Results for "Dylan Rees"

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Observation of three-state nematicity in the triangular lattice antiferromagnet Fe$_{1/3}$ NbS$_2$Aug 01 2019Nematic order is the breaking of rotational symmetry in the presence of translational invariance. While originally defined in the context of liquid crystals, the concept of nematic order has arisen in crystalline matter with discrete rotational symmetry, ... More
Persistent Markov partitions and hyperbolic components of rational mapsAug 03 2016Markov partitions persisting in a neighbourhood of hyperbolic components of rational maps were constructed under the condition that closures of Fatou components are disjoint in \cite{R1}. Given such a partition, we characterize all nearby hyperbolic components ... More
Persistent Markov partitions for rational mapsJun 26 2013Sep 30 2016A construction is given of Markov partitions for some rational maps, which persist over regions of parameter space, not confined to single hyperbolic components. The set on which the Markov partition exists, and its boundary, are analysed.
Hairdressing in groups: a survey of combings and formal languagesOct 29 1998A group is combable if it can be represented by a language of words satisfying a fellow traveller property; an automatic group has a synchronous combing which is a regular language. This article surveys results for combable groups, in particular in the ... More
A Curvature Flow and Applications to an Isoperimetric InequalityOct 19 2016Long time existence and convergence to a circle is proved for radial graph solutions to a mean curvature type curve flow in warped product surfaces (under a weak assumption on the warp potential of the surface). This curvature flow preserves the area ... More
Quantum Cluster CharactersSep 29 2011Aug 13 2012Let $\FF$ be a finite field and $(Q,\bfd)$ an acyclic valued quiver with associated exchange matrix $\tilde{B}$. We follow Hubery's approach \cite{hub1} to prove our main conjecture of \cite{rupel}: the quantum cluster character gives a bijection from ... More
The Fully Quantized Axion and Dark EnergyDec 17 2012This letter reviews the exact evolution equation for the axion effective potential with the axion scale factor f and phenomenological consequences of the flat effective potential solution are discussed. It is shown that the corresponding vacuum energy ... More
Rank Two Non-Commutative Laurent Phenomenon and Pseudo-PositivityJul 10 2017Feb 24 2019We study polynomial generalizations of the Kontsevich automorphisms acting on the skew-field of formal rational expressions in two non-commuting variables. Our main result is the Laurentness and pseudo-positivity of iterations of these automorphisms. ... More
Power operations for $\text{H}\underline{\mathbb{F}}_2$ and a cellular construction of $\text{BP}\mathbf{R}$Nov 21 2016Jul 02 2017We study some power operations for ordinary $C_2$-equivariant homology with coefficients in the constant Mackey functor $\underline{\mathbb{F}}_2$. In addition to a few foundational results, we calculate the action of these power operations on a $C_2$-equivariant ... More
Proof of the Kontsevich Non-Commutative Cluster Positivity ConjectureJan 17 2012Feb 01 2012We extend the Lee-Schiffler Dyck path model to give a proof of the Kontsevich non-commutative cluster positivity conjecture with unequal parameters.
An algorithm for enumerating difference setsJul 05 2018The DifSets package for GAP implements an algorithm for enumerating all difference sets in a group up to equivalence and provides access to a library of results. The algorithm functions by finding difference sums, which are potential images of difference ... More
Why is the CMB fluctuation level 10^{-5}?Sep 08 1997Dec 12 1997We explore the qualitative changes that would occur if the amplitude Q ~ 10^{-5} of cosmological density fluctuations were different. If is less than about 10^{-6}, the cosmological objects that form would have so low virial temperatures that they may ... More
Holographic renormalization for irrelevant operators and multi-trace countertermsFeb 10 2011We investigate the structure of holographic renormalization in the presence of sources for irrelevant operators. By working perturbatively in the sources we avoid issues related to the non-renormalizability of the dual field theory. We find new classes ... More
Positivity in Quantum Cluster Algebras and Flags of Valued Quiver RepresentationsApr 04 2011Apr 05 2011In this paper we give a direct proof of the positivity conjecture for adapted quantum cluster variables. Moreover, our process allows one to explicitly compute formulas for all adapted cluster monomials and certain ordered products of adapted cluster ... More
Coefficients of Gaussian Polynomials Modulo $N$Dec 30 2017The $q$-analogue of the binomial coefficient, known as a $q$-binomial coefficient, is typically denoted $\left[{n \atop k}\right]_q$. These polynomials are important combinatorial objects, often appearing in generating functions related to permutations ... More
