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The Parameterised Complexity of List Problems on Graphs of Bounded TreewidthOct 18 2011Aug 04 2016We consider the parameterised complexity of several list problems on graphs, with parameter treewidth or pathwidth. In particular, we show that List Edge Chromatic Number and List Total Chromatic Number are fixed parameter tractable, parameterised by ... More

The complexity of flood-filling games on graphsJan 31 2011Oct 18 2011We consider the complexity of problems related to the combinatorial game Free-Flood-It, in which players aim to make a coloured graph monochromatic with the minimum possible number of flooding operations. Although computing the minimum number of moves ... More

Randomised enumeration of small witnesses using a decision oracleSep 18 2015Aug 08 2016Many combinatorial problems involve determining whether a universe of $n$ elements contains a witness consisting of $k$ elements which have some specified property. In some cases it is necessary to consider the entire universe in order to determine whether ... More

Deleting edges to restrict the size of an epidemicApr 22 2015Apr 19 2017Motivated by applications in network epidemiology, we consider the problem of determining whether it is possible to delete at most $k$ edges from a given input graph (of small treewidth) so that the resulting graph avoids a set $\mathcal{F}$ of forbidden ... More

Changing times to optimise reachability in temporal graphsFeb 16 2018Temporal graphs (in which edges are active only at specified time steps) are an increasingly important and popular model for a wide variety of natural and social phenomena. We propose a new extension of classical graph modification problems into the temporal ... More

Spanning trees and the complexity of flood-filling gamesMar 12 2012May 29 2013We consider problems related to the combinatorial game (Free-)Flood-It, in which players aim to make a coloured graph monochromatic with the minimum possible number of flooding operations. We show that the minimum number of moves required to flood any ... More

The complexity of Free-Flood-It on 2xn boardsJan 28 2011Jun 13 2013We consider the complexity of problems related to the combinatorial game Free-Flood-It, in which players aim to make a coloured graph monochromatic with the minimum possible number of flooding operations. Our main result is that computing the length of ... More

Counting small subgraphs in multi-layer networksOct 24 2017Feb 16 2018Motivated by the prevalence of multi-layer network structures in biological and social systems, we investigate the problem of counting the number of occurrences of (small) subgraphs or motifs in multi-layer graphs in which each layer of the graph has ... More

Extremal properties of flood-filling gamesApr 02 2015Mar 07 2019The problem of determining the number of "flooding operations" required to make a given coloured graph monochromatic in the one-player combinatorial game Flood-It has been studied extensively from an algorithmic point of view, but basic questions about ... More

Extremal properties of flood-filling gamesApr 02 2015Apr 15 2015The problem of determining the number of "flooding operations" required to make a given coloured graph monochromatic in the one-player combinatorial game Flood-It has been studied extensively from an algorithmic point of view, but basic questions about ... More

Approximately counting and sampling small witnesses using a colourful decision oracleJul 10 2019In this paper, we prove "black box" results for turning algorithms which decide whether or not a witness exists into algorithms to approximately count the number of witnesses, or to sample from the set of witnesses approximately uniformly, with essentially ... More

Normal amenable subgroups of the automorphism group of shifts of finite typeMay 07 2018Let $(X, \sigma)$ be a transitive shift of finite type and let $\rm{Aut}(X)$ denote its automorphism group. We generalize a result of Frisch, Schlank, and Tamuz to show that any normal amenable subgroup of $\rm{Aut}(X)$ must be contained in the subgroup ... More

Manifold Learning Using Kernel Density Estimation and Local Principal Components AnalysisSep 11 2017We consider the problem of recovering a $d-$dimensional manifold $\mathcal{M} \subset \mathbb{R}^n$ when provided with noiseless samples from $\mathcal{M}$. There are many algorithms (e.g., Isomap) that are used in practice to fit manifolds and thus reduce ... More

Deleting edges to restrict the size of an epidemic in temporal networksMay 17 2018A variety of potentially disease-spreading contact networks can be naturally modeled with graphs whose structure is subject to discrete changes over time, i.e. with temporal graphs. In such a temporal graph, vertices represent meaningful entities (such ... More

