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A highly inclined orbit for the 110-day period M-dwarf companion KOI-368.01Jul 08 2013Sep 11 2013We report the detection of asymmetry in the transit light curves of the 110-day period companion to KOI-368, a rapidly rotating A-dwarf. The significant distortion in the transit light curve is attributed to spin-orbit misalignment between the transiting ... More

Braided commutative algebras over quantized enveloping algebrasJan 25 2019Feb 10 2019We produce braided commutative algebras in braided monoidal categories by generalizing Davydov's full center construction of commutative algebras in centers of monoidal categories. Namely, we build braided commutative algebras in relative monoidal centers ... More

Dependence of Small Planet Frequency on Stellar Metallicity Hidden by Their PrevalenceMay 13 2016Sep 15 2016The dependence of gas giant planet occurrence rate on stellar metallicity has been firmly established. We extend this so-called planet-metallicity correlation to broader ranges of metallicities and planet masses/radii. In particular, we assume that the ... More

Dynamically hot Super-Earths from outer giant planet scatteringSep 26 2016Mar 28 2017The hundreds of multiple planetary systems discovered by the \textit{Kepler} mission are typically observed to reside in close-in ($\lesssim0.5$ AU), low-eccentricity, and low-inclination orbits. We run N-body experiments to study the effect that unstable ... More

Bayesian Ages for Early-Type Stars from Isochrones Including Rotation, and a Possible Old Age for the HyadesJan 19 2015May 28 2015We combine recently computed models of stellar evolution using a new treatment of rotation with a Bayesian statistical framework to constrain the ages and other properties of early-type stars. We find good agreement for early-type stars and clusters with ... More

Rotating Stellar Models Can Account for the Extended Main Sequence Turnoffs in Intermediate Age ClustersApr 16 2015May 28 2015We show that the extended main sequence turnoffs seen in intermediate age Large Magellanic Cloud (LMC) clusters, often attributed to age spreads of several hundred Myr, may be easily accounted for by variable stellar rotation in a coeval population. We ... More

The Age and Age Spread of the Praesepe and Hyades Clusters: a Consistent, ~800 Myr Picture from Rotating Stellar ModelsMar 31 2015May 29 2015We fit the upper main sequence of the Praesepe and Hyades open clusters using stellar models with and without rotation. When neglecting rotation, we find that no single isochrone can fit the entire upper main sequence at the clusters' spectroscopic metallicity: ... More

Testing the Titius-Bode law predictions for Kepler multi-planet systemsMay 09 2014We use three and half years of Kepler Long Cadence data to search for the 97 predicted planets of Bovaird & Lineweaver (2013) in 56 of the multi-planet systems, based on a general Titius-Bode relation. Our search yields null results in the majority of ... More

Expected Yields of Planet discoveries from the TESS primary and extended missionsJul 30 2018We present a prediction of the transiting exoplanet yield of the TESS primary mission, in order to guide follow-up observations and science projects utilizing TESS discoveries. Our new simulations differ from previous work by using (1) an updated photometric ... More

Dynamically hot Super-Earths from outer giant planet scatteringSep 26 2016The hundreds of multiple planetary systems discovered by the Kepler mission are typically observed to reside in close-in ($\lesssim0.5$ AU), low-eccentricity, and low-inclination orbits. We run N-body experiments to study the effect that unstable outer ... More

The Hunt for Exomoons with Kepler (HEK): V. A Survey of 41 Planetary Candidates for ExomoonsMar 18 2015Sep 24 2015We present a survey of 41 Kepler Objects of Interest (KOIs) for exomoons using Bayesian photodynamics, more than tripling the number of KOIs surveyed with this technique. We find no compelling evidence for exomoons although thirteen KOIs yield spurious ... More

Constraining the Oblateness of Kepler PlanetsOct 01 2014We use Kepler short cadence light curves to constrain the oblateness of planet candidates in the Kepler sample. The transits of rapidly rotating planets that are deformed in shape will lead to distortions in the ingress and egress of their light curves. ... More

