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Learning unknown pure quantum statesMay 17 2018We propose a learning method for estimating unknown pure quantum states. The basic idea of our method is to learn a unitary operation $\hat{U}$ that transforms a given unknown state $|\psi_\tau\rangle$ to a known fiducial state $|f\rangle$. Then, after ... More

Optimal Usage of Quantum Random Access Memory in Quantum Machine LearningSep 13 2018Jan 17 2019By considering an unreliable oracle in a query-based model of quantum learning, we present a tradeoff relation between the oracle's reliability and the reusability of quantum state of the input data. The tradeoff relation manifests as the fundamental ... More

A genetic-algorithm-based method to find the unitary transformations for any de- sired quantum computation and application to a one-bit oracle decision problemMar 12 2014Jan 07 2015We propose a genetic-algorithm-based method to find the unitary transformations for any desired quantum computation. We formulate a simple genetic algorithm by introducing the "genetic parameter vector" of the unitary transformations to be found. In the ... More

Preparation-Attack-Immune Quantum Secure Direct Communication Using Two-Fold Photon Degree of FreedomApr 05 2017Quite recently, enhancing security against device-attack vulnerability has been theoretically challenging but also practically important in quantum cryptographic communication. For dealing with this issue in a general and strict scenario, we design a ... More

Fidelity deviation in quantum teleportationJan 18 2018Mar 01 2018We analyze the performance of quantum teleportation in terms of average fidelity and fidelity deviation. The average fidelity is defined as the average value of the fidelities over all possible input states and the fidelity deviation is their standard ... More

Fisher information as an indicator of quantum phenomenaFeb 27 2018Sep 30 2018Fisher information quantifies how well we can detect small changes in a parameter. According to the parameter that we focus on, the Fisher information presents different quantum phenomena. Here we investigate quantum interference of two particles in a ... More

Protocol for secure quantum machine learning at a distant placeApr 20 2015Aug 05 2015The application of machine learning to quantum information processing has recently attracted keen interest, particularly for the optimization of control parameters in quantum tasks without any pre-programmed knowledge. By adapting the machine learning ... More

Two-particle indistinguishability and identification of boson-and-fermion species: a Fisher information approachFeb 27 2018Jul 22 2019We present a study on two-particle indistinguishability and particle-species identification by introducing a Fisher-information (FI) approach---in which two particles pass through a two-wave mixing operation and the number of particles is counted in one ... More

Notes on the Quadratic Integers and Real Quadratic Number FieldsAug 27 2012Nov 26 2015It is shown that when a real quadratic integer $\xi$ of fixed norm $\mu$ is considered, the fundamental unit $\varepsilon_d$ of the field $\mathbb{Q}(\xi) = \mathbb{Q}(\sqrt{d})$ satisfies $\log \varepsilon_d \gg (\log d)^2$ almost always. An easy construction ... More

On the Regulators of Real Quadratic Number FieldsJul 04 2012Dec 03 2012This paper deals with the quadratic integers of small norms and asserts that in some sense R >> (log D)^2 is true for almost all real quadratic number fields. (A few errata is corrected.)

A quantum speedup in machine learning: Finding a N-bit Boolean function for a classificationMar 25 2013Oct 14 2014We compare quantum and classical machines designed for learning an N-bit Boolean function in order to address how a quantum system improves the machine learning behavior. The machines of the two types consist of the same number of operations and control ... More

Quantum Learning MachineMar 20 2008Mar 31 2008We propose a novel notion of a quantum learning machine for automatically controlling quantum coherence and for developing quantum algorithms. A quantum learning machine can be trained to learn a certain task with no a priori knowledge on its algorithm. ... More

Inseparability Criterion Using Higher-Order Schrödinger-Robertson Uncertainty RelationMar 10 2014We formulate an inseparability criterion based on the recently derived generalized Schr\"odinger-Robertson uncertainty relation (SRUR) [Ivan {\it et al.} J. Phys. A :Math. Theor. {\bf 45}, 195305 (2012)] together with the negativity of partial transpose ... More

