arXiv subjects

Tao Yang

Publications and source records attributed to Tao Yang.

At least 307 records · Page 17Linked to original sources

arXiv2021

Exact solutions of the $C_n$ quantum spin chain

We study the exact solutions of quantum integrable model associated with the $C_n$ Lie algebra, with either a periodic or an open one with off-diagonal boundary reflections, by generalizing the nested off-diagonal Bethe ansatz method. Taking the $C_3$ as an example we demonstrate how the generalized method works. We give the fusion structures of the model and provide a way to close fusion processes. Based on the resulted operator product identities among fused transfer matrices and some necessary additional constraints such as asymptotic behaviors and relations at some special points, we obtain the eigenvalues of transfer matrices and parameterize them as homogeneous $T-Q$ relations in the periodic case or inhomogeneous ones in the open case. We also give the exact solutions of the $C_n$ model with an off-diagonal open boundary condition. The method and results in this paper can be generalized to other high rank integrable models associated with other Lie algebras.

math-ph↗

arXiv2021

Multiplicity and asymptotics of standing waves for the energy critical half-wave

In this paper, we consider the multiplicity and asymptotics of standing waves with prescribed mass $\int_{{\mathbb{R}^N}} {{u}^2}=a^2$ to the energy critical half-wave \begin{equation}\label{eqA0.1} \sqrt{-Δ}u=λu+μ|u|^{q-2} u+|u|^{2^*-2}u,\ \ u\in H^{1/2}(\R^N), \end{equation} where $N\!\geq\! 2$, $a\!>\!0$, $q \!\in\!\big(2,2+\frac{2}{N}\big)$, $2^*\!=\!\frac{2N}{N-1}$ and $λ\!\in\!\R$ appears as a Lagrange multiplier. We show that \eqref{eqA0.1} admits a ground state $u_a$ and an excited state $v_a$, which are characterised by a local minimizer and a mountain-pass critical point of the corresponding energy functional. Several asymptotic properties of $\{u_a\}$, $\{v_a\}$ are obtained and it is worth pointing out that we get a precise description of $\{u_a\}$ as $a\!\to\! 0^+$ without needing any uniqueness condition on the related limit problem. The main contribution of this paper is to extend the main results in J. Bellazzini et al. [Math. Ann. 371 (2018), 707-740] from energy subcritical to energy critical case. Furthermore, these results can be extended to the general fractional nonlinear Schrödinger equation with Sobolev critical exponent, which generalize the work of H. J. Luo-Z. T. Zhang [Calc. Var. Partial Differ. Equ. 59 (2020)] from energy subcritical to energy critical case.

math.AP↗

arXiv2021

Maximizing Marginal Fairness for Dynamic Learning to Rank

Rankings, especially those in search and recommendation systems, often determine how people access information and how information is exposed to people. Therefore, how to balance the relevance and fairness of information exposure is considered as one of the key problems for modern IR systems. As conventional ranking frameworks that myopically sorts documents with their relevance will inevitably introduce unfair result exposure, recent studies on ranking fairness mostly focus on dynamic ranking paradigms where result rankings can be adapted in real-time to support fairness in groups (i.e., races, genders, etc.). Existing studies on fairness in dynamic learning to rank, however, often achieve the overall fairness of document exposure in ranked lists by significantly sacrificing the performance of result relevance and fairness on the top results. To address this problem, we propose a fair and unbiased ranking method named Maximal Marginal Fairness (MMF). The algorithm integrates unbiased estimators for both relevance and merit-based fairness while providing an explicit controller that balances the selection of documents to maximize the marginal relevance and fairness in top-k results. Theoretical and empirical analysis shows that, with small compromises on long list fairness, our method achieves superior efficiency and effectiveness comparing to the state-of-the-art algorithms in both relevance and fairness for top-k rankings.

cs.IR↗

arXiv2021

Performance Analysis for Correlated AoI and Energy Efficiency in Heterogeneous CR-IoT System

We consider a cognitive radio based Internet of Things (CR-IoT) system where the secondary IoT device (SD) accesses the licensed channel during the transmission vacancies of the primary IoT device (PD). We focus on the impact of the IoT devices' heterogeneous traffic pattern on the energy efficiency and on the age of information (AoI) performance of the SD. We first derive closed-form expressions of the energy efficiency and the average AoI, and subsequently explore their convexity and monotonicity to the transmit power. Following these characterizations, an optimal transmit power optimization algorithm (TPOA) is proposed for the SD to maximize the energy efficiency while maintaining the average AoI under a predefined threshold. Numerical results verify the different preferences of the SD toward different PD traffic patterns, and provides insights into the tradeoff between the energy efficiency and the average AoI.

