The asymptotic stable region and long-time decay rate of solutions to linear homogeneous Caputo time fractional ordinary differential equations (F-ODEs) are known to be completely determined by the eigenvalues of the coefficient matrix. Very differen
t from the exponential decay of solutions to classical ODEs, solutions of F-ODEs decay only polynomially, leading to the so-called Mittag-Leffler stability, which was already extended to semi-linear F-ODEs with small perturbations. This work is mainly devoted to the qualitative analysis of the long-time behavior of numerical solutions. By applying the singularity analysis of generating functions developed by Flajolet and Odlyzko (SIAM J. Disc. Math. 3 (1990), 216-240), we are able to prove that both $mathcal{L}$1 scheme and strong $A$-stable fractional linear multistep methods (F-LMMs) can preserve the numerical Mittag-Leffler stability for linear homogeneous F-ODEs exactly as in the continuous case. Through an improved estimate of the discrete fractional resolvent operator, we show that strong $A$-stable F-LMMs are also Mittag-Leffler stable for semi-linear F-ODEs under small perturbations. For the numerical schemes based on $alpha$-difference approximation to Caputo derivative, we establish the Mittag-Leffler stability for semi-linear problems by making use of properties of the Poisson transformation and the decay rate of the continuous fractional resolvent operator. Numerical experiments are presented for several typical time fractional evolutional equations, including time fractional sub-diffusion equations, fractional linear system and semi-linear F-ODEs. All the numerical results exhibit the typical long-time polynomial decay rate, which is fully consistent with our theoretical predictions.
This paper introduces the sixth Oriental Language Recognition (OLR) 2021 Challenge, which intends to improve the performance of language recognition systems and speech recognition systems within multilingual scenarios. The data profile, four tasks, t
wo baselines, and the evaluation principles are introduced in this paper. In addition to the Language Identification (LID) tasks, multilingual Automatic Speech Recognition (ASR) tasks are introduced to OLR 2021 Challenge for the first time. The challenge this year focuses on more practical and challenging problems, with four tasks: (1) constrained LID, (2) unconstrained LID, (3) constrained multilingual ASR, (4) unconstrained multilingual ASR. Baselines for LID tasks and multilingual ASR tasks are provided, respectively. The LID baseline system is an extended TDNN x-vector model constructed with Pytorch. A transformer-based end-to-end model is provided as the multilingual ASR baseline system. These recipes will be online published, and available for participants to construct their own LID or ASR systems. The baseline results demonstrate that those tasks are rather challenging and deserve more effort to achieve better performance.
The mass spectrum of hidden charm pentaquark states composed of two diquarks and an antiquark are calculated by use of an effective Hamiltonian which includes explicitly the spin, color, and flavor dependent interactions. The results show that the $P
_c(4312)^+$ and $P_c(4440)^+$ states could be explained as hidden charm pentaquark states with isospin and spin-parity $IJ^P=1/2left(3/2^-right)$, the $P_c(4457)^+$ state could be explained as a hidden charm pentaquark state with $IJ^P=1/2left(5/2^-right)$, and the $P_{cs}(4459)^+$ state could be explained as a hidden charm pentaquark state with $IJ^P=0left(1/2^-right)$ or $0left(3/2^-right)$. Predications for the masses of other possible pentaquark states are also given, and the possible decay channels of these hidden charm pentaquark states are discussed.
A fundamental challenge for sequential recommenders is to capture the sequential patterns of users toward modeling how users transit among items. In many practical scenarios, however, there are a great number of cold-start users with only minimal log
ged interactions. As a result, existing sequential recommendation models will lose their predictive power due to the difficulties in learning sequential patterns over users with only limited interactions. In this work, we aim to improve sequential recommendation for cold-start users with a novel framework named MetaTL, which learns to model the transition patterns of users through meta-learning. Specifically, the proposed MetaTL: (i) formulates sequential recommendation for cold-start users as a few-shot learning problem; (ii) extracts the dynamic transition patterns among users with a translation-based architecture; and (iii) adopts meta transitional learning to enable fast learning for cold-start users with only limited interactions, leading to accurate inference of sequential interactions.
