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Positively Scale-Invariant Flatness of ReLU Neural NetworksMar 06 2019It was empirically confirmed by Keskar et al.\cite{SharpMinima} that flatter minima generalize better. However, for the popular ReLU network, sharp minimum can also generalize well \cite{SharpMinimacan}. The conclusion demonstrates that the existing definitions ... More

Discrete energy levels of Caroli-de Gennes-Martricon states in quantum limit due to small Fermi energy in FeTe$_{0.55}$Se$_{0.45}$Sep 27 2017Caroli-de Gennes-Martricon (CdGM) states were predicted in 1964 as low energy excitations within vortex cores of type-II superconductors. In the quantum limit, namely $T/T_\mathrm{c} \ll \Delta/E_\mathrm{F}$, the energy levels of these states were predicted ... More

Zero-Energy Modes on Superconducting Bismuth Islands Deposited on Fe(Te,Se)May 14 2019Topological superconductivity is one of the frontier research directions in condensed matter physics. One of the unique elementary excitations in topological superconducting state is the Majorana fermion (mode) which is its own antiparticle and obeys ... More

The Roper PuzzleMar 26 2014We carried out a calculation of the Roper state with the Sequential Empirical Bayesian (SEB) method with overlap valence fermion on 2+1-flavor domain-wall fermion configurations on the 24^3 x 64 lattice with a^{-1} = 1.73 GeV. The light sea quark mass ... More

Studying Cultural Differences in Emoji Usage across the East and the WestApr 04 2019Global acceptance of Emojis suggests a cross-cultural, normative use of Emojis. Meanwhile, nuances in Emoji use across cultures may also exist due to linguistic differences in expressing emotions and diversity in conceptualizing topics. Indeed, literature ... More

MIMS: Towards a Message Interface based Memory SystemJan 01 2013Memory system is often the main bottleneck in chipmultiprocessor (CMP) systems in terms of latency, bandwidth and efficiency, and recently additionally facing capacity and power problems in an era of big data. A lot of research works have been done to ... More

Multi-source weak supervision for saliency detectionApr 01 2019The high cost of pixel-level annotations makes it appealing to train saliency detection models with weak supervision. However, a single weak supervision source usually does not contain enough information to train a well-performing model. To this end, ... More

Ratio of strange to $u/d$ momentum fraction in disconnected insertionsJan 22 2019The ratio of the strange momentum fraction $\langle x\rangle_{s+\bar{s}}$ to that of $u/d$ in the disconnected insertion is calculated on the lattice with overlap fermions on four domain wall fermion ensembles. These ensembles cover three lattice spacings, ... More

HAKE: Human Activity Knowledge EngineApr 13 2019Human activity understanding is crucial for building automatic intelligent system. With the help of deep learning, activity understanding has made huge progress recently. But some challenges such as imbalanced data distribution, action ambiguity, complex ... More

HAKE: Human Activity Knowledge EngineApr 13 2019May 08 2019Human activity understanding is crucial for building automatic intelligent system. With the help of deep learning, activity understanding has made huge progress recently. But some challenges such as imbalanced data distribution, action ambiguity, complex ... More

Multi-band superconductivity and possible nodal gap in RbCr$_{3}$As$_{3}$ revealed by Andreev reflection and single-particle tunneling measurementsJan 24 2019By measuring point-contact Andreev reflection spectra in the newly discovered chromium-based quasi-one-dimensional superconductor RbCr$_{3}$As$_{3}$, we find clear evidence of two superconducting components, one has a gap value of about 1.8 meV and another ... More

Photon-counting Brillouin optical time-domain reflectometry based on up-conversion detector and fiber Fabry-Perot scanning interferometerApr 06 2015A direct-detection Brillouin optical time-domain reflectometry (BOTDR) is proposed and demonstrated by using an up-conversion single-photon detector and a fiber Fabry-Perot scanning interferometer (FFP-SI). Taking advantage of high signal-to-noise ratio ... More

