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Variable Selection for Latent Class Analysis with Application to Low Back Pain DiagnosisDec 10 2015Feb 05 2018The identification of most relevant clinical criteria related to low back pain disorders may aid the evaluation of the nature of pain suffered in a way that usefully informs patient assessment and treatment. Data concerning low back pain can be of categorical ... More

Motor Insurance Accidental Damage Claims Modeling with Factor Collapsing and Bayesian Model AveragingOct 10 2017Accidental damage is a typical component of motor insurance claim. Modeling of this nature generally involves analysis of past claim history and different characteristics of the insured objects and the policyholders. Generalized linear models (GLMs) have ... More

Products of Differences over Arbitrary Finite FieldsMay 18 2017Nov 13 2018There exists an absolute constant $\delta > 0$ such that for all $q$ and all subsets $A \subseteq \mathbb{F}_q$ of the finite field with $q$ elements, if $|A| > q^{2/3 - \delta}$, then \[ |(A-A)(A-A)| = |\{ (a -b) (c-d) : a,b,c,d \in A\}| > \frac{q}{2}. ... More

A Second Wave of Expanders over Finite FieldsJan 06 2017This is an expository survey on recent sum-product results in finite fields. We present a number of sum-product or "expander" results that say that if $|A| > p^{2/3}$ then some set determined by sums and product of elements of $A$ is nearly as large as ... More

Popular Products and Continued FractionsAug 17 2018Aug 23 2018We prove bounds for the popularity of products of sets with weak additive structure, and use these bounds to prove results about continued fractions. Namely, we obtain a nearly sharp upper bound for the cardinality of Zaremba's set modulo $p$.

Bivariate Gamma Mixture of Experts Models for Joint Insurance Claims ModelingApr 09 2019In general insurance, risks from different categories are often modeled independently and their sum is regarded as the total risk the insurer takes on in exchange for a premium. The dependence from multiple risks is generally neglected even when correlation ... More

Mixture of Latent Trait Analyzers for Model-Based Clustering of Categorical DataJan 10 2013Feb 19 2013Model-based clustering methods for continuous data are well established and commonly used in a wide range of applications. However, model-based clustering methods for categorical data are less standard. Latent class analysis is a commonly used method ... More

Joint Modelling of Multiple Network ViewsJan 16 2013Sep 25 2014Latent space models (LSM) for network data were introduced by Hoff et al. (2002) under the basic assumption that each node of the network has an unknown position in a D-dimensional Euclidean latent space: generally the smaller the distance between two ... More

Exponential Family Mixed Membership Models for Soft~Clustering of Multivariate DataAug 10 2016For several years, model-based clustering methods have successfully tackled many of the challenges presented by data-analysts. However, as the scope of data analysis has evolved, some problems may be beyond the standard mixture model framework. One such ... More

Mixed-Membership of Experts Stochastic BlockmodelApr 01 2014Social network analysis is the study of how links between a set of actors are formed. Typically, it is believed that links are formed in a structured manner, which may be due to, for example, political or material incentives, and which often may not be ... More

Terahertz nonlinear conduction and absorption saturation in silicon waveguidesMar 19 2015We employ a silicon dielectric waveguide to confine and concentrate terahertz pulses, and observe that the absorption saturates under strong terahertz fields. By comparing the response between lightly-doped and intrinsic silicon waveguides, we confirm ... More

Prophet Inequalities Made Easy: Stochastic Optimization by Pricing Non-Stochastic InputsDec 09 2016Jul 09 2017We present a general framework for stochastic online maximization problems with combinatorial feasibility constraints. The framework establishes prophet inequalities by constructing price-based online approximation algorithms, a natural extension of threshold ... More

Variational Learning in Mixed-State Dynamic Graphical ModelsJan 23 2013Many real-valued stochastic time-series are locally linear (Gassian), but globally non-linear. For example, the trajectory of a human hand gesture can be viewed as a linear dynamic system driven by a nonlinear dynamic system that represents muscle actions. ... More

Model-based clustering for random hypergraphsAug 15 2018A probabilistic model for random hypergraphs is introduced to represent unary, binary and higher order interactions among objects in real-world problems. This model is an extension of the Latent Class Analysis model, which captures clustering structures ... More

