arXiv subjects

Chengyuan Wu

Publications and source records attributed to Chengyuan Wu.

54 records · Page 3Linked to original sources

arXiv2020

Topological Machine Learning for Multivariate Time Series

We develop a framework for analyzing multivariate time series using topological data analysis (TDA) methods. The proposed methodology involves converting the multivariate time series to point cloud data, calculating Wasserstein distances between the persistence diagrams and using the $k$-nearest neighbors algorithm ($k$-NN) for supervised machine learning. Two methods (symmetry-breaking and anchor points) are also introduced to enable TDA to better analyze data with heterogeneous features that are sensitive to translation, rotation, or choice of coordinates. We apply our methods to room occupancy detection based on 5 time-dependent variables (temperature, humidity, light, CO2 and humidity ratio). Experimental results show that topological methods are effective in predicting room occupancy during a time window. We also apply our methods to an Activity Recognition dataset and obtained good results.

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arXiv2020

Can Helium-detonation Model Explain the Observed Diversity of Type Ia Supernovae?

We study a sample of 16 Type Ia supernovae (SNe Ia) having both spectroscopic and photometric observations within 2 $-$ 3 days after the first light. The early $B-V$ colors of such a sample tends to show a continuous distribution. For objects with normal ejecta velocity (NV), the C~II $λ$6580 feature is always visible in the early spectra while it is absent or very weak in the high-velocity (HV) counterpart. Moreover, the velocities of the detached high-velocity features (HVFs) of Ca~II NIR triplet (CaIR3) above the photosphere are found to be much higher in HV objects than in NV objects, with typical values exceeding 30,000 km~s$^{-1}$ at 2 $-$ 3 days. We further analyze the relation between %velocities of Si~II~$λ$6355 at maximum, $v_{\rm Si,max}$, the velocity shift of late-time [Fe~II] lines ($v_{\rm [Fe~II]}$) and host galaxy mass. We find that all HV objects have redshifted $v_{\rm [Fe~II]}$ while NV objects have both blue- and redshifted $v_{\rm [Fe~II]}$. It is interesting to point out that the objects with redshifted $v_{\rm [Fe~II]}$ are all located in massive galaxies, implying that HV and a portion of NV objects may have similar progenitor metallicities and explosion mechanisms. We propose that, with a geometric/projected effect, the He-detonation model may account for the similarity in birthplace environment and the differences seen in some SNe Ia, including $B-V$ colors, C~II feature, CaIR3 HVFs at early time and $v_{\rm [Fe~II]}$ in the nebular phase. Nevertheless, some features predicted by He-detonation simulation, such as the rapidly decreasing light curve, deviate from the observations, and some NV objects with blueshifted nebular $v_{\rm [Fe~II]}$ may involve other explosion mechanisms.

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arXiv2020

He-shell flashes on the surface of oxygen-neon white dwarfs

Accretion induced collapse (AIC) may be responsible for the formation of some interesting neutron star binaries, e.g., millisecond pulsars, intermediate-mass binary pulsars, etc. It has been suggested that oxygen-neon white dwarfs (ONe WDs) can increase their mass to the Chandrasekhar limit by multiple He-shell flashes, leading to AIC events. However, the properties of He-shell flashes on the surface of ONe WDs are still not well understood. In this article, we aim to study He-shell flashes on the surface of ONe WDs in a systematic approach. We investigated the long-term evolution of ONe WDs accreting He-rich material with various constant mass-accretion rates by time-dependent calculations with the stellar evolution code Modules for Experiments in Stellar Astrophysics (MESA), in which the initial ONe WD masses range from 1.1 to 1.35 M . We found that the mass-retention efficiency increases with the ONe WD mass and the mass-accretion rate, whereas both the nova cycle duration and the ignition mass decrease with the ONe WD mass and the mass-accretion rate. We also present the nuclear products in different accretion scenarios. The results presented in this article can be used in the future binary population synthesis studies of AIC events.

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arXiv2020

Topological Machine Learning for Mixed Numeric and Categorical Data

Topological data analysis is a relatively new branch of machine learning that excels in studying high dimensional data, and is theoretically known to be robust against noise. Meanwhile, data objects with mixed numeric and categorical attributes are ubiquitous in real-world applications. However, topological methods are usually applied to point cloud data, and to the best of our knowledge there is no available framework for the classification of mixed data using topological methods. In this paper, we propose a novel topological machine learning method for mixed data classification. In the proposed method, we use theory from topological data analysis such as persistent homology, persistence diagrams and Wasserstein distance to study mixed data. The performance of the proposed method is demonstrated by experiments on a real-world heart disease dataset. Experimental results show that our topological method outperforms several state-of-the-art algorithms in the prediction of heart disease.