cs.IT↗

arXiv2021

g-SiC6 Monolayer: A New Graphene-like Dirac Cone Material with a High Fermi Velocity

Two-dimensional (2D) materials with Dirac cones have been intrigued by many unique properties, i.e., the effective masses of carriers close to zero and Fermi velocity of ultrahigh, which yields a great possibility in high-performance electronic devices. In this work, using first-principles calculations, we have predicted a new Dirac cone material of silicon carbide with the new stoichiometries, named g-SiC6 monolayer, which is composed of sp2 hybridized with a graphene-like structure. The detailed calculations have revealed that g-SiC6 has outstanding dynamical, thermal, and mechanical stabilities, and the mechanical and electronic properties are still isotropic. Of great interest is that the Fermi velocity of g-SiC6 monolayer is the highest in silicon carbide Dirac materials until now. The Dirac cone of the g-SiC6 is controllable by an in-plane uniaxial strain and shear strain, which is promised to realize a direct application in electronics and optoelectronics. Moreover, we found that new stoichiometries AB6 (A, B = C, Si, and Ge) compounds with the similar SiC6 monolayer structure are both dynamics stable and possess Dirac cones, and their Fermi velocity was also calculated in this paper. Given the outstanding properties of those new types of silicon carbide monolayer, which is a promising 2D material for further exploring the potential applications.

cond-mat.mtrl-sci↗

arXiv2021

A Risk-Sensitive Task Offloading Strategy for Edge Computing in Industrial Internet of Things

Edge computing has become one of the key enablers for ultra-reliable and low-latency communications in the industrial Internet of Things in the fifth generation communication systems, and is also a promising technology in the future sixth generation communication systems. In this work, we consider the application of edge computing to smart factories for mission-critical task offloading through wireless links. In such scenarios, although high end-to-end delays from the generation to completion of tasks happen with low probability, they may incur severe casualties and property loss, and should be seriously treated. Inspired by the risk management theory widely used in finance, we adopt the Conditional Value at Risk to capture the tail of the delay distribution. An upper bound of the Conditional Value at Risk is derived through analysis of the queues both at the devices and the edge computing servers. We aim to find out the optimal offloading policy taking into consideration both the average and the worst case delay performance of the system. Given that the formulated optimization problem is a non-convex mixed integer non-linear programming problem, a decomposition into sub-problems is performed and a two-stage heuristic algorithm is proposed. Simulation results validate our analysis and indicate that the proposed algorithm can reduce the risk in both the queuing and end-to-end delay.

cs.IT↗

arXiv2021

Active Anomaly Detection with Switching Cost

The problem of detecting a single anomalous process among multiple independent processes is considered. Under a constraint on the number of processes that can be probed simultaneously, the decision maker should decide which processes to probe at each time and when to terminate the probing. Compared with previous work considering only the observation costs, the switching costs of switchings across processes also need to be taken into account in many practical scenarios. The objective is an active inference strategy that minimizes the Bayesian risk taking into account of the sample complexity, switching cost, as well as detection errors. Based on the framework of sequential design of experiments, we propose a low-complexity, low-switching deterministic policy for two scenarios where the total switching cost is negligible and the total switching cost is comparable to the total observation cost. We show that the proposed algorithm is asymptotically optimal in the former scenario and is order optimal in the latter scenario. Simulation results demonstrate strong performance in the finite regime for both scenarios.

eess.SP↗

arXiv2020

TexSmart: A Text Understanding System for Fine-Grained NER and Enhanced Semantic Analysis

This technique report introduces TexSmart, a text understanding system that supports fine-grained named entity recognition (NER) and enhanced semantic analysis functionalities. Compared to most previous publicly available text understanding systems and tools, TexSmart holds some unique features. First, the NER function of TexSmart supports over 1,000 entity types, while most other public tools typically support several to (at most) dozens of entity types. Second, TexSmart introduces new semantic analysis functions like semantic expansion and deep semantic representation, that are absent in most previous systems. Third, a spectrum of algorithms (from very fast algorithms to those that are relatively slow but more accurate) are implemented for one function in TexSmart, to fulfill the requirements of different academic and industrial applications. The adoption of unsupervised or weakly-supervised algorithms is especially emphasized, with the goal of easily updating our models to include fresh data with less human annotation efforts. The main contents of this report include major functions of TexSmart, algorithms for achieving these functions, how to use the TexSmart toolkit and Web APIs, and evaluation results of some key algorithms.

