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Robust Dynamic Hamiltonian Engineering of Many-Body Spin SystemsJul 08 2019We introduce a new framework for the robust control of quantum dynamics of strongly interacting many-body systems. Our approach involves the design of periodic global control pulse sequences to engineer desired target Hamiltonians that are robust against ... More

Quantum Approximate Optimization Algorithm: Performance, Mechanism, and Implementation on Near-Term DevicesDec 03 2018The Quantum Approximate Optimization Algorithm (QAOA) is a hybrid quantum-classical variational algorithm designed to tackle combinatorial optimization problems. Despite its promise for near-term quantum applications, not much is currently understood ... More

Computational complexity of the Rydberg blockade in two dimensionsSep 13 2018We discuss the computational complexity of finding the ground state of the two-dimensional array of quantum bits that interact via strong van der Waals interactions. Specifically, we focus on systems where the interaction strength between two spins depends ... More

Quantum Convolutional Neural NetworksOct 09 2018We introduce and analyze a novel quantum machine learning model motivated by convolutional neural networks (CNN). Our quantum convolutional neural network (QCNN) makes use of only $O(\log(N))$ variational parameters for input sizes of $N$ qubits, allowing ... More

Symmetry-protected dissipative preparation of matrix product statesJun 06 2017We propose and analyze a method for efficient dissipative preparation of matrix product states that exploits their symmetry properties. Specifically, we construct an explicit protocol that makes use of driven-dissipative dynamics to prepare the Affleck-Kennedy-Lieb-Tasaki ... More

Dynamical engineering of interactions in qudit ensemblesMar 28 2017We propose and analyze a method to engineer effective interactions in an ensemble of d-level systems (qudits) driven by global control fields. In particular, we present (i) a necessary and sufficient condition under which a given interaction can be turned ... More

Quantum Kibble-Zurek mechanism and critical dynamics on a programmable Rydberg simulatorSep 14 2018Apr 01 2019Quantum phase transitions (QPTs) involve transformations between different states of matter that are driven by quantum fluctuations. These fluctuations play a dominant role in the quantum critical region surrounding the transition point, where the dynamics ... More

Quantum Control of Many-body Localized StatesAug 27 2015We propose and analyze a new approach to the coherent control and manipulation of quantum degrees of freedom in disordered, interacting systems in the many-body localized phase. Our approach leverages a number of unique features of many-body localization: ... More

Quantum metrology based on strongly correlated matterDec 29 2017We propose and analyze a new method for quantum metrology based on stable non-equilibrium states of quantum matter. Our approach utilizes quantum correlations stabilized by strong interactions and periodic driving. As an example, we present an explicit ... More

Dynamically induced many-body localizationMar 10 2017We show that a quantum phase transition from ergodic to many-body localized (MBL) phases can be induced via periodic pulsed manipulation of spin systems. Such a transition is enabled by the interplay between weak disorder and slow heating rates. Specifically, ... More

Periodic orbits, entanglement and quantum many-body scars in constrained models: matrix product state approachJul 04 2018Jan 30 2019We analyze quantum dynamics of strongly interacting, kinetically constrained many-body systems. Motivated by recent experiments demonstrating surprising long-lived, periodic revivals after quantum quenches in Rydberg atom arrays, we introduce a manifold ... More

Photonic tensor networks produced by a single quantum emitterFeb 07 2017We propose and analyze a protocol to generate two dimensional tensor network states using a single quantum system that sequentially interacts with a 1D string of qubits. This is accomplished by using parts of the string itself as a quantum queue memory. ... More

Quantum error correction and entanglement phase transition in random unitary circuits with projective measurementsMar 12 2019We analyze the dynamics of entanglement entropy in a generic quantum many-body open system from the perspective of quantum information and error corrections. We introduce a random unitary circuit model with intermittent projective measurements, in which ... More