Tunable superconductivity in parent cuprate Pr$_{2}$CuO$_{4\pmδ}$ thin filmsJul 03 2018In this article, we studied the role of oxygen in Pr$_{2}$CuO$_{4\pm\delta}$ thin films fabricated by polymer assisted deposition method. The magnetoresistance and Hall resistivity of Pr$_{2}$CuO$_{4\pm\delta}$ samples were systematically investigated. ... More

Coherent heteronuclear spin dynamics in an ultracold spin-1 mixtureFeb 13 2015We report the observation of coherent heteronuclear spin dynamics driven by inter-species spin-spin interaction in an ultracold spinor mixture, which manifests as periodical and well correlated spin oscillations between two atomic species. In particular, ... More

Direct visualization of sign reversal s^+- superconducting gaps in FeTe0.55Se0.45Oct 15 2018In many unconventional superconductors, the pairing of electrons is driven by the repulsive interaction, which leads to the sign reversal of superconducting gaps along the Fermi surfaces (FS) or between them. However, to measure this sign change is not ... More

Enhancing countries' fitness with recommender systems on the international trade networkApr 04 2019Prediction is one of the major challenges in complex systems. The prediction methods have shown to be effective predictors of the evolution of networks. These methods can help policy makers to solve practical problems successfully and make better strategy ... More

Joint training framework for text-to-speech and voice conversion using multi-source Tacotron and WaveNetMar 29 2019We investigated the training of a shared model for both text-to-speech (TTS) and voice conversion (VC) tasks. We propose using an extended model architecture of Tacotron, that is a multi-source sequence-to-sequence model with a dual attention mechanism ... More

Strange quark momentum fraction from overlap fermionFeb 19 2015Mar 10 2015We present a calculation of $< x >_s$ for the strange quark in the nucleon. We also report the ratio of the strange $< x >$ to that of $u/d$ in the disconnected insertion which will be useful in constraining the global fit of parton distribution functions ... More

Joint training framework for text-to-speech and voice conversion using multi-source Tacotron and WaveNetMar 29 2019Apr 07 2019We investigated the training of a shared model for both text-to-speech (TTS) and voice conversion (VC) tasks. We propose using an extended model architecture of Tacotron, that is a multi-source sequence-to-sequence model with a dual attention mechanism ... More

High-resolution Internal State Control of Ultracold $^{23}$Na$^{87}$Rb MoleculesDec 30 2017We report the full control over the internal states of ultracold $^{23}$Na$^{87}$Rb molecules, including vibrational, rotational and hyperfine degrees of freedom. Starting from a sample of weakly bound Feshbach molecules, we realize the creation of molecules ... More

Exploring Few-Body Processes with an Ultracold Light-Heavy Bose-Bose MixtureNov 10 2016We report the observation of several few-body processes with an ultracold Bose-Bose mixture consisting of sodium and rubidium atoms and weakly-bound NaRb Feshbach dimers. Preparing a pure dimer sample and tuning the scattering length between Na and Rb ... More

PointSIFT: A SIFT-like Network Module for 3D Point Cloud Semantic SegmentationJul 02 2018Nov 24 2018Recently, 3D understanding research sheds light on extracting features from point cloud directly, which requires effective shape pattern description of point clouds. Inspired by the outstanding 2D shape descriptor SIFT, we design a module called PointSIFT ... More

Towards Instance-level Image-to-Image TranslationMay 05 2019Unpaired Image-to-image Translation is a new rising and challenging vision problem that aims to learn a mapping between unaligned image pairs in diverse domains. Recent advances in this field like MUNIT and DRIT mainly focus on disentangling content and ... More

Learning data augmentation policies using augmented random searchNov 12 2018Previous attempts for data augmentation are designed manually, and the augmentation policies are dataset-specific. Recently, an automatic data augmentation approach, named AutoAugment, is proposed using reinforcement learning. AutoAugment searches for ... More

Unsupervised Cross-spectral Stereo Matching by Learning to SynthesizeMar 04 2019Unsupervised cross-spectral stereo matching aims at recovering disparity given cross-spectral image pairs without any supervision in the form of ground truth disparity or depth. The estimated depth provides additional information complementary to individual ... More

