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Liping Li

Publications and source records attributed to Liping Li.

At least 55 records · Page 3Linked to original sources
arXiv2024

Constructions of Waldhausen categories via Grothendieck opfibrations

Given a Grothendieck opfibration $p: \mathcal{T} \to \mathcal{B}$, we describe a method to construct a Waldhausen category structure on the total category $\mathcal{T}$ via combining Waldhausen category structures on the fibers $\mathcal{T}_A$ for $A \in \mathrm{Ob}(\mathcal{B})$ and the basis category $\mathcal{B}$. As an application, we show that if $\mathsf{E}$ is a Waldhausen category with small coproducts such that the class of cofibrations is the left part of a weak factorization system in $\mathsf{E}$, then the representation category $\mathsf{Rep}(Q, \mathsf{coE})$ of a left rooted quiver $Q$ is a Waldhausen category, where $\mathsf{coE}$ is the subcategory of $\mathsf{E}$ whose morphisms are cofibrations.

math.RT↗
arXiv2024

Early-Time Observations of SN 2023wrk: A Luminous Type Ia Supernova with Significant Unburned Carbon in the Outer Ejecta

We present extensive photometric and spectroscopic observations of the nearby Type Ia supernova (SN) 2023wrk at a distance of about 40 Mpc. The earliest detection of this SN can be traced back to a few hours after the explosion. Within the first few days the light curve shows a bump feature, while the B - V color is blue and remains nearly constant. The overall spectral evolution is similar to that of an SN 1991T/SN 1999aa-like SN Ia, while the C II $\lambda6580$ absorption line appears to be unusually strong in the first spectrum taken at $t \approx -$15.4 days after the maximum light. This carbon feature disappears quickly in subsequent evolution but it reappears at around the time of peak brightness. The complex evolution of the carbon line and the possible detection of Ni III absorption around 4700 Å and 5300 Å in the earliest spectra indicate macroscopic mixing of fuel and ash. The strong carbon lines is likely related to collision of SN ejecta with unbound carbon, consistent with the predictions of pulsational delayed-detonation or carbon-rich circumstellar-matter interaction models. Among those carbon-rich SNe Ia with strong C II $\lambda6580$ absorption at very early times, the line-strength ratio of C II to Si II and the B-V color evolution are found to exhibit large diversity, which may be attributed to different properties of unbound carbon and outward-mixing $^{56}$Ni.

astro-ph.SR↗
arXiv2024

Probing the Shock Breakout Signal of SN 2024ggi from the Transformation of Early Flash Spectroscopy

We present early-time, hour-to-day cadence spectroscopy of the nearby type II supernova (SN II) 2024ggi, which was discovered at a phase when the SN shock just emerged from the red-supergiant (RSG) progenitor star. Over the first few days after the first light, SN 2024ggi exhibited prominent narrow emission lines formed through intense and persistent photoionization of the nearby circumstellar material (CSM). In the first 63 hours, spectral lines of He, C, N, and O revealed a rapid rise in ionization, as a result of the progressive sweeping-up of the CSM by the shock. The duration of the IIn-like spectra indicates a dense and relatively confined CSM distribution extending up to $\sim 4 \times 10^{14}$ cm. Spectral modeling reveals a CSM mass loss rate at this region exceeding $5 \times 10^{-3}{\rm M}_{\odot}$ yr$^{-1}$ is required to reproduce low-ionization emissions, which dramatically exceeds that of an RSG. Analyzing H$α$ emission shift implies the velocity of the unshocked outer CSM to be between 20 and 40 km s$^{-1}$, matching the typical wind velocity of an RSG. The differences between the inner and outer layers of the CSM and an RSG progenitor highlight a complex mass loss history before the explosion of SN 2024ggi.

astro-ph.HE↗
arXiv2024

SN 2021dbg: A Luminous Type IIP-IIL Supernova Exploding from a Massive Star with a Layered Shell

We present extensive observations and analysis of supernova (SN) 2021dbg, utilizing optical photometry and spectroscopy. For approximately 385 days following the explosion, SN 2021dbg exhibited remarkable luminosity, surpassing most SNe II. This initial high luminosity is potentially attributed to the interaction between the ejected material and the surrounding circumstellar material (CSM), as evidenced by the pronounced interaction signatures observed in its spectra. The subsequent high luminosity is primarily due to the significant $^{56}$Ni ($0.17 \pm 0.05$ M$_{\odot}$) produced in the explosion. Based on the flux of flash emission lines detected in the initial spectra, we estimate that the CSM mass near the progenitor amounted to $\sim$(1.0--2.0) $\times 10^{-3}$ M$_{\odot}$, likely resulting from intense stellar wind activity 2--3 yr preceding the explosion. Considering the bolometric light curve, nebular spectrum modeling, and mass-loss rate, we suggest that the progenitor of SN 2021dbg was a red supergiant (RSG) with a mass of $\sim 20$ M$_{\odot}$ and a radius of 1200 R$_{\odot}$. This RSG featured a thick hydrogen shell, which may have contained a region with a sharp decrease in material density, electron density, and temperature, contributing to its layered structure. This object demonstrates mixed features of SNe IIP and SNe IIL, making it as a transitional event linking the above two subclasses of SNe II.

