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Snapshot projection optical tomographyJun 11 2019We present a new plenoptic microscopy configuration consisting of an objective lens and a micro-lens array (MLA), which is used as a tube lens. The new system that we named as snapshot projection optical tomography (SPOT) can directly record the projection ... More

Two Symmetric Properties of Mersenne Numbers and Fermat NumbersApr 27 2013May 09 2013Mersenne numbers and Fermat numbers are two hot and difficult issues in number theory. This paper constructs a special group for every positive odd number other than 1, and discovers an algorithm for determining the multiplicative order of 2 modulo q ... More

Configuration space, moduli space and 3-fold covering spaceFeb 02 2018A function from configuration space to moduli space of surface may induce a homomorphism between their fundamental groups which are braid groups and mapping class groups of surface, respectively. This map $\phi: B_k \rightarrow \Gamma_{g,b}$ is induced ... More

Pillar switchings and acyclic embedding in mapping class groupFeb 15 2012The braid group $B_g$ is embedded in the ribbon braid group that is defined to be the mapping class group $\Gamma_{0,(g),1}$. By gluing two copies of surface $S_{0,g+2}$ along $g+1$ holes, we get surface $S_{g,1}$. A pillar switching is a self-homeomorphism ... More

D-UNet: a dimension-fusion U shape network for chronic stroke lesion segmentationAug 14 2019Assessing the location and extent of lesions caused by chronic stroke is critical for medical diagnosis, surgical planning, and prognosis. In recent years, with the rapid development of 2D and 3D convolutional neural networks (CNN), the encoder-decoder ... More

The braidings in the mapping class groups of surfacesMay 08 2012The disjoint union of mapping class groups of surfaces forms a braided monoidal category $\mathcal M$, as the disjoint union of the braid groups $\mathcal B$ does. We give a concrete, and geometric meaning of the braiding $\beta_{r,s}$ in $\M$. Moreover, ... More

Validity condition of the Jarzynski relation for a classical mechanical systemJun 09 2005Oct 05 2005Recently, Jarzynski suggested a striking thermodynamic equation that relates free energy change of a system and work done on the system during arbitrary nonequilibrium processes, which has been believed to hold irrespective of detailed nature of the nonequilibrium ... More

Finite group actions and G-monopole classes on smooth 4-manifoldsAug 19 2011Aug 27 2014On a smooth closed oriented $4$-manifold $M$ with a smooth action by a compact Lie group $G$, we define a $G$-monopole class as an element of $H^2(M;\Bbb Z)$ which is the first Chern class of a $G$-equivariant Spin$^c$ structure which has a solution of ... More

Transfer maps and nonexistence of joint determinantMar 31 2008Jun 29 2009Transfer Maps, sometimes called norm maps, for Milnor's $K$-theory were first defined by Bass and Tate (1972) for simple extensions of fields via tame symbol and Weil's reciprocity law, but their functoriality had not been settled until Kato (1980). On ... More

Surgery and equivariant Yamabe invariantApr 18 2006May 12 2006We consider the equivariant Yamabe problem, i.e. the Yamabe problem on the space of G-invariant metrics for a compact Lie group G. The G-Yamabe invariant is analogously defined as the supremum of the constant scalar curvatures of unit volume G-invariant ... More

Syzygies of A Tower of Compact Local Hermitian Symmetric Spaces of Finite TypeJan 30 2019Let $X$ be a $n$ dimensional compact local Hermitian symmetric space of non-compact type and $L=\shO(K_X)\tens\shO(qM)$ be an adjoint line bundle. Let $c>0$ be a constant. Assume the curvature of $M$ is $\ge c\omega$, where $\omega$ is the k\"ahler form ... More

On multilinearity and skew-symmetry of certain symbols in motivic cohomology of fieldsJan 09 2008Sep 15 2008The purpose of the present article is to show the multilinearity for symbols in Goodwillie-Lichtenbaum complex in two cases. The first case shown is where the degree is equal to the weight. In this case, the motivic cohomology groups of a field are isomorphic ... More