View Inter-Prediction GAN: Unsupervised Representation Learning for 3D Shapes by Learning Global Shape Memories to Support Local View PredictionsNov 07 2018In this paper we present a novel unsupervised representation learning approach for 3D shapes, which is an important research challenge as it avoids the manual effort required for collecting supervised data. Our method trains an RNN-based neural network ... More

OPUS-Beta: A Statistical Potential for Beta-Sheet Contact Pattern in ProteinsAug 03 2015Developing an accurate scoring function is essential for successfully predicting protein structures. In this study, we developed a statistical potential function, called OPUS-Beta, for energetically evaluating beta-sheet contact pattern (the entire residue-residue ... More

A Visual Attention Grounding Neural Model for Multimodal Machine TranslationAug 24 2018Aug 28 2018We introduce a novel multimodal machine translation model that utilizes parallel visual and textual information. Our model jointly optimizes the learning of a shared visual-language embedding and a translator. The model leverages a visual attention grounding ... More

High Speed Tracking With A Fourier Domain Kernelized Correlation FilterNov 08 2018Feb 22 2019It is challenging to design a high speed tracking approach using l1-norm due to its non-differentiability. In this paper, a new kernelized correlation filter is introduced by leveraging the sparsity attribute of l1-norm based regularization to design ... More

Distant IE by Bootstrapping Using Lists and Document StructureJan 04 2016Distant labeling for information extraction (IE) suffers from noisy training data. We describe a way of reducing the noise associated with distant IE by identifying coupling constraints between potential instance labels. As one example of coupling, items ... More

2D LiDAR Map Prediction via Estimating Motion Flow with GRUFeb 19 2019It is a significant problem to predict the 2D LiDAR map at next moment for robotics navigation and path-planning. To tackle this problem, we resort to the motion flow between adjacent maps, as motion flow is a powerful tool to process and analyze the ... More

Quark Spin in Proton from Anomalous Ward IndentityApr 15 2015We report a quark spin calculation from the anomalous Ward identity with overlap fermions on 2+1 flavor dynamical fermion configurations with light sea quark masses. Such a formulation decomposes the divergence of the flavor-singlet axial-vector current ... More

Off-Policy Evaluation of Probabilistic Identity Data in Lookalike ModelingJan 04 2019We evaluate the impact of probabilistically-constructed digital identity data collected from Sep. to Dec. 2017 (approx.), in the context of Lookalike-targeted campaigns. The backbone of this study is a large set of probabilistically-constructed "identities", ... More

Cutting Away the Confusion From CrowdtestingMay 07 2018Nov 13 2018Crowdtesting is effective especially when it comes to the feedback on GUI systems, or subjective opinions about features. Despite of this, we find crowdtesting reports are highly replicated, i.e., 82% of them are replicates of others. Hence automatically ... More

Reflexive Regular Equivalence for Bipartite DataFeb 16 2017Bipartite data is common in data engineering and brings unique challenges, particularly when it comes to clustering tasks that impose on strong structural assumptions. This work presents an unsupervised method for assessing similarity in bipartite data. ... More

FreeSense:Indoor Human Identification with WiFi SignalsAug 11 2016Human identification plays an important role in human-computer interaction. There have been numerous methods proposed for human identification (e.g., face recognition, gait recognition, fingerprint identification, etc.). While these methods could be very ... More

Observability-aware Self-Calibration of Visual and Inertial Sensors for Ego-Motion EstimationJan 22 2019External effects such as shocks and temperature variations affect the calibration of visual-inertial sensor systems and thus they cannot fully rely on factory calibrations. Re-calibrations performed on short user-collected datasets might yield poor performance ... More

Online Bearing Remaining Useful Life Prediction Based on a Novel Degradation Indicator and Convolutional Neural NetworksDec 08 2018In industrial applications, nearly half the failures of motors are caused by the degradation of rolling element bearings (REBs). Therefore, accurately estimating the remaining useful life (RUL) for REBs are of crucial importance to ensure the reliability ... More

