)}+b_2(z)e^{p_2(z)}+b_3(z)]f=0$, where $b_3(z)$ is a polynomial. We also prove a theorem on certain first-order linear differential equation related to complex dynamics.

math.CV↗

arXiv2020

TPLinker: Single-stage Joint Extraction of Entities and Relations Through Token Pair Linking

Extracting entities and relations from unstructured text has attracted increasing attention in recent years but remains challenging, due to the intrinsic difficulty in identifying overlapping relations with shared entities. Prior works show that joint learning can result in a noticeable performance gain. However, they usually involve sequential interrelated steps and suffer from the problem of exposure bias. At training time, they predict with the ground truth conditions while at inference it has to make extraction from scratch. This discrepancy leads to error accumulation. To mitigate the issue, we propose in this paper a one-stage joint extraction model, namely, TPLinker, which is capable of discovering overlapping relations sharing one or both entities while immune from the exposure bias. TPLinker formulates joint extraction as a token pair linking problem and introduces a novel handshaking tagging scheme that aligns the boundary tokens of entity pairs under each relation type. Experiment results show that TPLinker performs significantly better on overlapping and multiple relation extraction, and achieves state-of-the-art performance on two public datasets.

cs.CL↗

arXiv2019

Encoding Visual Sensitivity by MaxPol Convolution Filters for Image Sharpness Assessment

In this paper, we propose a novel design of Human Visual System (HVS) response in a convolution filter form to decompose meaningful features that are closely tied with image sharpness level. No-reference (NR) Image sharpness assessment (ISA) techniques have emerged as the standard of image quality assessment in diverse imaging applications. Despite their high correlation with subjective scoring, they are challenging for practical considerations due to high computational cost and lack of scalability across different image blurs. We bridge this gap by synthesizing the HVS response as a linear combination of Finite Impulse Response (FIR) derivative filters to boost the falloff of high band frequency magnitudes in natural imaging paradigm. The numerical implementation of the HVS filter is carried out with MaxPol filter library that can be arbitrarily set for any differential orders and cutoff frequencies to balance out the estimation of informative features and noise sensitivities. We then design an innovative NR-ISA metric called `HVS-MaxPol' that (a) requires minimal computational cost, (b) produce high correlation accuracy with image blurriness, and (c) scales to assess synthetic and natural image blur. Specifically, the synthetic blur images are constructed by blurring the raw images using Gaussian filter, while natural blur is observed from real-life application such as motion, out-of-focus, etc. Furthermore, we create a natural benchmark database in digital pathology for validation of image focus quality in whole slide imaging systems called `FocusPath' consisting of 864 blurred images. Thorough experiments are designed to test and validate the efficiency of HVS-MaxPol across different blur databases and state-of-the-art NR-ISA metrics. The experiment result indicates that our metric has the best overall performance with respect to speed, accuracy and scalability.

eess.IV↗

arXiv2018

Focus Quality Assessment of High-Throughput Whole Slide Imaging in Digital Pathology

One of the challenges facing the adoption of digital pathology workflows for clinical use is the need for automated quality control. As the scanners sometimes determine focus inaccurately, the resultant image blur deteriorates the scanned slide to the point of being unusable. Also, the scanned slide images tend to be extremely large when scanned at greater or equal 20X image resolution. Hence, for digital pathology to be clinically useful, it is necessary to use computational tools to quickly and accurately quantify the image focus quality and determine whether an image needs to be re-scanned. We propose a no-reference focus quality assessment metric specifically for digital pathology images, that operates by using a sum of even-derivative filter bases to synthesize a human visual system-like kernel, which is modeled as the inverse of the lens' point spread function. This kernel is then applied to a digital pathology image to modify high-frequency image information deteriorated by the scanner's optics and quantify the focus quality at the patch level. We show in several experiments that our method correlates better with ground-truth $z$-level data than other methods, and is more computationally efficient. We also extend our method to generate a local slide-level focus quality heatmap, which can be used for automated slide quality control, and demonstrate the utility of our method for clinical scan quality control by comparison with subjective slide quality scores.

eess.IV↗

arXiv2018

A lemma on the difference quotients

Using a new Borel type growth lemma, we extend the difference analogue of the lemma on the logarithmic derivative due to Halburd and Korhonen to the case of meromorphic functions $f(z)$ such that $\log T(r,f)\leq r/(\log r)^{2+ν}$, $ν>0$, for all sufficiently large $r$. The method by Halburd and Korhonen implies an estimate for the lemma on difference quotients, where the exceptional set is of finite logarithmic measure. We show the necessity of this set by proving that it must be of infinite linear measure for meromorphic functions whose deficiency is dependent on the choice of the origin. In addition, we show that there is an infinite sequence of $r$ in the set for which $m(r,f(z+c)/f(z))$ is not small compared to $T(r,f)$ for entire functions constructed by Miles. We also give a discrete version of Borel type growth lemma and use it to extend Halburd's result on first order discrete equations of Malmuist type.