Procedures for realizing an approximate universal NOT gateAug 10 2012Dec 19 2012We consider procedures to realize an approximate universal NOT gate in terms of average fidelity and fidelity deviation. The average fidelity indicates the optimality of operation on average, while the fidelity deviation does the universality of operation. ... More

Strategy for quantum algorithm design assisted by machine learningJan 07 2013Jul 17 2014We propose a method for quantum algorithm design assisted by machine learning. The method uses a quantum-classical hybrid simulator, where a "quantum student" is being taught by a "classical teacher." In other words, in our method, the learning system ... More

Experimental Demonstration on Quantum Sensitivity to Available Information in Decision MakingApr 30 2018Jan 26 2019We present an experimental illustration on the quantum sensitivity of decision making machinery. In the decision making process, we consider the role of available information, say hint, whether it influences the optimal choices. To the end, we consider ... More

A quantum algorithm for obtaining the lowest eigenstate of a Hamiltonian assisted with an ancillary qubit systemDec 28 2012Sep 17 2014We propose a quantum algorithm to obtain the lowest eigenstate of any Hamiltonian simulated by a quantum computer. The proposed algorithm begins with an arbitrary initial state of the simulated system. A finite series of transforms is iteratively applied ... More

Neighbor Discovery in a Wireless Sensor Network: Multipacket Reception Capability and Physical-Layer Signal ProcessingDec 27 2011In randomly deployed networks, such as sensor networks, an important problem for each node is to discover its \textit{neighbor} nodes so that the connectivity amongst nodes can be established. In this paper, we consider this problem by incorporating the ... More

Channel-Aware Random Access in the Presence of Channel Estimation ErrorsFeb 19 2013In this work, we consider the random access of nodes adapting their transmission probability based on the local channel state information (CSI) in a decentralized manner, which is called CARA. The CSI is not directly available to each node but estimated ... More

Asymptotic FRESH Properizer for Block Processing of Improper-Complex Second-Order Cyclostationary Random ProcessesApr 27 2013In this paper, the block processing of a discrete-time (DT) improper-complex second-order cyclostationary (SOCS) random process is considered. In particular, it is of interest to find a pre-processing operation that enables computationally efficient near-optimal ... More

Low-lying zeros of cubic Dirichlet $L$-functions and the Ratios ConjectureFeb 06 2018Jan 22 2019We compute the one-level density for the family of cubic Dirichlet $L$-functions when the support of the Fourier transform of a test function is in $(-1,1)$. We also establish the Ratios conjecture prediction for the one-level density for this family, ... More

Volovik effect in the $\pm$s-wave state for the iron-based superconductorsDec 28 2009May 10 2010We studied the field dependencies of specific heat coefficient $\gamma(H) = \lim_{T \rightarrow 0} C(T,H)/T $ and thermal conductivity coefficient $\lim_{T \rightarrow 0} \kappa(T ,H)/T$ of the $\pm$s-wave state in the mixed state. We found that it is ... More

Phonon Boost Effect on the $S^{\pm}$-wave Superconductor with Incipient BandMay 30 2018We showed that the all phonons -- not only forward-scattering phonon but also local (all-momentum-scattering) phonon -- contribute to boosting $T_c$ of the $s^{\pm}$-wave pairing state in the incipient band model. In particular, when the incipient band ... More

Can a stochastic ensemble computing machine imitate quantum computation?Apr 26 2016"Where do classical and quantum computers fit in?" or "what can and cannot they do?" have been long-standing questions. In particular, drawing a clear borderline between classical and quantum computations is obscure and still remains controversial. With ... More

Experimental demonstration of error-insensitive approximate universal-NOT gatesMar 17 2014We propose and experimentally demonstrate an approximate universal-NOT (U-NOT) operation that is robust against operational errors. In our proposal, the U-NOT operation is composed of stochastic unitary operations represented by the vertices of regular ... More

Much easing learning-with-errors problem with small-sized quantum samplesAug 17 2019Learning-with-errors (LWE) problem has been a long-standing challenge in computation science and machine learning. In particular, the LWE problem offers useful primitives in modern post-quantum cryptography, since it is believed to be "intractable" even ... More