The origin of the occurrence rate profile of gas giants inside 100 daysApr 21 2017Jun 02 2017We investigate the origin of the period distribution of giant planets. We fit the bias-corrected distribution of gas-giant planets inside 300 days found by Santerne et al. (2016) using a planet formation model based on pebble accretion. We investigate ... More

Warm Jupiters are less lonely than hot Jupiters: close neighboursJan 19 2016Apr 27 2016Exploiting the Kepler transit data, we uncover a dramatic distinction in the prevalence of sub-Jovian companions, between systems that contain hot Jupiters (periods inward of 10 days) and those that host warm Jupiters (periods between 10 and 200 days). ... More

Saturation of the magnetorotational instability in the unstratified shearing box with zero net flux: convergence in taller boxesDec 03 2015Previous studies of the nonlinear regime of the magnetorotational instability in one particular type of shearing box model -- unstratified with no net magnetic flux -- find that without explicit dissipation (viscosity and resistivity) the saturation amplitude ... More

On the Edit Distance of Powers of CyclesSep 24 2015The edit distance between two graphs on the same labeled vertex set is defined to be the size of the symmetric difference of the edge sets. The edit distance function of a hereditary property $\mathcal{H}$ is a function of $p\in [0,1]$ that measures, ... More

Spin-Orbit Misalignment and Precession in the Kepler-13Ab Planetary SystemNov 07 2017Gravity darkening induced by rapid stellar rotation provides us with a unique opportunity to characterize the spin-orbit misalignment of a planetary system through analysis of its photometric transit. We use the gravity-darkened transit modeling code ... More

On the IMF in a Triggered Star Formation ContextSep 16 2015The origin of the stellar initial mass function (IMF) is a fundamental issue in the theory of star formation. It is generally fit with a composite power law. Some clues on the progenitors can be found in dense starless cores that have a core mass function ... More

An Invitation to Noncommutative AlgebraAug 09 2018Feb 23 2019This is a brief introduction to the world of Noncommutative Algebra aimed at advanced undergraduate and beginning graduate students.

Data-Driven Control of Distributed Reconfigurable Production-Inventory SystemsFeb 23 2019We analyze the value of mobile production capacity and transshipment in a supply chain with geographically distributed production facilities and epoch-dependent demands. We describe the L location, Y mobile production unit problem as a problem of sequential ... More

CO Emission in Infrared-Selected Active Galactic NucleiMay 16 2019In order to better understand how active galactic nuclei (AGN) effect the interstellar media of their host galaxies, we perform a meta-analysis of the CO emission for a sample of $z=0.01-4$ galaxies from the literature with existing CO detections and ... More

Degenerate Sklyanin algebras and Generalized Twisted Homogeneous Coordinate ringsDec 02 2008Dec 23 2011In this work, we introduce the point parameter ring B, a generalized twisted homogeneous coordinate ring associated to a degenerate version of the three-dimensional Sklyanin algebra. The surprising geometry of these algebras yields an analogue to a result ... More

Modeling the residential electricity consumption within a restructured power marketMay 28 2018Jun 12 2018The United States' power market is featured by the lack of judicial power at the federal level. The market thus provides a unique testing environment for the market organization structure. At the same time, the econometric modeling and forecasting of ... More

Representation theory of three-dimensional Sklyanin algebrasJul 14 2011Jan 19 2012We determine the dimensions of the irreducible representations of the Sklyanin algebras with global dimension 3. This contributes to the study of marginal deformations of the N=4 super Yang-Mills theory in four dimensions in supersymmetric string theory. ... More

Domain Specific Language for Modular Knitting Pattern Definitions: PurlJun 25 2016Purl is a language to be used for modular definition and verification of knitting patterns. The syntax is similar to the standard knitting pattern notation provided by the Craft Yarn Council. Purl provides constructs not available in the standard notation ... More

TOI-216b and TOI-216c: Two warm, large exoplanets in or slightly wide of the 2:1 orbital resonanceApr 26 2019Warm, large exoplanets with 10-100 day orbital periods pose a major challenge to our understanding of how planetary systems form and evolve. Although high eccentricity tidal migration has been invoked to explain their proximity to their host stars, a ... More