Critical Time Crystals in Dipolar SystemsMar 14 2017Jul 07 2017We analyze the quantum dynamics of periodically driven, disordered systems in the presence of long-range interactions. Focusing on the stability of discrete time crystalline (DTC) order in such systems, we use a perturbative procedure to evaluate its ... More

Quantum Optimization for Maximum Independent Set Using Rydberg Atom ArraysAug 31 2018We describe and analyze an architecture for quantum optimization to solve maximum independent set (MIS) problems using neutral atom arrays trapped in optical tweezers. Optimizing independent sets is one of the paradigmatic, NP-hard problems in computer ... More

Numerical study of the chiral $\mathbb{Z}_3$ quantum phase transition in one spatial dimensionJun 05 2018Jul 16 2018Recent experiments on a one-dimensional chain of trapped alkali atoms [arXiv:1707.04344] have observed a quantum transition associated with the onset of period-3 ordering of pumped Rydberg states. This spontaneous $\mathbb{Z}_3$ symmetry breaking is described ... More

Probing entanglement in a many-body-localized systemMay 24 2018Jun 13 2018An interacting quantum system that is subject to disorder may cease to thermalize due to localization of its constituents, thereby marking the breakdown of thermodynamics. The key to our understanding of this phenomenon lies in the system's entanglement, ... More

Depolarization dynamics in a strongly interacting solid-state spin ensembleAug 19 2016Oct 18 2016We study the depolarization dynamics of a dense ensemble of dipolar interacting spins, associated with nitrogen-vacancy centers in diamond. We observe anomalously fast, density-dependent, and non-exponential spin relaxation. To explain these observations, ... More

Depolarization dynamics in a strongly interacting solid-state spin ensembleAug 19 2016We study the depolarization dynamics of a dense ensemble of dipolar interacting spins, associated with nitrogen-vacancy centers in diamond. We observe anomalously fast, density-dependent, and non-exponential spin relaxation. To explain these observations, ... More

Critical thermalization of a disordered dipolar spin system in diamondSep 26 2016Statistical mechanics underlies our understanding of macroscopic quantum systems. It is based on the assumption that out-of-equilibrium systems rapidly approach their equilibrium states, forgetting any information about their microscopic initial conditions. ... More

Probing quantum thermalization of a disordered dipolar spin ensemble with discrete time-crystalline orderJun 26 2018We investigate thermalization dynamics of a driven dipolar many-body quantum system through the stability of discrete time crystalline order. Using periodic driving of electronic spin impurities in diamond, we realize different types of interactions between ... More

Emergent SU(2) dynamics and perfect quantum many-body scarsDec 13 2018Motivated by recent experimental observations of coherent many-body revivals in a constrained Rydberg atom chain, we construct a weak quasi-local deformation of the Rydberg blockade Hamiltonian, which makes the revivals virtually perfect. Our analysis ... More

Imaging the local charge environment of nitrogen-vacancy centers in diamondSep 05 2018Characterizing the local internal environment surrounding solid-state spin defects is crucial to harnessing them as nanoscale sensors of external fields. This is especially germane to the case of defect ensembles which can exhibit a complex interplay ... More

Probing many-body dynamics on a 51-atom quantum simulatorJul 13 2017Nov 30 2017Controllable, coherent many-body systems can provide insights into the fundamental properties of quantum matter, enable the realization of new quantum phases and could ultimately lead to computational systems that outperform existing computers based on ... More

Critical thermalization of a disordered dipolar spin system in diamondSep 26 2016Oct 25 2017Statistical mechanics underlies our understanding of macroscopic quantum systems. It is based on the assumption that out-of-equilibrium systems rapidly approach their equilibrium states, forgetting any information about their microscopic initial conditions. ... More

Observation of discrete time-crystalline order in a disordered dipolar many-body systemOct 25 2016Understanding quantum dynamics away from equilibrium is an outstanding challenge in the modern physical sciences. It is well known that out-of-equilibrium systems can display a rich array of phenomena, ranging from self-organized synchronization to dynamical ... More