Triviality of a trace on the space of commuting trace-class self-adjoint operatorsMar 17 2008Mar 26 2008In the present article, we investigate a possibility of a real-valued map on the space of tuples of commuting trace-class self-adjoint operators, which behaves like the usual trace map on the space of trace-class linear operators. It turns out that such ... More

T-structure and the Yamabe invariantDec 24 2008Nov 22 2010The Yamabe invariant is an invariant of a closed smooth manifold, which contains information about possible scalar curvature on it. It is well-known that a product manifold T^m\times B where T^m$ is the m-dimensional torus, and B is a closed spin manifold ... More

Connected sums with HP^n or CaP^2 and the Yamabe invariantOct 12 2007Feb 24 2011Let $M$ be a smooth closed $4k$-manifold whose Yamabe invariant $Y(M)$ is nonpositive. We show that $$Y(M\sharp l \Bbb HP^k\sharp m \bar{\Bbb HP^k})=Y(M),$$ where $l,m$ are nonnegative integers, and $\Bbb HP^k$ is the quaternionic projective space. When ... More

Probing the Gauge Content of Heavy Resonances with Soft RadiationAug 26 2009The use of energy flow is investigated as a diagnostic tool for determining the color SU(3) representation of new resonances. It is found that the pattern of soft gluon radiation into a rapidity gap depends on color flow in the hard scattering, and reflects ... More

Breakdown of the Jarzynski relation for an adiabatic stretching of an isotropic springOct 05 2005Oct 11 2005We perform a theoretical test of Jarzynski relation for an adiabatic stretching of an isotropic spring, which is an exactly solvable model. It turns out that Jarzynski relation does not hold even when the entire infinite momentum space of the system state ... More

Reply to Note on cond-mat/0510270: Jarzynski equation for adiabatically stretched rotorDec 12 2005Although the analysis in cond-mat/0510270 is correct, this doesn't mean Jarzynski relation holds always for an arbitrary process. There exists a sufficient and necessary condition for Jarzynski relation to hold for an adiabatic parameter switching process. ... More

Surgery, Yamabe invariant, and Seiberg-Witten theoryOct 12 2007Nov 06 2010By using the gluing formula of the Seiberg-Witten invariant, we compute the Yamabe invariant Y(X) of 4-manifolds X obtained by performing surgeries along points, circles or tori on compact Kaehler surfaces. For instance, if M is a compact Kaehler surface ... More

Ricci curvature and monopole classes on 3-manifoldsMar 03 2009May 17 2012We prove an L^2-estimate involving Ricci curvature and a harmonic 1-form on a closed oriented Riemannian 3-manifold admitting a solution of any rescaled Seiberg-Witten equations. We also give a necessary condition to be a monopole class on some special ... More

Global attractor for a nonlinear one-dimensional compressible viscous micropolar fluidJun 05 2018This paper considers the dynamical behavior of solutions of constitutive systems for 1D compressible viscous and heat-conducting micropolar fluids. With proper constraints on initial data, we prove the existence of global attractors in generalized Sobolev ... More

Liouville-type theorems and applications to geometry on complete Riemannian manifoldsNov 06 2010On a complete Riemannian manifold M with Ricci curvature satisfying $$\textrm{Ric}(\nabla r,\nabla r) \geq -Ar^2(\log r)^2(\log(\log r))^2...(\log^{k}r)^2$$ for $r\gg 1$, where A>0 is a constant, and r is the distance from an arbitrarily fixed point in ... More

Non-equilibrium spin polarization effects in spin-orbit coupling system and contacting metallic leadsOct 25 2005Nov 08 2006We study theoretically the current-induced spin polarization effect in a two-terminal mesoscopic structure which is composed of a semiconductor two-dimensional electron gas (2DEG) bar with Rashba spin-orbit (SO) interaction and two attached ideal leads. ... More

G-monopole invariants on some connected sums of 4-manifoldsJun 17 2014On a smooth closed oriented $4$-manifold $M$ with a smooth action of a finite group $G$ on a Spin$^c$ structure, $G$-monopole invariant is defined by "counting" $G$-invariant solutions of Seiberg-Witten equations for any $G$-invariant Riemannian metric ... More

