arXiv subjects
Publications and source records attributed to Yi Zhang.
Using the tools of the Markov Decision Processes, we justify the dynamic programming approach to the optimal impulse control of deterministic dynamical systems. We prove the equivalence of the integral and differential forms of the optimality equation. The theory is illustrated by an example from mathematical epidemiology. The developed methods can be also useful for the study of piecewise deterministic Markov processes.
In this paper, we study the desingularization problem in the first $q$-Weyl algebra. We give an order bound for desingularized operators, and thus derive an algorithm for computing desingularized operators in the first $q$-Weyl algebra. Moreover, an algorithm is presented for computing a generating set of the first $q$-Weyl closure of a given $q$-difference operator. As an application, we certify that several instances of the colored Jones polynomial are Laurent polynomial sequences by computing the corresponding desingularized operator.
This paper addresses the topological structure of steady, anisotropic, inhomogeneous diffusion problems. Two discrete formulations: a) mixed and b) direct formulations are discussed. Differential operators are represented by sparse incidence matrices, while weighted mass matrices play the role of metric-dependent Hodge matrices. The resulting mixed formulations are point-wise divergence-free if the right hand side function f = 0. The method is inf-sup stable and displays optimal convergence on orthogonal and non-affine grids.
We give a polynomial-time algorithm for learning latent-state linear dynamical systems without system identification, and without assumptions on the spectral radius of the system's transition matrix. The algorithm extends the recently introduced technique of spectral filtering, previously applied only to systems with a symmetric transition matrix, using a novel convex relaxation to allow for the efficient identification of phases.
Compressive sensing (CS) has proved effective for tomographic reconstruction from sparsely collected data or under-sampled measurements, which are practically important for few-view CT, tomosynthesis, interior tomography, and so on. To perform sparse-data CT, the iterative reconstruction commonly use regularizers in the CS framework. Currently, how to choose the parameters adaptively for regularization is a major open problem. In this paper, inspired by the idea of machine learning especially deep learning, we unfold a state-of-the-art "fields of experts" based iterative reconstruction scheme up to a number of iterations for data-driven training, construct a Learned Experts' Assessment-based Reconstruction Network ("LEARN") for sparse-data CT, and demonstrate the feasibility and merits of our LEARN network. The experimental results with our proposed LEARN network produces a competitive performance with the well-known Mayo Clinic Low-Dose Challenge Dataset relative to several state-of-the-art methods, in terms of artifact reduction, feature preservation, and computational speed. This is consistent to our insight that because all the regularization terms and parameters used in the iterative reconstruction are now learned from the training data, our LEARN network utilizes application-oriented knowledge more effectively and recovers underlying images more favorably than competing algorithms. Also, the number of layers in the LEARN network is only 12, reducing the computational complexity of typical iterative algorithms by orders of magnitude.
We analyze the Sun's shadow observed with the Tibet-III air shower array and find that the shadow's center deviates northward (southward) from the optical solar disc center in the "Away" ("Toward") IMF sector. By comparing with numerical simulations based on the solar magnetic field model, we find that the average IMF strength in the "Away" ("Toward") sector is $1.54 \pm 0.21_{\rm stat} \pm 0.20_{\rm syst}$ ($1.62 \pm 0.15_{\rm stat} \pm 0.22_{\rm syst}$) times larger than the model prediction. These demonstrate that the observed Sun's shadow is a useful tool for the quantitative evaluation of the average solar magnetic field.
In recent years, finger vein recognition has become an important sub-field in biometrics and been applied to real-world applications. The development of finger vein recognition algorithms heavily depends on large-scale real-world data sets. In order to motivate research on finger vein recognition, we released the largest finger vein data set up to now and hold finger vein recognition competitions based on our data set every year. In 2017, International Competition on Finger Vein Recognition(ICFVR) is held jointly with IJCB 2017. 11 teams registered and 10 of them joined the final evaluation. The winner of this year dramatically improved the EER from 2.64% to 0.483% compared to the winner of last year. In this paper, we introduce the process and results of ICFVR 2017 and give insights on development of state-of-art finger vein recognition algorithms.
A novel predictor for traffic flow forecasting, namely spatio-temporal Bayesian network predictor, is proposed. Unlike existing methods, our approach incorporates all the spatial and temporal information available in a transportation network to carry our traffic flow forecasting of the current site. The Pearson correlation coefficient is adopted to rank the input variables (traffic flows) for prediction, and the best-first strategy is employed to select a subset as the cause nodes of a Bayesian network. Given the derived cause nodes and the corresponding effect node in the spatio-temporal Bayesian network, a Gaussian Mixture Model is applied to describe the statistical relationship between the input and output. Finally, traffic flow forecasting is performed under the criterion of Minimum Mean Square Error (M.M.S.E.). Experimental results with the urban vehicular flow data of Beijing demonstrate the effectiveness of our presented spatio-temporal Bayesian network predictor.