A mixture of experts model for rank data with applications in election studiesJan 27 2009A voting bloc is defined to be a group of voters who have similar voting preferences. The cleavage of the Irish electorate into voting blocs is of interest. Irish elections employ a ``single transferable vote'' electoral system; under this system voters ... More

Variable Selection for Latent Class Analysis with Application to Low Back Pain DiagnosisDec 10 2015The identification of most relevant clinical criteria related to low back pain disorders is a crucial task for a quick and correct diagnosis of the nature of pain and its treatment. Data concerning low back pain can be of categorical nature, in form of ... More

A robust approach to model-based classification based on trimming and constraintsApr 12 2019In a standard classification framework a set of trustworthy learning data are employed to build a decision rule, with the final aim of classifying unlabelled units belonging to the test set. Therefore, unreliable labelled observations, namely outliers ... More

Bayesian variable selection for latent class analysis using a collapsed Gibbs samplerFeb 27 2014Apr 30 2015Latent class analysis is used to perform model based clustering for multivariate categorical responses. Selection of the variables most relevant for clustering is an important task which can affect the quality of clustering considerably. This work considers ... More

Delayed Dynamical Systems: Networks, Chimeras and Reservoir ComputingAug 14 2018We present a systematic approach to reveal the correspondence between time delay dynamics and networks of coupled oscillators. After early demonstrations of the usefulness of spatio-temporal representations of time-delay system dynamics, extensive research ... More

Using Synchronization for Prediction of High-Dimensional Chaotic DynamicsSep 22 2008We experimentally observe the nonlinear dynamics of an optoelectronic time-delayed feedback loop designed for chaotic communication using commercial fiber optic links, and we simulate the system using delay differential equations. We show that synchronization ... More

Scalable parallel physical random number generator based on a superluminescent LEDMar 15 2011We describe an optoelectronic system for simultaneously generating parallel, independent streams of random bits using spectrally separated noise signals obtained from a single optical source. Using a pair of non-overlapping spectral filters and a fiber-coupled ... More

Experimental observation of chimera and cluster states in a minimal globally coupled networkDec 05 2015Jan 13 2016A "chimera state" is a dynamical pattern that occurs in a network of coupled identical oscillators when the symmetry of the oscillator population is broken into synchronous and asynchronous parts. We report the experimental observation of chimera and ... More

Harvesting entropy and quantifying the transition from noise to chaos in a photon-counting feedback loopMar 27 2015Aug 07 2015Some physical processes, including the intensity fluctuations of a chaotic laser, the detection of single photons, and the Brownian motion of a microscopic particle in a fluid are unpredictable, at least on long timescales. This unpredictability can be ... More

Variable selection and updating in model-based discriminant analysis for high dimensional data with food authenticity applicationsOct 14 2009Oct 07 2010Food authenticity studies are concerned with determining if food samples have been correctly labeled or not. Discriminant analysis methods are an integral part of the methodology for food authentication. Motivated by food authenticity applications, a ... More

Bayesian nonparametric Plackett-Luce models for the analysis of preferences for college degree programmesNov 21 2012Aug 01 2014In this paper we propose a Bayesian nonparametric model for clustering partial ranking data. We start by developing a Bayesian nonparametric extension of the popular Plackett-Luce choice model that can handle an infinite number of choice items. Our framework ... More

Latent Space Modeling of Multidimensional Networks with Application to the Exchange of Votes in Eurovision Song ContestMar 13 2018The Eurovision Song Contest is a popular TV singing competition held annually among country members of the European Broadcasting Union. In this competition, each member can be both contestant and jury, as it can participate with a song and/or vote for ... More

A bi-criteria path planning algorithm for robotics applicationsNov 04 2015Jan 08 2017Realistic path planning applications often require optimizing with respect to several criteria simultaneously. Here we introduce an efficient algorithm for bi-criteria path planning on graphs. Our approach is based on augmenting the state space to keep ... More

On Estimation of Parameter Uncertainty in Model-Based ClusteringOct 02 2015Mixture models are a popular tool in model-based clustering. Such a model is often fitted by a procedure that maximizes the likelihood, such as the EM algorithm. At convergence, the maximum likelihood parameter estimates are typically reported, but in ... More