On the Imbedding Problem for Three-state Time Homogeneous Markov Chains with Coinciding Negative EigenvaluesSep 11 2010For an indecomposable $3\times 3$ stochastic matrix (i.e., 1-step transition probability matrix) with coinciding negative eigenvalues, a new necessary and sufficient condition of the imbedding problem for time homogeneous Markov chains is shown by means ... More

Minimum K_2,3-saturated GraphsDec 19 2010Nov 11 2012A graph is K_{2,3}-saturated if it has no subgraph isomorphic to K_{2,3}, but does contain a K_{2,3} after the addition of any new edge. We prove that the minimum number of edges in a K_{2,3}-saturated graph on n >= 5 vertices is sat(n, K_{2,3}) = 2n ... More

On the anti-canonical geometry of weak $\mathbb{Q}$-Fano threefolds, IIAug 16 2017By a canonical (resp. terminal) weak $\mathbb{Q}$-Fano $3$-fold we mean a normal projective one with at worst canonical (resp. terminal) singularities on which the anti-canonical divisor is $\mathbb{Q}$-Cartier, nef and big. For a canonical weak $\mathbb{Q}$-Fano ... More

On the anti-canonical geometry of $\mathbb{Q}$-Fano 3-foldsAug 27 2014Feb 02 2015For a $\mathbb{Q}$-Fano 3-fold $X$ on which $K_X$ is a canonical divisor, we investigate the geometry induced from the linear system $|-mK_X|$ in this paper and prove that the anti-$m$-canonical map $\varphi_{-m}$ is birational onto its image for all ... More

Orthogonal Quantum Group Invariants of LinksJul 09 2010We study the Chern-Simons partition function of orthogonal quantum group invariants, and propose a new orthogonal Labastida-Mari\~{n}o-Ooguri-Vafa conjecture as well as degree conjecture for free energy associated to the orthogonal Chern-Simons partition ... More

Hidden space reconstruction inspires link prediction in complex networksMar 25 2017As a fundamental challenge in vast disciplines, link prediction aims to identify potential links in a network based on the incomplete observed information, which has broad applications ranging from uncovering missing protein-protein interaction to predicting ... More

A globally attractive cycle driven by sequential bifurcations containing ghost effects in a 3-node yeast cell cycle modelDec 18 2013Sep 11 2014Yeast cells produce daughter cells through a DNA replication and mitosis cycle associated with checkpoints and governed by the cell cycle regulatory network. To ensure genome stability and genetic information inheritance, this regulatory network must ... More

Glue Spin $S_G$ in The Longitudinally Polarized NucleonDec 22 2014Mar 03 2015We present a lattice QCD calculation of the glue spin $S_G$ in the nucleon for the first time. It was recently shown that the first moment of the glue helicity distribution could be obtained through the cross-product of the the electric field $\vec{E}$ ... More

Measurement of accelerator neutron radiation field spectrum by Extended Range Neutron Multisphere Spectrometers and unfolding programNov 10 2015This paper described a measurement of accelerator neutron radiation field at a transport beam line of Beijing-TBF. The experiment place was be selected around a Faraday Cup with a graphite target impacted by electron beam at 2.5GeV. First of all, we simulated ... More

Gravitational instantons with faster than quadratic curvature decay (III)Mar 28 2016Oct 06 2016This is our third paper in a series on the gravitational instantons. In this paper, we classify ALG and ALH gravitational instantons. In ALG case, we extend Hein's construction slightly and show that it's the only ALG gravitational instanton. In ALH case, ... More

Gravitational instantons with faster than quadratic curvature decay (II)Aug 31 2015Jun 23 2016This is our second paper in a series to study gravitational instantons, i.e. complete hyperk\"aler 4-manifolds with faster than quadratic curvature decay. We prove two main theorems: 1.The asymptotic rate of gravitational instantons to the standard models ... More

