arXiv subjects

Hao Hu

Publications and source records attributed to Hao Hu.

At least 163 records · Page 9Linked to original sources

arXiv2019

Learning to Adaptively Scale Recurrent Neural Networks

Recent advancements in recurrent neural network (RNN) research have demonstrated the superiority of utilizing multiscale structures in learning temporal representations of time series. Currently, most of multiscale RNNs use fixed scales, which do not comply with the nature of dynamical temporal patterns among sequences. In this paper, we propose Adaptively Scaled Recurrent Neural Networks (ASRNN), a simple but efficient way to handle this problem. Instead of using predefined scales, ASRNNs are able to learn and adjust scales based on different temporal contexts, making them more flexible in modeling multiscale patterns. Compared with other multiscale RNNs, ASRNNs are bestowed upon dynamical scaling capabilities with much simpler structures, and are easy to be integrated with various RNN cells. The experiments on multiple sequence modeling tasks indicate ASRNNs can efficiently adapt scales based on different sequence contexts and yield better performances than baselines without dynamical scaling abilities.

cs.LG↗

arXiv2019

New insights on Multi-Solution Distribution of the P3P Problem

Traditionally, the P3P problem is solved by firstly transforming its 3 quadratic equations into a quartic one, then by locating the roots of the resulting quartic equation and verifying whether a root does really correspond to a true solution of the P3P problem itself. However, a root of the quartic equation does not always correspond to a solution of the P3P problem. In this work, we show that when the optical center is outside of all the 6 toroids defined by the control point triangle, each positive root of the Grunert's quartic equation must correspond to a true solution of the P3P problem, and the corresponding P3P problem cannot have a unique solution, it must have either 2 positive solutions or 4 positive solutions. In addition, we show that when the optical center passes through any one of the 3 toroids among these 6 toroids ( except possibly for two concentric circles) , the number of the solutions of the corresponding P3P problem always changes by 1, either increased by 1 or decreased by 1.Furthermore we show that such changed solutions always locate in a small neighborhood of control points, hence the 3 toroids are critical surfaces of the P3P problem and the 3 control points are 3 singular points of solutions. A notable example is that when the optical center passes through the outer surface of the union of the 6 toroids from the outside to inside, the number of the solutions must always decrease by 1. Our results are the first to give an explicit and geometrically intuitive relationship between the P3P solutions and the roots of its quartic equation. It could act as some theoretical guidance for P3P practitioners to properly arrange their control points to avoid undesirable solutions.

cs.CV↗

arXiv2019

Geometric Interpretation of side-sharing and point-sharing solutions in the P3P Problem

It is well known that the P3P problem could have 1, 2, 3 and at most 4 positive solutions under different configurations among its 3 control points and the position of the optical center. Since in any real applications, the knowledge on the exact number of possible solutions is a prerequisite for selecting the right one among all the possible solutions, the study on the phenomenon of multiple solutions in the P3P problem has been an active topic . In this work, we provide some new geometric interpretations on the multi-solution phenomenon in the P3P problem, our main results include: (1): The necessary and sufficient condition for the P3P problem to have a pair of side-sharing solutions is the two optical centers of the solutions both lie on one of the 3 vertical planes to the base plane of control points; (2): The necessary and sufficient condition for the P3P problem to have a pair of point-sharing solutions is the two optical centers of the solutions both lie on one of the 3 so-called skewed danger cylinders;(3): If the P3P problem has other solutions in addition to a pair of side-sharing ( point-sharing) solutions, these remaining solutions must be a point-sharing ( side-sharing ) pair. In a sense, the side-sharing pair and the point-sharing pair are companion pairs. In sum, our results provide some new insights into the nature of the multi-solution phenomenon in the P3P problem, in addition to their academic value, they could also be used as some theoretical guidance for practitioners in real applications to avoid occurrence of multiple solutions by properly arranging the control points.

cs.CV↗

arXiv2018

Ultra-compact graphene plasmonic photodetector with the bandwidth over 110GHz

Graphene-based photodetectors, taking advantage of high carrier mobility and broadband absorption in graphene, have recently experienced rapid development. However, their performances with respect to the responsivity and bandwidth are still limited by either weak light-graphene interaction or large resistance-capacitance product. Here, we demonstrate a waveguide coupled integrated graphene plasmonic photodetector on the silicon-on-insulator platform. Benefiting from plasmonic enhanced graphene-light interactions and subwavelength confinement of the optical energy, we present a small-footprint graphene-plasmonic photodetector with bandwidth beyond 110GHz and intrinsic responsivity of 360mA/W. Attributed to the unique electronic bandstructure of graphene and its ultra-broadband absorption, the operational wavelength range extending beyond mid-infrared, and possibly further, can be anticipated. Our results show that the combination of graphene with plasmonic devices has great potential to realize ultra-compact and high-speed optoelectronic devices for graphene-based optical interconnects.