On the Enumeration of Minimal Hitting Sets in Lexicographical OrderMay 03 2018It is a long-standing open problem whether there exists an output-polynomial algorithm enumerating all minimal hitting sets of a hypergraph. A stronger requirement is to ask for an algorithm that outputs them in lexicographical order. We show that there ... More

The Mapping Class Group of a Minimal SubshiftOct 20 2018For a homeomorphism $T \colon X \to X$ of a Cantor set $X$, the mapping class group $\mathcal{M}(T)$ is the group of isotopy classes of orientation-preserving self-homeomorphisms of the suspension $\Sigma_{T}X$. The group $\mathcal{M}(T)$ can be interpreted ... More

A Characterization of Prediction ErrorsNov 18 2016Understanding prediction errors and determining how to fix them is critical to building effective predictive systems. In this paper, we delineate four types of prediction errors and demonstrate that these four types characterize all prediction errors. ... More

Structure and Parameter Learning for Causal Independence and Causal Interaction ModelsFeb 06 2013May 16 2015This paper discusses causal independence models and a generalization of these models called causal interaction models. Causal interaction models are models that have independent mechanisms where a mechanism can have several causes. In addition to introducing ... More

Quantifier Elimination for Statistical ProblemsJan 23 2013Recent improvement on Tarski's procedure for quantifier elimination in the first order theory of real numbers makes it feasible to solve small instances of the following problems completely automatically: 1. listing all equality and inequality constraints ... More

Inference for Multiplicative ModelsJun 13 2012The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture multiple forms of ... More

Models and Selection Criteria for Regression and ClassificationFeb 06 2013When performing regression or classification, we are interested in the conditional probability distribution for an outcome or class variable Y given a set of explanatoryor input variables X. We consider Bayesian models for this task. In particular, we ... More

Graphical Models and Exponential FamiliesJan 30 2013We provide a classification of graphical models according to their representation as subfamilies of exponential families. Undirected graphical models with no hidden variables are linear exponential families (LEFs), directed acyclic graphical models and ... More

Structural Risk Minimization for $C^{1,1}(\mathbb{R}^d)$ RegressionMar 29 2018Mar 30 2018One means of fitting functions to high-dimensional data is by providing smoothness constraints. Recently, the following smooth function approximation problem was proposed: given a finite set $E \subset \mathbb{R}^d$ and a function $f: E \rightarrow \mathbb{R}$, ... More

Automatic classification of time-variable X-ray sourcesMar 02 2014To maximize the discovery potential of future synoptic surveys, especially in the field of transient science, it will be necessary to use automatic classification to identify some of the astronomical sources. The data mining technique of supervised classification ... More

Autoclassification of the Variable 3XMM Sources Using the Random Forest Machine Learning AlgorithmSep 12 2015In the current era of large surveys and massive data sets, autoclassification of astrophysical sources using intelligent algorithms is becoming increasingly important. In this paper we present the catalog of variable sources in the Third XMM-Newton Serendipitous ... More

Measuring the mode volume of plasmonic nanocavities using coupled optical emittersJul 04 2012Metallic optical systems can confine light to deep sub-wavelength dimensions, but verifying the level of confinement at these length scales typically requires specialized techniques and equipment for probing the near-field of the structure. We experimentally ... More

Practically PerfectOct 19 2012The property of perfectness plays an important role in the theory of Bayesian networks. First, the existence of perfect distributions for arbitrary sets of variables and directed acyclic graphs implies that various methods for reading independence from ... More

Properly immersed surfaces in hyperbolic 3-manifoldsMar 07 2016Sep 09 2016We study complete finite topology immersed surfaces $\Sigma$ in complete Riemannian $3$-manifolds $N$ with sectional curvature $K_N\leq -a^2\leq 0$, such that the absolute mean curvature function of $\Sigma$ is bounded from above by $a$ and its injectivity ... More

Analysis of a Design Pattern for Teaching with Features and LabelsNov 18 2016We study the task of teaching a machine to classify objects using features and labels. We introduce the Error-Driven-Featuring design pattern for teaching using features and labels in which a teacher prefers to introduce features only if they are needed. ... More

On the toric algebra of graphical modelsAug 02 2006We formulate necessary and sufficient conditions for an arbitrary discrete probability distribution to factor according to an undirected graphical model, or a log-linear model, or other more general exponential models. For decomposable graphical models ... More