The definability criterions for convex projective polyhedral reflection groupsJun 11 2012Oct 14 2013Following Vinberg, we find the criterions for a subgroup generated by reflections $\Gamma \subset \SL^{\pm}(n+1,\mathbb{R})$ and its finite-index subgroups to be definable over $\mathbb{A}$ where $\mathbb{A}$ is an integrally closed Noetherian ring in ... More

Quantum Virtual CoolingDec 05 2018We propose a quantum information based scheme to reduce the temperature of quantum many-body systems, and access regimes beyond the current capability of conventional cooling techniques. We show that collective measurements on multiple copies of a system ... More

Probing quantum critical dynamics on a programmable Rydberg simulatorSep 14 2018Quantum phase transitions (QPTs) involve transformations between different states of matter that are driven by quantum fluctuations. These fluctuations play a dominant role in the quantum critical region surrounding the transition point, where the dynamics ... More

Distributed Source Coding with One Distortion Criterion and Correlated MessagesAug 15 2009In this paper, distributed (or multiterminal) source coding with one distortion criterion and correlated messages is considered. This problem can be also called ``Berger-Yeung problem with correlated messages''. It corresponds to the source coding part ... More

Construction of a Kinematic Variable Sensitive to the Mass of the Standard Model Higgs Boson in H->WW*->l l nu nu-bar using Symbolic RegressionJun 25 2010We derive a kinematic variable that is sensitive to the mass of the Standard Model Higgs boson (M_H) in the H->WW*->l l nu nu-bar channel using symbolic regression method. Explicit mass reconstruction is not possible in this channel due to the presence ... More

Adiabatic Quantum Algorithms for the NP-Complete Maximum-Weight Independent Set, Exact Cover and 3SAT ProblemsApr 13 2010The problem Hamiltonian of the adiabatic quantum algorithm for the maximum-weight independent set problem (MIS) that is based on the reduction to the Ising problem (as described in [Choi08]) has flexible parameters. We show that by choosing the parameters ... More

Multiplicity of the Protostar Serpens SMM 1 Revealed by Millimeter ImagingOct 13 2009The Serpens SMM 1 region was observed in the 6.9 mm continuum with an angular resolution of about 0.6 arcsec. Two sources were found to have steep positive spectra suggesting emission from dust. The stronger one, SMM 1a, is the driving source of the bipolar ... More

Injective convolution operators on ${\ell}^{\infty}(Γ)$ are surjectiveJun 15 2006Aug 01 2007Let $\Gamma$ be a discrete group and let $f \in \ell^1(\Gamma)$. We observe that if the natural convolution operator $\rho_f:\ell^{\infty}(\Gamma)\to \ell^{\inf ty}(\Gamma)$ is injective, then f is invertible in $\ell^1(\Gamma)$. Our proof simplifies ... More

Near-Online Multi-target Tracking with Aggregated Local Flow DescriptorApr 09 2015In this paper, we focus on the two key aspects of multiple target tracking problem: 1) designing an accurate affinity measure to associate detections and 2) implementing an efficient and accurate (near) online multiple target tracking algorithm. As the ... More

Maximal multiplier on Stratified groupsJun 13 2012Mar 17 2013In this paper, we prove Lp boundedness of maximal multipliers on stratified groups and maximal multipliers on product spaces of those groups.

Oscillating convolution operators on the Heisenberg groupApr 25 2012Jun 13 2012In this paper, we consider oscillating convolution operotors on the Heisenberg group $H^n_a$ with respect to the norm $\rho(x,t) = \rho_1(b x, b t)$ with $\rho_1(x,t)= (|x|^4 + t^2)^{1/4}$. We obtain $L^2$ boundedness properties using the oscillatory ... More

A Semidefinite Program for Structured BlockmodelsNov 16 2016Semidefinite programs have recently been developed for the problem of community detection, which may be viewed as a special case of the stochastic blockmodel. Here, we develop a semidefinite program that can be tailored to other instances of the blockmodel, ... More