Mod 2 power operations revisitedApr 30 2019In this mostly expository note we take advantage of homotopical and algebraic advances to give a modern account of power operations on the mod 2 homology of $\mathbb{E}_{\infty}$-ring spectra. The main advance is a quick proof of the Adem relations utilizing ... More
Orientations and Topological Modular Forms with Level StructureJul 17 2015Using the methods of Ando-Hopkins-Rezk, we describe the characteristic series arising from E-infinity genera valued in topological modular forms with level structure. We give examples of such series for tmf_0(N) and show that the Ochanine genus comes ... More
Bach flow on homogeneous productsMar 21 2018Aug 15 2019Qualitative behavior of Bach flow is established on compact four-dimensional locally homogeneous product manifolds. This is achieved by lifting to the homogeneous universal cover and, in most cases, capitalizing on the resultant group structure. The resulting ... More
Non-perturbative Treatments of the Bosonic String and the Axion with Cosmological ImplicationsJun 28 2012This paper is about the use of a novel, exact functional quantization method as applied to two commonly studied actions in theoretical physics. The functional method in question has its roots in the exact renormalisation group flow techniques pioneered ... More
Greedy bases in rank 2 generalized cluster algebrasSep 10 2013In this note we extend the notion of greedy bases developed by Lee, Li, and Zelevinsky to rank two generalized cluster algebras, i.e. binomial exchange relations are replaced by polynomial exchange relations. In the process we give a combinatorial construction ... More
On categories of slicesNov 09 2017In this paper we give an algebraic description of the category of $n$-slices for an arbitrary group $G$, in the sense of Hill-Hopkins-Ravenel. Specifically, given a finite group $G$ and an integer $n$, we construct an explicit $G$-spectrum $W$ (called ... More
The Feigin TetrahedronJan 17 2014Mar 19 2015The first goal of this note is to extend the well-known Feigin homomorphisms taking quantum groups to quantum polynomial algebras. More precisely, we define generalized Feigin homomorphisms from a quantum shuffle algebra to quantum polynomial algebras ... More
On Quantum Analogue of The Caldero-Chapoton FormulaMar 12 2010Apr 24 2010Let $Q$ be any invertible valued quiver without oriented cycles. We study connections between the category of valued representations of $Q$ and expansions of cluster variables in terms of the initial cluster in quantum cluster algebras. We show that an ... More
Weighted Power Counting and Perturbative UnitarityDec 10 2010Feb 28 2011We consider the relationship between renormalizability and unitarity at a Lifshitz point in d dimensions. We test tree unitarity for theories containing only scalars and fermions, and for pure gauge theory. In both cases, we find the requirement of weighted ... More
Bach flow on homogeneous productsMar 21 2018Qualitative behavior of Bach flow is established on compact four-dimensional locally homogeneous product manifolds. This is achieved by lifting to the homogeneous universal cover and, in most cases, capitalizing on the resultant group structure. The resulting ... More
$C_2$-equivariant Homology Operations: Results and FormulasApr 30 2019In this note we state corrected and expanded versions of our previous results on power operations for $C_2$-equivariant Bredon homology with coefficients in the constant Mackey functor on $\mathbb{F}_2$. In particular, we give a version of the Adem relations. ... More
Omega from Velocities in VoidsAug 23 1993We propose a method for deriving a dynamical lower bound on $\Omega$ from diverging flows in low-density regions, based on the fact that large outflows are not expected in a low-$\Omega$ universe. The velocities are assumed to be induced by gravity from ... More
Biautomatic structures in systolic Artin groupsJul 06 2018We examine the construction of Huang and Osajda that was used in their proof of the biautomaticity of Artin groups of almost large type. We describe a slightly simpler variant of that biautomatic structure, with explicit descriptions of a few small examples, ... More
Rewriting systems in sufficiently large Artin-Tits groupsNov 09 2015Jul 16 2016A conjecture of Dehornoy claims that, given a presentation of an Artin-Tits group, every word that represents the identity can be transformed into the trivial word using the braid relations, together with certain rules (between pairs of words that are ... More
Using administrative data to improve the estimation of immigration to local areas in EnglandMar 03 2009Aug 24 2009International migration is now a significant driver of population change across Europe but the methods available to estimate its true impact upon sub-national areas remain inconsistent, constrained by inadequate systems of measurement and data capture. ... More
Large magneto-optical Kerr effect and imaging of magnetic octupole domains in an antiferromagnetic metalMay 17 2018When a polarized light beam is incident upon the surface of a magnetic material, the reflected light undergoes a polarization rotation. This magneto-optical Kerr effect (MOKE) has been intensively studied in a variety of ferro- and ferrimagnetic materials ... More