Minimal surfaces with the area growth of two planes; the case of infinite symmetryJan 08 2005We prove that a connected properly immersed minimal surface in Euclidean 3-space with infinite symmetry group whose intersection with a ball of radius R is less than 2\piR^2 is a plane, a catenoid or a Scherk singly-periodic minimal surface. In particular, ... More

Limit lamination theorem for H-disksOct 17 2015Nov 03 2015In this paper we prove a theorem concerning lamination limits of sequences of compact disks $M_n$ embedded in $\mathbb{R}^3$ with constant mean curvature $H_n$, when the boundaries of these disks tend to infinity. This theorem generalizes to the non-zero ... More

The rigidity of embedded constant mean curvature surfacesJan 22 2008We study the rigidity of complete, embedded constant mean curvature surfaces in R^3. Among other things, we prove that when such a surface has finite genus, then intrinsic isometries of the surface extend to isometries of R^3 or its isometry group contains ... More

A Bayesian Approach to Learning Bayesian Networks with Local StructureFeb 06 2013May 16 2015Recently several researchers have investigated techniques for using data to learn Bayesian networks containing compact representations for the conditional probability distributions (CPDs) stored at each node. The majority of this work has concentrated ... More

Large-Sample Learning of Bayesian Networks is NP-HardOct 19 2012In this paper, we provide new complexity results for algorithms that learn discrete-variable Bayesian networks from data. Our results apply whenever the learning algorithm uses a scoring criterion that favors the simplest model able to represent the generative ... More

Finite topology minimal surfaces in homogeneous three-manifoldsMay 25 2015Nov 09 2015We prove that any complete, embedded minimal surface $M$ with finite topology in a homogeneous three-manifold $N$ has positive injectivity radius. When one relaxes the condition that $N$ be homogeneous to that of being locally homogeneous, then we show ... More

Asymptotic Model Selection for Directed Networks with Hidden VariablesFeb 13 2013May 16 2015We extend the Bayesian Information Criterion (BIC), an asymptotic approximation for the marginal likelihood, to Bayesian networks with hidden variables. This approximation can be used to select models given large samples of data. The standard BIC as well ... More

Factorization of Discrete Probability DistributionsDec 12 2012We formulate necessary and sufficient conditions for an arbitrary discrete probability distribution to factor according to an undirected graphical model, or a log-linear model, or other more general exponential models. This result generalizes the well ... More

New Bounds on van der Waerden-type Numbers for Generalized 3-term Arithmetic ProgressionsJan 18 2012Jan 19 2012Let a and b be positive integers with a \leq b. An (a,b)-triple is a set {x,ax+d,bx+ 2d}, where x,d \geq 1. Define T(a,b;r) to be the least positive integer n such that any r-coloring of {1,2...,n} contains a monochromatic (a,b)-triple. Earlier results ... More

Properly immersed surfaces in hyperbolic 3-manifoldsMar 07 2016Jul 29 2017We study complete finite topology immersed surfaces $\Sigma$ in complete Riemannian $3$-manifolds $N$ with sectional curvature $K_N\leq -a^2\leq 0$, such that the absolute mean curvature function of $\Sigma$ is bounded from above by $a$ and its injectivity ... More

CMC foliations of closed manifoldsApr 07 2014Apr 09 2015We prove that every closed, smooth $n$-manifold $X$ admits a Riemannian metric together with a smooth, transversely oriented CMC foliation if and only if its Euler characteristic is zero, where by CMC foliation we mean a codimension-one, transversely ... More

A Stark decelerator on a chipDec 08 2008A microstructured array of 1254 electrodes on a substrate has been configured to generate an array of local minima of electric field strength with a periodicity of 120 $\mu$m about 25 $\mu$m above the substrate. By applying sinusoidally varying potentials ... More

The Topological Classification of Minimal Surfaces in R^3Sep 22 2002We give a complete topological classification of minimal surfaces in Euclidian three-space.