cs.CL↗

arXiv2020

Thermodynamic limit of the spin-$\frac{1}{2}$ XYZ spin chain with the antiperiodic boundary condition

Based on its off-diagonal Bethe ansatz solution, we study the thermodynamic limit of the spin-$\frac{1}{2}$ XYZ spin chain with the antiperiodic boundary condition. The key point of our method is that there exist some degenerate points of the crossing parameter $η_{m,l}$, at which the associated inhomogeneous $T-Q$ relation becomes a homogeneous one. This makes extrapolating the formulae deriving from the homogeneous one to an arbitrary $η$ with $O(N^{-2})$ corrections for a large $N$ possible. The ground state energy and elementary excitations of the system are obtained. By taking the trigonometric limit, we also give the results of antiperiodic XXZ spin chain within the gapless region in the thermodynamic limit, which does not have any degenerate points.

math-ph↗

arXiv2020

Cosmography and flat $Λ$CDM tensions at high redshift

Risaliti, Lusso \& collaborators have constructed a high-redshift Hubble diagram of supernovae (SNe); quasars (QSO) and gamma-ray bursts (GRB) that shows a "$\sim 4 \, σ$ tension with the $Λ$CDM model" based on a log polynomial cosmographic expansion (Risaliti et.al 2018, Lusso et.al 2019). In this work, we demonstrate that the log polynomial expansion generically fails to recover flat $Λ$CDM beyond $z \sim 2$, thus undermining the $\sim 4 \, σ$ tension claim. Moreover, through direct fits of both the flat $Λ$CDM and the log polynomial model to the SNe+QSO+GRB dataset, we confirm that the flat $Λ$CDM model is preferred. Ultimately, we trace the tension to the QSO data and show that a best-fit of the flat $Λ$CDM model to the QSO data leads to a flat $Λ$CDM Universe with no dark energy within $1 \, σ$. This marks an irreconcilable tension between the Risaliti-Lusso QSOs and flat $Λ$CDM.

astro-ph.CO↗

arXiv2020

Normalized solutions for a fourth-order Schrödinger equation with positive second-order dispersion coefficient

We are concerned with the existence and asymptotic properties of solutions to the following fourth-order Schrödinger equation \begin{equation}\label{1} Δ^{2}u+μΔu-λu={|u|}^{p-2}u, ~~~~x \in \R^{N}\\ \end{equation} under the normalized constraint $$\int_{{\mathbb{R}^N}} {{u}^2}=a^2,$$ where $N\!\geq\!2$, $a,μ\!>\!0$, $2+\frac{8}{N}\!<\!p\!<\! 4^{*}\!=\!\frac{2N}{(N-4)^{+}}$ and $λ\in\R$ appears as a Lagrange multiplier. Since the second-order dispersion term affects the structure of the corresponding energy functional $$ E_μ(u)=\frac{1}{2}{||Δu||}_2^2-\fracμ{2}{||\nabla u||}_2^2-\frac{1}{p}{||u||}_p^p $$ we could find at least two normalized solutions to (\ref{1}) if $2\!+\!\frac{8}{N}\!<\! p\!<\!{ 4^{*} }$ and $μ^{pγ_p-2}a^{p-2}\!<\!C$ for some explicit constant $C\!=\!C(N,p)\!>\!0$ and $γ_p\!=\!\frac{N(p\!-\!2)}{4p}$. Furthermore, we give some asymptotic properties of the normalized solutions to (\ref{1}) as $μ\to0^+$ and $a\to0^+$, respectively. In conclusion, we mainly extend the results in \cite{DBon,dbJB}, which deal with (\ref{1}), from $μ\leq0$ to the case of $μ>0$, and also extend the results in \cite{TJLu,Nbal}, which deal with (\ref{1}), from $L^2$-subcritical and $L^2$-critical setting to $L^2$-supercritical setting.

math.AP↗

arXiv2020

Two-Timescale Resource Allocation for Cooperative D2D Communication: A Matching Game Approach