Bayesian model averaging in model-based clustering and density estimationJun 30 2015We propose Bayesian model averaging (BMA) as a method for postprocessing the results of model-based clustering. Given a number of competing models, appropriate model summaries are averaged, using the posterior model probabilities, instead of being taken ... More

Node-specific effects in latent space modelling of multidimensional networksJul 10 2018Observed multidimensional network data can have different levels of complexity, as nodes may be characterized by heterogeneous individual-specific features. Also, such characteristics may vary across the networks. This article discusses a novel class ... More

On Isolated Umbilic PointsDec 09 2018Counter-examples to the famous conjecture of Caratheodory, as well as the bound on umbilic index proposed by Hamburger, are constructed with respect to Riemannian metrics that are arbitrarily close to the flat metric on Euclidean 3-space. In particular, ... More

Limiting Empirical Singular Value Distribution of Restrictions of Unitary MatricesMar 04 2010We determine the limiting empirical singular value distribution for random unitary matrices with Haar distribution and discrete Fourier transform (DFT) matrices when a random set of columns and rows is removed.

Cohomology classes of interval positroid varieties and a conjecture of LiuOct 08 2014Jul 24 2018To each finite subset of $\mathbb{Z}^2$ (a diagram), one can associate a subvariety of a complex Grassmannian (a diagram variety), and a representation of a symmetric group (a Specht module). Liu has conjectured that the cohomology class of a diagram ... More

Decorated CospansFeb 03 2015Aug 11 2015Let $\mathcal C$ be a category with finite colimits, writing its coproduct $+$, and let $(\mathcal D, \otimes)$ be a braided monoidal category. We describe a method of producing a symmetric monoidal category from a lax braided monoidal functor $F: (\mathcal ... More

Classification of simple weight modules with finite-dimensional weight spaces over the Schrödinger algebraSep 05 2013We classify simple weight modules with finite-dimensional weight spaces over the (centrally extended complex) Schr\"odinger algebra in (1+1)-dimensional space-time. Our arguments use the description of lowest weight modules by Dobrev, Doebner and Mrugalla; ... More

Beyond Equilibria: Mechanisms for Repeated Combinatorial AuctionsSep 30 2009We study the design of mechanisms in combinatorial auction domains. We focus on settings where the auction is repeated, motivated by auctions for licenses or advertising space. We consider models of agent behaviour in which they either apply common learning ... More

Incidence category of the Young lattice, injections between finite sets, and KoszulityJul 01 2016Oct 04 2018We describe the Gabriel quiver with defining relations of the category of injections between finite sets, show that it is quadratic self-dual, and construct linear resolutions for its simple modules.

Induction and restriction on representations of dihedral groupsMay 07 2018We study the algebras generated by restriction and induction operations on complex modules over dihedral groups. In the case where the orders of all dihedral groups involved are not divisible by four, we describe the relations, a basis, the center, and ... More

Cubic fourfolds, K3 surfaces, and rationality questionsJan 21 2016Jul 17 2016This is a survey of the geometry of complex cubic fourfolds with a view toward rationality questions. Topics include classical constructions of rational examples, Hodge structures and special cubic fourfolds, associated K3 surfaces and their geometric ... More

Convexity and multi-dimensional screening for spaces with different dimensionsAug 18 2011We study the principal-agent problem. We show that $b$-convexity of the space of products, a condition which appears in a recent paper by Figalli, Kim and McCann \cite{fkm}, is necessary to formulate the problem as a maximization over a convex set. We ... More

Abelian Analytic Torsion and Symplectic VolumeAug 12 2012Aug 17 2015This article studies the abelian analytic torsion on a closed, oriented, Sasakian three-manifold and identifies this quantity as a specific multiple of the natural unit symplectic volume form on the moduli space of flat abelian connections. This identification ... More

Localization in Abelian Chern-Simons TheoryAug 08 2012Jul 18 2014Chern-Simons theory on a closed contact three-manifold is studied when the Lie group for gauge transformations is compact, connected and abelian. A rigorous definition of an abelian Chern-Simons partition function is derived using the Faddeev-Popov gauge ... More