Some refined higher type adjunction inequalities on 4-manifoldsJun 17 2014We further sharpen higher type adjunction inequalities of P. Ozsv\'ath and Z. Szab\'o on a 4-manifold $M$ with a nonzero Seiberg-Witten invariant for a Spin$^c$ structure $\frak{s}$, when an embedded surface $\Sigma\subset M$ satisfies $[\Sigma]\cdot ... More

On the nonexistence of Einstein metric on 4-manifoldsSep 29 2008Nov 16 2010By using the gluing formulae of the Seiberg-Witten invariant, we show the nonexistence of Einstein metric on manifolds obtained from a 4-manifold with nontrivial Seiberg-Witten invariant by performing sufficiently many connected sums or appropriate surgeries ... More

Scattering wave function approach to multi-terminal mesoscopic system with spin-orbit couplingMay 13 2006In this paper,we present a detailed formulation to solve the scattering wave function for a multi-terminal mesoscopic system with spin-orbit coupling. In addition to terminal currents, all local quantities can be calculated explicitly by taking proper ... More

Morse functions on the moduli space of $G_2$ structuresOct 04 2002May 04 2003Let $ \mathfrak{M}$ be the moduli space of torsion free $ G_2$ structures on a compact 7-manifold $ M$, and let $ \mathfrak{M}_1 \subset \mathfrak{M}$ be the $ G_2$ structures with volume($M$) $=1$. The cohomology map $ \pi^3: \mathfrak{M} \to H^3(M, ... More

Ring class fields by eta-quotientsApr 12 2014Jul 14 2016We generate ring class fields of imaginary quadratic fields in terms of the special values of certain eta-quotients, which are related to the relative norms of Siegel-Ramachandra invariants. These give us minimal polynomials with relatively small coefficients ... More

Temperature and Polarization Patterns in Anisotropic CosmologiesApr 06 2010Apr 15 2010We study the coherent temperature and polarization patterns produced in homogeneous but anisotropic cosmological models. We show results for all Bianchi types with a Friedman-Robertson-Walker limit (i.e. Types I, V, VII$_{0}$, VII$_{h}$ and IX) to illustrate ... More

State dependent spread of entanglement in relatively local HamiltoniansNov 17 2018Feb 15 2019Relatively local Hamiltonians are a class of background independent non-local Hamiltonians from which local theories emerge within a set of short-range entangled states. The dimension, topology and geometry of the emergent local theory is determined by ... More

Stochastic quantization and holographic Wilsonian renormalization group of free massive fermionFeb 01 2017Jun 05 2018We extend the relation between stochstic quantization and Holographic Wilsonian Renormalization Group to the massive fermion case in Euclidean AdS space. The original suggestion about the explicit relation between the two theories is in arXiv:1209.2242. ... More

Additive uniqueness of $\mathtt{PRIMES}-1$ for multiplicative functionsAug 10 2017Let $\mathtt{PRIMES}$ be the set of all primes. We show that a multiplicative function which satisfies \[ f(p+q-2) = f(p) + f(q) - f(2) \text{ for }p,q \in \mathtt{PRIMES} \] is one of the following: \begin{enumerate} \item $f$ is the identity function ... More

Online Sequence Training of Recurrent Neural Networks with Connectionist Temporal ClassificationNov 21 2015Feb 02 2017Connectionist temporal classification (CTC) based supervised sequence training of recurrent neural networks (RNNs) has shown great success in many machine learning areas including end-to-end speech and handwritten character recognition. For the CTC training, ... More

Robust Chinese Word Segmentation with Contextualized Word RepresentationsJan 17 2019In recent years, after the neural-network-based method was proposed, the accuracy of the Chinese word segmentation task has made great progress. However, when dealing with out-of-vocabulary words, there is still a large error rate. We used a simple bidirectional ... More

A New Approach to User Scheduling in Massive Multi-User MIMO Broadcast ChannelsMar 27 2014In this paper, a new user-scheduling-and-beamforming method is proposed for multi-user massive multiple-input multiple-output (massive MIMO) broadcast channels in the context of two-stage beamforming. The key ideas of the proposed scheduling method are ... More

Embeddedness of minimal submanifolds in homogeneous spacesFeb 01 2010Nov 18 2010This paper has been withdrawn.