The Possible Moon of Kepler-90g is a False PositiveNov 25 2014The discovery of an exomoon would provide deep insights into planet formation and the habitability of planetary systems, with transiting examples being particularly sought after. Of the hundreds of Kepler planets now discovered, the seven-planet system ... More

High Precision Photometry for K2 Campaign 1Jul 27 2015Sep 14 2015The two reaction wheel K2 mission promises and has delivered new discoveries in the stellar and exoplanet fields. However, due to the loss of accurate pointing, it also brings new challenges for the data reduction processes. In this paper, we describe ... More

Heuristics for Selecting Predicates for Partial Predicate AbstractionDec 30 2017In this paper we consider the problem of configuring partial predicate abstraction that combines two techniques that have been effective in analyzing infinite-state systems: predicate abstraction and fixpoint approximations. A fundamental problem in partial ... More

Braided Commutative Algebras over Quantized Enveloping AlgebrasJan 25 2019We produce braided commutative algebras in braided monoidal categories by generalizing Davydov's full center construction of commutative algebras in centers of monoidal categories. Namely, we build braided commutative algebras in relative monoidal centers ... More

PBW deformations of braided productsJan 10 2016Jan 27 2018We present new examples of deformations of smash product algebras that arise from Hopf algebra actions on pairs of module algebras. These examples involve module algebras that are Koszul, in which case a PBW theorem we established previously applies. ... More

Cocycle deformations and Galois objects for semisimple Hopf algebras of dimension $p^3$ and $pq^2$Oct 12 2016Jun 21 2017Let $p$ and $q$ be distinct prime numbers. We study the Galois objects and cocycle deformations of the noncommutative, noncocommutative, semisimple Hopf algebras of odd dimension $p^3$ and of dimension $pq^2$. We obtain that the $p+1$ non-isomorphic self-dual ... More

Finite dimensional Hopf actions on algebraic quantizationsMay 02 2016Dec 01 2016Let k be an algebraically closed field of characteristic zero. In joint work with J. Cuadra [arxiv.org/abs/1409.1644, arxiv.org/abs/1509.01165], we showed that a semisimple Hopf action on a Weyl algebra over a polynomial algebra k[z_1,...,z_s] factors ... More

The Use of Mutual Coherence to Prove $\ell^1/\ell^0$-Equivalence in Classification ProblemsJan 09 2019We consider the decomposition of a signal over an overcomplete set of vectors. Minimization of the $\ell^1$-norm of the coefficient vector can often retrieve the sparsest solution (so-called "$\ell^1/\ell^0$-equivalence"), a generally NP-hard task, and ... More

The Value of Misinformation and DisinformationJan 05 2019Information is a critical dimension in warfare. Inaccurate information such as misinformation or disinformation further complicates military operations. In this paper, we examine the value of misinformation and disinformation to a military leader who ... More

Finite dimensional Hopf actions on algebraic quantizationsMay 02 2016Let k be an algebraically closed field of characteristic zero. In joint work with J. Cuadra [arxiv.org/abs/1409.1644, arxiv.org/abs/1509.01165], we showed that a semisimple Hopf action on a Weyl algebra over a polynomial algebra k[z_1,...,z_s] factors ... More

Deep Visual Foresight for Planning Robot MotionOct 03 2016A key challenge in scaling up robot learning to many skills and environments is removing the need for human supervision, so that robots can collect their own data and improve their own performance without being limited by the cost of requesting human ... More

Finite dimensional Hopf actions on deformation quantizationsFeb 01 2016Jul 03 2016We study when a finite dimensional Hopf action on a quantum formal deformation A of a commutative domain A_0 (i.e., a deformation quantization) must factor through a group algebra. In particular, we show that this occurs when the Poisson center of the ... More

Poincare-Birkhoff-Witt deformations of smash product algebras from Hopf actions on Koszul algebrasAug 27 2013Apr 28 2017Let H be a Hopf algebra and let B be a Koszul H-module algebra. We provide necessary and sufficient conditions for a filtered algebra to be a Poincare-Birkhoff-Witt (PBW) deformation of the smash product algebra B#H. Many examples of these deformations ... More