Multi-marginal optimal transport and multi-agent matching problems: uniqueness and structure of solutionsOct 27 2012We prove uniqueness and Monge solution results for multi-marginal optimal transportation problems with a certain class of surplus functions; this class arises naturally in multi-agent matching problems in economics. This result generalizes a seminal result ... More

Regularity properties of optimal transportation problems arising in hedonic pricing modelsOct 12 2011We study a form of optimal transportation surplus functions which arise in hedonic pricing models. We derive a formula for the Ma-Trudinger-Wang curvature of these functions, yielding necessary and sufficient conditions for them to satisfy \textbf{(A3w)}. ... More

Koszulity of some path categoriesFeb 22 2015Jun 06 2015We prove Koszulity of certain linear path categories obtained from connected graphs with some infinite directed walk. These categories can be viewed as locally quadratic dual to preprojective algebras.

A point-line incidence identity in finite fields, and applicationsJan 15 2016Feb 20 2016Let $E \subseteq \mathbb{F}_q^2$ be a set in the 2-dimensional vector space over a finite field with $q$ elements. We prove an identity for the second moment of its incidence function and deduce a variety of existing results from the literature, not all ... More

Kakeya Configurations in Lie Groups and Homogeneous SpacesMar 04 2013In this paper, we study continuous Kakeya line and needle configurations, of both the oriented and unoriented varieties, in connected Lie groups and some associated homogenous spaces. These are the analogs of Kakeya line (needle) sets (subsets of $\mathbb{R}^n$ ... More

Complete Characterization of Stability of Cluster Synchronization in Complex Dynamical NetworksJul 15 2015Dec 03 2015Synchronization is an important and prevalent phenomenon in natural and engineered systems. In many dynamical networks, the coupling is balanced or adjusted in order to admit global synchronization, a condition called Laplacian coupling. Many networks ... More

Symmetries, Cluster Synchronization, and Isolated Desynchronization in Complex NetworksSep 25 2013Synchronization is of central importance in power distribution, telecommunication, neuronal, and biological networks. Many networks are observed to produce patterns of synchronized clusters, but it has been difficult to predict these clusters or understand ... More

Dynamic synchronization of a time-evolving optical network of chaotic oscillatorsDec 07 2010We present and experimentally demonstrate a technique for achieving and maintaining a global state of identical synchrony of an arbitrary network of chaotic oscillators even when the coupling strengths are unknown and time-varying. At each node an adaptive ... More

Robustness of Optimal Synchronization in Real NetworksJun 20 2011Experimental studies of synchronization properties on networks with controlled connection topology can provide powerful insights into the physics of complex networks. Here, we report experimental results on the influence of connection topology on synchronization ... More

Multiresolution network modelsAug 26 2016Sep 08 2016Social networks exhibit two key topological features: global sparsity and local density. That is, the overall propensity for interaction between any two randomly selected actors is infinitesimal, but for any given individual there is massive variability ... More

Modeling the social media relationships of Irish politicians using a generalized latent space stochastic blockmodelJul 16 2018D\'ail \'Eireann is the principal chamber of the Irish parliament. The 31st D\'ail \'Eireann is the principal chamber of the Irish parliament. The 31st D\'ail was in session from March 11th, 2011 to February 6th, 2016. Many of the members of the D\'ail ... More

Model-based clustering in networks with Stochastic Community FindingMay 09 2012Oct 28 2012In the model-based clustering of networks, blockmodelling may be used to identify roles in the network. We identify a special case of the Stochastic Block Model (SBM) where we constrain the cluster-cluster interactions such that the density inside the ... More

Multiresolution network modelsAug 26 2016Jul 05 2018Many existing statistical and machine learning tools for social network analysis focus on a single level of analysis. Methods designed for clustering optimize a global partition of the graph, whereas projection based approaches (e.g. the latent space ... More

Clustering in networks with the collapsed Stochastic Block ModelMar 14 2012Nov 08 2012An efficient MCMC algorithm is presented to cluster the nodes of a network such that nodes with similar role in the network are clustered together. This is known as block-modelling or block-clustering. The model is the stochastic blockmodel (SBM) with ... More

Multiresolution network modelsAug 26 2016Nov 22 2016Social networks exhibit two key topological features: global sparsity and local density. That is, the overall propensity for interaction between any two randomly selected actors is infinitesimal, but for any given individual there is massive variability ... More