astro-ph.HE↗
arXiv2024

Flat model structures and Gorenstein objects in functor categories

We construct a flat model structure on the category $_{\mathcal{Q},R}{\mathsf{Mod}}$ of additive functors from a small preadditive category $\mathcal{Q}$ satisfying certain conditions to the module category $_{R}{\mathsf{Mod}}$ over an associative ring $R$, whose homotopy category is the $\mathcal{Q}$-shaped derived category introduced by Holm and Jorgensen. Moreover, we prove that for an arbitrary associative ring $R$, an object in $_{\mathcal{Q},R}{\mathsf{Mod}}$ is Gorenstein projective (resp., Gorenstein injective, Gorenstein flat, projective coresolving Gorenstein flat) if and only if so is its value on each object of $\mathcal{Q}$, and hence improve a result by Dell'Ambrogio, Stevenson and Šťov\'ıček.

math.RT↗
arXiv2023

Circumstellar Material Ejected Violently by A Massive Star Immediately before its Death

Type II supernovae represent the most common stellar explosions in the Universe, for which the final stage evolution of their hydrogen-rich massive progenitors towards core-collapse explosion are elusive. The recent explosion of SN 2023ixf in a very nearby galaxy, Messier 101, provides a rare opportunity to explore this longstanding issue. With the timely high-cadence flash spectra taken within 1-5 days after the explosion, we can put stringent constraints on the properties of the surrounding circumstellar material around this supernova. Based on the rapid fading of the narrow emission lines and luminosity/profile of $\rm Hα$ emission at very early times, we estimate that the progenitor of SN 2023ixf lost material at a mass-loss rate $\dot{\rm M} \approx 6 \times 10^{-4}\, \rm M_{\odot}\,a^{-1}$ over the last 2-3 years before explosion. This close-by material, moving at a velocity $v_{\rm w} \approx 55\rm \, km\,s^{-1}$, accumulates a compact CSM shell at the radius smaller than $7 \times 10^{14}$ cm from the progenitor. Given the high mass-loss rate and relatively large wind velocity presented here, together with the pre-explosion observations made about two decades ago, the progenitor of SN 2023ixf could be a short-lived yellow hypergiant that evolved from a red supergiant shortly before the explosion.

astro-ph.HE↗
arXiv2023

Representations over diagrams of abelian categories I: Global structure and homological objects

Representations over diagrams of abelian categories unify quite a few notions appearing widely in literature such as representations of categories, presheaves of modules over categories, representations of species, etc. In this series of papers we study them systematically, characterizing special homological objects in representation category and constructing various structures (such as model structures and Wandhuasen category strcutres) on it. In the first paper we investigate the Grothendieck structure of the representation category, describe important functors and adjunction relations between them, and characterize special homological objects. These results lay a foundation for our future works.

math.RT↗
arXiv2023

On the restriction of a right process outside a negligible set

The objective of this paper is to examine the restriction of a right process on a Radon topological space, excluding a negligible set, and investigate whether the restricted object can induce a Markov process with desirable properties. We address this question in three aspects: the induced process necessitates only right continuity; it is a right process, and the semi-Dirichlet form of the induced process is quasi-regular. The main findings characterize the negligible set that meets the requirements within a universally measurable framework. These characterizations can be employed to generate instances of Markov processes that are non-right or (semi-)Dirichlet forms that are non-quasi-regular. Specifically, we will construct an example of a non-tight, strong Feller, symmetric right process on a non-Lusin Radon topological space, whose Dirichlet form is not quasi-regular.