physics.app-ph↗

arXiv2018

Geometric properties of the Fortuin-Kasteleyn representation of the Ising model

We present a Monte Carlo study of the Fortuin-Kasteleyn (FK) clusters of the Ising model on the square (2D) and simple-cubic (3D) lattices. The wrapping probability, a dimensionless quantity characterizing the topology of the FK clusters on a torus, is found to suffer from smaller finite-size corrections than the well-known Binder ratio, and yields a high-precision critical coupling as $K_c(3\rm D)=0.221\,654\,631(8)$. We then study geometric properties of the FK clusters at criticality. It is demonstrated that the distribution of the critical largest-cluster size $C_1$ follows a single-variable function as $P(C_1,L){\rm d}C_1=\tilde P(x){\rm d}x$ with $x\equiv C_1/L^{d_{\rm F}}$ ($L$ is the linear size), and that the fractal dimension $d_{\rm F}$ is identical to the magnetic exponent. An interesting bimodal feature is observed in distribution $\tilde P(x)$ in 3D, and attributed to the different approaching behaviors for $K \to K_c+0^\pm$. For a critical FK configuration, the cluster number per site $n(s,L)$ of size $s$ is confirmed to obey the standard scaling form $n(s,L)\sim s^{-τ}\tilde n(s/L^{d_{\rm F}})$, with hyper-scaling relation $τ=1+d/d_{\rm F}$ and the spatial dimension $d$. To further characterize the compactness of the FK clusters, we measure their graph distances and determine the shortest-path exponents as $d_{\rm min}(3\rm D)=1.259\,4(2)$ and $d_{\rm min}(2\rm D)=1.094\,0(3)$. Further, by excluding all the bridges from the occupied bonds, we obtain bridge-free configurations and determine the backbone exponents as $d_{\rm B}(3\rm D)=2.167\,3(15)$ and $d_{\rm B}(2\rm D)=1.732\,1(4)$. The estimates of the universal wrapping probabilities for the 3D Ising model and of the geometric critical exponents $d_{\rm min}$ and $d_{\rm B}$ either improve over the existing results or have not been reported yet.

cond-mat.stat-mech↗

arXiv2018

Spatially controlled electrostatic doping in graphene p-i-n junction for hybrid silicon photodiode

Sufficiently large depletion region for photocarrier generation and separation is a key factor for two-dimensional material optoelectronic devices, but few device configurations has been explored for a deterministic control of a space charge region area in graphene with convincing scalability. Here we investigate a graphene-silicon p-i-n photodiode defined in a foundry processed planar photonic crystal waveguide structure, achieving visible - near-infrared, zero-bias and ultrafast photodetection. Graphene is electrically contacting to the wide intrinsic region of silicon and extended to the p an n doped region, functioning as the primary photocarrier conducting channel for electronic gain. Graphene significantly improves the device speed through ultrafast out-of-plane interfacial carrier transfer and the following in-plane built-in electric field assisted carrier collection. More than 50 dB converted signal-to-noise ratio at 40 GHz has been demonstrated under zero bias voltage, with quantum efficiency could be further amplified by hot carrier gain on graphene-i Si interface and avalanche process on graphene-doped Si interface. With the device architecture fully defined by nanomanufactured substrate, this study is the first demonstration of post-fabrication-free two-dimensional material active silicon photonic devices.

physics.app-ph↗

arXiv2018

Image Classification Based on Quantum KNN Algorithm

Image classification is an important task in the field of machine learning and image processing. However, the usually used classification method --- the K Nearest-Neighbor algorithm has high complexity, because its two main processes: similarity computing and searching are time-consuming. Especially in the era of big data, the problem is prominent when the amount of images to be classified is large. In this paper, we try to use the powerful parallel computing ability of quantum computers to optimize the efficiency of image classification. The scheme is based on quantum K Nearest-Neighbor algorithm. Firstly, the feature vectors of images are extracted on classical computers. Then the feature vectors are inputted into a quantum superposition state, which is used to achieve parallel computing of similarity. Next, the quantum minimum search algorithm is used to speed up searching process for similarity. Finally, the image is classified by quantum measurement. The complexity of the quantum algorithm is only O((kM)^(1/2)), which is superior to the classical algorithms. Moreover, the measurement step is executed only once to ensure the validity of the scheme. The experimental results show that, the classification accuracy is 83.1% on Graz-01 dataset and 78% on Caltech-101 dataset, which is close to existing classical algorithms. Hence, our quantum scheme has a good classification performance while greatly improving the efficiency.