Interpreting, forecasting, and controlling feeding behaviour using high-resolution dataFeb 22 2019Mar 14 2019Better understanding of feeding behaviour will be vital in reducing obesity and metabolic syndrome, but we lack a standard model that captures the complexity of feeding behaviour. We construct an accurate stochastic model of rodent feeding at the bout ... More

Affine embeddings of a reductive groupDec 17 2010We classify affine varieties with an action of a connected, reductive algebraic group such that the group is isomorphic to an open orbit in the variety. This is accomplished by associating a set of one-parameter subgroups of the group to the variety, ... More

Adaptive synchronization of coupled chaotic oscillatorsJul 22 2009Oct 05 2009We experimentally demonstrate and numerically simulate a new adaptive method to maintain synchronization between coupled nonlinear chaotic oscillators, when the coupling between the systems is unknown and time-varying (e.g., due to environmental parameter ... More

Overcoming Small Minirhizotron Datasets Using Transfer LearningMar 22 2019Minirhizotron technology is widely used for studying the development of roots. Such systems collect visible-wavelength color imagery of plant roots in-situ by scanning an imaging system within a clear tube driven into the soil. Automated analysis of root ... More

Loose Legendrian embeddings in high dimensional contact manifoldsJan 11 2012Mar 11 2019We give an $h$--principle type result for a class of Legendrian embeddings in contact manifolds of dimension at least $5$. These Legendrians, referred to as loose, have trivial pseudo-holomorphic invariants. We demonstrate they are classified up to Legendrian ... More

Terahertz Nonlinearity in Graphene PlasmonsDec 23 2015Sub-wavelength graphene structures support localized plasmonic resonances in the terahertz and mid-infrared spectral regimes. The strong field confinement at the resonant frequency is predicted to significantly enhance the light-graphene interaction, ... More

Reflection in a Translation Invariant SurfaceOct 23 2005We prove that the focal set generated by the reflection of a point source off a translation invariant surface consists of two sets: a curve and a surface. The focal curve lies in the plane orthogonal to the symmetry direction containing the source, while ... More

The Geometry of Focal SetsNov 09 2004Nov 29 2005The space ${\Bbb{L}}$ of oriented lines, or rays, in ${\Bbb{R}}^3$ is a 4-dimensional space with an abundance of natural geometric structure. In particular, it boasts a neutral K\"ahler metric which is closely related to the Euclidean metric on ${\Bbb{R}}^3$. ... More

On Hamilton's Characteristic Functions for ReflectionFeb 01 2006We review the complex differential geometry of the space of oriented affine lines in ${\Bbb{R}}^3$ and give a description of Hamilton's characteristic functions for reflection in an oriented C$^1$ surface in terms of this geometry.

A characterization of Weingarten surfaces in hyperbolic 3-spaceSep 15 2007Mar 08 2009We study 2-dimensional submanifolds of the space ${\mathbb{L}}({\mathbb{H}}^3)$ of oriented geodesics of hyperbolic 3-space, endowed with the canonical neutral K\"ahler structure. Such a surface is Lagrangian iff there exists a surface in ${\mathbb{H}}^3$ ... More

Log minimal model program for the moduli space of stable curves: The first flipJun 20 2008We give a geometric invariant theory (GIT) construction of the log canonical model $\bar M_g(\alpha)$ of the pairs $(\bar M_g, \alpha \delta)$ for $\alpha \in (7/10 - \epsilon, 7/10]$ for small $\epsilon \in \mathbb Q_+$. We show that $\bar M_g(7/10)$ ... More

On area-stationary surfaces in certain neutral Kaehler 4-manifoldsNov 22 2006We study surfaces in TN that are area-stationary with respect to a neutral Kaehler metric constructed on TN from a riemannian metric g on N. We show that holomorphic curves in TN are area-stationary, while lagrangian surfaces that are area-stationary ... More

A Neutral Kaehler Metric on Space of Time-like Lines in Lorentzian 3-spaceAug 31 2006Nov 24 2006We study the neutral K\"ahler metric on the space of time-like lines in Lorentzian ${\Bbb{E}}^3_1$, which we identify with the total space of the tangent bundle to the hyperbolic plane. We find all of the infinitesimal isometries of this metric, as well ... More

