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Graph Convolutional Gaussian ProcessesMay 14 2019We propose a novel Bayesian nonparametric method to learn translation-invariant relationships on non-Euclidean domains. The resulting graph convolutional Gaussian processes can be applied to problems in machine learning for which the input observations ... More

Is Texture Predictive for Age and Sex in Brain MRI?Jul 25 2019Deep learning builds the foundation for many medical image analysis tasks where neuralnetworks are often designed to have a large receptive field to incorporate long spatialdependencies. Recent work has shown that large receptive fields are not always ... More

Distance Metric Learning using Graph Convolutional Networks: Application to Functional Brain NetworksMar 07 2017Jun 14 2017Evaluating similarity between graphs is of major importance in several computer vision and pattern recognition problems, where graph representations are often used to model objects or interactions between elements. The choice of a distance or similarity ... More

Implicit Weight Uncertainty in Neural NetworksNov 03 2017May 25 2018Modern neural networks tend to be overconfident on unseen, noisy or incorrectly labelled data and do not produce meaningful uncertainty measures. Bayesian deep learning aims to address this shortcoming with variational approximations (such as Bayes by ... More

DLTK: State of the Art Reference Implementations for Deep Learning on Medical ImagesNov 18 2017We present DLTK, a toolkit providing baseline implementations for efficient experimentation with deep learning methods on biomedical images. It builds on top of TensorFlow and its high modularity and easy-to-use examples allow for a low-threshold access ... More

Nonparametric Density Flows for MRI Intensity NormalisationJun 07 2018With the adoption of powerful machine learning methods in medical image analysis, it is becoming increasingly desirable to aggregate data that is acquired across multiple sites. However, the underlying assumption of many analysis techniques that corresponding ... More

Improving RetinaNet for CT Lesion Detection with Dense Masks from Weak RECIST LabelsJun 05 2019Accurate, automated lesion detection in Computed Tomography (CT) is an important yet challenging task due to the large variation of lesion types, sizes, locations and appearances. Recent work on CT lesion detection employs two-stage region proposal based ... More

Ensembles of Multiple Models and Architectures for Robust Brain Tumour SegmentationNov 04 2017Deep learning approaches such as convolutional neural nets have consistently outperformed previous methods on challenging tasks such as dense, semantic segmentation. However, the various proposed networks perform differently, with behaviour largely influenced ... More

Towards continual learning in medical imagingNov 06 2018This work investigates continual learning of two segmentation tasks in brain MRI with neural networks. To explore in this context the capabilities of current methods for countering catastrophic forgetting of the first task when a new one is learned, we ... More

Overfitting of neural nets under class imbalance: Analysis and improvements for segmentationJul 25 2019Overfitting in deep learning has been the focus of a number of recent works, yet its exact impact on the behavior of neural networks is not well understood. This study analyzes overfitting by examining how the distribution of logits alters in relation ... More

Efficient variational Bayesian neural network ensembles for outlier detectionMar 20 2017Apr 22 2017In this work we perform outlier detection using ensembles of neural networks obtained by variational approximation of the posterior in a Bayesian neural network setting. The variational parameters are obtained by sampling from the true posterior by gradient ... More

Graph Saliency Maps through Spectral Convolutional Networks: Application to Sex Classification with Brain ConnectivityJun 05 2018Graph convolutional networks (GCNs) allow to apply traditional convolution operations in non-Euclidean domains, where data are commonly modelled as irregular graphs. Medical imaging and, in particular, neuroscience studies often rely on such graph representations, ... More

WESD - Weighted Spectral Distance for Measuring Shape DissimilarityAug 24 2012This article presents a new distance for measuring shape dissimilarity between objects. Recent publications introduced the use of eigenvalues of the Laplace operator as compact shape descriptors. Here, we revisit the eigenvalues to define a proper distance, ... More