Distribution of integral Fourier Coefficients of a Modular Form of Half Integral Weight Modulo PrimesMar 31 2007Recently, Bruinier and Ono classified cusp forms $f(z) := \sum_{n=0}^{\infty} a_f(n)q ^n \in S_{\lambda+1/2}(\Gamma_0(N),\chi)\cap \mathbb{Z}[[q]]$ that does not satisfy a certain distribution property for modulo odd primes $p$. In this paper, using Rankin-Cohen ... More

Thermal Production of Axino Dark MatterFeb 21 2012We discuss certain features of the low energy effective interactions of axion supermultiplet, which are relevant for axino cosmology, and examine the implication to thermal production of axino in the early Universe.

Axino as a sterile neutrinoApr 14 2001We present a supersymmetric axion model in which the fermionic superpartner of axion, i.e. the axino, corresponds to a sterile neutrino which would accommodate the LSND data with atmospheric and solar neutrino oscillations.

Light Quark Masses and Quarkonium DecaysJun 24 1992After discussing the intrinsic ambiguity in determining the light quark mass ratio $m_u/m_d$, we reexamine the recent proposal that this ambiguity can be resolved by applying the QCD multipole expansion for the heavy quarkonium decays. It is observed ... More

Group representations with empty residual spectrumJun 16 2009Jan 19 2010Let $X$ be a Banach space on which a discrete group $\Gamma$ acts by isometries. For certain natural choices of $X$, every element of the group algebra, when regarded as an operator on $X$, has empty residual spectrum. We show, for instance, that this ... More

Genus zero BPS invariants for local P^1Jun 23 2011Oct 09 2012We study the equivariant version of the genus zero BPS invariants of the total space of a rank 2 bundle on P^1 whose determinant is O(-2). We define the equivariant genus zero BPS invariants by the residue integrals on the moduli space of stable sheaves ... More

A note on some group $C^*$-algebras which are quasi-directly finiteMar 08 2010Jun 06 2010An algebra is said to be quasi-directly finite when any left-invertible element in its unitization is automatically right-invertible. It is an old observation of Kaplansky that the von Neumann algebra of a discrete group has this property; in this note, ... More

Directly finite algebras of pseudofunctions on locally compact groupsMay 19 2012Nov 12 2014An algebra $A$ is said to be directly finite if each left invertible element in the (conditional) unitization of $A$ is right invertible. We show that the reduced group ${\rm C}^\ast$-algebra of a unimodular group is directly finite, extending known results ... More

Persistence of Hölder continuity for non-local integro-differential equationsDec 28 2011In this paper, we consider non-local integro-differential equations under certain natural assumptions on the kernel, and obtain persistence of H\"{o}lder continuity for their solutions. In other words, we prove that a solution stays in $C^\beta$ for all ... More

Dimensionally Constrained Symbolic RegressionJun 20 2011We describe dimensionally constrained symbolic regression which has been developed for mass measurement in certain classes of events in high-energy physics (HEP). With symbolic regression, we can derive equations that are well known in HEP. However, in ... More

The maximal tubes under the deformations of a class of 3-dimensional hyperbolic cone-manifoldsMay 14 2004Recently, Hodgson and Kerckhoff found a small bound on Dehn surgered 3-manifolds from hyperbolic knots not admitting hyperbolic structures using deformations of hyperbolic cone-manifolds. They asked whether the area normalized meridian length squared ... More

The module category weight of compact exceptional Lie groupsJul 14 2013We compute the lower bound estimate for the module category weight of compact exceptional Lie groups by analyzing several Eilenberg--Moore type spectral sequences.