Angora: Efficient Fuzzing by Principled SearchMar 04 2018Mar 27 2018Fuzzing is a popular technique for finding software bugs. However, the performance of the state-of-the-art fuzzers leaves a lot to be desired. Fuzzers based on symbolic execution produce quality inputs but run slow, while fuzzers based on random mutation ... More

Modeling the Annual Growth Rate of Electricity Consumption of China in the 21st Century: Trends and PredictionOct 21 2017In this paper, the annual growth rate of electricity consumption in China in the first 15 years of the 21st century is modeled using multiple linear regression. Historical data and trends of gross domestic product, fixed assets investment and share of ... More

Notes on "Einstein metrics on compact simple Lie groups attached to standard triples"Jan 06 2017In the paper "Einstein metrics on compact simple Lie groups attached to standard triples", the authors introduced the definition of standard triples and proved that every compact simple Lie group $G$ attached to a standard triple $(G,K,H)$ admits a left-invariant ... More

Characterizations of asymptotic distributions of continuous-time Pólya processesNov 29 2016Sep 02 2018We propose an elementary but effective approach to studying a general class of Poissonized tenable and balanced urns on two colors. We characterize the asymptotic behavior of the process via a partial differential equation that governs the process, coupled ... More

Gravitational instantons with faster than quadratic curvature decay (I)May 07 2015In this paper, we study gravitational instantons (i.e., complete hyperk\"aler 4-manifolds with faster than quadratic curvature decay). We prove three main theorems: 1.Any gravitational instanton must have known end----ALE, ALF, ALG or ALH. 2.In ALG and ... More

Exact Methods for Multistage Estimation of a Binomial ProportionFeb 13 2013We first review existing sequential methods for estimating a binomial proportion. Afterward, we propose a new family of group sequential sampling schemes for estimating a binomial proportion with prescribed margin of error and confidence level. In particular, ... More

Embedding of tenable and balanced urn scheme into continuous-time Pólya processNov 29 2016We study poissonized tenable and balanced urns on two colors, say white and blue. In particular, we look at the process obtained by embedding a generalized P\'{o}lya-Eggenberger urn into continuous time. We analyze the number of white and blue balls after ... More

Some sufficient conditions for infinite collisions of simple random walks on a wedge combOct 26 2010In this paper, we give some sufficient conditions for the infinite collisions of independent simple random walks on a wedge comb with profile $\{f(n), n\in \ZZ\}$. One interesting result is that if $f(n)$ has a growth order as $n\log n$, then two independent ... More

HSEARCH: fast and accurate protein sequence motif search and clusteringJan 02 2017Protein motifs are conserved fragments occurred frequently in protein sequences. They have significant functions, such as active site of an enzyme. Search and clustering protein sequence motifs are computational intensive. Most existing methods are not ... More

Mathematical foundation of nonequilibrium fluctuation-dissipation theorems for inhomogeneous diffusion processes with unbounded coefficientsAug 30 2017Sep 24 2017Nonequilibrium fluctuation-dissipation theorems (FDTs) are one of the most important advances in stochastic thermodynamics over the past two decades. Here we provide a rigourous mathematical theory of two types of nonequilibrium FDTs for inhomogeneous ... More

Unsupervised Learning-based Depth Estimation aided Visual SLAM ApproachJan 22 2019The RGB-D camera maintains a limited range for working and is hard to accurately measure the depth information in a far distance. Besides, the RGB-D camera will easily be influenced by strong lighting and other external factors, which will lead to a poor ... More

Dipolar Collisions of Ultracold Ground-state Bosonic MoleculesDec 01 2018The dipolar collision between ultracold polar molecules is an important topic both by its own right from the fundamental point of view and for the successful exploration of many-body physics with strong and long-range dipolar interactions. Here, we report ... More

Transient supersolid properties in an array of dipolar quantum dropletsJan 23 2019Mar 08 2019We study theoretically and experimentally the emergence of supersolid properties in a dipolar Bose-Einstein condensate. The theory reveals a ground state phase diagram with three distinct regimes - a regular Bose-Einstein condensate, incoherent and coherent ... More