Scalar Curvature Functions of Almost-Kähler MetricsSep 14 2014Sep 18 2014For a closed smooth manifold $M$ admitting a symplectic structure, we define a smooth topological invariant $Z(M)$ using almost-K\"ahler metrics, i.e. Riemannian metrics compatible with symplectic structures. We also introduce $Z(M, [[\omega]])$ depending ... More

Is repulsive Casimir force physical?Aug 30 2004The Casimir force for charge-neutral, perfect conductors of non-planar geometric configurations have been investigated. The configurations are: (1) the plate-hemisphere, (2) the hemisphere-hemisphere and (3) the spherical shell. The resulting Casimir ... More

Symmetric lens with extended depth of focusNov 27 2008Feb 03 2009The lens surface profile is derived based on the instantaneous focal length versus the lens radius data. The lens design based on instantaneous focal length versus the lens radius data has many useful applications in software assisted image focusing technology. ... More

Counting Rational Points on Kummer surfacesJan 30 2019Aug 03 2019We consider the problem of counting the number of rational points on the family of Kummer surfaces associated with two non-isogenous elliptic curves. For this two-parameter family we prove Manin's unity, using the presentation of the Kummer surfaces as ... More

Holographic description of large N gauge theoryNov 05 2010Jun 28 2011Based on the earlier work [S.-S. Lee, Nucl. Phys. B 832, 567 (2010)], we derive a holographic dual for the D-dimensional U(N) lattice gauge theory from a first principle construction. The resulting theory is a lattice field theory of closed loops, dubbed ... More

A Competitive Algorithm for Online Multi-Robot Exploration of a Translating PlumeNov 07 2018In this paper, we study the problem of exploring a translating plume with a team of aerial robots. The shape and the size of the plume are unknown to the robots. The objective is to find a tour for each robot such that they collectively explore the plume. ... More

Dimension-Wise Importance Sampling Weight Clipping for Sample-Efficient Reinforcement LearningMay 07 2019In importance sampling (IS)-based reinforcement learning algorithms such as Proximal Policy Optimization (PPO), IS weights are typically clipped to avoid large variance in learning. However, policy update from clipped statistics induces large bias in ... More

Character-Level Incremental Speech Recognition with Recurrent Neural NetworksJan 25 2016Jan 28 2016In real-time speech recognition applications, the latency is an important issue. We have developed a character-level incremental speech recognition (ISR) system that responds quickly even during the speech, where the hypotheses are gradually improved ... More

Enhancing Non-Orthogonal Multiple Access By Forming Relaying Broadcast ChannelsOct 26 2015In this paper, using relaying broadcast channels (RBCs) as component channels for non-orthogonal multiple access (NOMA) is proposed to enhance the performance of NOMA in single-input single-output (SISO) cellular downlink systems. To analyze the performance ... More

The capacity for the linear time-invariant Gaussian relay channelSep 26 2011In this paper, the Gaussian relay channel with linear time-invariant relay filtering is considered. Based on spectral theory for stationary processes, the maximum achievable rate for this subclass of linear Gaussian relay operation is obtained in finite-letter ... More

Simple proofs for universal binary Hermitian latticesMar 26 2008If a positive definite Hermitian lattice represents all positive integers, we call it universal. Several mathematicians, including the author, found 25 universal binary Hermitian lattices. But their ad hoc proofs are complicated. We give simple and unified ... More

1-rigidity of CR submanifolds in spheresJun 08 2005Aug 16 2005We propose a unified computational framework for the problem of deformation and rigidity of submanifolds in a homogeneous space under geometric constraint. A notion of 1-rigidity of a submanifold under admissible deformations is introduced. It measures ... More

