arXiv subjects
Publications and source records attributed to Yuan Gao.
This work considers the rigorous derivation of continuum models of step motion starting from a mesoscopic Burton-Cabrera-Frank (BCF) type model following the work [Xiang, SIAM J. Appl. Math. 2002]. We prove that as the lattice parameter goes to zero, for a finite time interval, a modified discrete model converges to the strong solution of the limiting PDE with first order convergence rate.
Many man-made objects have intrinsic symmetries and Manhattan structure. By assuming an orthographic projection model, this paper addresses the estimation of 3D structures and camera projection using symmetry and/or Manhattan structure cues, which occur when the input is single- or multiple-image from the same category, e.g., multiple different cars. Specifically, analysis on the single image case implies that Manhattan alone is sufficient to recover the camera projection, and then the 3D structure can be reconstructed uniquely exploiting symmetry. However, Manhattan structure can be difficult to observe from a single image due to occlusion. To this end, we extend to the multiple-image case which can also exploit symmetry but does not require Manhattan axes. We propose a novel rigid structure from motion method, exploiting symmetry and using multiple images from the same category as input. Experimental results on the Pascal3D+ dataset show that our method significantly outperforms baseline methods.
This paper addresses the problem of face recognition when there is only few, or even only a single, labeled examples of the face that we wish to recognize. Moreover, these examples are typically corrupted by nuisance variables, both linear (i.e., additive nuisance variables such as bad lighting, wearing of glasses) and non-linear (i.e., non-additive pixel-wise nuisance variables such as expression changes). The small number of labeled examples means that it is hard to remove these nuisance variables between the training and testing faces to obtain good recognition performance. To address the problem we propose a method called Semi-Supervised Sparse Representation based Classification (S$^3$RC). This is based on recent work on sparsity where faces are represented in terms of two dictionaries: a gallery dictionary consisting of one or more examples of each person, and a variation dictionary representing linear nuisance variables (e.g., different lighting conditions, different glasses). The main idea is that (i) we use the variation dictionary to characterize the linear nuisance variables via the sparsity framework, then (ii) prototype face images are estimated as a gallery dictionary via a Gaussian Mixture Model (GMM), with mixed labeled and unlabeled samples in a semi-supervised manner, to deal with the non-linear nuisance variations between labeled and unlabeled samples. We have done experiments with insufficient labeled samples, even when there is only a single labeled sample per person. Our results on the AR, Multi-PIE, CAS-PEAL, and LFW databases demonstrate that the proposed method is able to deliver significantly improved performance over existing methods.
We study Lagrangian correspondences between Liouville manifolds and construct functors between wrapped Fukaya categories. The study naturally brings up the question on comparing two versions of wrapped Fukaya categories of the product manifold, which we prove quasi-isomorphism on the level of wrapped Floer cohomology. To prove representability of these functors constructed from Lagrangian correspondences, we introduce the geometric compositions of Lagrangian correspondences under wrapping, as new classes of objects in the wrapped Fukaya category, which we prove to represent the functors by establishing a canonical isomorphism of quilted version of wrapped Floer cohomology under geometric composition.
Generalized matrix-fractional (GMF) functions are a class of matrix support functions introduced by Burke and Hoheisel as a tool for unifying a range of seemingly divergent matrix optimization problems associated with inverse problems, regularization and learning. In this paper we dramatically simplify the support function representation for GMF functions as well as the representation of their subdifferentials. These new representations allow the ready computation of a range of important related geometric objects whose formulations were previously unavailable.
Motivated by a model proposed by Peng et al. [Advances in Coll. and Interf. Sci. 206 (2014)] for break-up of tear films on human eyes, we study the dynamics of a generalized thin film model. The governing equations form a fourth-order coupled system of nonlinear parabolic PDE for the film thickness and salt concentration subject to non-conservative effects representing evaporation. We analytically prove the global existence of solutions to this model with mobility exponents in several different ranges and the results are then validated against PDE simulations. We also numerically capture other interesting dynamics of the model, including finite-time rupture-shock phenomenon due to the instabilities caused by locally elevated evaporation rates, convergence to equilibrium and infinite-time thinning.
We study in this work a continuum model derived from 1D attachment-detachment-limited (ADL) type step flow on vicinal surface, $ u_t=-u^2(u^3)_{hhhh}$, where $u$, considered as a function of step height $h$, is the step slope of the surface. We formulate a notion of weak solution to this continuum model and prove the existence of a global weak solution, which is positive almost everywhere. We also study the long time behavior of weak solution and prove it converges to a constant solution as time goes to infinity. The space-time Hölder continuity of the weak solution is also discussed as a byproduct.
