arXiv subjects
Publications and source records attributed to Mei Zhang.
In this paper, we consider a critical Galton-Watson branching process with immigration stopped at zero $\mathbf{W}$. Some precise estimation on the generation function of the $n$-th population are obtained, and the tail probability of the life period of $\mathbf{W}$ is studied. Based on above results, two conditional limit theorems for $\mathbf{W}$ are established.
Experiments with both qualitative and quantitative factors occur frequently in practical applications. Many construction methods for this kind of designs, such as marginally coupled designs, were proposed to pursue some good space-filling structures. However, few criteria can be adapted to quantify the space-filling property of designs involving both qualitative and quantitative factors. As the uniformity is an important space-filling property of a design, in this paper, a new uniformity criterion, qualitative-quantitative discrepancy (QQD), is proposed for assessing the uniformity of designs with both types of factors. The closed form and lower bounds of the QQD are presented to calculate the exact QQD values of designs and recognize the uniform designs directly. In addition, a connection between the QQD and the balance pattern is derived, which not only helps to obtain a new lower bound but also provides a statistical justification of the QQD. Several examples show that the proposed criterion is reasonable and useful since it can distinguish distinct designs very well.
Multi-wavelength observations of prominence eruptions provide an opportunity to uncover the physical mechanism of the triggering and the evolution process of the eruption. In this paper, we investigated an erupting prominence on October 14, 2012, recorded in Hα, EUV, and X-ray wavelengths. The process of the eruption gives evidences on the existence of a helical magnetic structure and showing the twist being converting to writhe. The estimated twist is ~6π (3 turns), exceeding the threshold of the kink instability. The rising plasma then reached a high speed, estimated at 228 km s-1, followed by a sudden rapid acceleration at 2715 m s-2, and synchronous with a solar are. Co-spatial cusp shaped structures were observed in both AIA 131Å and 94Å images, signifying the location of the magnetic reconnection. The erupted flux rope finally undergone a deceleration with a maximum value of 391 m s-2, which is even larger than the free-fall acceleration on the Sun (273 m s-2) , suggesting that the eruption finally failed, possibly due to an inward magnetic tension force.
Filaments are very common physical phenomena on the Sun and are often taken as important proxies of solar magnetic activities. The study of filaments has become a hot topic in the space weather research. For a more comprehensive understanding of filaments, especially for an understanding of solar activities of multiple solar cycles, it is necessary to perform a combined multifeature analysis by constructing a data set of multiple solar cycle data. To achieve this goal, we constructed a centennial data set that covers the H$α$ data from five observatories around the world. During the data set construction, we encountered varieties of problems, such as data fusion, accurate determination of the solar edge, classifying data by quality, dynamic threshold, and so on, which arose mainly due to multiple sources and a large time span of data. But fortunately, these problems were well solved. The data set includes seven types of data products and eight types of feature parameters with which we can implement the functions of data searching and statistical analyses. It has the characteristics of better continuity and highly complementary to space observation data, especially in the wavelengths not covered by space observations, and covers many solar cycles (including more than 60 yr of high-cadence data). We expect that this new comprehensive data set as well as the tools will help researchers to significantly speed up their search for features or events of interest, for either statistical or case study purposes, and possibly help them get a better and more comprehensive understanding of solar filament mechanisms.
Extreme public health interventions play a critical role in mitigating the local and global prevalence and pandemic potential of COVID-19. Here, we use population size for pathogen transmission to measure the intensity of public health interventions, which is a key characteristic variable for nowcasting and forecasting of the epidemic. By formulating a hidden Markov dynamic system and using nonlinear filtering theory, we have developed a stochastic epidemic dynamic model under public health interventions. The model parameters and states are estimated in time from internationally available public data by combining an unscented filter and an interacting multiple model filter. Moreover, we consider the computability of the population size and provide its selection criterion. We estimate the mean of the basic reproductive number of China and the rest of the globe except China (GEC) to be 2.46 (95% CI: 2.41-2.51) and 3.64 (95% CI: (3.55-3.72), respectively. We infer that the number of latent infections of GEC is about 7.47*10^5 (95% CI: 7.32*10^5-7.62*10^5) as of April 2, 2020. We predict that the peak of infections in hospitals of GEC may reach 3.00*10^6 on the present trajectory, i.e., if the population size for pathogen transmission and epidemic parameters remains unchanged. If the control intensity is strengthened, e.g., 50% reduction or 75% reduction of the population size for pathogen transmission, the peak would decline to 1.84*10^6, 1.27*10^6, respectively.