Identifying the production process of new physics at colliders; symmetric or asymmetric?Mar 07 2016Aug 23 2016We propose a class of kinematic variables, which is a smooth generalization of min-max type mass variables such as the Cambridge-$M_{T2}$ and $M_2$, for measuring a mass spectrum of intermediate resonances in a semi-invisibly decaying pair production. ... More

Beam Design and User Scheduling for Non-Orthogonal Multiple Access with Multiple Antennas Based on Pareto-OptimalityMay 19 2017In this paper, an efficient transmit beam design and user scheduling method is proposed for multi-user (MU) multiple-input single-output (MISO) non-orthogonal multiple access (NOMA) downlink, based on Pareto-optimality. The proposed beam design and user ... More

Holomorphic maps between closed SU(l,m)-orbits in GrassmannianSep 06 2018Orbits of $SU(\ell, m)$ in a Grassmannian manifold have homogeneous CR structures. In this paper, we study germs of smooth CR mappings sending a closed orbit of $SU(\ell,m)$ into a closed orbit of $SU(\ell',m')$ in Grassmannian manifolds. We show that ... More

Recent Developments in Non-Fermi Liquid TheoryMar 23 2017Non-Fermi liquids arise when metals are subject to singular interactions mediated by soft collective modes. In the absence of well-defined quasiparticle, universal physics of non-Fermi liquids is captured by interacting field theories which replace Landau ... More

On positiveness and contractiveness of the integral operator arising from the beam deflection problem on elastic foundationAug 21 2014We provide a complete proof that there are no nontrivial eigenvalues of the integral operator $\mathcal{K}_l$ outside the interval $(0,1/k)$. $\mathcal{K}_l$ arises naturally from the deflection problem of a beam with length $l$ resting horizontally on ... More

Single Stream Parallelization of Recurrent Neural Networks for Low Power and Fast InferenceMar 30 2018As neural network algorithms show high performance in many applications, their efficient inference on mobile and embedded systems are of great interests. When a single stream recurrent neural network (RNN) is executed for a personal user in embedded systems, ... More

Conservation laws for a class of Third order Evolutionary differential systemsSep 15 1999The conservation laws of the third order quasilinear scalar evolution equations are considered via differential system and characteristic cohomology. We find a subspace of 2 forms in the infinite prolonged space in which every conservation law has a unique ... More

Mechanism behind self-sustained oscillations in direct current glow discharges and dusty plasmasFeb 28 2013Apr 09 2013An alternative explanation to the mechanism behind self-sustained oscillations of ions in direct current (DC) glow discharges is provided. Such description is distinguished from the one provided by the fluid models, where oscillations are attributed to ... More

A Novel Device for Generating Terahertz Radiation PulsesJun 13 2011May 11 2012The dynamics of a core-shell structured ionized particle between two parallel conductor plates, which is biased with a direct current (DC) voltage, have been investigated. It has been found that an ionized particle oscillates rapidly between the DC voltage ... More

Nucleon Transversity and Hyperon PolarizationAug 09 2016We calculate the transverse polarizations of the produced hyperons in the semi-inclusive deep inelastic scattering of unpolarized lepton beam on transversely polarized nucleon, since these polarizations provide a potential method for extracting the transversity ... More

Transverse Spin Polarization of $τ^-$ in ${\bar{B}}^0\rightarrow D^{+} τ^- {\barν}$ and Charged Higgs BosonApr 27 2015May 06 2015The spin of the $\tau$ lepton in the semiletonic process ${\bar{B}}^0\rightarrow D^{+} \tau^- {\bar{\nu}}$ can be polarized in the direction which is normal to the reaction plane, if the charged Higgs boson exists and its coupling to quarks has a complex ... More

Online Sequence Training of Recurrent Neural Networks with Connectionist Temporal ClassificationNov 21 2015Jan 07 2016Connectionist temporal classification (CTC) based supervised sequence training of recurrent neural networks (RNNs) has shown great success in many machine learning areas including end-to-end speech and handwritten character recognition. For the CTC training, ... More