Quantum macroscopicity measure for arbitrary spin systems and its application to quantum phase transitionsOct 10 2015Nov 29 2016We explore a previously unknown connection between two important problems in physics, i.e., quantum macroscopicity and the quantum phase transition. We devise a general and computable measure of quantum macroscopicity that can be applied to arbitrary ... More

Quantum heuristic algorithm for traveling salesman problemApr 23 2010Nov 06 2012We propose a quantum heuristic algorithm to solve a traveling salesman problem by generalizing Grover search. Sufficient conditions are derived to greatly enhance the probability of finding the tours with extremal costs, reaching almost to unity and they ... More

Quantum-mechanical machinery for rational decision-making in classical guessing gameAug 20 2015Nov 23 2015In quantum game theory, one of the most intriguing and important questions is, "Is it possible to get quantum advantages without any modification of the classical game?" The answer to this question so far has largely been negative. So far, it has usually ... More

Pairing Mechanism of the Heavily Electron Doped FeSe Systems: Dynamical Tuning of the Pairing Cutoff EnergyMay 05 2016Jun 03 2016We studied pairing mechanism of the heavily electron doped FeSe (HEDIS) systems, which commonly have one incipient hole band -- a band top below the Fermi level by a finite energy distance $\epsilon_b$ -- at $\Gamma$ point and ordinary electron bands ... More

Geometric distance-regular graphs without 4-clawsJan 03 2011A non-complete \drg $\Gamma$ is called geometric if there exists a set $\mathcal{C}$ of Delsarte cliques such that each edge of $\Gamma$ lies in a unique clique in $\mathcal{C}$. In this paper, we determine the non-complete distance-regular graphs satisfying ... More

Measure of Quantum Macroscopicity for Arbitrary Spin Systems and Quantum Phase Transition as a Genuine Macroscopic Quantum PhenomenonOct 10 2015We propose a general and computable measure of quantum macroscopicity for arbitrary spin states by quantifying interference fringes in phase space. It effectively discriminates genuine macroscopic quantum effects from mere accumulations of microscopic ... More

Quantifiable simulation of quantum computation beyond stochastic ensemble computationApr 26 2016Aug 24 2018In this study, a distinctive feature of quantum computation (QC) is characterized. To this end, a seemingly-powerful classical computing model, called "stochastic ensemble machine (SEnM)," is considered. The SEnM runs with an ensemble consisting of finite ... More

A classical-quantum hybrid oracle architecture for Boolean oracle identification in the noisy intermediate-scale quantum eraMay 14 2019Quantum algorithms have the potential to be very powerful. However, to exploit quantum parallelism, some quantum algorithms require an embedding of large classical data into quantum states. This embedding can cost a lot of resources, for instance by implementing ... More

Experimental demonstration of quantum learning speed-up with classical input dataJun 05 2017Nov 23 2018We consider quantum-classical hybrid machine learning in which large-scale input channels remain classical and small-scale working channels process quantum operations conditioned on classical input data. This does not require the conversion of classical ... More

Ricci tensor on smooth metric measure space with boundarySep 28 2017The aim of this note is to study the measure-valued Ricci tensor on smooth metric measure space with boundary, which is a generalization of Bakry-Emery's modified Ricci tensor on weighted Riemannian manifold. As an application, we offer a new approach ... More

On Wintgen ideal surfacesJul 07 2013Wintgen proved in [P. Wintgen, Sur l'in\'egalit\'e de Chen-Willmore, C. R. Acad. Sci. Paris, 288 (1979), 993--995] that the Gauss curvature $K$ and the normal curvature $K^D$ of a surface in the Euclidean 4-space $E^4$ satisfy $$K+|K^D|\leq H^2,$$ where ... More

Segre embedding and related maps and immersions in differential geometryJul 01 2013Segre embedding was introduced by C. Segre (1863--1924) in his famous 1891 article \cite{segre}. The Segre embedding plays an important roles in algebraic geometry as well as in differential geometry, mathematical physics, and coding theory. In this article, ... More