Severi Degrees in Cogenus 4Jan 15 1996Jan 15 1996In this paper, we give closed-form formulae for Severi degrees in cogenus 3 and 4 using Ran's method. These formulae coincide with those of I. Vainsencher and for cogenus 3 case, that of J. Harris and R. Pandharipande. Another result of this paper is ... More

Minor-Embedding in Adiabatic Quantum Computation: I. The Parameter Setting ProblemApr 30 2008We show that the NP-hard quadratic unconstrained binary optimization (QUBO) problem on a graph $G$ can be solved using an adiabatic quantum computer that implements an Ising spin-1/2 Hamiltonian, by reduction through minor-embedding of $G$ in the quantum ... More

Faster Algorithms for Constructing a Concept (Galois) LatticeFeb 19 2006Jun 01 2006In this paper, we present a fast algorithm for constructing a concept (Galois) lattice of a binary relation, including computing all concepts and their lattice order. We also present two efficient variants of the algorithm, one for computing all concepts ... More

On commutative, operator amenable subalgebras of finite von Neumann algebrasDec 20 2010Sep 12 2011An open question, raised independently by several authors, asks if a closed amenable subalgebra of ${\mathcal B}({\mathcal H})$ must be similar to an amenable C*-algebra; the question remains open even for singly-generated algebras. In this article we ... More

Singly generated operator algebras satisfying weakened versions of amenabilityFeb 06 2012Aug 03 2012We construct a singly generated subalgebra of ${\mathcal K}({\mathcal H})$ which is non-amenable, yet is boundedly approximately contractible. The example embeds into a homogeneous von Neumann algebra. We also observe that there are singly generated, ... More

Generalized Faraday law derived from classical forces in a rotating frameApr 02 2009Aug 19 2009We show the additional spin dependent classical force due to the rotation of an electron spin's rest frame is essential to derive a spin-Faraday law by using an analogy with the usual Faraday law. The contribution of the additional spin dependent force ... More

The Lane-Emden system near the critical hyperbola on nonconvex domainsMay 26 2015Jan 05 2016In this paper we study the asymptotic behavior of minimal energy solutions to the Lane-Emden system $-\Delta u = v^p$ and $-\Delta v = u^q$ on bounded domains as the index $(p,q)$ approaches to the critical hyperbola from below. Precisely, we remove the ... More

The convex real projective orbifolds with radial or totally geodesic ends: a survey of some partial resultsJan 26 2016Oct 26 2017A real projective orbifold has a radial end if a neighborhood of the end is foliated by projective geodesics that develop into geodesics ending at a common point. It has a totally geodesic end if the end can be completed to have the totally geodesic boundary. ... More

Small Flavor Conserving CP Violation in Superstring ModelsFeb 21 1994It is well known that supersymmetric models allow new sources for CP violation that arise from soft supersymmetry breaking terms. If unsuppressed, these new CP-violating phases would give too large a neutron electric dipole moment. We discuss a mechanism ... More

Small SUSY phases in string-inspired supergravityNov 24 1993In supersymmetric models, there are new CP violating phases which, if unsuppressed, would give a too large neutron electric dipole moment. We examine the possibility of small SUSY phases in string-inspired supergravity models in which supersymmetry is ... More

Dynamical gauge coupling unification from moduli stabilizationJun 12 2006In D-brane models, different part of the 4-dimensional gauge group might originate from D-branes wrapping different cycles in the internal space, and then the standard model gauge couplings at the compactification scale are determined by different cycle-volume ... More

Flavor Structure of Scherk-Schwarz Supersymmetry Breaking for Quasi-Localized Matter FieldDec 27 2003We discuss the flavor structure of soft supersymmetry breaking parameters in 5-dimensional orbifold field theories in which N=1 supersymmetry is broken by the Scherk-Schwarz boundary condition and hierarchical 4-dimensional Yukawa couplings are obtained ... More

Twisted traces of singular moduli of weakly holomorphic modular functionsMay 06 2011Zagier proved that the generating series for the traces of singular moduli is a \textit{weakly holomorphic} modular form of weight 3/2 on $\Gamma_0(4)$. Bruinier and Funke extended the results of Zagier to modular curves of arbitrary genus. Zagier also ... More