Pointed Hopf actions on fields, IINov 30 2015Apr 21 2016This is a continuation of the authors' study of finite-dimensional pointed Hopf algebras H which act inner faithfully on commutative domains. As mentioned in Part I of this work, the study boils down to the case where H acts inner faithfully on a field. ... More

Pointed Hopf actions on fields, IMar 19 2014Nov 30 2015Actions of semisimple Hopf algebras H over an algebraically closed field of characteristic zero on commutative domains were classified recently by the authors. The answer turns out to be very simple- if the action is inner faithful, then H has to be a ... More

PBW deformations of braided productsJan 10 2016We present new examples of deformations of smash product algebras that arise from Hopf algebra actions on pairs of module algebras. These examples involve module algebras that are Koszul, in which case a PBW theorem we established previously applies. ... More

Poincare-Birkhoff-Witt deformations of smash product algebras from Hopf actions on Koszul algebrasAug 27 2013Aug 07 2014Let H be a Hopf algebra and let B be a Koszul H-module algebra. We provide necessary and sufficient conditions for a filtered algebra to be a Poincare-Birkhoff-Witt (PBW) deformation of the smash product algebra B#H. Many examples of these deformations ... More

Corrigendum to "Degenerate Sklyanin algebras and Generalized Twisted Homogeneous Coordinate rings", J. Algebra 322 (2009) 2508-2527Dec 22 2011Feb 03 2012There is an error in the computation of the truncated point schemes of the degenerate Sklyanin algebra S(1, 1, 1); they are larger than was claimed in Proposition 3.13 of the above paper. We provide a description of the correct truncated point schemes. ... More

The warm Neptunes around HD 106315 have low stellar obliquitiesJun 29 2018We present the obliquity of the warm Neptune HD 106315c measured via a series of spectroscopic transit observations. HD 106315c is a 4.4 REarth warm Neptune orbiting a moderately rotating late F-star with a period of 21.05 days. HD 106315 also hosts a ... More

Measurement of Source Star Colors with the K2C9-CFHT Multi-color Microlensing SurveyMar 25 2018K2 Campaign 9 (K2C9) was the first space-based microlensing parallax survey capable of measuring microlensing parallaxes of free-floating planet candidate microlensing events. Simultaneous to K2C9 observations we conducted the K2C9 Canada-France-Hawaii ... More

A Machine Learns to Predict the Stability of Tightly Packed Planetary SystemsOct 17 2016The requirement that planetary systems be dynamically stable is often used to vet new discoveries or set limits on unconstrained masses or orbital elements. This is typically carried out via computationally expensive N-body simulations. We show that characterizing ... More

Extracting Microlensing Signals from K2 Campaign 9Apr 27 2017Aug 20 2017The reduction of the \emph{K2}'s Campaign 9 (K2C9) microlensing data is challenging mostly because of the very crowded field and the unstable pointing of the spacecraft. In this work, we present the first method that can extract microlensing signals from ... More

Aztec: A Platform to Render Biomedical Software Findable, Accessible, Interoperable, and ReusableJun 19 2017Precision medicine and health requires the characterization and phenotyping of biological systems and patient datasets using a variety of data formats. This scenario mandates the centralization of various tools and resources in a unified platform to render ... More

A Machine Learns to Predict the Stability of Tightly Packed Planetary SystemsOct 17 2016Nov 21 2016The requirement that planetary systems be dynamically stable is often used to vet new discoveries or set limits on unconstrained masses or orbital elements. This is typically carried out via computationally expensive N-body simulations. We show that characterizing ... More

Improving Sparse Representation-Based Classification Using Local Principal Component AnalysisJul 04 2016Nov 18 2016Sparse representation-based classification (SRC), proposed by Wright et al., seeks the sparsest decomposition of a test sample over the dictionary of training samples, with classification to the most-contributing class. Because it assumes test samples ... More