High-throughput investigation of tunable superconductivity in FeSe filmsJul 03 2018Mar 11 2019There is an ongoing debate about the relative importance of structural change versus doping charge carriers on the mechanism of superconductivity in Fe-based materials. Elucidating this issue is a major challenge since it would require a large number ... More

Temporal similarity metrics for latent network reconstruction: The role of time-lag decayApr 04 2019When investigating the spreading of a piece of information or the diffusion of an innovation, we often lack information on the underlying propagation network. Reconstructing the hidden propagation paths based on the observed diffusion process is a challenging ... More

Error Reduction Network for DBLSTM-based Voice ConversionSep 26 2018So far, many of the deep learning approaches for voice conversion produce good quality speech by using a large amount of training data. This paper presents a Deep Bidirectional Long Short-Term Memory (DBLSTM) based voice conversion framework that can ... More

Visual-inertial self-calibration on informative motion segmentsAug 08 2017Environmental conditions and external effects, such as shocks, have a significant impact on the calibration parameters of visual-inertial sensor systems. Thus long-term operation of these systems cannot fully rely on factory calibration. Since the observability ... More

Scene Graph Generation with External Knowledge and Image ReconstructionApr 01 2019Scene graph generation has received growing attention with the advancements in image understanding tasks such as object detection, attributes and relationship prediction,~\etc. However, existing datasets are biased in terms of object and relationship ... More

Y^2Seq2Seq: Cross-Modal Representation Learning for 3D Shape and Text by Joint Reconstruction and Prediction of View and Word SequencesNov 07 2018A recent method employs 3D voxels to represent 3D shapes, but this limits the approach to low resolutions due to the computational cost caused by the cubic complexity of 3D voxels. Hence the method suffers from a lack of detailed geometry. To resolve ... More

UWB/LiDAR Fusion For Cooperative Range-Only SLAMNov 07 2018We equip an ultra-wideband (UWB) node and a 2D LiDAR sensor a.k.a. 2D laser rangefinder on a mobile robot, and place UWB beacon nodes at unknown locations in an unknown environment. All UWB nodes can do ranging with each other thus forming a cooperative ... More

High Resolution Molecular Spectroscopy for Producing Ultracold Absolute Ground-State $^{23}$Na$^{87}$Rb MoleculesOct 13 2017We report a detailed molecular spectroscopy study on the lowest excited electronic states of $^{23}\rm{Na}^{87}\rm{Rb}$ for producing ultracold $^{23}\rm{Na}^{87}\rm{Rb}$ molecules in the electronic, rovibrational and hyperfine ground state. Starting ... More

Fine Residual Carrier Frequency and Sampling Frequency Estimation in Wireless OFDM SystemsNov 08 2012This paper presents a novel algorithm for residual phase estimation in wireless OFDM systems, including the carrier frequency offset (CFO) and the sampling frequency offset (SFO). The subcarriers are partitioned into several regions which exhibit pairwise ... More

Faster Deterministic Algorithms for Packing, Matching and $t$-Dominating Set ProblemsJun 15 2013In this paper, we devise three deterministic algorithms for solving the $m$-set $k$-packing, $m$-dimensional $k$-matching, and $t$-dominating set problems in time $O^*(5.44^{mk})$, $O^*(5.44^{(m-1)k})$ and $O^*(5.44^{t})$, respectively. Although recently ... More

Exact Sample Size Methods for Estimating Parameters of Discrete DistributionsNov 08 2012Nov 19 2012In this paper, we develop an approach for the exact determination of the minimum sample size for estimating the parameter of an integer-valued random variable, which is parameterized by its expectation. Under some continuity and unimodal property assumptions, ... More

Gröbner-Shirshov bases for metabelian Lie algebrasJun 13 2011In this paper, we establish the Gr\"{o}bner-Shirshov bases theory for metabelian Lie algebras. As applications, we find the Gr\"{o}bner-Shirshov bases for partial commutative metabelian Lie algebras related to circuits, trees and some cubes.