Deep Generative Models in the Real-World: An Open Challenge from Medical ImagingJun 14 2018Recent advances in deep learning led to novel generative modeling techniques that achieve unprecedented quality in generated samples and performance in learning complex distributions in imaging data. These new models in medical image computing have important ... More

Medical Imaging with Deep Learning: MIDL 2019 -- Extended Abstract TrackMay 21 2019Jul 22 2019This compendium gathers all the accepted extended abstracts from the Second International Conference on Medical Imaging with Deep Learning (MIDL 2019), held in London, UK, 8-10 July 2019. Note that only accepted extended abstracts are listed here, the ... More

Attention Gated Networks: Learning to Leverage Salient Regions in Medical ImagesAug 22 2018Jan 20 2019We propose a novel attention gate (AG) model for medical image analysis that automatically learns to focus on target structures of varying shapes and sizes. Models trained with AGs implicitly learn to suppress irrelevant regions in an input image while ... More

Needles in Haystacks: On Classifying Tiny Objects in Large ImagesAug 16 2019In some computer vision domains, such as medical or hyperspectral imaging, we care about the classification of tiny objects in large images. However, most Convolutional Neural Networks (CNNs) for image classification were developed and analyzed using ... More

Image-and-Spatial Transformer Networks for Structure-Guided Image RegistrationJul 22 2019Image registration with deep neural networks has become an active field of research and exciting avenue for a long standing problem in medical imaging. The goal is to learn a complex function that maps the appearance of input image pairs to parameters ... More

High-Resolution Mammogram Synthesis using Progressive Generative Adversarial NetworksJul 09 2018The ability to generate synthetic medical images is useful for data augmentation, domain transfer, and out-of-distribution detection. However, generating realistic, high-resolution medical images is challenging, particularly for Full Field Digital Mammograms ... More

PnP-AdaNet: Plug-and-Play Adversarial Domain Adaptation Network with a Benchmark at Cross-modality Cardiac SegmentationDec 19 2018Deep convolutional networks have demonstrated the state-of-the-art performance on various medical image computing tasks. Leveraging images from different modalities for the same analysis task holds clinical benefits. However, the generalization capability ... More

Disease Prediction using Graph Convolutional Networks: Application to Autism Spectrum Disorder and Alzheimer's DiseaseJun 05 2018Graphs are widely used as a natural framework that captures interactions between individual elements represented as nodes in a graph. In medical applications, specifically, nodes can represent individuals within a potentially large population (patients ... More

NeuroNet: Fast and Robust Reproduction of Multiple Brain Image Segmentation PipelinesJun 11 2018NeuroNet is a deep convolutional neural network mimicking multiple popular and state-of-the-art brain segmentation tools including FSL, SPM, and MALPEM. The network is trained on 5,000 T1-weighted brain MRI scans from the UK Biobank Imaging Study that ... More

Quantitative Error Prediction of Medical Image Registration using Regression ForestsMay 18 2019Predicting registration error can be useful for evaluation of registration procedures, which is important for the adoption of registration techniques in the clinic. In addition, quantitative error prediction can be helpful in improving the registration ... More

Morpho-MNIST: Quantitative Assessment and Diagnostics for Representation LearningSep 27 2018Feb 28 2019Revealing latent structure in data is an active field of research, having introduced exciting technologies such as variational autoencoders and adversarial networks, and is essential to push machine learning towards unsupervised knowledge discovery. However, ... More

Attention-Gated Networks for Improving Ultrasound Scan Plane DetectionApr 15 2018In this work, we apply an attention-gated network to real-time automated scan plane detection for fetal ultrasound screening. Scan plane detection in fetal ultrasound is a challenging problem due the poor image quality resulting in low interpretability ... More

Spectral Graph Convolutions for Population-based Disease PredictionMar 08 2017Jun 21 2017Exploiting the wealth of imaging and non-imaging information for disease prediction tasks requires models capable of representing, at the same time, individual features as well as data associations between subjects from potentially large populations. ... More