Triply periodic constant mean curvature surfacesNov 17 2016Given a closed flat 3-torus $N$, for each $H>0$ and each non-negative integer $g$, we obtain area estimates for closed surfaces with genus $g$ and constant mean curvature $H$ embedded in $N$. This result contrasts with the theorem of Traizet [33], who ... More

Curvature estimates for constant mean curvature surfacesFeb 21 2015Sep 27 2016We derive extrinsic curvature estimates for compact disks embedded in $\mathbb{R}^3$ with nonzero constant mean curvature.

A Comprehensive Trainable Error Model for Sung Music QueriesJun 30 2011We propose a model for errors in sung queries, a variant of the hidden Markov model (HMM). This is a solution to the problem of identifying the degree of similarity between a (typically error-laden) sung query and a potential target in a database of musical ... More

Staged Mixture Modelling and BoostingDec 12 2012In this paper, we introduce and evaluate a data-driven staged mixture modeling technique for building density, regression, and classification models. Our basic approach is to sequentially add components to a finite mixture model using the structural expectation ... More

CFW: A Collaborative Filtering System Using Posteriors Over Weights Of EvidenceDec 12 2012May 16 2015We describe CFW, a computationally efficient algorithm for collaborative filtering that uses posteriors over weights of evidence. In experiments on real data, we show that this method predicts as well or better than other methods in situations where the ... More

Perfect Tree-Like Markovian DistributionsJan 16 2013We show that if a strictly positive joint probability distribution for a set of binary random variables factors according to a tree, then vertex separation represents all and only the independence relations enclosed in the distribution. The same result ... More

The geometry of constant mean curvature surfaces in $\mathbb{R}^3$Sep 26 2016We derive intrinsic curvature and radius estimates for compact disks embedded in $\mathbb{R}^3$ with nonzero constant mean curvature and apply these estimates to study the global geometry of complete surfaces embedded in $\mathbb{R}^3$ with nonzero constant ... More

Properly embedded minimal planar domains with infinite topology are Riemann minimal examplesSep 12 2009These notes outline recent developments in classical minimal surface theory that are essential in classifying the properly embedded minimal planar domains M in R^3 with infinite topology (equivalently, with an infinite number of ends). This final classification ... More

Finite type annular ends for harmonic functionsSep 10 2009Mar 29 2016In this paper we describe the notion of an annular end of a Riemann surface being of finite type with respect to some harmonic function and prove some theoretical results relating the conformal structure of such an annular end to the level sets of the ... More

Chord arc properties for constant mean curvature disksAug 24 2014Apr 10 2017We prove a chord arc bound for disks embedded in $\mathbb{R}^3$ with constant mean curvature. This bound does not depend on the value of the mean curvature. It is inspired by and generalizes the work of Colding and Minicozzi in [2] for embedded minimal ... More

Chord arc properties for constant mean curvature disksAug 24 2014Nov 03 2015We prove a chord arc bound for disks embedded in $\mathbb{R}^3$ with constant mean curvature. This bound does not depend on the value of the mean curvature. It is inspired by and generalizes the work of Colding and Minicozzi in [2] for embedded minimal ... More

Limit lamination theorems for H-surfacesOct 26 2015Apr 29 2016In this paper we prove some general results on constant mean curvature lamination limits of certain sequences of compact surfaces $M_n$ embedded in $\mathbb R^3$ with constant mean curvature $H_n$ and fixed finite genus, when the boundaries of these surfaces ... More

One-sided curvature estimates for H-disksAug 22 2014Nov 03 2015In this paper we prove an extrinsic one-sided curvature estimate for disks embedded in $\mathbb{R}^3$ with constant mean curvature which is independent of the value of the constant mean curvature. We apply this extrinsic one-sided curvature estimate in ... More

Existence of regular neighborhoods for H-surfacesFeb 26 2010In this paper, we study the global geometry of complete, constant mean curvature hypersurfaces embedded in n-manifolds. More precisely, we give conditions that imply properness of such surfaces and prove the existence of fixed size one-sided regular neighborhoods ... More

The Dynamics Theorem for CMC surfaces in R^3May 09 2008In this paper, we study the space of translational limits T(M) of a surface M properly embedded in R^3 with nonzero constant mean curvature and bounded second fundamental form. There is a natural map T which assigns to any surface M' in T(M), the set ... More

