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We present photometric and spectroscopic observations of supernova (SN) 2014C, primarily emphasizing the initial month after the explosion at approximately daily intervals. During this time, it was classified as a Type Ib SN exhibiting a notably higher peak luminosity ($L_{\rm peak}\approx4.3\times10^{42}\rm erg\,s^{-1}$), a faster rise to brightness ($t_{\rm rise} \approx 11.6$ d), and a more gradual dimming ($\Delta m_{15}^{V} \approx 0.48$ mag) compared to typical SNe Ib. Analysis of the velocity evolution over the first $\sim$ 20 days after the explosion supports the view that the absorption near 6200\AA is due to high-velocity H$\alpha$ in the outer layers of the ejecta, indicating the presence of a small amount of hydrogen in the envelope of progenitor before the explosion. Assuming the peak luminosity is entirely attributed to radioactive decay, we estimate that 0.14 ${\rm M}_{\odot}$ of$^{56}$Ni was synthesized in the explosion. However, this amount of nickel could no longer maintain observed brightness approximately ten days after peak luminosity, suggesting additional energy sources beyond radioactive decay. This supplementary energy likely originates from interaction with the circumstellar medium (CSM). Consequently, the timing of the SN-CSM interaction in SN 2014C may occur much earlier than the emergence of IIn-like features during the nebular phase., Comment: 22 pages, 15 figures, submitted to ApJ

As the role of variable renewables in electricity markets expands, new market products help system operators manage imbalances caused by uncertainty and variability. Whereas work in the last decade has focused on constructing demand curves for central procurement of those products, little attention has been paid to designing their settlement scheme and understanding the connections between the economic value of these products, the schedule of variable resources, and the cost of flexibility. In this article, we compare a new product called Flexibility Options, which addresses these gaps, with a traditional reserve product using a case study similar to the 2019 Texas (ERCOT) system. Our findings suggest that both products are equally effective in managing imbalances, but Flexibility Options have superior risk management properties and keep the system operator revenue adequate.

Reconfigurable intelligent surfaces (RIS) can actively perform beamforming and have become a crucial enabler for wireless systems in the future. The direction-of-arrival (DOA) estimates of RIS received signals can help design the reflection control matrix and improve communication quality. In this paper, we design a RIS-assisted system and propose a robust Lawson norm-based multiple-signal-classification (LN-MUSIC) DOA estimation algorithm for impulsive noise, which is divided into two parts. The first one, the non-convex Lawson norm is used as the error criterion along with a regularization constraint to formulate the optimization problem. Then, a Bregman distance based alternating direction method of multipliers is used to solve the problem and recover the desired signal. The second part is to use the multiple signal classification (MUSIC) to find out the DOAs of targets based on their sparsity in the spatial domain. In addition, we also propose a RIS control matrix optimization strategy that requires no channel state information, which effectively enhances the desired signals and improves the performance of the LN-MUSIC algorithm. A Cramer-Rao-lower-bound (CRLB) of the proposed DOA estimation algorithm is presented and verifies its feasibility. Simulated results show that the proposed robust DOA estimation algorithm based on the Lawson norm can effectively suppress the impact of large outliers caused by impulsive noise on the estimation results, outperforming existing methods., Comment: 10 figures, 28 pages

The birth-death process is a special type of continuous-time Markov chain with index set $\mathbb{N}$. Its resolvent matrix can be fully characterized by a set of parameters $(\gamma, \beta, \nu)$, where $\gamma$ and $\beta$ are non-negative constants, and $\nu$ is a positive measure on $\mathbb{N}$. By employing the Ray-Knight compactification, the birth-death process can be realized as a c\`adl\`ag process with strong Markov property on the one-point compactification space $\overline{\mathbb{N}}_{\partial}$, which includes an additional cemetery point $\partial$. In a certain sense, the three parameters that determine the birth-death process correspond to its killing, reflecting, and jumping behaviors at $\infty$ used for the one-point compactification, respectively. In general, providing a clear description of the trajectories of a birth-death process, especially in the pathological case where $|\nu|=\infty$, is challenging. This paper aims to address this issue by studying the birth-death process using approximation methods. Specifically, we will approximate the birth-death process with simpler birth-death processes that are easier to comprehend. For two typical approximation methods, our main results establish the weak convergence of a sequence of probability measures, which are induced by the approximating processes, on the space of all c\`adl\`ag functions. This type of convergence is significantly stronger than the convergence of transition matrices typically considered in the theory of continuous-time Markov chains.

The main result of this paper demonstrates that every Feller's Brownian motion, specifically, the Brownian motion with general boundary conditions as examined by Ito and McKean, can be transformed into a birth-death process through a time-change. Additionally, we have derived the parameters of the birth-death processes in terms of those associated with Feller's Brownian motion.