Controlling Meshes via Curvature: Spin Transformations for Pose-Invariant Shape ProcessingMar 06 2019We investigate discrete spin transformations, a geometric framework to manipulate surface meshes by controlling mean curvature. Applications include surface fairing -- flowing a mesh onto say, a reference sphere -- and mesh extrusion -- e.g., rebuilding ... More

Small Organ Segmentation in Whole-body MRI using a Two-stage FCN and Weighting SchemesJul 30 2018Accurate and robust segmentation of small organs in whole-body MRI is difficult due to anatomical variation and class imbalance. Recent deep network based approaches have demonstrated promising performance on abdominal multi-organ segmentations. However, ... More

FastReg: Fast Non-Rigid Registration via Accelerated Optimisation on the Manifold of DiffeomorphismsMar 05 2019Apr 23 2019We present an implementation of a new approach to diffeomorphic non-rigid registration of medical images. The method is based on optical flow and warps images via gradient flow with the standard $L^2$ inner product. To compute the transformation, we rely ... More

FastReg: Fast Non-Rigid Registration via Accelerated Optimisation on the Manifold of DiffeomorphismsMar 05 2019Apr 24 2019We present an implementation of a new approach to diffeomorphic non-rigid registration of medical images. The method is based on optical flow and warps images via gradient flow with the standard $L^2$ inner product. To compute the transformation, we rely ... More

FastReg: Fast Non-Rigid Registration via Accelerated Optimisation on the Manifold of DiffeomorphismsMar 05 2019We present a new approach to diffeomorphic non-rigid registration of medical images. The method is based on optical flow and warps images via gradient flow with the standard $L^2$ inner product. To compute the transformation, we rely on accelerated optimisation ... More

Semi-Supervised Learning via Compact Latent Space ClusteringJun 07 2018Jul 29 2018We present a novel cost function for semi-supervised learning of neural networks that encourages compact clustering of the latent space to facilitate separation. The key idea is to dynamically create a graph over embeddings of labeled and unlabeled samples ... More

Domain Adaptation for MRI Organ Segmentation using Reverse Classification AccuracyJun 01 2018The variations in multi-center data in medical imaging studies have brought the necessity of domain adaptation. Despite the advancement of machine learning in automatic segmentation, performance often degrades when algorithms are applied on new data acquired ... More

Reverse Classification Accuracy: Predicting Segmentation Performance in the Absence of Ground TruthFeb 11 2017When integrating computational tools such as automatic segmentation into clinical practice, it is of utmost importance to be able to assess the level of accuracy on new data, and in particular, to detect when an automatic method fails. However, this is ... More

Predicting Slice-to-Volume Transformation in Presence of Arbitrary Subject MotionFeb 28 2017Mar 04 2017This paper aims to solve a fundamental problem in intensity-based 2D/3D registration, which concerns the limited capture range and need for very good initialization of state-of-the-art image registration methods. We propose a regression approach that ... More

Efficient Multi-Scale 3D CNN with Fully Connected CRF for Accurate Brain Lesion SegmentationMar 18 2016Jan 08 2017We propose a dual pathway, 11-layers deep, three-dimensional Convolutional Neural Network for the challenging task of brain lesion segmentation. The devised architecture is the result of an in-depth analysis of the limitations of current networks proposed ... More

Efficient Multi-Scale 3D CNN with Fully Connected CRF for Accurate Brain Lesion SegmentationMar 18 2016Apr 01 2016We propose a dual pathway, 11-layers deep, three-dimensional Convolutional Neural Network for the challenging task of brain lesion segmentation. The devised architecture is the result of an in-depth analysis of the limitations of current networks proposed ... More

Anatomically Constrained Neural Networks (ACNN): Application to Cardiac Image Enhancement and SegmentationMay 22 2017Dec 05 2017Incorporation of prior knowledge about organ shape and location is key to improve performance of image analysis approaches. In particular, priors can be useful in cases where images are corrupted and contain artefacts due to limitations in image acquisition. ... More