Solutions to homogeneous Monge-Ampère equations of homothetic functions and their applications to production models in economicsJul 01 2013Jul 05 2013Mathematically, a homothetic function is a function of the form $f({\bf x})=F(h(x_1,...,x_n))$, where $h$ is a homogeneous function of any degree $d\ne 0$ and $F$ is a monotonically increasing function. In economics homothetic functions are production ... More

The maximum disjoint paths problem on multi-relations social networksApr 22 2011Motivated by applications to social network analysis (SNA), we study the problem of finding the maximum number of disjoint uni-color paths in an edge-colored graph. We show the NP-hardness and the approximability of the problem, and both approximation ... More

SO(3) invariants of Seifert manifolds and their algebraic integralityMay 31 2000For Seifert manifold $M=X({p_1}/_{\f{q_1}},{p_2}/_{\f{q_2}}, ...,{p_n}/_ {\f{q_n}}), \tau^{'}_r(M)$ is calculated for all $r$ odd $\geq 3$. If $r$ is coprime to at least $n-2$ of $p_k$ (e.g. when $M$ is the Poincare homology sphere), it is proved that ... More

Highly sensitive refractometer with photonic crystal fiber long-period gratingNov 19 2007We present highly sensitive refractometers based on a long-period grating in a large mode area PCF. The maximum sensitivity is 1500 nm/RIU at a refractive index of 1.33, the highest reported for any fiber grating. The minimal detectable index change is ... More

Phase transition for the once-excited random walk on general treesDec 05 2018Dec 27 2018The phase transition of $M$-digging random on a general tree was studied by Collevecchio, Huynh and Kious (2018). In this paper, we study particularly the critical $M$-digging random walk on a superperiodic tree that is proved to be recurrent. We keep ... More

Some open problems and conjectures on submanifolds of finite type: recent developmentJan 15 2014Submanifolds of finite type were introduced by the author during the late 1970s. The first results on this subject were collected in author's books [26,29]. In 1991, a list of twelve open problems and three conjectures on finite type submanifolds was ... More

Riemannian Submanifolds: A SurveyJul 07 2013Submanifold theory is a very active vast research field which plays an important role in the development of modern differential geometry. This branch of differential geometry is still so far from being exhausted; only a small portion of an exceedingly ... More

Recent developments of biharmonic conjecture and modified biharmonic conjecturesJun 30 2013Jul 14 2013A submanifold $M$ of a Euclidean $m$-space is said to be biharmonic if $\Delta \overrightarrow H=0$ holds identically, where $\overrightarrow H$ is the mean curvature vector field and $\Delta$ is the Laplacian on $M$. In 1991, the author conjectured that ... More

A survey on geometry of warped product submanifoldsJun 30 2013The warped product $N_1\times_f N_2$ of two Riemannian manifolds $(N_1,g_1)$ and $(N_2,g_2)$ is the product manifold $N_1\times N_2$ equipped with the warped product metric $g=g_1+f^2 g_2$, where $f$ is a positive function on $N_1$. The notion of warped ... More

On purely real surfaces in Kaehler surfaces and Lorentz surfaces in Lorentzian Kaehler surfacesJul 07 2013An immersion $\phi \colon M \to \tilde M$ of a manifold $M$ into an indefinite Kaehler manifold $\tilde M$ is called purely real if the almost complex structure $J$ on $\tilde M$ carries the tangent bundle of $M$ into a transversal bundle. In this article ... More

The sharp $p$-Poincaré inequality under the measure contraction propertyMay 28 2019We obtain sharp estimate on $p$-spectral gaps, or equivalently optimal constant in $p$-Poincar\'e inequalities, for metric measure spaces satisfying measure contraction property. We also prove the rigidity for the sharp $p$-spectral gap.