Torus actions on cohomology complex generalized Bott manifoldsJan 29 2011Aug 31 2012A torus manifold is a closed smooth manifold of dimension $2n$ having an effective smooth $T^n = (S^1)^n$-action with non-empty fixed points. Petrie \cite{petrie:1973} has shown that any homotopy equivalence between a complex projective space $\CP^n$ ... More

Splitting maps and norm bounds for the cyclic cohomology of biflat Banach algebrasOct 27 2009Apr 25 2010We revisit the old result that biflat Banach algebras have the same cyclic cohomology as $\mathbb C$, and obtain a quantitative variant (which is needed in forthcoming joint work of the author). Our approach does not rely on the Connes-Tsygan exact sequence, ... More

Uniform bounds for point cohomology of $\ell^1({\mathbb Z}_+)$ and related algebrasAug 16 2008May 14 2009It is well-known that the point cohomology of the convolution algebra $\ell^1({\mathbb Z}_+)$ vanishes in degrees 2 and above. We sharpen this result by obtaining splitting maps whose norms are bounded independently of the choice of point module. Our ... More

Simplicial cohomology of augmentation ideals in ${\ell}^1(G)$Nov 23 2007Aug 14 2008Let $G$ be a discrete group. We give a decomposition theorem for the Hochschild cohomology of $\ell^1(G)$ with coefficients in certain $G$-modules. Using this we show that if $G$ is commutative-transitive, the canonical inclusion of bounded cohomology ... More

A classification of radial and totally geodesic ends of properly convex real projective orbifolds III: the convex but nonproperly convex and non-complete-affine radial endsJul 03 2015Real projective structures on $n$-orbifolds are useful in understanding the space of representations of discrete groups into $\mathrm{SL}(n+1, \mathbb{R})$ or $\mathrm{PGL}(n+1, \mathbb{R})$. A recent work shows that many hyperbolic manifolds deform to ... More

Different Adiabatic Quantum Optimization Algorithms for the NP-Complete Exact Cover and 3SAT ProblemsOct 06 2010May 31 2011One of the most important questions in studying quantum computation is: whether a quantum computer can solve NP-complete problems more efficiently than a classical computer? In 2000, Farhi, et al. (Science, 292(5516):472--476, 2001) proposed the adiabatic ... More

Spectroscopy results from BelleJan 29 2011We report recent results on the charmonium and charmoniumlike states based on a large data sample recorded at the $\Upsilon(4S)$ and $\Upsilon(5S)$ resonances with the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider.

A classification of radial or totally geodesic ends of real projective orbifolds I: a survey of resultsJan 02 2015Jan 26 2016Real projective structures on $n$-orbifolds are useful in understanding the space of representations of discrete groups into $\mathrm{SL}(n+1, \mathbb{R})$ or $\mathrm{PGL}(n+1, \mathbb{R})$. A recent work shows that many hyperbolic manifolds deform to ... More

Convex and concave decompositions of affine $3$-manifoldsNov 05 2014Sep 27 2016An (flat) affine $3$-manifold is a $3$-manifold with an atlas of charts to an affine space ${\mathbf R}^3$ with transition maps in the affine transformation group $Aff({\mathbf R}^3)$. We will show that a closed affine $3$-manifold is either an affine ... More

Relativistic spin operator and Lorentz transformation of spin state of a massive Dirac particleSep 20 2012Jul 08 2013We have shown the covariant relativistic spin operator is equivalent to the spin operator commuting with the free Dirac Hamiltonian. This implies that the covariant relativistic spin operator is a good quantum observable. The covariant relativistic spin ... More

The PL-methods for hyperbolic 3-manifolds to prove tamenessFeb 23 2006Using PL-methods, we prove the Marden's conjecture that a hyperbolic 3-manifold $M$ with finitely generated fundamental group and with no parabolics are topologically tame. Our approach is to form an exhaustion $M_i$ of $M$ and modify the boundary to ... More

A gap theorem for the ZL-amenability constant of a finite groupOct 20 2014May 19 2015It was shown in [A. Azimifard, E. Samei, N. Spronk, JFA 2009; arxiv 0805.3685] that the ZL-amenability constant of a finite group is always at least 1, with equality if and only if the group is abelian. It was also shown in the same paper that for any ... More