Computing CNN Loss and Gradients for Pose Estimation with Riemannian GeometryMay 02 2018Jul 17 2018Pose estimation, i.e. predicting a 3D rigid transformation with respect to a fixed co-ordinate frame in, SE(3), is an omnipresent problem in medical image analysis with applications such as: image rigid registration, anatomical standard plane detection, ... More

Unsupervised domain adaptation in brain lesion segmentation with adversarial networksDec 28 2016Significant advances have been made towards building accurate automatic segmentation systems for a variety of biomedical applications using machine learning. However, the performance of these systems often degrades when they are applied on new data that ... More

3D Reconstruction in Canonical Co-ordinate Space from Arbitrarily Oriented 2D ImagesSep 19 2017Jan 23 2018Limited capture range, and the requirement to provide high quality initialization for optimization-based 2D/3D image registration methods, can significantly degrade the performance of 3D image reconstruction and motion compensation pipelines. Challenging ... More

Attention U-Net: Learning Where to Look for the PancreasApr 11 2018May 20 2018We propose a novel attention gate (AG) model for medical imaging that automatically learns to focus on target structures of varying shapes and sizes. Models trained with AGs implicitly learn to suppress irrelevant regions in an input image while highlighting ... More

A complex Frobenius theorem, multiplier ideal sheaves and Hermitian-Einstein metrics on stable bundlesJun 04 2003Aug 01 2003This paper describes how, in the case of algebraic surfaces, the well-known theorem of Donaldson-Uhlenbeck-Yau can be proved in a framework of generalized 'multiplier ideal sheaves', following the ideas of Siu. The key concept is that the destabilizing ... More

Lie algebra configuration pairingOct 22 2010Nov 04 2016We give a new description of the configuration pairing of Sinha-Walter by showing that it computes coefficients in the associative, preLie, or graph polynomial of a Lie bracket expression. We also connect the graph complexes of Sinha-Walter with preLie ... More

Polynomial Ergodic Averages Converge Rapidly: Variations on a Theorem of BourgainFeb 08 2014Let $L^2(X,\Sigma,\mu,\tau)$ be a measure-preserving system, with $\tau$ a $\mathbb{Z}$-action. In this note, we prove that the ergodic averages along integer-valued polynomials, $P(n)$, \[ M_N(f):= \frac{1}{N}\sum_{n \leq N} \tau^{P(n)} f \] converge ... More

Quantum Satake in type A: part IMar 21 2014We give an interpretation of sl_n webs as morphisms between certain singular Soergel bimodules. We explain how this is a combinatorial, algebraic version of the geometric Satake equivalence (in type A). We then q-deform the construction, giving an equivalence ... More

Doubly Quenched Convergence and the Entropy of Algebraic Actions of Sofic GroupsMar 21 2016Let G be a sofic group and X a compact group that G acts on by automorphisms. Using (and reformulating) the notion of doubly-quenched convergence developed by Austin, we show that in many cases the topological and the measure-theoretic entropy with respect ... More

Higher enveloping algebrasMay 04 2016We provide Lie algebras with enveloping algebras over the operad of little $n$-dimensional disks for any choice of $n$, and we give two complementary descriptions of these objects. The first description is an abstract characterization by a universal mapping ... More

Tools for extracting new physics in events with missing transverse momentumOct 20 2011Mar 26 2012We review tools that have been developed in recent years to maximize our ability to discover and characterize new physics appearing in LHC events with missing transverse momentum.