Minimal submanifolds in certain types of kaehler product manifoldDec 20 2016Jan 05 2017Let $M$ be a real $l$-dimensional minimal submanifold with flat normal connection in a kaehler product manifold $\overline{M}^m\times \overline{M}^n$ where $\overline{M}^m$ and $\overline{M}^n$ are complex $m$-dimensional and complex $n$-dimensional kaehler ... More

A simpler and more efficient algorithm for the next-to-shortest path problemMay 03 2011Given an undirected graph $G=(V,E)$ with positive edge lengths and two vertices $s$ and $t$, the next-to-shortest path problem is to find an $st$-path which length is minimum amongst all $st$-paths strictly longer than the shortest path length. In this ... More

Quark-antiquark and diquark condensates in vacuum in two-flavor four-fermion interaction models with any color number $N_c$Apr 29 2009The color number $N_c$-dependence of the interplay between quark-antiquark condensates $<\bar{q}q>$ and diquark condensates $<qq>$ in vacuum in two-flavor four-fermion interaction models is researched. The results show that the $G_S$-$H_S$ (the coupling ... More

Effective potential for composite operators and for an auxiliary scalar field in a Nambu-Jona-Lasinio modelDec 12 2003We derive the effective potentials for composite operators in a Nambu-Jona-Lasinio (NJL) model at zero and finite temperature and show that in each case they are equivalent to the corresponding effective potentials based on an auxiliary scalar field. ... More

Nambu-Goldstone mechanism at finite temperature in the imaginary-time and real-time formalismAug 01 2000Oct 14 2000In the imaginay-time formalism of thermal field theory, and also in the real-time formalism but by means of some redefined physical propagators for scalar bound states by diagonalization of four-point function matrices, we reexamine the Nambu-Goldstone ... More

Discrete symmetry breaking and restoration at finite temperature in 3D Gross-Neveu modelNov 11 1998Dynamical spontaneous breaking of some discrete symmetries including special parities and time reversal and their restoration at finite temperature T are researched in 3D Gross-Neveu model by means of Schwinger-Dyson equation in the real-time thermal ... More

Geometry of warped product and CR-warped product submanifolds in Kaehler manifolds: modified versionJun 27 2018The warped product $N_1\times_f N_2$ of two Riemannian manifolds $(N_1,g_1)$ and $(N_2,g_2)$ is the product manifold $N_1\times N_2$ equipped with the warped product metric $g=g_1+f^2 g_2$, where $f$ is a positive function on $N_1$. Warped products play ... More

New characterizations of Ricci curvature on RCD metric measure spacesFeb 02 2017Jul 16 2018We prove that on a large family of metric measure spaces, if the $L^p$-gradient estimate for heat flows holds for some $p>2$, then the $L^1$-gradient estimate also holds. This result extends Savar\'e's result on metric measure spaces, and provides a new ... More

Optimal Utilization of a Cognitive Shared Channel with a Rechargeable Primary Source NodeJul 31 2011This paper considers the scenario in which a set of nodes share a common channel. Some nodes have a rechargeable battery and the others are plugged to a reliable power supply and, thus, have no energy limitations. We consider two source-destination pairs ... More

Inverse problem for Pell equation and real quadratic fields of the least typeDec 03 2012Jul 09 2013The purpose of this article is to give the solutions of the inverse problem for Pellian equations. For any rational number $0< a/b < 1$, the fundamental discriminants $D$ satisfying $(\lfloor \sqrt{D} \rfloor b + a)^2 - D b^2 = 4$ are given in terms of ... More

Conformal transformation on metric measure spacesNov 10 2015We intrinsically study the conformal transformations on metric measure spaces, including the Sobolev space, the differential structure and the curvature-dimension condition under conformal transformations. As an application, we will show how the conformal ... More

Ricci tensor on ${\rm RCD}^*(K,N)$ spacesDec 01 2014Sep 14 2015We obtain an improved Bochner inequality based on the curvature-dimension condition ${\rm RCD}^*(K,N)$ and propose a definition of $N$-dimensional Ricci tensor on metric measure spaces.