Proof of the Caratheodory ConjectureAug 06 2008Jul 31 2013A well-known conjecture of Caratheodory states that the number of umbilic points on a closed convex surface in ${\mathbb E}^3$ must be greater than one. In this paper we prove this for $C^{3+\alpha}$-smooth surfaces. The Conjecture is first reformulated ... More

On Brauer groups of double covers of ruled surfacesJun 13 2013Oct 08 2014Let X be a smooth double cover of a geometrically ruled surface defined over a separably closed field of characteristic different from 2. The main result of this paper is a finite presentation of the 2-torsion in the Brauer group of X with generators ... More

A class of Ramsey-extremal hypergraphsAug 28 2016In 1991, McKay and Radziszowski proved that, however each 3-subset of a 13-set is assigned one of two colours, there is some 4-subset whose four 3-subsets have the same colour. More than 25 years later, this remains the only non-trivial classical Ramsey ... More

A note on the history of the four-colour conjectureJan 13 2012Feb 21 2012The four-colour conjecture was brought to public attention in 1854, most probably by Francis or Frederick Guthrie. This moves back by six years the date of the earliest known publication.

Corelations are the prop for extraspecial commutative Frobenius monoidsJan 11 2016Jan 30 2016Just as binary relations between sets may be understood as jointly monic spans, so too may equivalence relations on the disjoint union of sets be understood as jointly epic cospans. With the ensuing notion of composition inherited from the pushout of ... More

Extremal rays and automorphisms of holomorphic symplectic varietiesJun 26 2015We survey recent results on ample cones and birational contractions of holomorphic symplectic varieties of K3 type, focusing on explicit constructions and concrete examples.

Embedding pointed curves in K3 surfacesJan 30 2013We analyze morphisms from pointed curves to K3 surfaces with a distinguished rational curve, such that the marked points are taken to the rational curve, perhaps with specified cross ratios. This builds on work of Mukai and others characterizing embeddings ... More

Hodge theory and Lagrangian planes on generalized Kummer fourfoldsApr 01 2010We analyze the intersection properties of projective planes embedded in generalized Kummer fourfolds, with a view toward classifying the homology classes represented by these submanifolds.

User Satisfaction in Competitive Sponsored SearchOct 15 2013We present a model of competition between web search algorithms, and study the impact of such competition on user welfare. In our model, search providers compete for customers by strategically selecting which search results to display in response to user ... More

Rationality of complete intersections of two quadricsMar 21 2019We study rationality problems for smooth complete intersections of two quadrics. We focus on the three-dimensional case, with a view toward understanding the invariants governing the rationality of a geometrically rational threefold over a non-closed ... More

Unlinking information from 4-manifoldsMar 10 2015Nov 04 2015We generalise theorems of Cochran-Lickorish and Owens-Strle to the case of links with more than one component. This enables the use of linking forms on double branched covers, Heegaard Floer correction terms, and Donaldson's diagonalisation theorem to ... More

Approximation at places of bad reductionMay 10 2006This paper addresses weak approximation for rationally connected varieties defined over the function field of a curve, especially at places of bad reduction. Our approach entails analyzing the rational connectivity of the smooth locus of singular reductions ... More

A concordance invariant from the Floer homology of double branched coversAug 02 2005Ozsvath and Szabo defined an analog of the Froyshov invariant in the form of a correction term for the grading in Heegaard Floer homology. Applying this to the double cover of the 3-sphere branched over a knot K, we obtain an invariant delta of knot concordance. ... More

Subgraphs of dense random graphs with specified degreesFeb 16 2010Nov 27 2010Let d = (d1, d2, ..., dn) be a vector of non-negative integers with even sum. We prove some basic facts about the structure of a random graph with degree sequence d, including the probability of a given subgraph or induced subgraph. Although there are ... More

Noether charges and black hole mechanics in Einstein-aether theorySep 29 2005Dec 09 2005The Noether charge method for defining the Hamiltonian of a diffeomorphism-invariant field theory is applied to "Einstein-aether" theory, in which gravity couples to a dynamical, timelike, unit-norm vector field. Using the method, expressions are obtained ... More