On quantum groups associated to non-Noetherian regular algebras of dimension 2Mar 31 2015Feb 16 2016We investigate homological and ring-theoretic properties of universal quantum linear groups that coact on Artin-Schelter regular algebras A(n) of global dimension 2, especially with central homological codeterminant (or central quantum determinant). As ... More

Semisimple Hopf actions on commutative domainsJan 17 2013Oct 08 2013Let H be a semisimple (so, finite dimensional) Hopf algebra over an algebraically closed field k of characteristic zero and let A be a commutative domain over k. We show that if A arises as an H-module algebra via an inner faithful H-action, then H must ... More

Improving Sparse Representation-Based Classification Using Local Principal Component AnalysisJul 04 2016Jun 02 2018Sparse representation-based classification (SRC), proposed by Wright et al., seeks the sparsest decomposition of a test sample over the dictionary of training samples, with classification to the most-contributing class. Because it assumes test samples ... More

Actions of some pointed Hopf algebras on path algebras of quiversOct 28 2014Jan 06 2015We classify Hopf actions of Taft algebras T(n) on path algebras of quivers, in the setting where the quiver is loopless, finite, and Schurian. As a corollary, we see that every quiver admitting a faithful Z_n-action (by directed graph automorphisms) also ... More

Dark Matter, Mass Scales Sequence, and Superstructure in the Universe (with extension)Sep 18 1999Oct 26 2015There is a category of stable non-baryonic dark matter particles in the universe at the present time: fermions or bosons with mass ~10^(-1) eV. The existence of these do not contradict the dip phenomena of the ultra-high energy primary cosmic ray spectrum ... More

Dark Matter, Quasars, and Superstructures in the UniverseAug 10 2009Feb 02 2016From the observed results of the space distribution of quasars we deduced that neutrino mass is about 10^(-1) eV. The fourth stable elementary paticle (delta particle) with mass about 10^(0) eV can help explain the energy resource mechanism in quasars, ... More

On regular graphs with four distinct eigenvaluesMay 18 2016Sep 17 2016Let $\mathcal{G}(4,2)$ be the set of connected regular graphs with four distinct eigenvalues in which exactly two eigenvalues are simple, $\mathcal{G}(4,2,-1)$ (resp. $\mathcal{G}(4,2,0)$) the set of graphs belonging to $\mathcal{G}(4,2)$ with $-1$ (resp. ... More

On graphs with three or four distinct normalized Laplacian eigenvaluesNov 16 2016Mar 27 2017In this paper, we characterize all connected graphs with exactly three distinct normalized Laplacian eigenvalues of which one is equal to $1$, determine all connected bipartite graphs with at least one vertex of degree $1$ having exactly four distinct ... More

Large Number, Dark Matter, Dark Energy, and the Superstructures in the Universe (with Extension)Apr 16 2008Sep 12 2016Since there are dark matter particles (neutrino) with mass about 10^(-1)eV in the universe, the superstructures with a scale of 10^(19) solar mass [large number A is about 10^(19)] appeared around the era of the hydrogen recombination. The redshift z ... More

Note on the spectra of a class of graphs derived from set inclusion relationsSep 04 2018Sep 08 2018For any given integers $n$, $k$ and $l$ with $n\geq 1$ and $0\leq k<l\leq n$, we denote by $G(n,k,l)$ the graph whose vertex set consists of all $k$- and $l$-subsets of $[n]=\{1,2,\ldots,n\}$, where two distinct vertices are adjacent if one of them is ... More

The Auslander-Type Condition of Triangular Matrix RingsMar 26 2009Let $R$ be a left and right Noetherian ring and $n,k$ any non-negative integers. $R$ is said to satisfy the Auslander-type condition $G_n(k)$ if the right flat dimension of the $(i+1)$-st term in a minimal injective resolution of $R_R$ is at most $i+k$ ... More

Hierarchical low rank approximation of likelihoods for large spatial datasetsMay 28 2016Datasets in the fields of climate and environment are often very large and irregularly spaced. To model such datasets, the widely used Gaussian process models in spatial statis- tics face tremendous challenges due to the prohibitive computational burden. ... More