math.AT↗

arXiv2020

A Discrete Morse Theory for Hypergraphs

A hypergraph can be obtained from a simplicial complex by deleting some non-maximal simplices. By [11], a hypergraph gives an associated simplicial complex. By [4], the embedded homology of a hypergraph is the homology of the infimum chain complex, or equivalently, the homology of the supremum chain complex. In this paper, we generalize the discrete Morse theory for simplicial complexes by R. Forman [5-7] and give a discrete Morse theory for hypergraphs. We use the critical simplices of the associated simplicial complex to construct a sub-chain complex of the infimum chain complex and a sub-chain complex of the supremum chain complex, then prove that the embedded homology of a hypergraph is isomorphic to the homology of the constructed chain complexes. Moreover, we define discrete Morse functions on hypergraphs and compute the embedded homology in terms of the critical hyperedges. As by-products, we derive some Morse inequalities and collapse results for hypergraphs.

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arXiv2020

The formation of type Ia supernovae from carbon-oxygen-silicon white dwarfs

The carbon-oxygen white dwarf (CO WD) + He star channel has been thought to be one of the promising scnarios to produce young type Ia supernovae (SNe Ia). Previous studies found that if the mass-accretion rate is greater than a critical value, the He-accreting CO WD will undergo inwardly propagating (off-centre) carbon ignition when it increases its mass close to the Chandrasekhar limit. The inwardly propagating carbon flame was supposed to reach the centre by previous works, leading to the production of an oxygen-neon (ONe) WD that may collapse into a neutron star but not an SN Ia. However, it is still uncertain how the carbon flame propagates under the effect of mixing mechanisms. In the present work, we aim to investigate the off-centre carbon burning of the He-accreting CO WDs by considering the effect of convective mixing. We found that the temperature of the flame is high enough to burn the carbon into silicon-group elements in the outer part of the CO core even if the convective overshooting is considered, but the flame would quench somewhere inside the WD, resulting in the formation of a C-O-Si WD. Owing to the inefficiency of thermohaline mixing, the C-O-Si WD may explode as an SN Ia if it continues to grow in mass. Our radiation transfer simulations show that the SN ejecta with the silicon-rich outer layer will form high-velocity absorption lines in Si II, leading to some similarities to a class of the high-velocity SNe Ia in the spectral evolution. We estimate that the birthrate of SNe Ia with Si-rich envelope is ~ 10^(-4)/yr in our galaxy.

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arXiv2020

Weighted Fundamental Group

In this paper, we develop and study the theory of weighted fundamental groups of weighted simplicial complexes. When all weights are 1, the weighted fundamental group reduces to the usual fundamental group as a special case. We also study weighted versions of classical theorems like van Kampen's theorem. In addition, we also investigate the abelianization, lower central series and applications of weighted fundamental groups.

math.AT↗

arXiv2019

Discrete Morse Theory for Weighted Simplicial Complexes

In this paper, we study Forman's discrete Morse theory in the context of weighted homology. We develop weighted versions of classical theorems in discrete Morse theory. A key difference in the weighted case is that simplicial collapses do not necessarily preserve weighted homology. We work out some sufficient conditions for collapses to preserve weighted homology, as well as study the effect of elementary removals on weighted homology. An application to sequence analysis is included, where we study the weighted ordered complexes of sequences.

math.AT↗

arXiv2019

Computational Tools in Weighted Persistent Homology

In this paper, we study further properties and applications of weighted homology and persistent homology. We introduce the Mayer-Vietoris sequence and generalized Bockstein spectral sequence for weighted homology. For applications, we show an algorithm to construct a filtration of weighted simplicial complexes from a weighted network. We also prove a theorem that allows us to calculate the mod $p^2$ weighted persistent homology given some information on the mod $p$ weighted persistent homology.

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arXiv2019

Off-centre carbon burning in He-accreting carbon-oxygen white dwarfs

The carbon-oxygen white dwarf (CO WD) + He star channel is one of the promising ways for producing type Ia supernovae (SNe Ia) with short delay times. Recent studies found that carbon under the He-shell can be ignited if the mass-accretion rate of CO WD is higher than a critical rate (about 2 * 10^-6 Msun/yr), triggering an inwardly propagating carbon flame. Previous studies usually supposed that the off-centre carbon flame would reach the centre, resulting in the formation of an oxygen-neon (ONe) WD that will collapse into a neutron star. However, the process of off-centre carbon burning is not well studied. This may result in some uncertainties on the final fates of CO WDs. By employing MESA, we simulated the long-term evolution of off-centre carbon burning in He-accreting CO WDs. We found that the inwardly propagating carbon flame transforms the CO WDs into OSi cores directly but not ONe cores owing to the high temperature of the burning front. We suggest that the final fates of the CO WDs may be OSi WDs under the conditions of off-centre carbon burning, or explode as iron-core-collapse SNe if the mass-accretion continues. We also found that the mass-fractions of silicon in the OSi cores are sensitive to the mass-accretion rates.