Quasars at z=6: the survival of the fittestJul 05 2006The Sloan Digital Sky survey detected luminous quasars at very high redshift, z>6. Follow-up observations indicated that at least some of these quasars are powered by supermassive black holes (SMBHs) with masses in excess of billion solar masses. SMBHs, ... More
Massive Black Holes as Population III RemnantsJan 13 2001Mar 09 2001Recent numerical simulations of the fragmentation of primordial molecular clouds in hierarchical cosmogonies have suggested that the very first stars (the so-called Population III) may have been rather massive. Here we point out that a numerous population ... More
Capture of stellar--mass compact objects by massive black holes in galactic cuspsAug 14 1996A significant fraction of the stellar population in the cusp around central black holes of galaxies consists of compact remnants of evolved stars, such as white dwarfs, neutron stars and stellar mass black holes. We estimate the rate of capture of compact ... More
Population III Gamma Ray BurstsApr 12 2010We discuss a model of Poynting-dominated gamma-ray bursts from the collapse of very massive first generation (pop. III) stars. From redshifts of order 20, the resulting relativistic jets would radiate in the hard X-ray range around 50 keV and above, followed ... More
The Edge of a Gamma Ray Burst AfterglowJun 12 1998Jul 16 1998We discuss the formation of spectral features in the decelerating ejecta of gamma-ray bursts, including the possible effect of inhomogeneities. These should lead to blueshifted and broadened absorption edges and resonant features, especially from H and ... More
The Earliest Luminous Sources and the Damping Wing of the Gunn-Peterson TroughJun 20 2000Aug 18 2000Recent observations of high-redshift galaxies and quasars indicate that the hydrogen component of the intergalactic medium (IGM) must have been reionized at some redshift z>6. Prior to complete reionization, sources of ultraviolet radiation will be seen ... More
Optical and Long Wavelength Afterglow from Gamma-Ray BurstsJun 06 1996We discuss the evolution of cosmological gamma-ray burst remnants, consisting of the cooling and expanding fireball ejecta together with any swept-up external matter, after the gamma-ray event. We show that significant optical emission is predicted which ... More
GRB 990123: Reverse and Internal Shock Flashes and Late AfterglowFeb 25 1999The prompt $(t \siml 0.16$ days) light curve and initial 9-th magnitude optical flash from GRB 990123 can be attributed to a reverse external shock, or possibly to internal shocks. We discuss the time decay laws and spectral slopes expected under various ... More
Classical and quantum chaos in a circular billiard with a straight cutJul 09 1998We study classical and quantum dynamics of a particle in a circular billiard with a straight cut. This system can be integrable, nonintegrable with soft chaos, or nonintegrable with hard chaos, as we vary the size of the cut. We use a quantum web to show ... More
Steep Slopes and Preferred Breaks in GRB Spectra: the Role of Photospheres and ComptonizationAug 11 1999Oct 27 1999The role of a photospheric component and of pair breakdown is examined in the internal shock model of gamma-ray bursts. We discuss some of the mechanisms by which they would produce anomalously steep low energy slopes, X-ray excesses and preferred energy ... More
Gamma-Ray Bursts: Multiwaveband Spectral Predictions for Blast Wave ModelsSep 09 1993In almost any scenario for 'cosmological' gamma-ray bursts (and in many models where they originate in our own Galaxy), the initial energy density is so large that the resulting relativistic plasma expands with $v\sim c$ producing a blast wave ahead of ... More
Iron K-alpha Emission from a Decaying Magnetar Model of Gamma-Ray BurstsOct 13 2000The recent report of X-ray Fe features in the afterglow of the gamma-ray burst GRB 991216 may provide important clues for identifying the nature of its progenitor and constraining the burst mechanism. We argue that the strong line emission can be attributed ... More
Multi-GeV Neutrinos from Internal Dissipation in GRB FireballsJul 07 2000Sub-photospheric internal shocks and transverse differences of the bulk Lorentz factor in relativistic fireball models of GRB lead to neutron diffusion relative to protons, resulting in inelastic nuclear collisions. This produces significant fluxes of ... More
Delayed Gev Emission from Cosmological Gamma-Ray Bursts : Impact of a Relativistic Wind on External MatterApr 22 1994Sudden collapse of a compact object, or coalescence of a compact binary, can generate an unsteady relativistic wind that lasts for a few seconds. The wind is likely to carry a high magnetic field; and its Lorentz factor depends on the extent to which ... More
Consistent Anisotropic Repulsions for Simple MoleculesDec 01 2000We extract atom-atom potentials from the effective spherical potentials that suc cessfully model Hugoniot experiments on molecular fluids, e.g., $O_2$ and $N_2$. In the case of $O_2$ the resulting potentials compare very well with the atom-atom potentials ... More