FPGA Based Implementation of Deep Neural Networks Using On-chip Memory OnlyFeb 04 2016Aug 29 2016Deep neural networks (DNNs) demand a very large amount of computation and weight storage, and thus efficient implementation using special purpose hardware is highly desired. In this work, we have developed an FPGA based fixed-point DNN system using only ... More

Intrinsic Brightness Temperatures of Compact Radio Jets as a Function of FrequencyDec 10 2014We present results of our investigation of the radio intrinsic brightness temperatures of compact radio jets. The intrinsic brightness temperatures of about 100 compact radio jets at 2, 5, 8, 15, and 86 GHz are estimated based on large VLBI surveys conducted ... More

Prototype for Extended XDB Using WikiNov 24 2012This paper describes a prototype of extended XDB. XDB is an open-source and extensible database architecture developed by National Aeronautics and Space Administration (NASA) to provide integration of heterogeneous and distributed information resources ... More

On the Pareto-Optimal Beam Structure and Design for Multi-User MIMO Interference ChannelsNov 18 2012In this paper, the Pareto-optimal beam structure for multi-user multiple-input multiple-output (MIMO) interference channels is investigated and a necessary condition for any Pareto-optimal transmit signal covariance matrix is presented for the K-pair ... More

Embeddedness of proper minimal submanifolds in homogeneous spacesNov 18 2010We prove the three embeddedness results as follows. $({\rm i})$ Let $\Gamma_{2m+1}$ be a piecewise geodesic Jordan curve with $2m+1$ vertices in $\mathbb{R}^n$, where $m$ is an integer $\geq2$. Then the total curvature of $\Gamma_{2m+1}<2m\pi$. In particular, ... More

Dynamic Hand Gesture Recognition for Wearable Devices with Low Complexity Recurrent Neural NetworksAug 14 2016Gesture recognition is a very essential technology for many wearable devices. While previous algorithms are mostly based on statistical methods including the hidden Markov model, we develop two dynamic hand gesture recognition techniques using low complexity ... More

Willmore Legendrian surfaces in pseudoconformal 5-sphereJul 03 2007Let $ X: M \hook S^5$ be a compact Legendrian surface in pseudoconformal(CR) 5-sphere. We introduce a pseudoconformally invariant Willmore type second order functional $ \W(X)$, and study its critical points called Willmore Legendrian surfaces. The fifth ... More

An Omori-Yau maximum principle for semi-elliptic operators and Liouville-type theoremsNov 15 2011Jun 18 2013We generalize the Omori-Yau almost maximum principle of the Laplace-Beltrami operator on a complete Riemannian manifold $M$ to a second-order linear semi-elliptic operator $L$ with bounded coefficients and no zeroth order term. Using this result, we prove ... More

Bandwidth Extension on Raw Audio via Generative Adversarial NetworksMar 21 2019Neural network-based methods have recently demonstrated state-of-the-art results on image synthesis and super-resolution tasks, in particular by using variants of generative adversarial networks (GANs) with supervised feature losses. Nevertheless, previous ... More

Binarization Trees and Random Number GenerationFeb 19 2016May 11 2018An m-extracting procedure produces unbiased random bits from a loaded dice with m faces. A binarization takes inputs from an m-faced dice and produce bit sequences to be fed into a (binary) extracting procedure to obtain random bits. Thus, binary extracting ... More

Peres-Style Recursive AlgorithmsMay 11 2018May 22 2018Peres algorithm applies the famous von Neumann trick recursively to produce unbiased random bits from biased coin tosses. Its recursive nature makes the algorithm simple and elegant, and yet its output rate approaches the information-theoretic upper bound. ... More

Charged particle displayDec 15 2008Aug 17 2009An optical shutter based on charged particles is presented. The output light intensity of the proposed device has an intrinsic dependence on the interparticle spacing between charged particles, which can be controlled by varying voltages applied to the ... More

COMBINE: a novel drug discovery platform designed to capture insight and experience of usersNov 13 2017The insight and experience gained by a researcher are often lost because the current productive and analytics software are inherently data-centric, disconnected, and scattered. The connected nature of insight and experience can be captured if the applications ... More