cs.CV↗

arXiv2018

Global versus Localized Generative Adversarial Nets

In this paper, we present a novel localized Generative Adversarial Net (GAN) to learn on the manifold of real data. Compared with the classic GAN that {\em globally} parameterizes a manifold, the Localized GAN (LGAN) uses local coordinate charts to parameterize distinct local geometry of how data points can transform at different locations on the manifold. Specifically, around each point there exists a {\em local} generator that can produce data following diverse patterns of transformations on the manifold. The locality nature of LGAN enables local generators to adapt to and directly access the local geometry without need to invert the generator in a global GAN. Furthermore, it can prevent the manifold from being locally collapsed to a dimensionally deficient tangent subspace by imposing an orthonormality prior between tangents. This provides a geometric approach to alleviating mode collapse at least locally on the manifold by imposing independence between data transformations in different tangent directions. We will also demonstrate the LGAN can be applied to train a robust classifier that prefers locally consistent classification decisions on the manifold, and the resultant regularizer is closely related with the Laplace-Beltrami operator. Our experiments show that the proposed LGANs can not only produce diverse image transformations, but also deliver superior classification performances.

cs.CV↗

arXiv2018

EMC design for the actuators of FAST reflector

The active reflector is one of the three main innovations of the Five-hundred-meter Aperture Spherical radio Telescope (FAST). The deformation of such a huge spherically shaped reflector into different transient parabolic shapes is achieved by using 2225 hydraulic actuators which change the position of the 2225 nodes through the connected down tied cables. For each different tracking process of the telescope, more than 1/3 of these 2225 actuators must be in operation to tune the parabolic aperture accurately to meet the surface error restriction. It means that some of these actuators are inevitably located within the main beam of the receiver, and the Electromagnetic Interference (EMI) from the actuators must be mitigated to ensure the scientific output of the telescope. Based on the threshold level of interference detrimental to radio astronomy presented in ITU-R Recommendation RA.769 and EMI measurements, the shielding efficiency (SE) requirement of each actuator is set to be 80dB in the frequency range from 70MHz to 3GHz. Therefore, Electromagnetic Compatibility (EMC) was taken into account in the actuator design by measures such as power line filters, optical fibers, shielding enclosures and other structural measures. In 2015, all the actuators had been installed at the FAST site. Till now, no apparent EMI from the actuators has been detected by the receiver, which proves the effectiveness of these EMC measures.

astro-ph.IM↗

arXiv2018

Entropy stabilizes floppy crystals of mobile DNA-coated colloids

Grafting linkers with open ends of complementary single-stranded DNA makes a flexible tool to tune interactions between colloids,which facilitates the design of complex self-assembly structures. Recently, it has been proposed to coat colloids with mobile DNA linkers, which alleviates kinetic barriers without high-density grafting, and also allows the design of valency without patches.However, the self-assembly mechanism of this novel system is poorly understood.Using a combination of theory and simulation, we obtain phase diagrams forthe system in both two and three dimensional spaces, and find stable floppy squareand CsCl crystals when the binding strength is strong, even in the infinite bindingstrength limit. We demonstrate that these floppy phases are stabilized by vibrational entropy, and "floppy" modes play an important role in stabilizing the floppy phases for the infinite binding strength limit. This special entropic effect in the self-assembly of mobile DNA-coated colloids is very different from conventional molecular self-assembly, and it offers new axis to help design novel functional materials using mobile DNA-coated colloids.

cond-mat.soft↗

arXiv2017

Special cases of the quadratic shortest path problem

The quadratic shortest path problem (QSPP) is \textcolor{black}{the problem of finding a path with prespecified start vertex $s$ and end vertex $t$ in a digraph} such that the sum of weights of arcs and the sum of interaction costs over all pairs of arcs on the path is minimized. We first consider a variant of the QSPP known as the adjacent QSPP. It was recently proven that the adjacent QSPP on cyclic digraphs cannot be approximated unless P=NP. Here, we give a simple proof for the same result. We also show that if the quadratic cost matrix is a symmetric weak sum matrix \textcolor{black}{ and all $s$-$t$ paths have the same length,} then an optimal solution for the QSPP can be obtained by solving the corresponding instance of the shortest path problem. Similarly, it is shown that the QSPP with a symmetric product cost matrix is solvable in polynomial time. Further, we provide sufficient and necessary conditions for a QSPP instance on a complete symmetric digraph with four vertices to be linearizable. We also characterize linearizable QSPP instances on complete symmetric digraphs with more than four vertices. Finally, we derive an algorithm that examines whether a QSPP instance on the directed grid graph $G_{pq}$ ($p,q\geq 2$) is linearizable. The complexity of this algorithm is ${\mathcal{O}(p^{3}q^{2}+p^{2}q^{3})}$.

math.OC↗

arXiv2017

Effective electro-optic modulation in low-loss graphene-plasmonic slot waveguides