Large surveys using modern telescopes are producing images that are increasing exponentially in size and quality. Identifying objects in the generated images by visual recognition is time-consuming and labor-intensive, while classifying the extracted
radio sources is even more challenging. To address these challenges, we develop a deep learning-based radio source detector, named textsc{HeTu}, which is capable of rapidly identifying and classifying radio sources in an automated manner for both compact and extended radio sources. textsc{HeTu} is based on a combination of a residual network (ResNet) and feature pyramid network (FPN). We classify radio sources into four classes based on their morphology. The training images are manually labeled and data augmentation methods are applied to solve the data imbalance between the different classes. textsc{HeTu} automatically locates the radio sources in the images and assigns them to one of the four classes. The experiment on the testing dataset shows an average operation time of 5.4 millisecond per image and a precision of 99.4% for compact point-like sources and 98.1% for double-lobe sources. We applied textsc{HeTu} to the images obtained from the GaLactic and the Galactic Extragalactic All-Object Murchison Wide-field Array (GLEAM) survey project. More than 96.9% of the textsc{HeTu}-detected compact sources are matched compared to the source finding software used in the GLEAM. We also detected and classified 2,298 extended sources (including Fanaroff-Riley type I and II sources, and core-jet sources) above $5sigma$. The cross-matching rates of extended sources are higher than 97%, showing excellent performance of textsc{HeTu} in identifying extended radio sources. textsc{HeTu} provides an efficient tool for radio source finding and classification and can be applied to other scientific fields.
The fifth Oriental Language Recognition (OLR) Challenge focuses on language recognition in a variety of complex environments to promote its development. The OLR 2020 Challenge includes three tasks: (1) cross-channel language identification, (2) diale
ct identification, and (3) noisy language identification. We choose Cavg as the principle evaluation metric, and the Equal Error Rate (EER) as the secondary metric. There were 58 teams participating in this challenge and one third of the teams submitted valid results. Compared with the best baseline, the Cavg values of Top 1 system for the three tasks were relatively reduced by 82%, 62% and 48%, respectively. This paper describes the three tasks, the database profile, and the final results. We also outline the novel approaches that improve the performance of language recognition systems most significantly, such as the utilization of auxiliary information.
Discoveries of extended rotation curves have suggested the presence of dark matter in spiral galaxy haloes. It has led to many studies that estimated the galaxy total mass, mostly by using the Navarro Frenk and White (NFW) density profile. We aim at
verifying how the choice of the dark-matter profile may affect the predicted values of extrapolated total masses. We have considered the recent Milky Way (MW) rotation curve, firstly because of its unprecedented accuracy, and secondly because the Galactic disk is amongst the least affected by past major mergers having fully reshaped the initial disk. We find that the use of NFW profile (or its generalized form, gNFW) for calculating the dark-matter contribution to the MW rotation curve generates apparently inconsistent results, e.g., an increase of the baryonic mass leads to increase of the dark matter mass. Furthermore we find that NFW and gNFW profile narrow the total mass range, leading to a possible methodological bias particularly against small MW masses. By using the Einasto profile that is more appropriate to represent cold dark matter haloes, we finally find that the Milky Way slightly decreasing rotation curve favors total mass that can be as small as 2.6 $times 10^{11}$ $M_{odot}$, disregarding any other dynamical tracers further out in the MW. It is inconsistent with values larger than 18 $times 10^{11}$ $M_{odot}$ for any kind of CDM dark-matter halo profiles, under the assumption that stars and gas do not influence the predicted dark matter distribution in the MW. This methodological paper encourages the use of the Einasto profile for characterizing rotation curves with the aim of evaluating their total masses.