math.CV↗

arXiv2018

Existence of meromorphic solutions of first order difference equations

It is shown that if It is shown that if \begin{equation}\label{abstract_eq} f(z+1)^n=R(z,f),\tag† \end{equation} where $R(z,f)$ is rational in $f$ with meromorphic coefficients and $°_f(R(z,f))=n$, has an admissible meromorphic solution, then either $f$ satisfies a difference linear or Riccati equation with meromorphic coefficients, or \eqref{abstract_eq} can be transformed into one in a list of ten equations with certain meromorphic or algebroid coefficients. In particular, if \eqref{abstract_eq}, where the assumption $°_f(R(z,f))=n$ has been discarded, has rational coefficients and a transcendental meromorphic solution $f$ of hyper-order $<1$, then either $f$ satisfies a difference linear or Riccati equation with rational coefficients, or \eqref{abstract_eq} can be transformed into one in a list of five equations which consists of four difference Fermat equations and one equation which is a special case of the symmetric QRT map. Solutions to all of these equations are presented in terms of Weierstrass or Jacobi elliptic functions, or in terms of meromorphic functions which are solutions to a difference Riccati equation. This provides a natural difference analogue of Steinmetz' generalization of Malmquist's theorem.

math.CV↗

arXiv2017

Test of Weak Equivalence Principle with the multi-band timing of the Crab Pulsar

Weak Equivalent Principle (WEP) can be tested through the parameterized post-Newtonian parameter $γ$, representing the space curvature produced by unit rest mass. The parameter $γ$ in turn has been constrained by comparing the arrival times of photons originating in distant transient events, such as gamma-ray bursts, fast radio bursts as well as giant pulses of pulsars. Those measurements normally correspond to an individual burst event with very limited energy bands and signal-to-noise ratio (S/N). In this letter, the discrepancy in the pulse arrival times of the Crab Pulsar between different energy bands is obtained by the phase difference between corresponding pulse profiles. This allows us to compare the pulse arrival times at the largest energy band differences, between radio and optical, radio and X-ray, radio and gamma-ray respectively. As the pulse profiles are generated by phase-folding thousands of individual pulses, the time discrepancies between two energy bands are actually measured from thousands of events at each energy band, which corresponds to much higher S/N. The upper limit of the $γ$ discrepancy set by such an extensively-observed and well-modeled source is as follows: $γ_{radio}-γ_{γ-ray}<3.28\times10^{-9}$ at the energy difference of $E_{γ-ray}/E_{radio}\sim10^{13}$, $γ_{radio}-γ_{X-ray}<4.01\times10^{-9}$ at the energy difference of $E_{X-ray}/E_{radio}\sim10^{9}$, $γ_{radio}-γ_{optical}<2.63\times10^{-9}$ at $E_{optical}/E_{radio}\sim10^{5}$, and $γ_{optical}-γ_{γ-ray}<3.03\times10^{-10}$ at $E_{γ-ray}/E_{optical}\sim10^8$. This actually measures the arrival times of freely-falling photons in the gravitational field of the Milky Way with the largest amount of events and with data of the highest S/N, which tests WEP at the energy band differences that has never been reached before.

gr-qc↗

arXiv2012

LAMOST Experiment for Galactic Understanding and Exploration (LEGUE) The survey science plan

We describe the current plans for a spectroscopic survey of millions of stars in the Milky Way galaxy using the Guo Shou Jing Telescope (GSJT, formerly the Large Area Multi-Object Spectroscopic Telescope - LAMOST). The survey will obtain spectra for 2.5 million stars brighter than $r<19$ during dark/grey time, and 5 million stars brighter than $r<17$ or $J<16$ on nights that are moonlit or have low transparency. The survey will begin in fall of 2012, and will run for at least four years. The telescope design constrains the optimal declination range for observations to $10^\circ<δ<50^\circ$, and site conditions lead to an emphasis on stars in the direction of the Galactic anticenter. The survey is divided into three parts with different target selection strategies: disk, anticenter, and spheroid. The resulting dataset will be used to study the merger history of the Milky Way, the substructure and evolution of the disks, the nature of the first generation of stars through identification of the lowest metallicity stars, and star formation through study of open clusters and the OB associations. Detailed design of the LEGUE survey will be completed after a review of the results of the pilot survey in summer 2012.