In this paper, we consider a cooperative device-todevice (D2D) communication system, where the D2D transmitters (DTs) act as relays to assist the densified cellular network users (CUs) for transmission quality of service (QoS) improvement. The proposed system achieves a win-win situation, i.e. improving the spectrum efficiency of the CUs that cannot meet their rate requirement while providing spectrum access for D2D pairs. Unlike previous works, to reduce the overhead, we design a novel two-timescale resource allocation scheme, in which the pairing between CUs and D2D pairs is decided at a long timescale and transmission time for CU and D2D pair is determined at a short timescale. Specifically, to characterize the long-term payoff of each potential CU-D2D pair, we investigate the optimal cooperation policy to decide the transmission time based on the instantaneous channel state information (CSI). We prove that the optimal policy is a threshold policy which can be achieved via binary search. Since CUs and D2D pairs are self-interested, they are paired only when they agree to cooperate mutually. Therefore, to study the cooperation behaviors of CUs and D2D pairs, we formulate the pairing problem as a matching game, based on the long-term payoff achieved by the optimal cooperation policy of each possible pairing. Furthermore, unlike most previous matching models in D2D networks, we allow transfer between CUs and D2D pairs to improve the performance. To solve the pairing problem, a distributed algorithm is proposed, which converges to an ε-stable matching. We show that there is a tradeoff between the optimality and the computational complexity of the algorithm. We also analyze the algorithm in terms of the robustness to the unilateral deviation of D2D pairs. Finally, the simulation results verify the efficiency of the proposed matching algorithm.

cs.IT↗

arXiv2020

Unbiased Learning to Rank: Online or Offline?

How to obtain an unbiased ranking model by learning to rank with biased user feedback is an important research question for IR. Existing work on unbiased learning to rank (ULTR) can be broadly categorized into two groups -- the studies on unbiased learning algorithms with logged data, namely the \textit{offline} unbiased learning, and the studies on unbiased parameters estimation with real-time user interactions, namely the \textit{online} learning to rank. While their definitions of \textit{unbiasness} are different, these two types of ULTR algorithms share the same goal -- to find the best models that rank documents based on their intrinsic relevance or utility. However, most studies on offline and online unbiased learning to rank are carried in parallel without detailed comparisons on their background theories and empirical performance. In this paper, we formalize the task of unbiased learning to rank and show that existing algorithms for offline unbiased learning and online learning to rank are just the two sides of the same coin. We evaluate six state-of-the-art ULTR algorithms and find that most of them can be used in both offline settings and online environments with or without minor modifications. Further, we analyze how different offline and online learning paradigms would affect the theoretical foundation and empirical effectiveness of each algorithm on both synthetic and real search data. Our findings could provide important insights and guideline for choosing and deploying ULTR algorithms in practice.

cs.IR↗

arXiv2020

$β$-As$_2$Te$_3$: Pressure-Induced 3D Dirac Semi-Metal

We report a theoretical \textit{ab-initio} study of $β$-As$_2$Te$_3$ ($R\bar{3}m$ symmetry) at hydrostatic pressures up to 12 GPa. We have systematically characterized the vibrational and electronic changes of the system induced by the pressure variation. The electronic band dispersions calculated at different pressures using \textit{QS}GW show an insulator-metal transition. At room pressure the system is a semiconductor with small band-gap, and the valence and conduction bands present a parabolic conventional dispersion. However around 2 GPa the parabolic shape of the bands become linear and touch at the Fermi level. This means that this compound undergoes a pressure-induced topological phase transition to a 3D analog of graphene, known as a 3D Dirac semi-metal, with gapless electronic excitations. At increasing pressures the gap reopens and variation of the character of the electronic band-gap from direct to indirect is evidenced. At 7 GPa we observe the formation of a negative band-gap character, which persists for pressures up to 12 GPa. Topological insulating features are evidenced from 2 to 12 GPa with a Z$_4$=3 topological index. Moreover by investigating the lattice thermal-conductivity at different pressures, we observe an ultra low value of $κ_\textrm{L}$ at 300 K for 0.5 GPa (0.294 and 0.486 Wm$^{-1}$K$^{-1}$ for the $x$-$y$-axis and for the $z$-axis, respectively) which is the result of existing low-frequency optical modes. At 2 GPa $κ_\textrm{L}$ increases to 1.170 and 0.669 Wm$^{-1}$K$^{-1}$, for the $x$-$y$-axis and for the $z$-axis, respectively. At 4 GPa the thermal-conductivity values between the two distinct crystallographic axis tend to approximate, with 1.495 and 1.433 Wm$^{-1}$K$^{-1}$, along the $x$-$y$-axis and the $z$-axis, respectively.

cond-mat.mtrl-sci↗

arXiv2020

Ground states for 3D dipolar Bose-Einstein condensate involving quantum fluctuations and three-body losses