Many objects, especially these made by humans, are symmetric, e.g. cars and aeroplanes. This paper addresses the estimation of 3D structures of symmetric objects from multiple images of the same object category, e.g. different cars, seen from various viewpoints. We assume that the deformation between different instances from the same object category is non-rigid and symmetric. In this paper, we extend two leading non-rigid structure from motion (SfM) algorithms to exploit symmetry constraints. We model the both methods as energy minimization, in which we also recover the missing observations caused by occlusions. In particularly, we show that by rotating the coordinate system, the energy can be decoupled into two independent terms, which still exploit symmetry, to apply matrix factorization separately on each of them for initialization. The results on the Pascal3D+ dataset show that our methods significantly improve performance over baseline methods.
This paper introduces two recurrent neural network structures called Simple Gated Unit (SGU) and Deep Simple Gated Unit (DSGU), which are general structures for learning long term dependencies. Compared to traditional Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU), both structures require fewer parameters and less computation time in sequence classification tasks. Unlike GRU and LSTM, which require more than one gates to control information flow in the network, SGU and DSGU only use one multiplicative gate to control the flow of information. We show that this difference can accelerate the learning speed in tasks that require long dependency information. We also show that DSGU is more numerically stable than SGU. In addition, we also propose a standard way of representing inner structure of RNN called RNN Conventional Graph (RCG), which helps analyzing the relationship between input units and hidden units of RNN.
An electric current in the presence of spin-orbit coupling can generate a spin accumulation that exerts torques on a nearby magnetization. We demonstrate that, even in the absence of materials with strong bulk spin-orbit coupling, a torque can arise solely due to interfacial spin-orbit coupling, namely Rashba-Eldestein effects at metal/insulator interfaces. In magnetically soft NiFe sandwiched between a weak spin-orbit metal (Ti) and insulator (Al$_2$O$_3$), this torque appears as an effective field, which is significantly larger than the Oersted field and sensitive to insertion of an additional layer between NiFe and Al$_2$O$_3$. Our findings point to new routes for tuning spin-orbit torques by engineering interfacial electric dipoles.
Descriptional complexity is the study of the conciseness of the various models representing formal languages. The state complexity of a regular language is the size, measured by the number of states of the smallest, either deterministic or nondeterministic, finite automaton that recognises it. Operational state complexity is the study of the state complexity of operations over languages. In this survey, we review the state complexities of individual regularity preserving language operations on regular and some subregular languages. Then we revisit the state complexities of the combination of individual operations. We also review methods of estimation and approximation of state complexity of more complex combined operations.
Electric-field modulation of magnetism in strain-mediated multiferroic heterostructures is considered a promising scheme for enabling memory and magnetic microwave devices with ultralow power consumption. However, it is not well understood how electric-field-induced strain influences magnetic relaxation, an important physical process for device applications. Here we investigate resonant magnetization dynamics in ferromagnet/ferrolectric multiferroic heterostructures, FeGaB/PMN-PT and NiFe/PMN-PT, in two distinct strain states provided by electric-field-induced ferroelectric phase transition. The strain not only modifies magnetic anisotropy but also magnetic relaxation. In FeGaB/PMN-PT, we observe a nearly two-fold change in intrinsic Gilbert damping by electric field, which is attributed to strain-induced tuning of spin-orbit coupling. By contrast, a small but measurable change in extrinsic linewidth broadening is attributed to inhomogeneous ferroelastic domain switching during the phase transition of the PMN-PT substrate.
To investigate how consensus is reached on a large self-organized peer-to-peer network, we extended the naming game model commonly used in language and communication to Naming Game in Groups (NGG). Differing from other existing naming game models, in NGG, everyone in the population (network) can be both speaker and hearer simultaneously, which resembles in a closer manner to real-life scenarios. Moreover, NGG allows the transmission (communication) of multiple words (opinions) for multiple intra-group consensuses. The communications among indirectly-connected nodes are also enabled in NGG. We simulated and analyzed the consensus process in some typical network topologies, including random-graph networks, small-world networks and scale-free networks, to better understand how global convergence (consensus) could be reached on one common word. The results are interpreted on group negotiation of a peer-to-peer network, which shows that global consensus in the population can be reached more rapidly when more opinions are permitted within each group or when the negotiating groups in the population are larger in size. The novel features and properties introduced by our model have demonstrated its applicability in better investigating general consensus problems on peer-to-peer networks.