A linear gyrokinetic particle-in-cell scheme, which is valid for arbitrary perpendicular wavelength $k_\perpρ_i$ and includes the parallel dynamic along the field line, is developed to study the local electrostatic drift modes in point and ring dipole plasmas. We find the most unstable mode in this system can be either electron mode or ion mode. The properties and relations of these modes are studied in detail as a function of $k_\perpρ_i$, the density gradient $κ_n$, the temperature gradient $κ_T$, electron to ion temperature ratio $τ=T_e/T_i$, and mass ratio $m_i/m_e$. For conventional weak gradient parameters, the mode is on ground state (with eigenstate number $l=0$) and especially $k_\parallel\sim0$ for small $k_\perpρ_i$. Thus, bounce averaged dispersion relation is also derived for comparison. For strong gradient and large $k_\perpρ_i$, most interestingly, higher order eigenstate modes with even (e.g., $l=2,4$) or odd (e.g., $l=1$) parity can be most unstable, which is not expected by previous studies. High order eigenstate can also easily be most unstable at weak gradient when $τ>10$. This work can be particularly important to understand the turbulent transport in laboratory and space magnetosphere.
Abbreviation is a common phenomenon across languages, especially in Chinese. In most cases, if an expression can be abbreviated, its abbreviation is used more often than its fully expanded forms, since people tend to convey information in a most concise way. For various language processing tasks, abbreviation is an obstacle to improving the performance, as the textual form of an abbreviation does not express useful information, unless it's expanded to the full form. Abbreviation prediction means associating the fully expanded forms with their abbreviations. However, due to the deficiency in the abbreviation corpora, such a task is limited in current studies, especially considering general abbreviation prediction should also include those full form expressions that do not have valid abbreviations, namely the negative full forms (NFFs). Corpora incorporating negative full forms for general abbreviation prediction are few in number. In order to promote the research in this area, we build a dataset for general Chinese abbreviation prediction, which needs a few preprocessing steps, and evaluate several different models on the built dataset. The dataset is available at https://github.com/lancopku/Chinese-abbreviation-dataset
This work presents a combined experimental and theoretical study of dynamic contact angle hysteresis using liquid bridges under cyclic compression and stretching between two identical plates. Under various loading rates, contact angle hysteresis for three different liquids was measured by examination of advancing and receding angles in liquid bridges, and the capillary forces were recorded. It is found that, for a given liquid, the hysteretic phenomenon of the contact angle is more pronounced at higher loading rates. By unifying the behaviour of the three liquids, power-law correlations were proposed to describe the relationship between the dynamic contact angle and the capillary number for advancing and receding cases. It is found that the exponents of obtained power-law correlations differ from those derived through earlier methods (e.g., capillary rise), due to the different kinematics of the triple-line. The various hysteretic loops of capillary force in liquid bridges under varied cyclic loading rates were also observed, which can be captured quantitatively by the prediction of our developed model incorporating the dynamic contact angle hysteresis. These results illustrate the importance of varying triple-line geometries during dynamic wetting and dewetting processes, and warrant an improved modelling approach for higher level phenomena involving these processes, e.g., multiphase flow in porous media and liquid transfer between surfaces with moving contact lines.
After decades of progress and effort, obtaining a phase diagram for a strongly-correlated topological system still remains a challenge. Although in principle one could turn to Wilson loops and long-range entanglement, evaluating these non-local observables at many points in phase space can be prohibitively costly. With growing excitement over topological quantum computation comes the need for an efficient approach for obtaining topological phase diagrams. Here we turn to machine learning using quantum loop topography (QLT), a notion we have recently introduced. Specifically, we propose a construction of QLT that is sensitive to quasi-particle statistics. We then use mutual statistics between the spinons and visons to detect a $\mathbb{Z}_{2}$ quantum spin liquid in a multi-parameter phase space. We successfully obtain the quantum phase boundary between the topological and trivial phases using a simple feed-forward neural network. Furthermore, we demonstrate advantages of our approach for the evaluation of phase diagrams relating to speed and storage. Such statistics-based machine learning of topological phases opens new efficient routes to studying topological phase diagrams in strongly correlated systems.
This work proposes a novel location-based multi-group multicast framework which is termed as non-orthogonal multiple access (NOMA) assisted multi-region geocast. This novel spectrum sharing framework exploits the NOMA technology to realize the simultaneous delivery of different messages to different user groups characterized by different geographical locations. The essence of the proposed framework is that the geographical information of user groups unites NOMA and multi-group multicast to enhance the spectral efficiency (SE) and the energy efficiency (EE) of wireless transmissions. Specifically, we investigate the downlink beamforming design of the proposed framework in multiple-input single-output (MISO) settings. The decoding strategy for NOMA is designed and guaranteed by users' geographical information and required quality of service (QoS). The majorization and minimization (MM) algorithm is exploited to solve the non-convex and intractable problems therein. Comprehensive numerical experiments are further provided to show that NOMA holds tremendous promise but also limitations in terms of SE and EE, compared with spatial division multiple access (SDMA) and orthogonal multiple access (OMA).