Physics of self-sustained oscillations in the positive glow coronaMar 28 2012Jul 18 2012The physics of self-sustained oscillations in the phenomenon of positive glow corona is presented. The dynamics of charged-particle oscillation under static electric field has been briefly outlined; and, the resulting self-sustained current oscillations ... More

Charged-particle oscillation in DC voltage biased plane-parallel conductorsJun 28 2011Mar 16 2012The phenomenon of charged-particle oscillation in DC voltage biased plane-parallel conductors is discussed. Traditionally accepted mechanism for explaining the oscillatory behavior of charged particles in such system attributes the phenomenon to a process ... More

Lens design based on instantaneous focal functionFeb 02 2009Feb 04 2009The formula for the lens is derived based on the information of instantaneous focal function. Focal function is an important tool in designing lenses with extended depth of focus (EDoF) because this allows EDoF lens designers to try out various mathematical ... More

Energy harvesting by utilization of nanohelicesJan 07 2009Mar 18 2009An energy harvesting device based on nanohelices is presented. The energy harvesting scheme based on nanohelices involves the same rectification circuitry found in many household electronic goods, which converts alternating current (AC) from a wall outlet ... More

The symmetry of Spin^c Dirac spectrums on Riemannian product manifoldsAug 24 2013It is well-known that the spectrum of a $\text{spin}^{\mathbb{C}}$ Dirac operator on a closed Riemannian $\text{spin}^{\mathbb{C}}$ manifold $M^{2k}$ of dimension $2k$ for $k \in \mathbb{N}$ is symmetric. In this article, we prove that over an odd-dimensional ... More

Character-Level Language Modeling with Hierarchical Recurrent Neural NetworksSep 13 2016Recurrent neural network (RNN) based character-level language models (CLMs) are extremely useful for modeling unseen words by nature. However, their performance is generally much worse than the word-level language models (WLMs), since CLMs need to consider ... More

Light-Cone Wavefunction Representations of Sivers and Boer-Mulders Distribution FunctionsMar 03 2010We find the light-cone wavefunction representations of the Sivers and Boer-Mulders distribution functions. A necessary condition for the existence of these representations is that the light-cone wavefunctions have complex phases. We induce the complex ... More

On the dual of the mobile coneNov 21 2010May 08 2011We prove that the cone of mobile divisors and the cone of curves birationally movable in codimension 1 are dual in the $(K+B)$-negative part for a klt pair $(X/Z,B)$. We also prove the structure theorem and the contraction theorem for the expanded cone ... More

Multiplicative functions preserving the sum-of-three-squares operationDec 04 2015If a multiplicative function $f$ satisfies $f(a^2+b^2+c^2) = f(a)^2+f(b)^2+f(c)^2$ for all positive integers $a$, $b$, and $c$, then $f$ is an identity function.

Polarized Spots in Anisotropic Open UniversesMay 14 2009Aug 17 2009We calculate the temperature and polarization patterns generated in anisotropic cosmological models drawn from the Bianchi classification. We show that localized features in the temperature pattern, perhaps similar to the cold spot observed in the Wilkinson ... More

Multiplicative functions which are additive on sums of two nonzero squaresMar 25 2019Let $f$ be a multiplicative function which satisfies \[ f(a^2+b^2+c^2+d^2) = f(a^2+b^2)+f(c^2+d^2) \] for positive integers $a$, $b$, $c$, and $d$. We show that $f$ is the identity function provided that $f(3)\,f(11) \ne 0$. Otherwise, $f(n)=0$ for all ... More

Character-Level Language Modeling with Hierarchical Recurrent Neural NetworksSep 13 2016Feb 02 2017Recurrent neural network (RNN) based character-level language models (CLMs) are extremely useful for modeling out-of-vocabulary words by nature. However, their performance is generally much worse than the word-level language models (WLMs), since CLMs ... More

Single stream parallelization of generalized LSTM-like RNNs on a GPUMar 10 2015Recurrent neural networks (RNNs) have shown outstanding performance on processing sequence data. However, they suffer from long training time, which demands parallel implementations of the training procedure. Parallelization of the training algorithms ... More