Bending the HelicoidNov 15 2005We construct Colding-Minicozzi limit minimal laminations in open domains in $\rth$ with the singular set of $C^1$-convergence being any properly embedded $C^{1,1}$-curve. By Meeks' $C^{1,1}$-regularity theorem, the singular set of convergence of a Colding-Minicozzi ... More

Calabi-Yau domains in three manifoldsJun 25 2009We prove that given any compact Riemannian 3-manifold with boundary M, there exists a smooth properly embedded one-manifold G, included in M, each of whose components is a simple closed curve and such that the domain D=Int(M)-G does not admit any properly ... More

The Riemann minimal examplesSep 19 2016Near the end of his life, Bernhard Riemann made the marvelous discovery of a 1-parameter family $R_{\lambda}$, $\lambda\in (0,\infty)$, of periodic properly embedded minimal surfaces in $\mathbb{R}^3$ with the property that every horizontal plane intersects ... More

Embedded minimal surfaces of finite topologyJun 25 2015In this paper we prove that a complete, embedded minimal surface $M$ in $\mathbb{R}^3$ with finite topology and compact boundary (possibly empty) is conformally a compact Riemann surface $\overline{M}$ with boundary punctured in a finite number of interior ... More

Finite topology minimal surfaces in homogeneous three-manifoldsMay 25 2015Oct 18 2016We prove that any complete, embedded minimal surface $M$ with finite topology in a homogeneous three-manifold $N$ has positive injectivity radius. When one relaxes the condition that $N$ be homogeneous to that of being locally homogeneous, then we show ... More

Two-Path Solid-State Interferometry Using Ultra-Subwavelength 2D Plasmonic WavesDec 17 2012We report an on-chip solid-state Mach-Zehnder interferometer operating on two-dimensional (2D) plasmonic waves at microwave frequencies. Two plasmonic paths are defined with GaAs/AlGaAs 2D electron gas 80 nm below a metallic gate. The gated 2D plasmonic ... More

Learning Mixtures of DAG ModelsJan 30 2013May 16 2015We describe computationally efficient methods for learning mixtures in which each component is a directed acyclic graphical model (mixtures of DAGs or MDAGs). We argue that simple search-and-score algorithms are infeasible for a variety of problems, and ... More

Causal Inference in the Presence of Latent Variables and Selection BiasFeb 20 2013We show that there is a general, informative and reliable procedure for discovering causal relations when, for all the investigator knows, both latent variables and selection bias may be at work. Given information about conditional independence and dependence ... More

The embedded Calabi-Yau conjecture for finite genusJun 08 2018Suppose $M$ is a complete, embedded minimal surface in $\mathbb{R}^3$ with an infinite number of ends, finite genus and compact boundary. We prove that the simple limit ends of $M$ have properly embedded representatives with compact boundary, genus zero ... More

The topology, geometry and conformal structure of properly embedded minimal surfacesJan 21 2004This paper develops new tools for understanding surfaces with more than one end (and usually, of infinite topology) which properly minimally embed into Euclidean three-space. On such a surface, the set of ends forms a compact Hausdorff space, naturally ... More

The Dynamics Theorem for properly embedded minimal surfacesJan 08 2014In this paper we prove two theorems. The first one is a structure result that describes the extrinsic geometry of an embedded surface with constant mean curvature (possibly zero) in a homogeneously regular Riemannian three-manifold, in any small neighborhood ... More

The geometry of stable minimal surfaces in metric Lie groupsOct 24 2016We study geometric properties of compact stable minimal surfaces with boundary in homogeneous 3-manifolds $X$ that can be expressed as a semidirect product of $\mathbb{R}^2$ with $\mathbb{R}$ endowed with a left invariant metric. For any such compact ... More

Precision spectra of $A\, ^2Σ^+,v'=0 \leftarrow X\, ^2Π_{3/2},v''=0,J''=3/2$ transitions in $^{16}$OH and $^{16}$ODMay 25 2018Nov 01 2018We report absolute optical frequencies of electronic transitions from the $X\, ^2\Pi_{3/2},v''=0,J''=3/2$ rovibronic ground state to the 12 lowest levels of the $A\, ^2\Sigma^+,v'=0$ vibronic state in $^{16}$OH, as well as to the 16 lowest levels of the ... More