A Mixture Model to Detect Edges in Sparse Co-expression GraphsApr 03 2018In the early days of microarray data, the medical and statistical communities focused on gene-level data, and particularly on finding differentially expressed genes. This usually involved making a simplifying assumption that genes are independent, which ... More

Measure rigidity of synthetic lower Ricci curvature bound on Riemannian manifoldsFeb 03 2019Feb 26 2019In this paper we investigate Lott-Sturm-Villani's synthetic lower Ricci curvature bound on Riemannian manifolds with boundary. We prove several measure rigidity results for some important functional and geometric inequalities, which completely characterize ... More

High Quality Bidirectional Generative Adversarial NetworksMay 28 2018Generative adversarial networks (GANs) have achieved outstanding success in generating the high quality data. Focusing on the generation process, existing GANs investigate unidirectional mapping from the latent vector to the data. Later, various studies ... More

A simple characterization of generalized Robertson-Walker spacetimesNov 02 2014A generalized Robertson-Walker spacetime is the warped product with base an open interval of the real line endowed with the opposite of its metric and base any Riemannian manifold. The family of generalized Robertson-Walker spacetimes widely extends the ... More

Construction of Hamiltonian-stationary Lagrangian submanifolds of constant curvature $\varepsilon$ in complex space forms $\tilde M^n(4\varepsilon)Jul 15 2013Lagrangian submanifolds of a Kaehler manifold are called Hamiltonian-stationary (or $H$-stationary for short) if it is a critical point of the area functional restricted to compactly supported Hamiltonian variations. In [B. Y. Chen, F. Dillen, L. Verstraelen ... More

Classification of minimal Lorentz surfaces in indefinite space forms with arbitrary codimension and arbitrary indexJul 15 2013Since J. L. Lagrange initiated in 1760 the study of minimal surfaces of Euclidean 3-space, minimal surfaces in real space forms have been studied extensively by many mathematicians during the last two and half centuries. In contrast, so far very few results ... More

Submanifolds with parallel mean curvature vector in Riemannian and indefinite space formsJul 01 2013A submanifold of a pseudo-Riemannian manifold is said to have parallel mean curvature vector if the mean curvature vector field H is parallel as a section of the normal bundle. Submanifolds with parallel mean curvature vector are important since they ... More

An Enhanced Random Access with Preamble-Assisted Short-Packet Transmissions for Cellular IoT CommunicationsApr 06 2019We propose an enhanced random access (RA) with preamble-assisted short-packet transmissions to support cellular Internet-of-things (IoT) communications. A key feature of the proposed scheme is that the base station (e.g., eNodeB in LTE networks) utilizes ... More

A simple approximation algorithm for the internal Steiner minimum treeJul 15 2013Jul 17 2013For a metric graph $G=(V,E)$ and $R\subset V$, the internal Steiner minimum tree problem asks for a minimum weight Steiner tree spanning $R$ such that every vertex in $R$ is not a leaf. This note shows a simple polynomial-time $2\rho$-approximation algorithm, ... More

Joint remote preparation of a four-dimensional quantum stateJun 22 2010We propose various protocols for joint remotely prepare a four-dimensional quantum state by using two- and three-particle four-dimensional entangled state as the quantum channel. The single- and two-particle generalized projective measurement and the ... More

Identity of the imaginary-time and real-time thermal propagators for scalar bound states in a one-generation Nambu-Jona-Lasinio modelOct 25 2001By rigorous reanalysis of the results, we have proven that the propagators at finite temperature for scalar bound states in one-generation fermion condensate scheme of electroweak symmetry breaking are in fact identical in the imaginary-time and the real-time ... More

Quark-Antiquark and Diquark Condensates in Vacuum in a 3D Two-Flavor Gross-Neveu ModelApr 06 2007Jun 23 2007The effective potential analysis indicates that, in a 3D two-flavor Gross-Neveu model in vacuum, depending on less or bigger than the critical value 2/3 of $G_S/H_P$, where $G_S$ and $H_P$ are respectively the coupling constants of scalar quark-antiquark ... More

Interplay between quark-antiquark and diquark condensates in vacuum in a two-flavor Nambu-Jona-Lasinio modelMar 07 2007Jun 26 2007By means of a relativistic effective potential, we have analytically researched competition between the quark-antiquark condensates $<\bar{q}q>$ and the diquark condensates $<qq>$ in vacuum in ground state of a two-flavor Nambu-Jona-Lasinio (NJL) model ... More

Propagators for scalar bound states at finite temperature in a NJL modelJun 11 2000Sep 03 2001We reexamine physical causal propagators for scalar and pseudoscalar bound states at finite temperature in a chiral $U_L(1)\times U_R(1)$ NJL model, defined by four-point amputated functions subtracted through the gap equation, and prove that they are ... More