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arXiv2018

The outcomes of carbon-oxygen white dwarfs accreting CO-rich material

The double-degenerate model, involving the merger of double carbon-oxygen white dwarfs (CO WDs), is one of the two classic models for the progenitors of type Ia supernovae (SNe Ia). Previous studies suggested that off-centre carbon burning would occur if the mass-accretion rate (Macc) is relatively high during the merging process, leading to the formation of oxygen-neon (ONe) cores that may collapse into neutron stars. However, the off-centre carbon burning is still incompletely understood, especially when the inwardly propagating burning wave reaches the centre. In this paper, we aim to investigate the propagating characteristics of burning waves and the subsequently evolutionary outcomes of these CO cores. We simulated the long-term evolution of CO WDs that accrete CO-rich material by employing the stellar evolution code MESA on the basis of the thick-disc assumption. We found that the final outcomes of CO WDs strongly depend on Macc (Msun/yr) based on the thick-disc assumption, which can be divided into four regions: (1) explosive carbon ignition in the centre, then SNe Ia (Macc < 2.45*10^-6); (2) OSi cores, then neutron stars (2.45*10^-6 < Macc < 4.5*10^-6); (3) ONe cores, then e-capture SNe (4.5*10^-6 < Macc < 1.05*10^-5); (4) off-centre oxygen and neon ignition, then off-centre explosion or Si-Fe cores (Macc > 1.05*10^-5). Our results indicate that the final fates of double CO WD mergers are strongly dependent on the merging processes (e.g. slow merger, fast merger, composite merger, violent merger, etc.).

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arXiv2018

Hodge Decompositions for Weighted Hypergraphs

Weighted hypergraphs are generalizations of weighted simplicial complexes. In recent years, weighted Laplacians of weighted simplicial complexes have been studied. In 2016, as a generalization of the homology of simplicial complexes, the embedded homology of hypergraphs was constructed. In this paper, we generalize the weighted Laplacians of weighted simplicial complexes to weighted hypergraphs. We study the relations between the weighted Laplacians and the weighted embedded homology of weighted hypergraphs. We generalize the Hodge decompositions of weighted simplicial complexes to weighted hypergraphs. Moreover, as a complement for the Hodge decompositions, we give some results for the nonzero eigenvalues of the weighted Laplacians of weighted hypergraphs.

math.AT↗

arXiv2018

Weighted Persistent Homology

In this paper we develop the theory of weighted persistent homology. In 1990, Robert J. Dawson was the first to study in depth the homology of weighted simplicial complexes. We generalize the definitions of weighted simplicial complex and the homology of weighted simplicial complex to allow weights in an integral domain $R$. Then we study the resulting weighted persistent homology. We show that weighted persistent homology can tell apart filtrations that ordinary persistent homology does not distinguish. For example, if there is a point considered as special, weighted persistent homology can tell when a cycle containing the point is formed or has disappeared.

math.AT↗

arXiv2018

Accreting CO material onto ONe white dwarfs towards accretion-induced collapse

The final outcomes of accreting ONe white dwarfs (ONe WDs) have been studied for several decades, but there are still some issues not resolved. Recently, some studies suggested that the deflagration of oxygen would occur for accreting ONe WDs with Chandrasekhar masses. In this paper, we aim to investigate whether ONe WDs can experience accretion-induced collapse (AIC) or explosions when their masses approach the Chandrasekhar limit. Employing the stellar evolution code modules for experiments in stellar astrophysics (MESA), we simulate the long-term evolution of ONe WDs by accreting CO material. The ONe WDs undergo weak multicycle carbon flashes during the mass-accretion process, leading to the mass increase of the WDs. We found that different initial WD masses and mass-accretion rates have influence on the evolution of central density and temperature. However, the central temperature cannot reach the explosive oxygen ignition temperature due to the neutrino cooling. This work implies that the final outcome of accreting ONe WDs is electron-capture induced collapse rather than thermonuclear explosion.