The Noether inequality for algebraic threefolds (With an Appendix by János Kollár)Mar 15 2018Jul 19 2018We establish the Noether inequality for projective $3$-folds. More precisely, we prove that the inequality $${\rm vol}(X)\geq \tfrac{4}{3}p_g(X)-{\tfrac{10}{3}}$$ holds for all projective $3$-folds $X$ of general type with either $p_g(X)\leq 4$ or $p_g(X)\geq ... More

Transient supersolid properties in an array of dipolar quantum dropletsJan 23 2019We study theoretically and experimentally the emergence of supersolid properties in a dipolar Bose-Einstein condensate. The theory reveals a ground state phase diagram with three distinct regimes - a regular Bose-Einstein condensate, incoherent and coherent ... More

Modularity of the metabolic gene network as a prognostic biomarker for hepatocellular carcinomaNov 24 2017Abnormal metabolism is an emerging hallmark of cancer. Cancer cells utilize both aerobic glycolysis and oxidative phosphorylation (OXPHOS) for energy production and biomass synthesis. Understanding the metabolic reprogramming in cancer can help design ... More

Collisions of ultracold ^{23}Na^{87}Rb molecules with controlled chemical reactivitiesJan 27 2018The collision of molecules at ultracold temperatures is of great importance for understanding the chemical interactions at the quantum regime. While much theoretical work has been devoted to this, experimental data are only available sparsely mainly due ... More

Urbanization, Ikization, and Replacement DynamicsNov 04 2015The phenomenon of Iks was first found by anthropologists and biologists, but it is actually a problem of human geography. However, it has not yet drawn extensive attention of geographers. In this paper, a hypothesis of ikization is presented that sudden ... More

The Tractability Frontier of Graph-Like First-Order Query SetsJul 13 2014We study first-order model checking, by which we refer to the problem of deciding whether or not a given first-order sentence is satisfied by a given finite structure. In particular, we aim to understand on which sets of sentences this problem is tractable, ... More

Regular balanced Cayley maps on ${\rm PSL}(2,p)$Jan 20 2016Jul 05 2016A {\it regular balanced Cayley map} (RBCM for short) on a finite group $\Gamma$ is an embedding of a Cayley graph on $\Gamma$ into a surface, with some special symmetric property. People have classified RBCM's for cyclic, dihedral, generalized quaternion, ... More

Cellular Automata to More Efficiently Compute the Collatz MapJan 14 2013The Collatz, or 3x+1, Conjecture claims that for every positive integer n, there exists some k such that T^k(n)=1, where T is the Collatz map. We present three cellular automata (CA) that transform the global problem of mimicking the Collatz map in bases ... More

Basis Collapse for Holographic Algorithms Over All Domain SizesNov 03 2015The theory of holographic algorithms introduced by Valiant represents a novel approach to achieving polynomial-time algorithms for seemingly intractable counting problems via a reduction to counting planar perfect matchings and a linear change of basis. ... More

Pseudo-holomorphic curves and the Weinstein conjectureAug 10 1997Feb 02 2000We established existence of periodic Reeb orbits for a large class of tight contact structures on closed 3-manifolds, notably the Stein fillable structures, based on a fundamental theorem of Cliff Taubes on symplectic 4-manifolds.

CRT-Based High Speed Parallel Architecture for Long BCH EncodingApr 21 2009BCH (Bose-Chaudhuri-Hocquenghen) error correcting codes ([1]-[2]) are now widely used in communication systems and digital technology. Direct LFSR(linear feedback shifted register)-based encoding of a long BCH code suffers from serial-in and serial-out ... More

Technical Report: Representing SES Cases Using OntologyJan 31 2016Socio-ecological System (SES) research studies the interaction between environment, users, and governance of environment resources. Data produced during the research cycle can be both long-tail (e.g. heterogeneous) and longitudinal data. For example, ... More

The evolution of Zipf's law indicative of city developmentApr 16 2015Zipf's law of city-size distributions can be expressed by three types of mathematical models: one-parameter form, two-parameter form, and three-parameter form. The one-parameter and one of the two-parameter models are familiar to urban scientists. However, ... More