$U_L(N)\times U_R(N)$-invariant four-fermion interactions and Nambu-Goldstone mechanism at finite temperatureJan 08 1999In a chiral $U_L(N)\times U_R(N)$ fermion model of NJL-form, we prove that, if all the fermions are assumed to have equal masses and equal chemical potentials, then at the finite temperature $T$ below the symmetry restoration temperature $T_c$, there ... More

Multiple Kernel $k$-means Clustering using Min-Max Optimization with $l_2$ RegularizationMar 06 2018As various types of biomedical data become available, multiple kernel learning approaches have been proposed to incorporate abundant yet diverse information collected from multiple sources (or views) to facilitate disease prediction and pattern recognition. ... More

Measure rigidity of synthetic lower Ricci curvature bound on Riemannian manifoldsFeb 03 2019In this paper we investigate Lott-Sturm-Villani's synthetic lower Ricci curvature bound on Riemannian manifolds with boundary. We prove several measure rigidity results for some important functional and geometric inequalities, which completely characterize ... More

Solitons in nonlocal nonlinear media: exact resultsJun 19 2000We investigate the propagation of one-dimensional bright and dark spatial solitons in a nonlocal Kerr-like media, in which the nonlocality is of general form. We find an exact analytical solution to the nonlinear propagation equation in the case of weak ... More

MGGAN: Solving Mode Collapse using Manifold Guided TrainingApr 12 2018Mode collapse is a critical problem in training generative adversarial networks. To alleviate mode collapse, several recent studies introduce new objective functions, network architectures or alternative training schemes. However, their achievement is ... More

Noncommutative weak $(1,1)$ type estimate for a square function from ergodic theoryJul 31 2019In this paper, we investigate the boundedness of a square function from ergodic theory on noncommutative $L_{p}$-spaces. The main result is a weak $(1,1)$ type estimate of this square function. We also show the $(L_{\infty},\mathrm{BMO})$ estimate, and ... More

Conformal transformation on metric measure spacesNov 10 2015Jul 16 2018We study several problems concerning conformal transformation on metric measure spaces, including the Sobolev space, the differential structure and the curvature-dimension condition under conformal transformations. This is the first result about preservation ... More

Multisensor Management Algorithm for Airborne Sensors Using Frank-Wolfe MethodJul 23 2018This study proposes an airborne multisensor management algorithm for target tracking, taking each of multiple unmanned aircraft as a sensor. The purpose of the algorithm is to determine the configuration of the sensor deployment and to guide the mobile ... More

Almost sure convergence of the forward-backward-forward splitting algorithmMay 19 2015In this paper, we propose a stochastic forward-backward-forward splitting algorithm and prove its almost sure weak convergence in real separable Hilbert spaces. Applications to composite monotone inclusion and minimization problems are demonstrated.

Distributed Optimal Dynamic State Estimation for Cyber Intrusion Detection in Networked DC MicrogridsJul 06 2019In this paper, we present a novel distributed state estimation approach in networked DC microgrids to detect the false data injection in the microgrid control network. Each microgrid monitored by a distributed state estimator will detect if there is manipulated ... More

Algorithms for the minimum non-separating path and the balanced connected bipartition problems on grid graphs (With erratum)May 30 2011Feb 08 2014For given a pair of nodes in a graph, the minimum non-separating path problem looks for a minimum weight path between the two nodes such that the remaining graph after removing the path is still connected. The balanced connected bipartition (BCP$_2$) ... More

Two-numbers and their applications - A surveyMay 12 2018The notion of two-numbers of connected Riemannian manifolds was introduced about 35 years ago in [Un invariant geometrique riemannien, C. R. Acad. Sci. Paris Math. 295 (1982), 389--391] by B.-Y. Chen and T. Nagano. Later, two-numbers have been studied ... More

A Wintgen type inequality for surfaces in 4D neutral pseudo-Riemannian space forms and its applications to minimal immersionsJul 11 2013Let $M$ be a space-like surface immersed in a 4-dimensional pseudo-Riemannian space form $R^4_2(c)$ with constant sectional curvature $c$ and index two. In the first part of this article, we prove that the Gauss curvature $K$, the normal curvature $K^D$, ... More