Explicit representations of 3-dimensional Sklyanin algebras associated to a point of order 2Dec 30 2015The representation theory of a three-dimensional Sklyanin algebra $S$ depends on its (noncommutative projective algebro-) geometric data: an elliptic curve $E$ in $\mathbb{P}^2$, and an automorphism $\sigma$ of $E$ given by translation by a point. Indeed, ... More

Optical variability of quasars: a damped random walkDec 13 2013A damped random walk is a stochastic process, defined by an exponential covariance matrix that behaves as a random walk for short time scales and asymptotically achieves a finite variability amplitude at long time scales. Over the last few years, it has ... More

Explicit representations of 3-dimensional Sklyanin algebras associated to a point of order 2Dec 30 2015Feb 23 2017The representation theory of a 3-dimensional Sklyanin algebra $S$ depends on its (noncommutative projective algebro-) geometric data: an elliptic curve $E$ in $\mathbb{P}^2$, and an automorphism $\sigma$ of $E$ given by translation by a point. Indeed, ... More

The universal enveloping algebra of the Witt algebra is not noetherianMar 30 2013Aug 07 2014This work is prompted by the long standing question of whether it is possible for the universal enveloping algebra of an infinite dimensional Lie algebra to be noetherian. To address this problem, we answer a 23-year-old question of Carolyn Dean and Lance ... More

On the quadratic dual of the Fomin-Kirillov algebrasJun 25 2018We study ring-theoretic and homological properties of the quadratic dual (or Koszul dual) $\mathcal{E}_n^!$ of the Fomin-Kirillov algebras $\mathcal{E}_n$; these algebras are connected $\mathbb{N}$-graded and are defined for $n \geq 2$. We establish that ... More

Maps from the enveloping algebra of the positive Witt algebra to regular algebrasAug 21 2015May 04 2016We construct homomorphisms from the universal enveloping algebra of the positive (part of the) Witt algebra to several different Artin-Schelter regular algebras, and determine their kernels and images. As a result, we produce elementary proofs that the ... More

Dark Matter Particles with Low Mass (and FTL)Mar 26 2010Apr 17 2012From the observed results of the space distribution of quasars and the mass scale sequence table, we deduced the existence of superstructure (feeble dark structure) with mass scale of 10^(19) solar mass, as well as the lightest stable fermion with mass ... More

Parameter Optimization of Multi-Agent Formations based on LQR DesignJan 24 2011In this paper we study the optimal formation control of multiple agents whose interaction parameters are adjusted upon a cost function consisting of both the control energy and the geometrical performance. By optimizing the interaction parameters and ... More

Automorphism group of the complete alternating group graphMay 21 2016Aug 26 2017Let $S_n$ and $A_n$ denote the symmetric group and alternating group of degree $n$ with $n\geq 3$, respectively. Let $S$ be the set of all $3$-cycles in $S_n$. The \emph{complete alternating group graph}, denoted by $CAG_n$, is defined as the Cayley graph ... More

Total Variation Depth for Functional DataNov 15 2016There has been extensive work on data depth-based methods for robust multivariate data analysis. Recent developments have moved to infinite-dimensional objects such as functional data. In this work, we propose a new notion of depth, the total variation ... More

The $hp$-version Error Analysis of A Mixed DG Method for Linear ElasticityAug 14 2016This paper focuses on the $hp$-version error analysis of a mixed discontinuous Galerkin (DG) method for the linear elasticity problem. We first derive some error estimates for two $L^2$ projection operators in terms of the results in [7,13,23]. Using ... More

TESS delivers its first Earth-sized planet and a warm sub-NeptuneDec 31 2018Apr 15 2019The future of exoplanet science is bright, as TESS once again demonstrates with the discovery of its longest-period confirmed planet to date. We hereby present HD 21749b (TOI 186.01), a sub-Neptune in a 36-day orbit around a bright (V = 8.1) nearby (16 ... More

TESS Discovery of an ultra-short-period planet around the nearby M dwarf LHS 3844Sep 19 2018Data from the newly-commissioned \textit{Transiting Exoplanet Survey Satellite} (TESS) has revealed a "hot Earth" around LHS 3844, an M dwarf located 15 pc away. The planet has a radius of $1.32\pm 0.02$ $R_\oplus$ and orbits the star every 11 hours. ... More