Gamma-Ray Burst Afterglow emission with a decaying magnetic fieldApr 24 2002Nov 06 2002In models for gamma ray burst afterglows, it is normally assumed that the external shock strongly amplifies the magnetic field and that this field maintains a steady value throughout the shocked region. We discuss the effects of modifying this (probably ... More
Tidal Interaction as the origin of early-type dwarf galaxies in group environmentOct 29 2014We present a sample of dwarf galaxies that suffer ongoing disruption by the tidal force of nearby massive galaxies. Analysing structural and stellar population properties using the archival imaging and spectroscopic data from the Sloan Digital Sky Survey ... More
Reprocessing of radiation by multi-phase gas in Low Luminosity Accretion FlowsJul 24 1998We discuss the role that magnetic fields in low luminosity accretion flows can play in creating and maintaining a multi-phase medium, and show that small magnetically-confined clouds or filaments of dense cold gas can dramatically reprocess the `primary' ... More
Gamma-Ray BurstsJan 13 2014Gamma-ray bursts are the most luminous explosions in the Universe. They appear connected to supernova remnants from massive stars or the merger of their remnants, and their brightness makes them temporarily detectable out to the larges distances yet explored ... More
Gamma-ray bursts as X-ray depth-gauges of the UniverseMay 07 2003May 31 2003We discuss the X-ray flux of gamma-ray burst afterglows at redshifts in the range 3-30, including the effects of the intergalactic He II absorption. We point out that strong X-ray lines may form locally in burst afterglows starting minutes after the trigger. ... More
Poynting Jets from Black Holes and Cosmological Gamma-Ray BurstsSep 07 1996Mar 20 1997We discuss the properties of magnetically dominated jet-like outflows from stellar mass black holes surrounded by debris tori resulting from neutron star disruption. These jets may have narrow cores (along the rotation axis) which are almost free of baryons ... More
GeV Emission from Collisional Magnetized Gamma Ray BurstsApr 26 2011Magnetic fields may play a dominant role in gamma-ray bursts, and recent observations by the Fermi satellite indicate that GeV radiation, when detected, arrives delayed by seconds from the onset of the MeV component. Motivated by this, we discuss a magnetically ... More
Collapsar Jets, Bubbles and Fe LinesApr 25 2001Jun 20 2001In the collapsar scenario, gamma ray bursts are caused by relativistic jets expelled along the rotation axis of a collapsing stellar core. We discuss how the structure and time-dependence of such jets depends on the stellar envelope and central engine ... More
Spectral Features from Ultrarelativistic Ions in Gamma-Ray Bursts?Apr 13 1998Jun 11 1998Gamma ray burst outflows may entrain small blobs or filaments of dense, highly ionized metal rich material. Such inhomogeneities, accelerated by the flow to Lorentz factors in the range 10-100, could have a significant coverage factor, and give rise to ... More
Unsteady Outflow Models for Cosmological Gamma-Ray BurstsApr 18 1994The 'event' that triggers a gamma ray burst cannot last for more than a few seconds. This is, however, long compared with the dynamical timescale of a compact stellar-mass object ($\sim 10^{-3}$ seconds). Energy is assumed to be released as an outflow ... More
Quasars and Galaxy FormationJan 04 1998The formation of massive black holes may precede the epoch that characterises the peak of galaxy formation, as characterized by the star formation history in luminous galaxies. Hence protogalactic star formation may be profoundly affected by quasar-like ... More
Accelerating Fast Fourier Transforms Using Hadoop and CUDAJul 25 2014There has been considerable research into improving Fast Fourier Transform (FFT) performance through parallelization and optimization for specialized hardware. However, even with those advancements, processing of very large files, over 1TB in size, still ... More
Generalising some results about right-angled Artin groups to graph products of groupsOct 12 2011Oct 25 2011We prove three results about the graph product $G=\G(\Gamma;G_v, v \in V(\Gamma))$ of groups $G_v$ over a graph $\Gamma$. The first result generalises a result of Servatius, Droms and Servatius, proved by them for right-angled Artin groups; we prove a ... More
Normality preserving operations for Cantor series expansions and associated fractals part IJul 03 2014Jul 08 2014It is well known that rational multiplication preserves normality in base $b$. We study related normality preserving operations for the $Q$-Cantor series expansions. In particular, we show that while integer multiplication preserves $Q$-distribution normality, ... More
Unexpected distribution phenomenon resulting from Cantor series expansionsMar 12 2014Mar 07 2015We explore in depth the number theoretic and statistical properties of certain sets of numbers arising from their Cantor series expansions. As a direct consequence of our main theorem we deduce numerous new results as well as strengthen known ones.