$δ$-Invariants, Inequalities of Submanifolds and Their ApplicationsJul 07 2013The famous Nash embedding theorem was aimed for in the hope that if Riemannian manifolds could be regarded as Riemannian submanifolds, this would then yield the opportunity to use extrinsic help. However, as late as 1985 (see \cite{G}) this hope had not ... More

Open problems and conjectures on submanifolds of finite type revisitedJul 24 2013Submanifolds of finite type were introduced by the author during the late 1970s. The first results on this subject had been collected in author's book [Total mean curvature and sub manifolds of finite type, World Scientific, NJ, 1984]. A list of ten open ... More

Conformal mappings and first eigenvalue of Laplacian on surfacesJul 23 2013In this note we give a simple relation between conformal mapping and the first eigenvalue of Laplacian for surfaces in Euclidean spaces.

Geometry of quasi-sum production functions with constant elasticity of substitution propertyJul 15 2013A production function $f$ is called quasi-sum if there are strict monotone functions $F, h_1,...,h_n$ with $F'>0$ such that $$f(x)= F(h_1 (x_1)+...+h_n (x_n)).$$ The justification for studying quasi-sum production functions is that these functions appear ... More

Dependence of the Gauss-Codazzi equations and the Ricci equation of Lorentz surfacesJul 15 2013The fundamental equations of Gauss, Codazzi and Ricci provide the conditions for local isometric embeddability. In general, the three fundamental equations are independent for surfaces in Riemannian 4-manifolds. In contrast, we prove in this article that ... More

Covering maps and ideal embeddings of compact homogeneous spacesJun 20 2017Jun 24 2017The notion of ideal embeddings was introduced in [B.-Y. Chen, {Strings of Riemannian invariants, inequalities, ideal immersions and their applications.} The Third Pacific Rim Geometry Conference (Seoul, 1996), 7-60, Int. Press, Cambridge, MA, 1998]. Roughly ... More

Top-quark condensate at finite temperature and electroweak symmetry restorationJan 08 1999The gap equation at finite temperature in the top-quark condensate scheme of electroweak symmetry breaking is proved to have the identical form in both the imaginary and the real time formalism of thermal field theory. By means of the gap equation, combined ... More

Possible Effects of Fierz Transformations on Vacua of Some Four-Fermion Interaction ModelsSep 24 2015A theoretical research on possible effects of the Fierz transformations on the ground states (vacua) of some 2-flavor and $N_c$-color four-fermion (quark) interaction models has been systematically conducted. It has been shown that, based on the known ... More

Current quark mass and nonzero-ness of chiral condensates in thermal Nambu-Jona-Lasinio modelJun 23 2015The effect that the current quark mass $M_0$ may result in nonzero-ness of chiral condensates is systematically reexamined and analyzed in a two-flavor Nambu-Jona-Lasinio model simulating Quantum Chromodynamics (QCD) at temperature $T$ and finite quark ... More

Difermion condensates in vacuum in 2-4D four-fermion interaction modelsApr 06 2007Feb 17 2008Theoretical analysis of interplay between the condensates $<\bar{q}q>$ and $<qq>$ in vacuum is generally made by relativistic effective potentials in the mean field approximation in 2D, 3D and 4D models with two flavor and $N_c$ color massless fermions. ... More

Critical analyses of order parameter and phase transitions at high density in Gross-Neveu modelOct 03 2002Dec 18 2002By critical analyses of the order parameter of symmetry breaking, we have researched the phase transitions at high density in D=2 and D=3 Gross-Neveu (GN) model and shown that the gap equation obeyed by the dynamical fermion mass has the same effectivenesss ... More

Exact Solutions of Linearized Schwinger-Dyson Equation of Fermion Self-EnergyOct 29 2001The Schwinger-Dyson equation of fermion self-energy in the linearization approximation is solved exactly in a theory with gauge and effective four-fermion interactions. Different expressions for the indepedent solutions which respectively submit to irregular ... More