HD 202772A B: A Transiting Hot Jupiter Around A Bright, Mildly Evolved Star In A Visual Binary Discovered By TessOct 04 2018We report the first confirmation of a hot Jupiter discovered by the Transiting Exoplanet Survey Satellite (TESS) mission: HD 202772A b. The transit signal was detected in the data from TESS Sector 1, and was confirmed to be of planetary origin through ... More

A heuristic view about the evolution and speciesApr 16 2010The controversy concerning both the definition of the species and methods for inferring the boundaries and numbers of species has occupied biologists for centuries, and the debate itself has become known as the species problem. The modern theory of evolution ... More

On Legendrian foliations in contact manifolds II: Deformation theoryNov 23 2014Using the structural theorems developed in [Hua13], we study the deformation theory of coisotropic submanifolds in contact manifolds, under the assumption that the characteristic foliation is nonsingular. In the "middle" dimensions, we find an interesting ... More

A polynomial-time algorithm for the ground state of one-dimensional gapped HamiltoniansJun 24 2014Oct 26 2015A (deterministic) polynomial-time algorithm is proposed for approximating the ground state of (general) one-dimensional gapped Hamiltonians. Let $\epsilon,n,\eta$ be the energy gap, the system size, and the desired precision, respectively. Neglecting ... More

Backwards uniqueness of the mean curvature flowJul 06 2009In this note we prove the backwards uniqueness of the mean curvature flow in codimension one case. More precisely,let $F_t, \widetilde{F}_t:M^n \to \overline{M}^{n+1}$ be two complete solutions of the mean curvature flow on $M^n \times [0,T]$ with bounded ... More

Greatest lower bounds on the transverse Ricci curvature of some toric Sasaki manifoldsSep 20 2016We determine the greatest lower bounds on the transverse Ricci curvature of compact toric Sasaki manifolds with positive basic first Chern class and with the first Chern class of the contact bundle being trivial. This is based on Wang-Zhu's and Futaki-Ono-Wang's ... More

Entanglement dynamics in critical random quantum Ising chain with perturbationsNov 15 2016We simulate the entanglement dynamics in a critical random quantum Ising chain with generic perturbations using the time-evolving block decimation algorithm. Starting from a product state, we observe super-logarithmic growth of entanglement entropy with ... More

On plastikstufe, bordered Legendrian open book and overtwisted contact structuresJul 27 2016Oct 06 2016In this paper we prove the presence of an embedded plastikstufe implies overtwistedness of the contact structure in any dimension. Moreover, we show in dimension 5 that the presence of an embedded bordered Legendrian open book (bLob) also implies overtwistedness. ... More

On Structure and History of Space-time with Variable Speed of LightOct 15 2004We apply the variable speed of light into general relativity in order to solve the problems we met in the standard cosmology. We're surprised to find that, the results from the general relativity in cosmology are exactly the same as those we got from ... More

An Eye Tracking Study into the Effects of Graph LayoutOct 24 2008Graphs are typically visualized as node-link diagrams. Although there is a fair amount of research focusing on crossing minimization to improve readability, little attention has been paid on how to handle crossings when they are an essential part of the ... More

An Aggregation-Based Overall Quality Measurement for VisualizationJun 11 2013Aesthetics are often used to evaluate the quality of graph drawings. However, the existing aesthetic criteria are useful in judging the extents to which a drawing conforms to particular drawing rules. They have limitations in evaluating overall quality. ... More

An explicit family of unitaries with exponentially minimal length Pauli geodesicsJan 28 2007Recently, Nielsen et al have proposed a geometric approach to quantum computation. They've shown that the size of the minimum quantum circuits implementing a unitary U, up to polynomial factors, equals to the length of minimal geodesic from identity I ... More

Synthesis of Sugar and fixation of CO2 through Artificial Photosynthesis driving by Hydrogen or ElectricitySep 02 2010The overall process of photosynthesis consists of two main phases, the so-called light and dark eactions: light energy is absorbed by chlorophyll molecules and transferred to regenerate NADH and ATP, then drive Calvin-Benson cycle to synthesize sugar. ... More