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arXiv2017

Computing the Homology of Hypergraphs

Hypergraph is a topological model for networks. In order to study the topology of hypergraphs, the homology of the associated simplicial complexes and the embedded homology have been invented. In this paper, we give some algorithms to compute the homology of the associated simplicial complexes and the embedded homology of hypergraphs as well as some heuristics for efficient computations.

math.AT↗

arXiv2017

Merging of a CO WD and a He-rich white dwarf to produce a type Ia supernovae

Context: Although type Ia supernovae (SNe Ia) play a key role in astrophysics, the companions of the exploding carbon-oxygen white dwarfs (CO WDs) are still not completely identified. It has been suggested recently that a He-rich WD (a He WD or a hybrid HeCO WD) merges with a CO WD may produce an SN Ia. This theory was based on the double-detonation model, in which the shock compression in the CO core caused by the surface explosion of the He-rich shell might lead to the explosion of the whole CO WD. However, so far, very few binary population synthesis (BPS) studies have been made on the merger scenario of a CO WD and a He-rich WD in the context of SNe Ia. Aims: We aim to systematically study the Galactic birthrates and delay-time distributions of SNe Ia based on the merger scenario of a CO WD and a He-rich WD. Methods: We performed a series of Monte Carlo BPS simulations to investigate the properties of SNe Ia from the merging of a CO WD and a He-rich WD based on the Hurley rapid binary evolution code. We also considered the influence of different metallicities on the final results. Results: From our simulations, we found that no more than 15% of all SNe Ia stem from the merger scenario of a CO WD and a He-rich WD, and their delay times range from ~110 Myr to the Hubble time. This scenario mainly contributes to SN Ia explosions with intermediate and long delay times. The present work indicates that the merger scenario of a CO WD and a He-rich WD can roughly reproduce the birthrates of SN 1991bg-like events, and cover the range of their delay times. We also found that SN Ia birthrates from this scenario would be higher for the cases with low metallicities.

astro-ph.SR↗

arXiv2016

The core-degenerate scenario for the progenitors of type Ia supernovae

The origin of the progenitors of type Ia supernovae (SNe Ia) is still uncertain. The core-degenerate (CD) scenario has been proposed as an alternative way for the production of SNe Ia. In this scenario, SNe Ia are formed at the final stage of common-envelope evolution from a merger of a carbon-oxygen white dwarf (CO WD) with the CO core of an asymptotic giant branch companion. However, the birthrates of SNe Ia from this scenario are still not well determined. In this work, we performed a detailed investigation on the CD scenario based on a binary population synthesis approach. The SN Ia delay times from this scenario are basically in the range of 90Myr-2500Myr, mainly contributing to the observed SNe Ia with short and intermediate delay times although this scenario can also produce some old SNe Ia. Meanwhile, our work indicates that the Galactic birthrates of SNe Ia from this scenario are no more than 20% of total SNe Ia due to more careful treatment of mass transfer. Although the SN Ia birthrates in the present work are lower than those in Ilkov & Soker, the CD scenario cannot be ruled out as a viable mechanism for the formation of SNe Ia. Especially, SNe Ia with circumstellar material from this scenario contribute to 0.7-10% of total SNe Ia, which means that the CD scenario can reproduce the observed birthrates of SNe Ia like PTF 11kx. We also found that SNe Ia happen systemically earlier for a high value of metallicity and their birthrates increase with metallicity.

astro-ph.SR↗

arXiv2015

A super-Eddington wind scenario for the progenitors of type Ia supernovae: binary population synthesis calculations

The super-Eddington wind scenario has been proposed as an alternative way for producing type Ia supernovae (SNe Ia). The super-Eddington wind can naturally prevent the carbon--oxygen white dwarfs (CO WDs) with high mass-accretion rates from becoming red-giant-like stars. Furthermore, it works in low-metallicity environments, which may explain SNe Ia observed at high redshifts. In this article, we systematically investigated the most prominent single-degenerate WD+MS channel based on the super-Eddington wind scenario. We combined the Eggleton stellar evolution code with a rapid binary population synthesis (BPS) approach to predict SN Ia birthrates for the WD+MS channel by adopting the super-Eddington wind scenario and detailed mass-accumulation efficiencies of H-shell flashes on the WDs. Our BPS calculations found that the estimated SN Ia birthrates for the WD+MS channel are ~0.009-0.315*10^{-3}{yr}^{-1} if we adopt the Eddington accretion rate as the critical accretion rate, which are much lower than that of the observations (<10% of the observed SN Ia birthrates). This indicates that the WD+MS channel only contributes a small proportion of all SNe Ia. The birthrates in this simulation are lower than previous studies, the main reason of which is that new mass-accumulation efficiencies of H-shell flashes are adopted. We also found that the critical mass-accretion rate has a significant influence on the birthrates of SNe Ia. Meanwhile, the results of our BPS calculations are sensitive to the values of the common-envelope ejection efficiency.

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