astro-ph.GA↗

arXiv2012

The site conditions of the Guo Shou Jing Telescope

The weather at Xinglong Observing Station, where the Guo Shou Jing Telescope (GSJT) is located, is strongly affected by the monsoon climate in north-east China. The LAMOST survey strategy is constrained by these weather patterns. In this paper, we present a statistics on observing hours from 2004 to 2007, and the sky brightness, seeing, and sky transparency from 1995 to 2011 at the site. We investigate effects of the site conditions on the survey plan. Operable hours each month shows strong correlation with season: on average there are 8 operable hours per night available in December, but only 1-2 hours in July and August. The seeing and the sky transparency also vary with seasons. Although the seeing is worse in windy winters, and the atmospheric extinction is worse in the spring and summer, the site is adequate for the proposed scientific program of LAMOST survey. With a Monte Carlo simulation using historical data on the site condition, we find that the available observation hours constrain the survey footprint from 22h to 16h in right ascension; the sky brightness allows LAMOST to obtain the limit magnitude of V = 19.5mag with S/N = 10.

astro-ph.IM↗

arXiv2012

The LEGUE Input Catalogue for Dark Night Observing in the LAMOST Pilot Survey

We outline the design of the dark nights portion of the LAMOST Pilot Survey, which began observations in October 2011. In particular, we focus on Milky Way stellar candidates that are targeted for the LEGUE (LAMOST Experiment for Galactic Understanding and Exploration) survey. We discuss the regions of sky in which spectroscopic candidates were selected, and the motivations for selecting each of these sky areas. Some limitations due to the unique design of the telescope are discussed, including the requirement that a bright (V < 8) star be placed at the center of each plate for wavefront sensing and active optics corrections. The target selection categories and scientific goals motivating them are briefly discussed, followed by a detailed overview of how these selection functions were realized. We illustrate the difference between the overall input catalog - Sloan Digital Sky Survey (SDSS) photometry - and the final targets selected for LAMOST observation.

astro-ph.IM↗

arXiv2012

The LEGUE High Latitude Bright Survey Design for the LAMOST Pilot Survey

We describe the footprint and input catalog for bright nights in the LAMOST Pilot Survey, which began in October 2011. Targets are selected from two stripes in the north and south Galactic Cap regions, centered at $α$= 29$^\circ$, with 10$^\circ$ width in declination, covering right ascension of 135$^\circ-290^\circ$ and -30$^\circ$ to 30$^\circ$ respectively. We selected spectroscopic targets from a combination of the SDSS and 2MASS point source catalogs. The catalog of stars defining the field centers (as required by the Shack-Hartmann wavefront sensor at the center of the LAMOST field) consists of all V < 8m stars from the Hipparcos catalog. We employ a statistical selection algorithm that assigns priorities to targets based on their positions in multidimensional color/magnitude space. This scheme overemphasizes rare objects and de-emphasizes more populated regions of magnitude and color phase space, while ensuring a smooth, well-understood selection function. A demonstration of plate design is presented based on the Shack-Hartmann star catalog and an input catalog that was generated by our target selection routines.

astro-ph.IM↗

arXiv2012

The selection of LEGUE disk targets for LAMOST's pilot survey

We describe the target selection algorithm for the low latitude disk portion of the LAMOST Pilot Survey, which aims to test systems in preparation for the LAMOST spectroscopic survey. We use the PPMXL (Roeser et al. 2010) astrometric catalog, which provides positions, proper motions, B/R/I magnitudes (mostly) from USNO-B (Monet et al. 2003) and J/H/Ks from The Two Micron All Sky Survey (2MASS, see Skrutskie et al. 2006) as well. We chose 8 plates along the Galactic plane, in the region $0^\circ<α<67^\circ$ and $42^\circ<δ<59^\circ$, that cover 22 known open clusters with a range of ages. Adjacent plates may have small overlapping. Each plate covers an area $2.5^\circ$ in radius,with central star (for Shack-Hartmann guider) brighter than $\sim8^{\rm th}$ magnitude. For each plate, we create an input catalog in the magnitude range $11.3<Imag<16.3$ and $Bmag$ available from PPMXL. The stars are selected to satisfy the requirements of the fiber positioning system and have a uniform distribution in the $I$ vs. $B-I$ color-magnitude diagram. Our final input catalog consists of 12,000 objects on each of 8 plates that are observable during the winter observing season in Xinglong Station of the National Astronomical Observatory of China.

astro-ph.GA↗