Basis entropy: A useful physical quantity about projective measurementJun 05 2016Sep 30 2016Projective measurement can increase the entropy of a state $\rho$, the increased entropy is not only up to the basis of projective measurement, but also has something to do with the properties of the state itself. In this paper we define this increased ... More

A Gentle Tutorial of Recurrent Neural Network with Error BackpropagationOct 08 2016We describe recurrent neural networks (RNNs), which have attracted great attention on sequential tasks, such as handwriting recognition, speech recognition and image to text. However, compared to general feedforward neural networks, RNNs have feedback ... More

Approximating the Minimum Breakpoint Linearization Problem for Genetic Maps without Gene StrandednessFeb 25 2015The study of genetic map linearization leads to a combinatorial hard problem, called the {\em minimum breakpoint linearization} (MBL) problem. It is aimed at finding a linearization of a partial order which attains the minimum breakpoint distance to a ... More

Xiao's Conjecture on Canonically Fibered SurfacesMay 20 2014A canonically fibered surface is a surface whose canonical series maps it to a curve. Using Miyaoka-Yau inequality, A. Beauville proved that a canonically fibered surface has relative genus at most 5 when its geometric genus is sufficiently large. G. ... More

Grand Challenges in Measuring and Characterizing Scholarly ImpactMar 02 2016The constantly growing body of scholarly knowledge of science, technology, and humanities is an asset of the mankind. While new discoveries expand the existing knowledge, they may simultaneously render some of it obsolete. It is crucial for scientists ... More

An ontology-based approach to the optimization of non-binary (2,v)-regular LDPC codesSep 06 2014A non-binary (2,v)-regular LDPC code is defined by a parity-check matrix with column weight 2 and row weight v. In this report, we give an ontology-based approach to the optimization for this class of codes. All possible inter-connected cycle patterns ... More

Revisit Consensus of Multiagent Systems and Synchronization of Complex Networks: A Unified ViewpointSep 20 2016In this paper, we revisit the topic "Consensus of Multiagent Systems and Synchronization of Complex Networks: A Unified Viewpoint". We also revisit the topic "New Approach to Synchronization Analysis of Linearly Coupled Ordinary Differential Systems" ... More

Smoothness and Smooth Extensions (I): Generalization of MWK Functions and Gradually Varied FunctionsMay 20 2010A mathematical smooth function means that the function has continuous derivatives to a certain degree C(k). We call it a k-smooth function or a smooth function if k can grow infinitively. Based on quantum physics, there is no such smooth surface in the ... More

Equivalence of Weak Galerkin Methods and Virtual Element Methods for Elliptic EquationsMar 16 2015We propose a modification of the weak Galerkin methods and show its equivalence to a new version of virtual element methods. We also show the original weak Galerkin method is equivalent to the non-conforming virtual element method. As a consequence, ideas ... More

A quantum algorithm for solving the 3-SAT problemOct 16 2012Oct 18 2012The method in this paper is wrong.

Bouchard-Klemm-Marino-Pasquetti Conjecture for $\mathbb{C}^3$Oct 20 2009In this paper, we give a proof of the Bouchard-Klemm-Marino-Pasquetti conjecture for a framed vertex, by using the symmetrized Cut-Join Equation developed in a previous paper.

Existence of the rhombohedral and tetragonal deformation families of the gyroidJan 13 2019We provide an existence proof for two 1-parameter families of triply periodic minimal surfaces of genus three, namely the tG family with tetragonal symmetry that contains the gyroid, and the rGL family with rhombohedral symmetry that contains the gyroid ... More

Minimal rPD-Twin SurfacesOct 25 2016We study a $2$-parameter family of minimal surfaces with twin structure, namely the rPD-twin surfaces. A (polysynthetic) rPD-twin surface can be seen as copies of an rPD-surface that are symmetric about parallel mirrors. Candidates of rPD-twin surfaces ... More