Transverse Observables and Mass Determination at Hadron CollidersSep 18 2007Feb 26 2008I consider the two-body decay of a particle at a hadron collider into a visible and an invisible particle, generalizing $W \to e \nu$, where the masses of the decaying particle and the invisible decay particle are, {\em a priori}, unknown. I prove that ... More

Koszul duality between Higgs and Coulomb categories $\mathcal{O}$Nov 20 2016We prove a Koszul duality theorem between the category of weight modules over the quantized Coulomb branch (as defined by Braverman, Finkelberg and Nakajima) attached to a group $G$ and representation $V$ and a category of $G$-equivariant D-modules on ... More

Cube number can detect chirality and Legendrian type of knotsJun 24 2010For a knot K the cube number is a knot invariant defined to be the smallest n for which there is a cube diagram of size n for K. We will show that the cube number detects chirality in all cases computed thus far, and distinguishes certain legendrian knots. ... More

Rouquier's conjecture and diagrammatic algebraJun 01 2013Mar 20 2017We prove a conjecture of Rouquier relating the decomposition numbers in category $\mathcal{O}$ for a cyclotomic rational Cherednik algebra to Uglov's canonical basis of a higher level Fock space. Independent proofs of this conjecture have also recently ... More

Tensor product algebras in type A are KoszulSep 13 2012Jun 09 2016In this note, we prove the Koszulity of the tensor product algebra defined in the author's previous work for sl(n) and a list of fundamental weights. This is achieved by constructing a graded Morita equivalence between the modules over this algebra and ... More

Unfurling Khovanov-Lauda-Rouquier algebrasMar 21 2016Dec 12 2018In this paper, we study the behavior of categorical actions of a Lie algebra $\mathfrak{g}$ under the deformation of their spectra. We give conditions under which the general point of a family of categorical actions of $\mathfrak{g}$ carry an action of ... More

Geometry and categorificationFeb 18 2016We describe a number of geometric contexts where categorification appears naturally: coherent sheaves, constructible sheaves and sheaves of modules over quantizations. In each case, we discuss how "index formulas" allow us to easily perform categorical ... More

Purity of critical cohomology and Kac's conjectureNov 27 2013Mar 10 2017We provide a new proof of the Kac positivity conjecture for an arbitrary quiver $Q$. The ingredients are the cohomological integrality theorem in Donaldson-Thomas theory, dimensional reduction, and an easy purity result. These facts imply the purity of ... More

An Arzelà-Ascoli theorem for the Hausdorff measure of noncompactnessMar 10 2013Mar 14 2013We generalize the Arzel\`a-Ascoli theorem in the space of continuous maps on a compact interval with values in Euclidean N-space by providing a quantitative link between the Hausdorff measure of noncompactness in this space and a natural measure of non-uniform ... More

Sarkozy's theorem in function fieldsMay 24 2016May 05 2017S\'ark\"ozy proved that dense sets of integers contain two elements differing by a $k$th power. The bounds in quantitative versions of this theorem are rather weak compared to what is expected. We prove a version of S\'ark\"ozy's theorem for polynomials ... More

Finite field models in additive combinatoricsSep 22 2004The study of many problems in additive combinatorics, such as Szemer\'edi's theorem on arithmetic progressions, is made easier by first studying models for the problem in F_p^n for some fixed small prime p. We give a number of examples of finite field ... More

1-bounded entropy and regularity problems in von Neumann algebrasMay 25 2015Jun 28 2017We investigate the singular subspace of an inclusion of tracial von Neumann algebras. The singular subspace is a canonical N-N subbimodule of L^{2}(M) and it contains the quasinormalizer introduced by Popa, one-sided quasinormalizer introduced by Fang-Gao-Smith, ... More

Local and doubly empirical convergence and the entropy of algebraic actions of sofic GroupsMar 21 2016Aug 29 2017Let G be a sofic group and X a compact group that G acts on by automorphisms. Using (and reformulating) the notion of doubly-quenched convergence developed by Austin, we show that in many cases the topological and the measure-theoretic entropy with respect ... More

Mixing and Spectral Gap Relative to Pinsker Factors for Sofic GroupsSep 25 2015Dec 12 2015Motivated by our previous results, we investigate structural properties of probability measure-preserving actions of sofic groups relative to their Pinsker factor. We also consider the same properties relative to the Outer Pinsker factor, which is another ... More