Structure theorems for singular minimal laminationsFeb 09 2016Nov 23 2016We apply the local removable singularity theorem for minimal laminations and the local picture theorem on the scale of topology to obtain two descriptive results for certain possibly singular minimal laminations of $\mathbb{R}^3$. These two global structure ... More

The classification of CMC foliations of $\mathbb{R}^3$ and $\mathbb{S}^3$ with countably many singularitiesJan 13 2014In this paper we generalize the Local Removable Singularity Theorem in [16] for minimal laminations to the case of weak $H$-laminations (with $H\in \mathbb{R}$ constant) in a punctured ball of a Riemannian three-manifold. We also obtain a curvature estimate ... More

Constant mean curvature surfacesMay 09 2016In this article we survey recent developments in the theory of constant mean curvature surfaces in homogeneous 3-manifolds, as well as some related aspects on existence and descriptive results for $H$-laminations and CMC foliations of Riemannian $n$-manifolds. ... More

Structure theorems for singular minimal laminationsFeb 09 2016We apply the local removable singularity theorem for minimal laminations and the local picture theorem on the scale of topology to obtain two descriptive results for certain possibly singular minimal laminations of $\mathbb{R}^3$. These two global structure ... More

A non-vanishing result for the CMC fluxJun 26 2016We prove the non-vanishing of the CMC flux of the boundaries of certain Riemannian manifolds with constant mean curvature.

A non-vanishing result for the CMC fluxJun 26 2016Jun 29 2017We prove the non-vanishing of the CMC flux of the boundaries of certain Riemannian manifolds with constant mean curvature.

Non-properly Embedded H-Planes in Hyperbolic 3-SpaceMar 16 2015For any H in [0,1), we construct complete, non-proper, stable, simply-connected surfaces with constant mean curvature H embedded in hyperbolic 3-space.

Limit leaves of a CMC lamination are stableJan 28 2008Feb 26 2008Suppose ${\cal L}$ is a lamination of a Riemannian manifold by hypersurfaces with the same constant mean curvature. We prove that every limit leaf of ${\cal L}$ is stable for the Jacobi operator. A simple but important consequence of this result is that ... More

Bounded domains which are universal for minimal surfacesApr 15 2005We construct open domains in Euclidean 3-space which do not admit complete properly immersed minimal surfaces with an annular end. These domains can not be smooth by a recent result of Martin and Morales

Isoperimetric domains of large volume in homogeneous three-manifoldsMar 18 2013Apr 03 2013Given a non-compact, simply connected homogeneous three-manifold $X$ and a sequence $\{\Omega_n\}_n$ of isoperimetric domains in $X$ with volumes tending to infinity, we prove that as $n\to \infty $: 1. The radii of the $\Omega_n$ tend to infinity. 2. ... More

Bounds on the topology and index of minimal surfacesMay 09 2016We prove that for every nonnegative integer $g$, there exists a bound on the number of ends of a complete, embedded minimal surface $M$ in $\mathbb{R}^3$ of genus $g$ and finite topology. This bound on the finite number of ends when $M$ has at least two ... More

Properly embedded minimal planar domainsJun 07 2013May 07 2014In 1997, Collin proved that any properly embedded minimal surface in $\mathbb{R}^3$ with finite topology and more than one end has finite total Gaussian curvature. Hence, by an earlier result of Lopez and Ros, catenoids are the only non-planar, non-simply ... More

Non-properly Embedded H-Planes in H^2xRSep 27 2016For any $H$ in (0,1/2), we construct complete, non-proper, stable, simply-connected surfaces embedded in $H^2xR$ with constant mean curvature $H$.

Embeddedness of spheres in homogeneous three-manifoldsJan 25 2016Let $X$ denote a metric Lie group diffeomorphic to $\mathbb{R}^3$ that admits an algebraic open book decomposition. In this paper we prove that if $\Sigma$ is an immersed surface in $X$ whose left invariant Gauss map is a diffeomorphism onto $\mathbb{S}^2$, ... More

The local picture theorem on the scale of topologyMay 25 2015Oct 16 2016We prove a descriptive theorem on the extrinsic geometry of an embedded minimal surface of injectivity radius zero in a homogeneously regular Riemannian three-manifold, in a certain small intrinsic neighborhood of a point of almost-minimal injectivity ... More