We consider ground states of three-dimensional dipolar Bose-Einstein condensate involving quantum fluctuations and three-body losses, which can be described equivalently by positive $L^2$-constraint critical point of the Gross-Pitaevskii energy functional \[E(u)\!=\!\frac{1}{2}\int_{{\mathbb{R}^3}} {|\nabla u|}^2dx+\frac{λ_{1}}{2}\int_{{\mathbb{R}^3}} {| u|}^4dx+\frac{λ_{2}}{2} \int_{\mathbb{R}^{3}}\left(K \star|u|^{2}\right)|u|^{2} d x+\frac{2λ_{3}}{p}\int_{{\mathbb{R}^3}} {|u|}^{p}dx,\] where $2 \!0$ with $V^c_{R_0} \!:=\!\left\{u \!\in\! S_c : \big(\int_{{\mathbb{R}^3}} {{|\nabla u|}^2dx}\big)^{\frac{1}{2}} \!<\!R_0\right\}$. We show that $m(c,R_0)$ is achieved by some $u_c>0$, which is a stable ground state. Furthermore, by refining the upper bound of $m(c, R_0)$, we provide a precise description of the asymptotic behavior of $u_c$ as the mass $c$ vanishes, i.e. $${[\frac{{p|{λ_3}|}}{2{γ_c}}]^{\frac{1}{p - 2}}}{u_c}(\frac{x + {y_c}}{{\sqrt {2{δ_p}{γ_c}} }}) \to {W_p}\;\;\;\;{\rm{in}}\;\;\;\;{H^1}({\mathbb{R}^3})\;\;\;\;{\rm{for some}}\;\;\;\;{y_c} \in {\mathbb{R}^3}\;\;\;\;{\rm{as}}\;\;\;\;c \to {0^ + }.$$

math.AP↗

arXiv2020

Is there an early Universe solution to Hubble tension?

We consider a low redshift $(z<0.7)$ cosmological dataset comprising megamasers, cosmic chronometers, type Ia SNe and BAO, which we bin according to their redshift. For each bin, we read the value of $H_0$ by fitting directly to the flat $Λ$CDM model. Doing so, we find that $H_0$ descends with redshift, allowing one to fit a line with a \textit{non-zero} slope of statistical significance $2.1 \, σ$. Our analysis rests on the use of cosmic chronometers to break a degeneracy in BAO data and it will be imperative to revisit this feature as data improves. Nevertheless, our results provide the first independent indication of the descending trend reported by the H0LiCOW collaboration. If substantiated going forward, early Universe solutions to the Hubble tension will struggle explaining this trend.

astro-ph.CO↗

arXiv2020

Model-Independent Perspectives on Coupled Dark Energy and the Swampland

We present a general model-independent approach to study the coupled dark energy and the string Swampland criteria. We show how the dark sector interaction is degenerated with the equation of state of dark energy in the context of the expansion of the Universe. With priors for either of them, the dynamics of dark energy and the dark sector interactions can be reconstructed together with the bounds of the Swampland criteria. Combining cosmic chronometers, baryon acoustic oscillation (BAO), and Type Ia supernovae our results suggest a mild $1 σ$ significance of dark sector interactions at low redshift for the coupled quintessence. The Lyman-$α$ BAO at $z=2.34$ leads a $2 σ$ signal of nonzero interactions at high redshift. The implications for coupled quintessence are discussed.

astro-ph.CO↗

arXiv2020

Quantum reflection of a Bose-Einstein condensate from a rapidly varying potential: the role of dark soliton

We study the dynamic behavior of a Bose-Einstein condensate (BEC) containing a dark soliton separately reflected from potential drops and potential barriers. It is shown that for a rapidly varying potential and in a certain regime of incident velocity, the quantum reflection probability displays the cosine of the deflection angle between the incident soliton and the reflected soliton, i.e., $R(θ) \sim \cos 2θ$. For a potential drop, $R(θ)$ is susceptible to the widths of potential drop up to the length of the dark soliton and the difference of the reflection rates between the orientation angle of the soliton $θ=0$ and $θ=π/2$, $δR_s$, displays oscillating exponential decay with increasing potential widths. However, for a barrier potential, $R(θ)$ is insensitive for the potential width less than the decay length of the matter wave and $δR_s$ presents an exponential trend. This discrepancy of the reflectances in two systems is arisen from the different behaviors of matter waves in the region of potential variation.

cond-mat.quant-gas↗