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 {\AA} and 5300 {\AA} 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., Comment: Accepted for publication in the Astrophysical Journal (27 pages, 14 figures, 7 tables)

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.

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.

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$\alpha$ 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., Comment: 10 pages and 5 figures in the main text (16 pages and 9 figures in total). https://iopscience.iop.org/article/10.3847/2041-8213/ad5da4

In this paper the concept of compatible weak factorization systems in general categories is introduced as a counterpart of compatible complete cotorsion pairs in abelian categories. We describe a method to construct model structures on general categories via two compatible weak factorization systems satisfying certain conditions, and hence generalize a very useful result by Gillespie for abelian model structures. As particular examples, we show that weak factorizations systems associated to some classical model structures (for example, the Kan-Quillen model structure on $\mathsf{sSet}$) satisfy these conditions., Comment: final version, to appear in Journal of Pure and Applied Algebra

In this paper we consider representations of certain combinatorial categories, including the poset $\D$ of positive integers and division, the Young lattice $\mathscr{Y}$ of partitions of finite sets, the opposite category of the orbit category $\mathscr{Z}$ of $(\mathbb{Z}, +)$ with respect to nontrivial subgroups, and the category $\mathscr{CI}$ of finite cyclic groups and injective homomorphisms. We describe explicit upper bounds for homological degrees of their representations, and deduce that finitely presented representations (resp., representations presented in finite degrees) over a field form abelian subcategories of the representation categories. We also give an explicit description for the category of sheaves over the ringed atomic site $(\mathscr{Z}, \, J_{at}, \, \underline{\mathbb{C}})$, and show that irreducible sheaves are parameterized by primitive roots of the unit.

Quasidiffusion is an extension of regular diffusion which can be described as a Feller process on $\mathbb{R}$ with infinitesimal operator $L=\frac{1}{2}D_mD_s$. Here, $s(x) = x$ and $m$ refers to the (not necessarily fully supported) speed measure. In this paper, we will examine an analogous operator where the scale function s is general and only assumed to be non-decreasing. We find that, like regular diffusion or quasidiffusion, the reproducing kernel can still be generated by two specific positive monotone solutions of the {\alpha}-harmonic equation $Lf = \alpha f$ for each $\alpha>0$. Our main result shows that this reproducing kernel is able to induce a Markov process, which is identical to that obtained in [25] using a semigroup approach or in [17] through Dirichlet forms. Further investigations into the properties of this process will be presented.

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 $\rm H\alpha$ 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., Comment: 10 pages, 6 figures in main body, Science Bulletin (Available online 14 September 2023)

This is the second one of the serial papers studying representations over diagrams of abelian categories. We show that under certain conditions a compatible family of abelian model categories indexed by a small category can amalgamate to an abelian model structure on the category of representations. Our strategy to realize this goal is to consider classes of morphisms rather than cotorsion pairs of objects. Moreover, we give an explicit description of cofibrant objects in this abelian model category. As applications, we construct Gorenstein injective and Gorenstein flat model structures on the category of presheaves of modules for a few special index categories, and give characterizations of Gorenstein homological objects in this category., Comment: arXiv admin note: text overlap with arXiv:2210.08558

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.

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.

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., Comment: arXiv admin note: substantial text overlap with arXiv:2208.02719

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., Comment: arXiv admin note: substantial text overlap with arXiv:2208.02719

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.

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.

A birth and death process is a continuous-time Markov chain with the minimal state space $\mathbb N$, whose transition matrix is standard and whose density matrix is the given birth-death matrix. Birth and death process is unique if and only if $\infty$ is an entrance or natural. When $\infty$ is neither an entrance nor natural, there are two ways in the literature to obtain all birth and death processes. The first one is an analytic treatment proposed by Feller in 1959, and the second one is a probabilistic construction completed by Wang in 1958. In this paper we will give another way to study birth and death processes using the Ray-Knight compactification. This way has the advantage of both the analytic and probabilistic treatments above. By applying the Ray-Knight compactification, every birth and death process can be modified into a c\`adl\`ag Ray process on $\mathbb N\cup \{\infty\}\cup\{\partial\}$, which is either a Doob processes or a Feller $Q$-process. Every birth and death process in the second class has a modification that is a Feller process on $\mathbb N\cup\{\infty\}\cup \{\partial\}$. We will derive the expression of its infinitesimal generator, which explains its boundary behaviours at $\infty$. Furthermore, by utilizing transformations of killing and Ikeda-Nagasawa-Watanabe's piecing out, we will also provide a probabilistic construction for birth and death processes. This construction relies on a triple determining the resolvent matrix introduced by Wang and Yang in their work (1992')}.

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 \v{S}\v{t}ov\'{\i}\v{c}ek., Comment: Final version, to appear in Proc. Roy. Soc. Edinburgh Sect. A

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., Comment: We reorganize the work in the original version as a series of papers, and this is the first one

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.

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.

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.