$L^{2}$ harmonic forms on complete special holonomy manifoldsJan 13 2018Apr 01 2018In this article, we consider $L^{2}$ harmonic forms on a complete non-compact Riemannian manifold $X$ with a non-zero parallel form $\omega$. The main result is that if $(X,\omega)$ is a complete $G_{2}$- ( or $Spin(7)$-) manifold with a $d$(linear) $G_{2}$- ... More

Magnetic loops above a small flux-emerging region observed by IRIS, Hinode and SDONov 08 2018I report on observations of a set of magnetic loops above a region with late-phase flux emergence taken by IRIS, Hinode and SDO. The loop system consists of many transition region loop threads with size of 5--12\arcsec\ in length and $\sim0.5$\arcsec ... More

On a topology property for moduli space of Kapustin-Witten equationsMar 20 2017Apr 17 2018In this article, we study the Kapustin-Witten equations on a closed, simply-connected, four-manifold. We using a compactness theorem due to Taubes to prove that if $(A,\phi)$ is a solution of Kapustin-Witten equations and the connection $A$ is closed ... More

A Cosmology Forecast Toolkit -- CosmoLibJan 28 2012Jun 11 2012The package CosmoLib is a combination of a cosmological Boltzmann code and a simulation toolkit to forecast the constraints on cosmological parameters from future observations. In this paper we describe the released linear-order part of the package. We ... More

Hall Viscosity Revealed via Density ResponseJan 21 2015Jun 03 2015Quantum Hall systems are recently shown to possess a quantity sensitive to the spatial geometry and topology of the system, dubbed the Hall viscosity $\eta_H$. Despite the extensive theoretical discussions on its properties, the question of how to measure ... More

Cyclic Descents for General Skew TableauxAug 14 2018A cyclic descent function on standard Young tableaux of size $n$ is a function that restricts to the usual descent function when $n$ is omitted, such that the number of standard Young tableaux of given shape with cyclic descent set $D\subset[n]$ is invariant ... More

An Averaging Theorem for Perturbed KdV EquationJan 08 2013We consider a perturbed KdV equation: [\dot{u}+u_{xxx} - 6uu_x = \epsilon f(x,u(\cdot)), \quad x\in \mathbb{T}, \quad\int_\mathbb{T} u dx=0.] For any periodic function $u(x)$, let $I(u)=(I_1(u),I_2(u),...)\in\mathbb{R}_+^{\infty}$ be the vector, formed ... More

$L^{2}$ vanishing theorem on some Kähler manifoldsNov 27 2018Let $E$ be a Hermitian vector bundle over a complete K\"{a}hler manifold $(X^{2n},\omega)$ with a $d$(bounded) fundamental form $\omega$, $A$ be a Hermitian connection on $E$. The goal of this article is to study the $L^{2}$-Hodge theory on the vector ... More

A compactness theorem of flat $SL(2,\mathbb{C})$ connections on $3$-foldsJun 12 2017In this article, we obtain a compactness theorem of flat $SL(2,\mathbb{C})$-connections by using a compactness theorem of Vafa-Witten equations proved by Tanaka (arXiv:1308.0862). We also using the compactness theorem to study the topology property of ... More

Non-existence of Higgs fields on Calabi-Yau ManifoldsMay 03 2017May 15 2017In this article, we study the Higgs $G$-bundles $(E,\theta)$ on a compact Calabi-Yau manifolds $X$. Our main result is that there is non-existence Higgs fields $\theta$ on a semistable Higgs $G$-bundle over a compact connected Calabi-Yau surface. The ... More

Probing Anomalous Top Quark Couplings at the Future Linear CollidersSep 05 2000Sep 20 2000In terms of an effective Lagrangian we investigate the possibilities of probing anomalous top quark couplings, $t \bar{t} H$, $\gamma t \bar{t}$, $Z t \bar{t}$ and $tWb$ at the future linear colliders. It is found that probing anomalous top quark couplings, ... More