Fuglede-Kadison Determinants and Sofic EntropyFeb 05 2014Jul 10 2016We relate Fuglede-Kadison determinants to entropy of algebraic actions of sofic groups in essentially complete generality. This generalizes recent results of Hanfeng Li and Andreas Thom from the amenable case to the sofic case, as well as results of David ... More

Metric Mean Dimension for Algebraic Actions of Sofic GroupsOct 15 2013Sep 28 2015Recently Bingbing Liang and Hanfeng Li computed the mean dimension and metric mean dimension for algebraic actions of amenable groups. We show how to extend their computation of metric mean dimension to the case of sofic groups, provided that the dual ... More

An l^{p}-Version of von Neumann Dimension for Banach Space Representation of Sofic Groups IIFeb 10 2013Aug 04 2015In previous work, we defined extended versions of von Neumann dimension for Banach space representations of sofic groups. The main application was a definition of l^{p}-dimension and, using this, a proof that the actions of a countable discrete group ... More

Measurements of Vector Bosons Produced in Association with JetsJul 27 2008The latest D0 and CDF measurements of the important $W+{\rm jets}$ and $Z/\gamma^{*}+{\rm jets}$ processes are described, along with a discussion of the comparisons that have been made to LO and NLO perturbative QCD predictions.

Simulating clusters of galaxies: a brief history of `N' and overmergingSep 15 2000I review four decades of numerical simulations of galaxy clusters focussing on the attempts to resolve their internal structure. Overmerging describes the numerical or physical disruption of dark matter halos within dense environments. This problem was ... More

An Upper Limit to the Mass of Black Holes in the Halo of our GalaxyJun 10 1993If massive black holes constitute the dark matter in the halo surrounding the Milky Way, the existence of low mass globular clusters in the halo suggests an upper limit to their mass, $M_{_{BH}}$. We use a combination of the impulse approximation and ... More

A Non-Linear Roth Theorem for Fractals of Sufficiently Large DimensionApr 23 2019Suppose that $d \geq 2$, and that $A \subset [0,1]$ has sufficiently large dimension, $1 - \epsilon_d < \dim_H(A) < 1$. Then for any polynomial $P$ of degree $d$ with no constant term, there exists a point configuration $\{ x, x-t,x-P(t) \} \subset A$ ... More

Weak equivalence to Bernoulli shifts for some algebraic actionsSep 15 2017Dec 20 2017Namely, we prove that if $G$ is a countable, discrete group and $f\in M_{n}(\Z(G))$ is invertible on $\ell^{2}(G)^{\oplus n},$ but $f$ is not invertible in $M_{n}(\Z(G))$, then the measure-preserving action of $G$ on $X_{f}$ equipped with the Haar measure ... More

Young Massive Clusters as probes of stellar evolutionMar 05 2009Mar 06 2009Young Massive Clusters (YMCs) represent ideal testbeds in which to study massive stellar evolution as they contain large, coeval, chemically homogeneous, samples of massive stars. By studying YMCs with a range of ages (and hence turn-off masses), we can ... More

An Algebraic Proof of Quillen's Resolution Theorem for K_1Jun 23 2009Mar 16 2011In his 1973 paper Quillen proved a resolution theorem for the K-Theory of an exact category; his proof was homotopic in nature. By using the main result of a paper by Nenashev, we are able to give an algebraic proof of Quillen's Resolution Theorem for ... More

Maximum hitting for n sufficiently largeMar 19 2012Nov 29 2012For a left-compressed intersecting family \A contained in [n]^(r) and a set X contained in [n], let \A(X) = {A in \A : A intersect X is non-empty}. Borg asked: for which X is |\A(X)| maximised by taking \A to be all r-sets containing the element 1? We ... More

Convergence of the J-flow on Kahler surfacesMay 31 2003Oct 19 2004Donaldson defined a parabolic flow on Kahler manifolds which arises from considering the action of a group of symplectomorphisms on the space of smooth maps between manifolds. One can define a moment map for this action, and then consider the gradient ... More

Pinching estimates and motion of hypersurfaces by curvature functionsFeb 19 2004Second derivative pinching estimates are proved for a class of elliptic and parabolic equations, including motion of hypersurfaces by curvature functions such as quotients of elementary symmetric functions of curvature. The estimates imply convergence ... More

Fully nonlinear parabolic equations in two space variablesFeb 14 2004H\"older estimates for second derivatives are proved for solutions of fully nonlinear parabolic equations in two space variables. Related techniques extend the regularity theory for fully nonlinear parabolic equations in higher dimensions.