Horizon as Critical PhenomenonMar 28 2016Sep 15 2016We show that renormalization group(RG) flow can be viewed as a gradual wave function collapse, where a quantum state associated with the action of field theory evolves toward a final state that describes an IR fixed point. The process of collapse is described ... More

AMBER: Adaptive Multi-Batch Experience Replay for Continuous Action ControlOct 12 2017Oct 02 2018In this paper, a new adaptive multi-batch experience replay scheme is proposed for proximal policy optimization (PPO) for continuous action control. On the contrary to original PPO, the proposed scheme uses the batch samples of past policies as well as ... More

Evolution of Cosmological Horizons of Wormhole CosmologyNov 17 2018Recently we solved the Einstein's field equations to obtain the exact solution of the cosmological model with the Morris-Thorne type wormhole. We found the apparent horizons and analyzed their geometric natures, including the causal tructures. We also ... More

Discriminants of stable rank two sheaves on some general type surfacesDec 05 2018Jan 10 2019We prove sharp bounds on the discriminants of stable rank two sheaves on surfaces in three-dimensional projective space. The key technical ingredient is to study them as torsion sheaves in projective space via tilt stability in the derived category. We ... More

Compact Deep Convolutional Neural Networks With Coarse PruningOct 30 2016The learning capability of a neural network improves with increasing depth at higher computational costs. Wider layers with dense kernel connectivity patterns furhter increase this cost and may hinder real-time inference. We propose feature map and kernel ... More

Counting Rational Points on Kummer surfacesJan 30 2019Jul 04 2019We consider the problem of counting the number of rational points on the family of Kummer surfaces associated with two non-isogenous elliptic curves. For this two-parameter family we prove Manin's unity, using the presentation of the Kummer surfaces as ... More

A positivity preserving iterative method for finding the ground states of saturable nonlinear Schrödinger equationsJul 10 2019In this paper, we propose an iterative method to compute the positive ground states of saturable nonlinear Schr\"odinger equations. A discretization of the saturable nonlinear Schr\"odinger equation leads to a nonlinear algebraic eigenvalue problem (NAEP). ... More

Evolution of Cosmological Horizons of Wormhole CosmologyNov 17 2018Jun 20 2019Recently we solved the Einstein's field equations to obtain the exact solution of the cosmological model with the Morris-Thorne type wormhole. We found the apparent horizons and analyzed their geometric natures, including the causal tructures. We also ... More

The Cosmological Model with a Wormhole and Hawking Temperature near Apparent HorizonJan 24 2018Mar 01 2018In this paper, a cosmological model with an isotropic form of the Morris-Thorne type wormhole was derived in a similar way to the McVittie solution to the black hole in the expanding universe. By solving Einstein's field equation with plausible matter ... More

State dependent spread of entanglement in relatively local HamiltoniansNov 17 2018May 16 2019Relatively local Hamiltonians are a class of background independent non-local Hamiltonians from which local theories emerge within a set of short-range entangled states. The dimension, topology and geometry of the emergent local theory is determined by ... More

Discriminants of stable rank two sheaves on some general type surfacesDec 05 2018Jul 09 2019We prove sharp bounds on the discriminants of stable rank two sheaves on surfaces in three-dimensional projective space. The key technical ingredient is to study them as torsion sheaves in projective space via tilt stability in the derived category. We ... More

PRE-render Content Using Tiles (PRECUT). 1. Large-Scale Compound-Target Relationship AnalysesNov 13 2017Visualizing a complex network is computationally intensive process and depends heavily on the number of components in the network. One way to solve this problem is not to render the network in real time. PRE-render Content Using Tiles (PRECUT) is a process ... More

Braids, mapping class groups, and categorical deloopingSep 21 2006May 10 2007Dehn twists around simple closed curves in oriented surfaces satisfy the braid relations. This gives rise to a group theoretic from the braid group to the mapping class group. We prove here that this map is trivial in stable homology with any trivial ... More