Half-space theorems and the embedded Calabi-Yau problem in Lie groupsDec 09 2010We study the embedded Calabi-Yau problem for complete embedded constant mean curvature surfaces of finite topology or of positive injectivity radius in a simply-connected three-dimensional Lie group X endowed with a left-invariant Riemannian metric. We ... More

Constant mean curvature spheres in homogeneous three-manifoldsJun 28 2017We prove that two spheres of the same constant mean curvature in an arbitrary homogeneous three-manifold only differ by an ambient isometry, and we determine the values of the mean curvature for which such spheres exist. This gives a complete classification ... More

ARMA Time-Series Modeling with Graphical ModelsJul 11 2012Aug 08 2012We express the classic ARMA time-series model as a directed graphical model. In doing so, we find that the deterministic relationships in the model make it effectively impossible to use the EM algorithm for learning model parameters. To remedy this problem, ... More

Trapping molecules on a chip in traveling potential wellsJan 18 2008Apr 23 2008A microstructured array of over 1200 electrodes on a substrate has been configured to generate an array of local minima of electric field strength with a periodicity of $120 \mu$m about $25 \mu$m above the substrate. By applying sinusoidally varying potentials ... More

Non-properly Embedded H-Planes in H^2xRSep 27 2016Apr 27 2017For any $H$ in (0,1/2), we construct complete, non-proper, stable, simply-connected surfaces embedded in $H^2xR$ with constant mean curvature $H$.

Existence of proper minimal surfaces of arbitrary topological typeMar 24 2009Consider a domain D in R^3 which is convex (possibly all R^3) or which is smooth and bounded. Given any open surface M, we prove that there exists a complete, proper minimal immersion f : M --> D. Moreover, if D is smooth and bounded, then we prove that ... More

Local removable singularity theorems for minimal laminationsAug 29 2013In this paper we prove a local removable singularity theorem for certain minimal laminations with isolated singularities in a Riemannian three-manifold. This removable singularity theorem is the key result used in our proof that a complete, embedded minimal ... More

Constant mean curvature spheres in homogeneous three-spheresAug 12 2013Aug 14 2013We give a complete classification of the immersed constant mean curvature spheres in a three-sphere with an arbitrary homogenous metric, by proving that for each $H\in\mathbb{R}$, there exists a constant mean curvature $H$-sphere in the space that is ... More

Half-space theorems for minimal surfaces in Nil_3 and Sol_3May 21 2010We prove some half-space theorems for minimal surfaces in the Heisenberg group Nil_3 and the Lie group Sol_3 endowed with their left-invariant Riemannian metrics. If S is a properly immersed minimal surface in Nil_3 that lies on one side of some entire ... More

Fourier transform spectroscopy around 3 microns with a broad difference frequency combFeb 25 2013We characterize a new mid-infrared frequency comb generator based on difference frequency generation around 3.2 microns. High power per comb mode (>10-7 W/mode) is obtained over a broad spectral span (>700 nm). The source is used for direct absorption ... More

An electrostatic elliptical mirror for neutral polar moleculesMar 29 2011Focusing optics for neutral molecules finds application in shaping and steering molecular beams. Here we present an electrostatic elliptical mirror for polar molecules consisting of an array of microstructured gold electrodes deposited on a glass substrate. ... More

Broadband high-resolution two-photon spectroscopy with laser frequency combsNov 24 2013Two-photon excitation spectroscopy with broad spectral span is demonstrated at Doppler-limited resolution. We describe first Fourier transform two-photon spectroscopy of an atomic sample with two mode-locked laser oscillators in a dual-comb technique. ... More

A non-invasive investigation of Egyptian faience using a long wavelength optical coherence tomography (OCT) at 2umMar 25 2019Egyptian faience is a non-clay ceramic semi-transparent material, formed of a quartz core and alkali lime glaze with some cases exhibiting an interaction layer between them. Several possible glazing methods have been identified. Previous investigations ... More

Is J enough? Comparison of gravitational waves emitted along the total angular momentum direction with other preferred orientationsJan 10 2012Aug 01 2012The gravitational wave signature emitted from a merging binary depends on the orientation of an observer relative to the binary. Previous studies suggest that emission along the total initial or total final angular momenta leads to both the strongest ... More