Triviality of the generalized Lau product associated to a Banach algebra homomorphismNov 24 2015Jan 08 2016Several papers have, as their raison d'etre, the exploration of the \emph{generalized Lau product} associated to a homomorphism $T:B\to A$ of Banach algebras. In this short note, we demonstrate that the generalized Lau product is isomorphic as a Banach ... More

Maximal multipliers on compact manifolds without boundaryJul 01 2012Mar 20 2014Hormander-Mihklin type multiplier theorem on compacts manifolds withour boundary has been obtained by using the wave kernels. We consider maximal multiplies on this setting. To obtain the result, we carefully deal with the remainder terms and find an ... More

Classification of Bott manifolds up to dimension eightDec 11 2011We show that three- and four-stage Bott manifolds are classified up to diffeomorphism by their integral cohomology rings. In addition, any cohomology ring isomorphism between two three-stage Bott manifolds can be realized by a diffeomorphism between the ... More

Atmospheric and Solar Neutrino Masses and Abelian Flavor SymmetryFeb 16 2001Recent atmospheric and solar neutrino experiments suggest that neutrinos have small but nonzero masses. They further suggest that mass eigenvalues have certain degree of hierarchical structures, and also some mixing angles are near-maximal while the others ... More

Gauge Unification and Flavor Hierarchy from Extra DimensionsJan 04 2004Extra dimension provides an attractive way to break symmetry by boundary conditions which can be useful to construct a natural grand unified theory avoiding the doublet-triplet splitting problem and the proton decay problem. It can provide also an elegant ... More

Relativistic hydrodynamic jets in the intracluster mediumMay 12 2017We have performed the first three-dimensional relativistic hydrodynamic simulations of extragalactic jets of pure leptonic and baryonic plasma compositions propagating into a hydrostatic intracluster medium environment. The numerical simulations use a ... More

Efficient Structured Surrogate Loss and Regularization in Structured PredictionSep 14 2018In this dissertation, we focus on several important problems in structured prediction. In structured prediction, the label has a rich intrinsic substructure, and the loss varies with respect to the predicted label and the true label pair. Structured SVM ... More

Quantum Key Distribution Using Quantum Faraday RotatorsDec 26 2006Aug 26 2007We propose a new quantum key distribution (QKD) protocol based on the fully quantum mechanical states of the Faraday rotators. The protocol is unconditionally secure against collective attacks for multi-photon source up to two photons on a noisy environment. ... More

The convex real projective orbifolds with radial or totally geodesic ends: a survey of some partial resultsJan 26 2016Aug 18 2016A real projective orbifold is an $n$-dimensional orbifold modeled on ${\mathbf R}P^n$ with the group $PGL(n+1, {\mathbf R})$-action. We concentrate on an orbifold that contains a compact codimension $0$ submanifold whose complement is a union of neighborhoods ... More

A twisted inclusion between tensor products of operator spaces, with an application to 2-cocyclesJun 20 2016Given operator spaces $V$ and $W$, let $\widetilde{W}$ denote the opposite operator space structure on the same underlying Banach space. Although the identity map $W\to \widetilde{W}$ is in general not completely bounded, we show that the identity map ... More

Geometric structures on orbifolds and holonomy representationsJul 24 2001Jul 29 2003An orbifold is a topological space modeled on quotient spaces of a finite group actions. We can define the universal cover of an orbifold and the fundamental group as the deck transformation group. Let $G$ be a Lie group acting on a space $X$. We show ... More

Realization of compact spaces as cb-Helson setsApr 14 2015Jul 29 2015We show that, given a compact Hausdorff space $\Omega$, there is a compact group ${\mathbb G}$ and a homeomorphic embedding of $\Omega$ into ${\mathbb G}$, such that the restriction map ${\rm A}({\mathbb G})\to C(\Omega)$ is a complete quotient map of ... More