In the framework of the isospin-dependent Boltzmann-Uehling-Uhlenbeck transport model, effects of the symmetry energy on the evolutions of free n/p ratio and charged pion ratio in the semi-central collision of $^{197}$Au+$^{197}$Au at an incident beam energy of 400 MeV/nucleon are studied. At the beginning of the reaction (before 11 fm/c) they are both affected by the low-density behavior of the symmetry energy but soon after are affected by the high-density behavior of the symmetry energy after nuclei are compressed (after 11 fm/c) and the effects of the symmetry energy are generally smaller compared with the central collision case. Interestingly, their dependences on the symmetry energy are shown to arise with increase of cone-azimuthal angle of the emitted particles. In the direction perpendicular to the reaction plane, the $π^{-}/π^{+}$ ratio or free n/p ratio especially at high kinetic energies exhibits significant sensitivity to the symmetry energy.
In the framework of the isospin-dependent Boltzmann-Uehling-Uhlenbeck transport model, effect of the momentum dependence of nuclear symmetry potential on nuclear transverse and elliptic flows in the neutron-rich reaction $^{132}$Sn+$^{124}$Sn at a beam energy of 400 MeV/nucleon is studied. We find that the momentum dependence of nuclear symmetry potential affects the rapidity distribution of the free neutron to proton ratio, the neutron and the proton transverse flows as a function of rapidity. The momentum dependence of nuclear symmetry potential affects the neutron-proton differential transverse flow more evidently than the difference of neutron and proton transverse flows as well as the difference of proton and neutron elliptic flows. It is thus better to probe the symmetry energy by using the difference of neutron and proton flows since the momentum dependence of nuclear symmetry potential is still an open question. And it is better to probe the momentum dependence of nuclear symmetry potential by using the neutron-proton differential transverse flow and the rapidity distribution of the free neutron to proton ratio.
Based on the isospin-dependent Boltzmann-Uehling-Uhlenbeck transport model plus the Skyrme force parameters, initialization effect is studied in heavy-ion collision at intermediate energies. We find that there are moderate initialization effects in the observables of free neutron to proton ratio (n/p), pion-/pion + ratio, as well as neutron to proton differential flow (F^x_n-p). Effects of initialization are larger for charged pion-/pion ratios than n/p ratios. And the effects of initialization are more evident in nuclear reactions at lower incident beam energies. We do not see large effects of initialization for light reaction systems or large asymmetric (neutron-richer) reaction systems. We also see relatively large effects of initialization on the neutron to proton differential flow at relatively lower incident beam energies or with large impact parameters. These results may be useful for the delicate studies of Equation of Sate (EoS) of asymmetric nuclear matter.
In the framework of the isospin-dependent Boltzmann-Uehling-Uhlenbeck transport model, effect of the momentum dependence of nuclear symmetry potential on pion-/pion+ ratio in the neutron-rich reaction 132Sn+124Sn at a beam energy of 400 MeV/nucleon is studied. We find that the momentum dependence of nuclear symmetry potential affects the compressed density of colliding nuclei, numbers of produced pion- and pion+, as well as the value of pion-/pion+ ratio. The momentum dependent nuclear symmetry potential increases the compressed density of colliding nuclei, numbers of produced resonances delta(1232), N*(1440), pion- and pion+, as well as the value of pion-/pion+ ratio.
We have demonstrated a metropolitan all-pass quantum communication network in field fiber for four nodes. Any two nodes of them can be connected in the network to perform quantum key distribution (QKD). An optical switching module is presented that enables arbitrary 2-connectivity among output ports. Integrated QKD terminals are worked out, which can operate either as a transmitter, a receiver, or even both at the same time. Furthermore, an additional link in another city of 60 km fiber (up to 130 km) is seamless integrated into this network based on a trusted relay architecture. On all the links, we have implemented protocol of decoy state scheme. All of necessary electrical hardware, synchronization, feedback control, network software, execution of QKD protocols are made by tailored designing, which allow a completely automatical and stable running. Our system has been put into operation in Hefei in August 2009, and publicly demonstrated during an evaluation conference on quantum network organized by the Chinese Academy of Sciences on August 29, 2009. Real-time voice telephone with one-time pad encoding between any two of the five nodes (four all-pass nodes plus one additional node through relay) is successfully established in the network within 60km.