Constructing Banach ideals using upper $\ell_p$-estimatesJul 22 2014Using upper $\ell_p$-estimates for normalized weakly null sequence images, we describe a new family of operator ideals $\mathcal{WD}_{\ell_p}^{(\infty,\xi)}$ with parameters $1\leq p\leq\infty$ and $1\leq\xi\leq\omega_1$. These classes contain the completely ... More

Closed ideals of operators acting on some families of sequence spacesJun 01 2018Jan 10 2019We study the lattice of closed ideals in the algebra of continuous linear operators acting on $p$th Tandori and $p'$th Ces\`{a}ro sequence spaces, $1\leqslant p<\infty$, which we show are isomorphic to the classical sequence spaces $(\oplus_{n=1}^\infty\ell_\infty^n)_p$ ... More

Non-collapsing in mean-convex mean curvature flowAug 01 2011We provide a direct proof of a non-collapsing estimate for compact hypersurfaces with positive mean curvature moving under the mean curvature flow: Precisely, if every point on the initial hypersurface admits an interior sphere with radius inversely proportional ... More

Bounding the weight choosability number of a graphOct 25 2012Jan 26 2014Let $G = (V,E)$ be a graph, and for each $e \in E(G)$, let $L_e$ be a list of real numbers. Let $w:E(G) \to \cup_{e \in E(G)}L_e$ be an edge weighting function such that $w(e) \in L_e$ for each $e \in E(G)$, and let $c_w$ be the vertex colouring obtained ... More

Roth's theorem in the primesFeb 25 2003Sep 07 2004We show that any set containing a positive proportion of the primes contains a 3-term arithmetic progression. An important ingredient is a proof that the primes enjoy the so-called Hardy-Littlewood majorant property. We derive this by giving a new proof ... More

Light ladders and clasp conjecturesOct 23 2015Morphisms between tensor products of fundamental representations of the quantum group of sl(n) are described by the sl(n)-webs of Cautis-Kamnitzer-Morrison. Using these webs, we provide an explicit, root-theoretic formula for the local intersection forms ... More

The two-color Soergel calculusAug 29 2013Mar 05 2016We give a diagrammatic presentation for the category of Soergel bimodules for the dihedral group W . The (two-colored) Temperley-Lieb category is embedded inside this category as the degree 0 morphisms between color-alternating objects. The indecomposable ... More

Gaitsgory's central sheaves via the diagrammatic Hecke categoryNov 15 2018We initiate the study of Gaitsgory's central sheaves using complexes of Soergel bimodules, in extended affine type A. We conjecture that the complex associated to the standard representation can be flattened to a central complex in finite type A, which ... More

Garling sequence spacesDec 04 2016May 28 2018By generalizing a construction of Garling, for each $1\leqslant p<\infty$ and each normalized, nonincreasing sequence of positive numbers $w\in c_0\setminus\ell_1$ we exhibit an $\ell_p$-saturated, complementably homogeneous Banach space $g(w,p)$ related ... More

A Peer-based Model of Fat-tailed OutcomesApr 02 2013It is well known that the distribution of returns from various financial instruments are leptokurtic, meaning that the distributions have "fatter tails" than a Normal distribution, and have skew toward zero. This paper presents a graceful micro-level ... More

Cohomological Hall algebras and character varietiesApr 01 2015May 14 2016In this paper we investigate the relationship between twisted and untwisted character varieties via a specific instance of the Cohomological Hall algebra for moduli of objects in 3-Calabi-Yau categories introduced by Kontsevich and Soibelman. In terms ... More