Spontaneous symmetry breaking of arbitrageJul 26 2011Apr 18 2012We introduce the concept of spontaneous symmetry breaking to arbitrage modeling. In the model, the arbitrage strategy is considered as being in the symmetry breaking phase and the phase transition between arbitrage mode and no-arbitrage mode is triggered ... More

Anisotropy universe in doubly warped product schemeAug 10 2014Jan 11 2016We study the GMGHS spacetimes to analyze the evolution of the anisotropy universe, which can be treated as a doubly warped products manifold possessing warping functions (or scale factor) having the Kantowski-Sachs solution which represents homogeneous ... More

Compressive random access with multiple resource blocks and fast retrialFeb 26 2019In this paper, we propose a compressive random access (CRA) scheme using multiple resource blocks (RBs) to support massive connections for machine type communications (MTC). The proposed CRA scheme is scalable. As a result, if the number of devices increases, ... More

A Game-Theoretic Approach for NOMA-ALOHAJan 08 2018Non-orthogonal multiple access (NOMA) can improve the spectral efficiency by exploiting the power domain and successive interference cancellation (SIC), and it can be applied to various transmission schemes including random access that plays a crucial ... More

The two components of the SO(3)-character space of the fundamental group of a closed surface of genus 2Feb 16 2010Sep 02 2010We use geometric techniques to explicitly find the topological structure of the space of SO(3)-representations of the fundamental group of a closed surface of genus 2 quotient by the conjugation action by SO(3). There are two components of the space. ... More

Cosmology of Radiatively Generated Axion ScaleJan 05 1997We discuss some cosmological aspects of supersymmetric axion models in which the axion scale is radiatively generated in terms of the weak scale and the Planck scale. They include thermal inflation, axions produced by the decay of oscillating Peccei-Quinn ... More

SUSY Breaking at the Tip of Throat and Mirage MediationMay 23 2007May 27 2007We discuss some features of supersymmetry breaking induced by a brane-localized source which is stabilized at the IR end of warped throat, and also the resulting mirage mediation pattern of soft terms of the visible fields which are localized in the bulk ... More

Axions and the Strong CP Problem in M-theoryJun 25 1997We examine the possibility that the strong CP problem is solved by string-theoretic axions in strong-coupling limit of the E_8 x E_8 heterotic string theory (M-theory). We first discuss some generic features of gauge kinetic functions in compactified ... More

Approximately multiplicative maps from weighted semilattice algebrasMar 30 2012May 06 2013We investigate which weighted convolution algebras $\ell^1_\omega(S)$, where $S$ is a semilattice, are AMNM in the sense of Johnson (JLMS, 1986). We give an explicit example where this is not the case. We show that the unweighted examples are all AMNM, ... More

Co-clustering of Nonsmooth GraphonsJul 22 2015Performance bounds are given for exploratory co-clustering/ blockmodeling of bipartite graph data, where we assume the rows and columns of the data matrix are samples from an arbitrary population. This is equivalent to assuming that the data is generated ... More

Different moment-angle manifolds arising from two polytopes having the same bigraded Betti numbersSep 04 2012Two simple polytopes of dimension 3 having the identical bigraded Betti numbers but non-isomorphic Tor-algebras are presented. These polytopes provide two homotopically different moment-angle manifolds having the same bigraded Betti numbers. These two ... More

On the estimate of distance traveled by a particle in a disk-like vortex patchMar 14 2019We consider the incompressible two-dimensional Euler equation in the plane in the case when its initial vorticity is the characteristic function of a bounded open set. We show that the travel distance grows linearly for most of fluid particles initially ... More

Convex and concave decompositions of affine $3$-manifoldsNov 05 2014Aug 22 2018A (flat) affine $3$-manifold is a $3$-manifold with an atlas of charts to an affine space $\mathbb{R}^3$ with transition maps in the affine transformation group $\mathrm{Aff}(\mathbb{R}^3)$. We will show that a connected closed affine $3$-manifold is ... More