math.PR↗
arXiv2023

Galaxy Morphology Classification Using Multi-Scale Convolution Capsule Network

The classification of galaxy morphology is a hot issue in astronomical research. Although significant progress has been made in the last decade in classifying galaxy morphology using deep learning technology, there are still some deficiencies in spatial feature representation and classification accuracy. In this study, we present a multi-scale convolutional capsule network (MSCCN) model for the classification of galaxy morphology. First, this model improves the convolutional layers through using a multi-branch structure to extract multi-scale hidden features of galaxy images. In order to further explore the hidden information in the features, the multi-scale features are encapsulated and fed into the capsule layer. Second, we use a sigmoid function to replace the softmax function in dynamic routing, which can enhance the robustness of MSCCN. Finally, the classification model achieving 97% accuracy, 96% precision, 98% recall, and 97% F1-score under macroscopic averaging. In addition, a more comprehensive model evaluation were accomplished in this study. We visualized the morphological features for the part of sample set, which using the t-distributed stochastic neighbor embedding (t-SNE) algorithm. The results shows that the model has the better generalization ability and robustness, it can be effectively used in the galaxy morphological classification.

astro-ph.GA↗
arXiv2023

Fukushima subspaces of quasidiffusions

Quasidiffusions are, by definition, time-changed Brownian motions on certain closed subset of $\mathbb{R}$. They admit an explicit representation of Dirichlet forms in terms of so-called speed measures. The Fukushima subspace of a Dirichlet form means another regular Dichichlet form on the same state space but having a smaller Dirichlet space. In this paper we aim to solve the problem of Fukushima subspaces for quasidiffusions. The main result obtains all Fukushima subspaces and characterizes their structures. In addition, we will also give criteria for the uniqueness of Fukushima subspaces and the existence of minimal Fukushima subspace.

math.PR↗
arXiv2023

On generalization of quasidiffusions

A quasidiffusion is by definition a time-changed Brownian motion on certain closed subset of $\mathbb{R}$. The aim of this paper is two-fold. On one hand, we will put forward a generation of quasidiffusion, called skip-free Hunt process, by way of a pathwise setup. As an analogue of regular diffusion on an interval, a skip-free Hunt process also admits a so-called scale function and a so-called speed measure. In addition, it is uniquely determined by scale function and speed measure. Particularly, a skip-free Hunt process is a quasidiffusion, if and only if it is on the natural scale. On the other hand, we will give an analytic characterization of skip-free Hunt processes by means of Dirichlet forms. The main result shows that a so-called strongly local-like property for associated Dirichlet forms is equivalent to the skip-free property of sample paths of skip-free Hunt processes. As a byproduct, the explicit expression of Dirichlet forms associated to skip-free Hunt processes will be formulated.

math.PR↗
arXiv2023

Dirichlet form approach to diffusions with discontinuous scale

It is well known that a regular diffusion on an interval $I$ without killing inside is uniquely determined by a canonical scale function $s$ and a canonical speed measure $m$. Note that $s$ is a strictly increasing and continuous function and $m$ is a fully supported Radon measure on $I$. In this paper we will associate a general triple $(I,s,m)$, where $s$ is only assumed to be increasing and $m$ is not necessarily fully supported, to certain Markov processes by way of Dirichlet forms. A straightforward generalization of Dirichlet form associated to regular diffusion will be first put forward, and we will find out its corresponding continuous Markov process $\dot X$, for which the strong Markov property fails whenever $s$ is not continuous. Then by operating regular representations on Dirichlet form and Ray-Knight compactification on $\dot X$ respectively, the same unique desirable symmetric Hunt process associated to $(I,s,m)$ is eventually obtained. This Hunt process is homeomorphic to a quasidiffusion, which is known as a celebrated generalization of regular diffusion.

math.PR↗
arXiv2023

Predictions of photophysical properties of phosphorescent platinum(II) complexes based on ensemble machine learning approach

Phosphorescent metal complexes have been under intense investigations as emissive dopants for energy efficient organic light emitting diodes (OLEDs). Among them, cyclometalated Pt(II) complexes are widespread triplet emitters with color-tunable emissions. To render their practical applications as OLED emitters, it is in great need to develop Pt(II) complexes with high radiative decay rate constant ($k_r$) and photoluminescence (PL) quantum yield. Thus, an efficient and accurate prediction tool is highly desirable. Here, we develop a general protocol for accurate predictions of emission wavelength, radiative decay rate constant, and PL quantum yield for phosphorescent Pt(II) emitters based on the combination of first-principles quantum mechanical method, machine learning (ML) and experimental calibration. A new dataset concerning phosphorescent Pt(II) emitters is constructed, with more than two hundred samples collected from the literature. Features containing pertinent electronic properties of the complexes are chosen. Our results demonstrate that ensemble learning models combined with stacking-based approaches exhibit the best performance, where the values of squared correlation coefficients ($R^2$), mean absolute error (MAE), and root mean square error (RMSE) are 0.96, 7.21 nm and 13.00 nm for emission wavelength prediction, and 0.81, 0.11 and 0.15 for PL quantum yield prediction. For radiative decay rate constant ($k_r$), the obtained value of $R^2$ is 0.67 while MAE and RMSE are 0.21 and 0.25 (both in log scale), respectively. The accuracy of the protocol is further confirmed using 24 recently reported Pt(II) complexes, which demonstrates its reliability for a broad palette of Pt(II) emitters.We expect this protocol will become a valuable tool, accelerating the rational design of novel OLED materials with desired properties.