Surface plasmon polaritons enable light concentration within subwavelength regions, opening thereby new avenues for miniaturizing the device and strengthening light-matter interactions. Here we realize effective electro-optic modulation in low-loss plasmonic waveguides with the aid of graphene, and the devices are fully integrated in the silicon-on-insulator platform. By advantageously exploiting low-loss plasmonic slot-waveguide modes, which weakly leak into a substrate while feature strong fields within the two-layer-graphene covered slots in metal, we successfully achieve a tunability of 0.13 dB/um for our fabricated graphene-plasmonic waveguide devices with extremely low insertion loss, which outperforms previously reported graphene-plasmonic devices. Our results highlight the potential of graphene plasmonic leaky-mode hybrid waveguides to realized active ultra-compact devices for optoelectronic applications.

physics.optics↗

arXiv2017

On Solving the Quadratic Shortest Path Problem

The quadratic shortest path problem is the problem of finding a path in a directed graph such that the sum of interaction costs over all pairs of arcs on the path is minimized. We derive several semidefinite programming relaxations for the quadratic shortest path problem with a matrix variable of order $m+1$, where $m$ is the number of arcs in the graph. We use the alternating direction method of multipliers to solve the semidefinite programming relaxations. Numerical results show that our bounds are currently the strongest bounds for the quadratic shortest path problem. We also present computational results on solving the quadratic shortest path problem using a branch and bound algorithm. Our algorithm computes a semidefinite programming bound in each node of the search tree, and solves instances with up to 1300 arcs in less than an hour (!).

math.OC↗

arXiv2017

On the Linear Extension Complexity of Stable Set Polytopes for Perfect Graphs

We study the linear extension complexity of stable set polytopes of perfect graphs. We make use of known structural results permitting to decompose perfect graphs into basic perfect graphs by means of two graph operations: 2-join and skew partitions. Exploiting the link between extension complexity and the nonnegative rank of an associated slack matrix, we investigate the behaviour of the extension complexity under these graph operations. We show bounds for the extension complexity of the stable set polytope of a perfect graph $G$ depending linearly on the size of $G$ and involving the depth of a decomposition tree of $G$ in terms of basic perfect graphs.

math.CO↗

arXiv2017

Computing indicators of Radford algebras

We compute higher Frobenius-Schur indicators of Radford algebras in positive characteristic and find minimal polynomials of these linearly recursive sequences. As a result of Kashina, Montgomery and Ng, we obtain gauge invariants for the monoidal categories of representations of Radford algebras.

math.RT↗

arXiv2017

Irreversible Markov chain Monte Carlo algorithm for self-avoiding walk

We formulate an irreversible Markov chain Monte Carlo algorithm for the self-avoiding walk (SAW), which violates the detailed balance condition and satisfies the balance condition. Its performance improves significantly compared to that of the Berretti-Sokal algorithm, which is a variant of the Metropolis-Hastings method. The gained efficiency increases with the spatial dimension (D), from approximately $10$ times in 2D to approximately $40$ times in 5D. We simulate the SAW on a 5D hypercubic lattice with periodic boundary conditions, for a system with a linear size up to $L=128$, and confirm that as for the 5D Ising model, the finite-size scaling of the SAW is governed by renormalized exponents $ν^*=2/d$ and $γ/ν^*=d/2$. The critical point is determined, which is approximately $8$ times more precise than the best available estimate.

cond-mat.stat-mech↗

arXiv2016

No-enclave percolation corresponds to holes in the cluster backbone

The no-enclave percolation (NEP) model introduced recently by Sheinman et al. can be mapped to a problem of holes within a standard percolation backbone, and numerical measurements of these holes gives the size-distribution exponent $τ= 1.82(1)$ of the NEP model. An argument is given that $τ=1 + d_B/2 \approx 1.822$ where $d_B$ is the backbone dimension. On the other hand, a model of simple holes within a percolation cluster implies $τ= 1 + d_f/2 = 187/96 \approx 1.948$, where $d_f$ is the fractal dimension of the cluster, and this value is consistent with Sheinman et al.'s experimental results of gel collapse which gives $τ= 1.91(6)$. Both models yield a discontinuous maximum hole size at $p_c$, signifying explosive percolation behavior. At $p_c$, the largest hole fills exactly half the system, due to symmetry. Extensive numerical simulations confirm our results.

cond-mat.dis-nn↗

arXiv2015

InAR:Inverse Augmented Reality

Augmented reality is the art to seamlessly fuse virtual objects into real ones. In this short note, we address the opposite problem, the inverse augmented reality, that is, given a perfectly augmented reality scene where human is unable to distinguish real objects from virtual ones, how the machine could help do the job. We show by structure from motion (SFM), a simple 3D reconstruction technique from images in computer vision, the real and virtual objects can be easily separated in the reconstructed 3D scene.

cs.CV↗