Hypohamiltonian planar cubic graphs with girth fiveJul 26 2015A graph is called hypohamiltonian if it is not hamiltonian but becomes hamiltonian if any vertex is removed. Many hypohamiltonian planar cubic graphs have been found, starting with constructions of Thomassen in 1981. However, all the examples found until ... More

Reduced words for clansJun 13 2018Clans are combinatorial objects indexing the orbits of $GL(\mathbb{C}^p) \times GL(\mathbb{C}^q)$ on the variety of flags in $\mathbb{C}^{p+q}$. This geometry leads to a partial order on the set of clans analogous to weak Bruhat order on the symmetric ... More

A recipe for black box functorsDec 10 2018The task of constructing compositional semantics for network-style diagrammatic languages, such as electrical circuits or chemical reaction networks, has been dubbed the black boxing problem, as it gives semantics that describes the properties of each ... More

Reflection of a wave off a surfaceJun 10 2004Recent advances in twistor theory are applied to geometric optics in ${\Bbb{R}}^3$. The general formulae for reflection of a wavefront in a surface are derived and in three special cases explicit descriptions are provided: when the reflecting surface ... More

On the three-dimensional Blaschke-Lebesgue problemJun 17 2009Aug 14 2010The width of a closed convex subset of Euclidean space is the distance between two parallel supporting planes. The Blaschke-Lebesgue problem consists of minimizing the volume in the class of convex sets of fixed constant width and is still open in dimension ... More

Parabolic Classical Curvature FlowsMar 06 2015Jun 18 2015We consider classical curvature flows: 1-parameter families of convex embeddings of the 2-sphere into Euclidean 3-space which evolve by an arbitrary (non-homogeneous) function of the radii of curvature. The associated flow of the radii of curvature is ... More

A Global Version of a Classical Result of JoachimsthalApr 22 2014Feb 18 2016A classical result attributed to Joachimsthal in 1846 states that if two surfaces intersect with constant angle along a line of curvature of one surface, then the curve of intersection is also a line of curvature of the other surface. In this note we ... More

Signatures, Heegaard Floer correction terms and quasi-alternating linksFeb 13 2013May 22 2013Turaev showed that there is a well-defined map assigning to an oriented link L in the three-sphere a Spin structure t_0 on Sigma(L), the 2-fold cover of S^3 branched along L. We prove, generalizing results of Manolescu-Owens and Donald-Owens, that for ... More

Solutions to multi-marginal optimal transport problems concentrated on several graphsJul 21 2015We study solutions to the multi-marginal Monge-Kantorovich problem which are concentrated on several graphs over the first marginal. We first present two general conditions on the cost function which ensure, respectively, that any solution must concentrate ... More

Recursive Sparse Pseudo-input Gaussian Process SARSANov 17 2018The class of Gaussian Process (GP) methods for Temporal Difference learning has shown promise for data-efficient model-free Reinforcement Learning. In this paper, we consider a recent variant of the GP-SARSA algorithm, called Sparse Pseudo-input Gaussian ... More

A Converging Lagrangian Curvature Flow in the Space of Oriented LinesOct 16 2013Jun 18 2015Under mean radius of curvature flow, a closed convex surface in Euclidean space is known to expand exponentially to infinity. In the 3-dimensional case we prove that the oriented normals to the flowing surface converge to the oriented normals of a round ... More

Strong field effects on binary systems in Einstein-aether theoryJun 05 2007Sep 23 2008"Einstein-aether" theory is a generally covariant theory of gravity containing a dynamical preferred frame. This article continues an examination of effects on the motion of binary pulsar systems in this theory, by incorporating effects due to strong ... More

Varieties of planes on intersections of three quadricsApr 12 2019We study the geometry of spaces of planes on smooth complete intersections of three quadrics, with a view toward rationality questions.

Quartic del Pezzo surfaces over function fields of curvesJan 30 2013We classify quartic del Pezzo surface fibrations over the projective line via numerical invariants, giving explicit examples for small values of the invariants. For generic such fibrations, we describe explicitly the geometry of spaces of sections to ... More

Potential density of rational points for K3 surfaces over function fieldsApr 10 2006We give examples of non-isotrivial K3 surfaces over complex function fields with Zariski-dense rational points and N'eron-Severi rank one.