cs.LG↗
arXiv2022

On diffusions with discontinuous scales

It is well known that a regular diffusion on an interval $I$ without killing inside is uniquely determined by a canonical scale function $s$ and a canonical speed measure $m$. Note that $s$ is a strictly increasing and continuous function and $m$ is a fully supported Radon measure on $I$. In this paper we will associate a general triple $(I,s,m)$, where $s$ is only assumed to be increasing and $m$ is not necessarily fully supported, to certain Markov processes by way of Dirichlet forms. Using two transformations, called scale completion and darning respectively, to rebuild the topology of $I$, we will successfully regularize the triple $(I,s,m)$ and obtain a regular Dirichlet form associated with it. The corresponding Markov process is called the regularized Markov process associated with $(I,s,m)$. In fact, it is the unique Markov process up to homeomorphism that can be associated with $(I,s,m)$ in the context of regular representations of Dirichlet forms. As a byproduct of regularized Markov process, a continuous simple Markov process, which does not satisfy the strong Markov property, will be also raised to be associated to $(I,s,m)$ without operating regularizing program. Furthermore, we will show that the regularized Markov process is identified with a skip-free Hunt process in one dimension as well as a quasidiffusion without killing inside. Note that the skip-free Hunt process generalizes the concept of regular diffusion and admits a scale function and a speed measure in an analogous manner.

math.PR↗
arXiv2022

Belief-selective Propagation Detection for MIMO Systems

Compared to the linear MIMO detectors, the Belief Propagation (BP) detector has shown greater capabilities in achieving near optimal performance and better nature to iteratively cooperate with channel decoders. Aiming at real applications, recent works mainly fall into the category of reducing the complexity by simplified calculations, at the expense of performance sacrifice. However, the complexity is still unsatisfactory with exponentially increasing complexity or required exponentiation operations. Furthermore, due to the inherent loopy structure, the existing BP detectors persistently encounter error floor in high signal-to-noise ratio (SNR) region, which becomes even worse with calculation approximation. This work aims at a revised BP detector, named {Belief-selective Propagation (BsP)} detector by selectively utilizing the \emph{trusted} incoming messages with sufficiently large \textit{a priori} probabilities for updates. Two proposed strategies: symbol-based truncation (ST) and edge-based simplification (ES) squeeze the complexity (orders lower than the Original-BP), while greatly relieving the error floor issue over a wide range of antenna and modulation combinations. For the $16$-QAM $8 \times 4$ MIMO system, the $\mathcal{B}(1,1)$ {BsP} detector achieves more than $4$\,dB performance gain (@$\text{BER}=10^{-4}$) with roughly $4$ orders lower complexity than the Original-BP detector. Trade-off between performance and complexity towards different application requirement can be conveniently obtained by configuring the ST and ES parameters.

cs.IT↗
arXiv2022

On order isomorphisms intertwining semigroups for Dirichlet forms

This paper is devoted to characterizing the so-called order isomorphisms intertwining the $L^2$-semigroups of two Dirichlet forms. We first show that every unitary order isomorphism intertwining semigroups is the composition of $h$-transformation and quasi-homeomorphism. In addition, under the absolute continuity condition on Dirichlet forms, every (not necessarily unitary) order isomorphism intertwining semigroups is the composition of $h$-transformation, quasi-homeomorphism, and multiplication by a certain step function.

math.FA↗
arXiv2022

Generalizing Dirichlet-to-Neumann operators

The aim of this paper is to study the Dirichlet-to-Neumann operators in the context of Dirichlet forms and especially to figure out their probabilistic counterparts. Regarding irreducible Dirichlet forms, we will show that the Dirichlet-to-Neumann operators for them are associated with the trace Dirichlet forms corresponding to the time changed processes on the boundary. Furthermore, the Dirichlet-to-Neumann operators for perturbations of Dirichlet forms will be also explored. It turns out that for typical cases such a Dirichlet-to-Neumann operator corresponds to a quasi-regular positivity preserving (symmetric) coercive form, so that there exists a family of Markov processes associated with it via Doob's $h$-transformations.

math.PR↗