Graphs are widely used to model the relational structure of data, and the research of graph machine learning (ML) has a wide spectrum of applications ranging from drug design in molecular graphs to friendship recommendation in social networks. Prevai
ling approaches for graph ML typically require abundant labeled instances in achieving satisfactory results, which is commonly infeasible in real-world scenarios since labeled data for newly emerged concepts (e.g., new categorizations of nodes) on graphs is limited. Though meta-learning has been applied to different few-shot graph learning problems, most existing efforts predominately assume that all the data from those seen classes is gold-labeled, while those methods may lose their efficacy when the seen data is weakly-labeled with severe label noise. As such, we aim to investigate a novel problem of weakly-supervised graph meta-learning for improving the model robustness in terms of knowledge transfer. To achieve this goal, we propose a new graph meta-learning framework -- Graph Hallucination Networks (Meta-GHN) in this paper. Based on a new robustness-enhanced episodic training, Meta-GHN is meta-learned to hallucinate clean node representations from weakly-labeled data and extracts highly transferable meta-knowledge, which enables the model to quickly adapt to unseen tasks with few labeled instances. Extensive experiments demonstrate the superiority of Meta-GHN over existing graph meta-learning studies on the task of weakly-supervised few-shot node classification.
Natural forking in blockchain refers to a phenomenon that there are a set of blocks at one block height at the same time, implying that various nodes have different perspectives of the main chain. Natural forking might give rise to multiple adverse i
mpacts on blockchain, jeopardizing the performance and security of the system consequently. However, the ongoing literature in analyzing natural forking is mainly from the macro point of view, which is not sufficient to incisively understand this phenomenon. In this paper, we fill this gap through leveraging the large deviation theory to conduct a microscopic study of natural forking, which resorts to investigating the instantaneous difference between block generation and dissemination in blockchain. Our work is derived comprehensively and complementarily via a three-step process, where both the natural forking probability and its decay rate are presented. Through solid theoretical derivation and extensive numerical simulations, we find 1) the probability of the mismatch between block generation and dissemination exceeding a given threshold dwindles exponentially with the increase of natural forking robustness related parameter or the difference between the block dissemination rate and block creation rate; 2) the natural forking robustness related parameter may emphasize a more dominant effect on accelerating the abortion of natural forking in some cases; 3) when the self-correlated block generation rate is depicted as the stationary autoregressive process with a scaling parameter, it is found that setting a lower scaling parameter may speed up the failure of natural forking. These findings are valuable since they offer a fresh theoretical basis to engineer optimal countermeasures for thwarting natural forking and thereby enlivening the blockchain network.
The purpose of the present study is to explore the mass spectrum of the hidden charm tetraquark states within a diquark model. Proposing that a tetraquark state is composed of a diquark and an antidiquark, the masses of all possible $[qc][bar{q}bar{c
}]$, $[sc][bar{s}bar{c}]$, and $[qc][bar{s}bar{c}]$ $left([sc][bar{q}bar{c}]right)$ hidden charm tetraquark states are systematically calculated by use of an effective Hamiltonian, which contains color, spin, and flavor dependent interactions. Apart from the $X(3872)$, $Z(3900)$, $chi_{c2}(3930)$, and $X(4350)$ which are taken as input to fix the model parameters, the calculated results support that the $chi_{c0}(3860)$, $X(4020)$, $X(4050)$ are $[qc][bar{q}bar{c}]$ states with $I^GJ^{PC}=0^+0^{++}$, $1^+1^{+-}$, and $1^-2^{++}$, respectively, the $chi_{c1}(4274)$ is an $[sc][bar{s}bar{c}]$ state with $I^GJ^{PC}=0^+1^{++}$, the $X(3940)$ is a $[qc][bar{q}bar{c}]$ state with $I^GJ^{PC}=1^-0^{++}$ or $1^-1^{++}$, the $Z_{cs}(3985)^-$ is an $[sc][bar{q}bar{c}]$ state with $J^{P}=0^{+}$ or $1^+$, and the $Z_{cs}(4000)^+$ and $Z_{cs}(4220)^+$ are $[qc][bar{s}bar{c}]$ states with $J^{P}=1^{+}$. Predictions for other possible tetraquark states are also given.