In this paper, a critical Galton-Watson branching process with immigration $Z_{n}$ is studied. We first obtain the convergence rate of the harmonic moment of $Z_{n}$. Then the large deviation of $S_{Z_n}:=\sum_{i=1}^{Z_n} X_i$ is obtained, where $\{X_i\}$ is a sequence of independent and identically distributed zero-mean random variables with tail index $α>2$. We shall see that the converging rate is determined by the immigration mean, the variance of reproducing and the tail index of $X_1^+$, comparing to previous result for supercritical case, where the rate depends on the Schröder constant and the tail index.
White-light flares (WLFs), first observed in 1859, refer to a type of solar flares showing an obvious enhancement of the visible continuum emission. This type of enhancement often occurs in most energetic flares, and is usually interpreted as a consequence of efficient heating in the lower solar atmosphere through non-thermal electrons propagating downward from the energy release site in the corona. However, this coronal-reconnection model has difficulty in explaining the recently discovered small WLFs. Here we report a C2.3 white-light flare, which are associated with several observational phenomena: fast decrease in opposite-polarity photospheric magnetic fluxes, disappearance of two adjacent pores, significant heating of the lower chromosphere, negligible increase of hard X-ray flux, and an associated U-shaped magnetic field configuration. All these suggest that this white-light flare is powered by magnetic reconnection in the lower part of the solar atmosphere rather than by reconnection higher up in the corona.
We consider subcritical branching processes with immigration which evolve under the influence of a random environment and study the tail distribution of life periods of such processes defined as the length of the time interval between the moment when first invader (or invaders) came to an empty site until the moment when the site becomes empty again. We prove that the tail distribution decays with exponential rate. The main tools are the change of measure and some conditional limit theorems for random walks.
We theoretically study the longitudinal relaxation of a nitrogen-vacancy (NV) center surrounded by a 13C nuclear spin bath in diamond. By incorporating electron spin in the cluster, we generalize the cluster-correlation expansion (CCE) to theoretically simulate the population dynamics of electron spin of NV center. By means of the generalized CCE, we numerically demonstrate the decay process of electronic state induced by cross relaxation at the ambient temperature. It is shown that the CCE method is not only capable of describing pure-dephasing effect at large-detuning regime, but it can also simulate the quantum dynamics of populations in the nearly-resonant regime.
Natural language question answering over knowledge graphs is an important and interesting task as it enables common users to gain accurate answers in an easy and intuitive manner. However, it remains a challenge to bridge the gap between unstructured questions and structured knowledge graphs. To address the problem, a natural discipline is building a structured query to represent the input question. Searching the structured query over the knowledge graph can produce answers to the question. Distinct from the existing methods that are based on semantic parsing or templates, we propose an effective approach powered by a novel notion, structural query pattern, in this paper. Given an input question, we first generate its query sketch that is compatible with the underlying structure of the knowledge graph. Then, we complete the query graph by labeling the nodes and edges under the guidance of the structural query pattern. Finally, answers can be retrieved by executing the constructed query graph over the knowledge graph. Evaluations on three question answering benchmarks show that our proposed approach outperforms state-of-the-art methods significantly.
Given a natural language phrase, relation linking aims to find a relation (predicate or property) from the underlying knowledge graph to match the phrase. It is very useful in many applications, such as natural language question answering, personalized recommendation and text summarization. However, the previous relation linking algorithms usually produce a single relation for the input phrase and pay little attention to a more general and challenging problem, i.e., combinational relation linking that extracts a subgraph pattern to match the compound phrase (e.g. mother-in-law). In this paper, we focus on the task of combinational relation linking over knowledge graphs. To resolve the problem, we design a systematic method based on the data-driven relation assembly technique, which is performed under the guidance of meta patterns. We also introduce external knowledge to enhance the system understanding ability. Finally, we conduct extensive experiments over the real knowledge graph to study the performance of the proposed method.