Gorenstein stable surfaces with $K_X^2 = 2$ and $χ(\mathcal O_X) = 4$Apr 28 2019We define and study a concrete stratification of the moduli space of Gorenstein stable surfaces $X$ satisfying $K_{X}^2 = 2$ and $\chi(\mathcal{O}_{X}) = 4$, by first establishing an isomorphism with the moduli space of plane octics with certain singularities, ... More

The mixing time for simple exclusionMay 10 2004Jul 12 2006We obtain a tight bound of $O(L^2\log k)$ for the mixing time of the exclusion process in $\mathbf{Z}^d/L\mathbf{Z}^d$ with $k\leq{1/2}L^d$ particles. Previously the best bound, based on the log Sobolev constant determined by Yau, was not tight for small ... More

The mixing time of the Thorp shuffleJul 15 2005The Thorp shuffle is defined as follows. Cut the deck into two equal piles. Drop the first card from the left pile or the right pile according to the outcome of a fair coin flip; then drop from the other pile. Continue this way until both piles are empty. ... More

A simple hierarchical Bayesian model for simultaneous inference of tournament graphs and informant errorApr 29 2013Oct 11 2013The paper presents a hierarchical Bayesian model for simultaneous inference of tournament graphs and informant error. From multiple informant reports or measurement instrument outputs, the model estimates the structure of a criterion (i.e., true) tournament ... More

The Calabi-Yau equation on almost-Kahler four-manifoldsApr 18 2006Mar 26 2007Let (M, \omega) be a compact symplectic 4-manifold with a compatible almost complex structure J. The problem of finding a J-compatible symplectic form with prescribed volume form is an almost-K\"ahler analogue of Yau's theorem and is connected to a programme ... More

Interest Point Detection for Reconstruction in High Granularity Tracking DetectorsJun 15 2010This paper presents an investigation of the use of interest point detection algorithms from image processing applied to reconstruction of interactions in high granularity tracking detectors. Their purpose is to extract keypoints from the data as input ... More

The Kähler-Ricci flow on compact Kähler manifoldsFeb 24 2015These notes are based on a lecture series given at the Park City Math Institute in the summer of 2013. The notes are intended as a leisurely introduction to the K\"ahler-Ricci flow on compact K\"ahler manifolds, aimed at graduate students with some background ... More

Some Optimizations for (Maximal) Multipliers in $L^p$Feb 08 2014We use Oberlin, Nazarov, and Thiele's Multi-Frequency Calder\'{o}n-Zygmund decomposition to lower estimates on maximal multipliers in $L^p$. We also improve on classical multiplier results of Coifman, Rubio de Francia, and Semmes.

Essential dimension and the flats spanned by a point setFeb 25 2016Oct 12 2016Let $P$ be a finite set of points in $\mathbb{R}^d$ or $\mathbb{C}^d$. We answer a question of Purdy on the conditions under which the number of hyperplanes spanned by $P$ is at least the number of $(d-2)$-flats spanned by $P$. In answering this question, ... More

Coxeter groups as Beauville groupsAug 11 2015Apr 21 2016We generalize earlier work of Fuertes and Gonz\'{a}lez-Diez as well as earlier work of Bauer, Catanese and Grunewald to Coxeter groups in general by classifying which of these are strongly real Beauville groups. As a consequence of this we determine which ... More

Recent work on Beauville surfaces, structures and groupsMay 29 2014Beauville surfaces are a class of complex surfaces defined by letting a finite group $G$ act on a product of Riemann surfaces. These surfaces possess many attractive geometric properties several of which are dictated by properties of the group $G$. In ... More

Ultraviolet Light from Old Stellar PopulationsNov 29 1996We consider the general theoretical problem of ultraviolet light from old stellar populations (t > 2 Gyr), and the interpretation of galaxy spectra at short wavelengths (lamda < 3200A) The sources believed to be responsible for the observed `ultraviolet ... More