Topological semimetal is a topic of general interest in material science. Recently, a new kind of topological semimetal called type-II Dirac semimetal with tilted Dirac cones is discovered in PtSe2 family. However, the further investigation is hindered due to the huge energy difference from Dirac points to Fermi level and the irrelevant conducting pockets at Fermi surface. Here we characterize the optimized type-II Dirac dispersions in a metastable 1T phase of IrTe2. Our strategy of Pt doping protects the metastable 1T phase in low temperature and tunes the Fermi level to the Dirac point. As demonstrated by angle-resolved photoemission spectra and first principle calculations, the Fermi surface of Ir1-xPtxTe2 is formed by only a single band with type-II Dirac cone which is tilted strongly along kz momentum direction. Interesting superconductivity is observed in samples for Dirac point close to Fermi level and even survives when Fermi level aligns with the Dirac point as finite density of states created by the tilted cone dispersion. This advantage offers opportunities for possible topological superconductivity and versatile Majorana devices in type-II Dirac semimetals.
Recent systems on structured prediction focus on increasing the level of structural dependencies within the model. However, our study suggests that complex structures entail high overfitting risks. To control the structure-based overfitting, we propose to conduct structure regularization decoding (SR decoding). The decoding of the complex structure model is regularized by the additionally trained simple structure model. We theoretically analyze the quantitative relations between the structural complexity and the overfitting risk. The analysis shows that complex structure models are prone to the structure-based overfitting. Empirical evaluations show that the proposed method improves the performance of the complex structure models by reducing the structure-based overfitting. On the sequence labeling tasks, the proposed method substantially improves the performance of the complex neural network models. The maximum F1 error rate reduction is 36.4% for the third-order model. The proposed method also works for the parsing task. The maximum UAS improvement is 5.5% for the tri-sibling model. The results are competitive with or better than the state-of-the-art results.
Cu2ZnSnS(e)4 (CZTS(e)) solar cells have attracted much attention due to the elemental abundance and the non-toxicity. However, the record efficiency of 12.6% for Cu2ZnSn(S,Se)4 (CZTSSe) solar cells is much lower than that of Cu(In,Ga)Se2 (CIGS) solar cells. One crucial reason is the recombination at interfaces. In recent years, large amount investigations have been done to analyze the interfacial problems and improve the interfacial properties via a variety of methods. This paper gives a review of progresses on interfaces of CZTS(e) solar cells, including: (1) the band alignment optimization at buffer/CZTS(e) interface, (2) tailoring the thickness of MoS(e)2 interfacial layers between CZTS(e) absorber and Mo back contact, (3) the passivation of rear interface, (4) the passivation of front interface, and (5) the etching of secondary phases.
We consider a piecewise deterministic Markov decision process, where the expected exponential utility of total (nonnegative) cost is to be minimized. The cost rate, transition rate and post-jump distributions are under control. The state space is Borel, and the transition and cost rates are locally integrable along the drift. Under natural conditions, we establish the optimality equation, justify the value iteration algorithm, and show the existence of a deterministic stationary optimal policy. Applied to special cases, the obtained results already significantly improve some existing results in the literature on finite horizon and infinite horizon discounted risk-sensitive continuous-time Markov decision processes.
We study a model of strongly-correlated systems that incorporates phases such as Fermi liquids, non-Fermi liquids, and superconductivity, in addition to potential intertwined orders. The model describes Fermi surfaces of spinful electron gas or electron liquid coupled to bosons via an intermediate gauge field. Effectively, the coupling imposes constraints and interactions between the fermion spin and the local boson density. This grants the bosons the meaning as the Schwinger boson of the magnetic order and allows us to probe a larger phase space, rather than around the quantum critical point. We design the initial model so that after the boson and gauge fields are integrated out exactly, the resulting fermion-only effective theory only consists of several local interactions, allowing controlled weak-coupling interpretation for certain parameter regions. Consequently, we find a non-Fermi liquid whose degrees of freedom in the effective theory take the form of an \emph{emergent} Fermi surface that has a different Luttinger volume from the original fermions, therefore explicitly violates the Luttinger theorem. Further, this allows a $d$-wave superconducting instability if the effective interacting induced by boson coupling is in the relevant pairing channel. When the emergent Fermi surface undergoes a Lifshitz transition, the carrier type changes. In addition, we attribute the Mott insulating behavior in the strong coupling limit to the loss of emergent Fermi surface and argue the possibility of coexisting magnetic order. Our effective theory also suggests the possibility of charge density waves as a consequence of \emph{effective} strong repulsion and is independent of the Fermi-surface-nesting scenario. We discuss the possible optimal conditions for higher superconducting transition temperature and potential relevances and implications for realistic materials.