In this paper, we prove the energy conservation for the weak solutions to the three-dimensional equations of compressible magnetohydrodynamic flows (MHD) under certain conditions only about density and velocity. This work is inspired by the seminal work by Yu [27] on the energy conservation of compressible Navier-Stokes equations. Our result indicates that even the magnetic field is taken into account, we only need some regularity conditions of the density and velocity as in [27] to ensure the energy conservation.
A critical branching process with immigration which evolve in a random environment is considered. Assuming that immigration is not allowed when there are no individuals in the aboriginal population we investigate the tail distribution of the so-called life period of the process, i.e., the length of the time interval between the moment when the process is initiated by a positive number of particles and the moment when there are no individuals in the population for the first time.
Hyperentangled Bell-state analysis (HBSA) is critical for high-capacity quantum communication. Here we design two effective schemes for error-heralded deterministic generation and self-assisted complete analysis of hyperentangled Bell states for two-photon systems in both the polarization and spatial-mode degrees of freedom, assisted by single-sided quantum-dot-cavity systems. We construct an error-heralded block with a singly charged quantum dot inside a single-sided optical microcavity, two circular polarization beam splitters, one half-wave plate, and one single-photon detector, in which the errors due to imperfect interactions between photons and quantum dot systems can be heralded. With this error-heralded block, the fidelity of our two schemes for hyperentangled Bell-state generation and complete HBSA can reach unit one. What interesting is that by using the measured spatial-mode state to assist the analysis of the polarization state, our complete HBSA scheme works in a self-assisted way, which greatly simplifies the analysis process and largely relaxes the requirements on nonlinearities. These advantages make our schemes much easier to implement experimentally, and have more practical applications in long-distance high-capacity quantum communication.
We consider a branching random walk with an absorbing barrier, where the step of the associated one-dimensional random walk is in the domain of attraction of an $α$-stable law with $1<α<2$. We shall prove that there is a barrier $an^{\frac{1}{1+α}}$ and a critical value $a_α$ such that if $a a_α$, then the process survives. The results generalize previous results in literature for the case $α=2$.
The light curves of solar-type stars present both periodic fluctuation and flare spikes. The gradual periodic fluctuation is interpreted as the rotational modulation of magnetic features on the stellar surface and is used to deduce magnetic feature activity properties. The flare spikes in light curves are used to derive flare activity properties. In this paper, we analyze the light curve data of three solar-type stars (KIC 6034120, KIC 3118883, and KIC 10528093) observed with Kepler space telescope and investigate the relationship between their magnetic feature activities and flare activities. The analysis shows that: (1) both the magnetic feature activity and the flare activity exhibit long-term variations as the Sun does; (2) unlike the Sun, the long-term variations of magnetic feature activity and flare activity are not in phase with each other; (3) the analysis of star KIC 6034120 suggests that the long-term variations of magnetic feature activity and flare activity have a similar cycle length. Our analysis and results indicate that the magnetic features that dominate rotational modulation and the flares possibly have different source regions, although they may be influenced by the magnetic field generated through a same dynamo process.
In this paper, a branching random walk $(V(x))$ in the boundary case is studied, where the associated one dimensional random walk is in the domain of attraction of an $α-$stable law with $1<α<2$. Let $M_n$ be the minimal position of $(V(x))$ at generation $n$. We established an integral test to describe the lower limit of $M_n-\frac{1}α\log n$ and a law of iterated logarithm for the upper limit of $M_n-(1+\frac{1}α)\log n$.
In this paper, we investigate the asymptotic behaviors of the critical branching process with immigration $\{Z_n, n\ge 0\}$. First we get some estimation for the probability generating function of $Z_n$. Based on it, we get a large deviation for $Z_{n+1}/Z_n$. Lower and upper deviations for $Z_n$ are also studied. As a by-product, an upper deviation for $\max_{1\le i\le n} Z_i$ is obtained.