On the Existence of Finite Type Link Homotopy InvariantsOct 21 2000We show that for links with at most 5 components, the only finite type homotopy invariants are products of the linking numbers. In contrast, we show that for links with at least 9 components, there must exist finite type homotopy invariants which are ... More
The cluster symplectic double and moduli spaces of local systemsSep 04 2015We prove a conjecture of Fock and Goncharov which provides a birational equivalence of a cluster variety called the cluster symplectic double and a certain moduli space of local systems associated to a surface.
Quantum cluster characters of Hall algebrasAug 13 2013Nov 28 2014The aim of the present paper is to introduce a generalized quantum cluster character, which assigns to each object V of a finitary Abelian category C over a finite field FF_q and any sequence ii of simple objects in C the element X_{V,ii} of the corresponding ... More
Wheeling: A diagrammatic analogue of the Duflo isomorphismJun 11 2000We construct and prove a diagrammatic version of the Duflo isomorphism between the invariant subalgebra of the symmetric algebra of a Lie algebra and the center of the universal enveloping algebra. This version implies the original for metrized Lie algebras ... More
Some consequences of categorificationDec 22 2017Several conjectures on acyclic skew-symmetrizable cluster algebras are proven as direct consequences of their categorification via valued quivers. These include conjectures of Fomin-Zelevinsky, Reading-Speyer, and Reading-Stella related to d-vectors, ... More
Maximal Invariant Set Computation and Design for Markov ChainsMay 02 2019We describe an algorithm for computing the maximal invariant set for a Markov chain with linear safety constraints on the distribution over states. We then propose a Markov chain synthesis method that guarantees finite determination of the maximal invariant ... More
Room-temperature stability of excitons and transverse-electric polarized deep-ultraviolet luminescence in atomically thin GaN quantum wellsMay 28 2019Quantum confinement profoundly affects the properties and interactions of electrons, holes, and excitons in nanomaterials. We apply first-principles calculations to study the effects of extreme quantum confinement on the electronic, excitonic, and radiative ... More
Measurement error and precision medicine: error-prone tailoring covariates in dynamic treatment regimesJul 26 2019Precision medicine incorporates patient-level covariates to tailor treatment decisions, seeking to improve outcomes. In longitudinal studies with time-varying covariates and sequential treatment decisions, precision medicine can be formalized with dynamic ... More
Second Order Backward Stochastic Differential Equations with Quadratic GrowthJan 03 2012Apr 11 2014We extend the wellposedness results for second order backward stochastic differential equations introduced by Soner, Touzi and Zhang \cite{stz} to the case of a bounded terminal condition and a generator with quadratic growth in the $z$ variable. More ... More
E-voting in EstoniaJun 28 2016Estonia has one of the most established e-voting systems in the world. Internet voting - remote e-voting using the voter's own equipment - was piloted in 2005 with the first real elections using e-voting being conducted the same year and has been in use ... More
Companion cluster algebras to a generalized cluster algebraApr 25 2015We study the $c$-vectors, $g$-vectors, and $F$-polynomials for generalized cluster algebras satisfying a normalization condition and a power condition recovering classical recursions and separation of additions formulas. We establish a relationship between ... More
Introduction to Cluster AlgebrasMar 23 2018These are notes for a series of lectures presented at the ASIDE conference 2016. The definition of a cluster algebra is motivated through several examples, namely Markov triples, the Grassmannians $Gr_2(\mathbb{C})$, and the appearance of double Bruhat ... More
Cell Decompositions for Rank Two Quiver GrassmanniansMar 18 2018We prove that all quiver Grassmannians for exceptional representations of a generalized Kronecker quiver admit a cell decomposition. In the process, we introduce a class of regular representations which arise as quotients of consecutive preprojective ... More
A $C_2$-equivariant analog of Mahowald's Thom spectrum theoremJul 09 2017Feb 03 2018We prove that the $C_2$-equivariant Eilenberg-MacLane spectrum associated to the constant Mackey functor $\underline{\mathbb{F}}_2$ is equivalent to a Thom spectrum over ${\Omega^\rho S^{\rho + 1}}$.
A calibrated sensitivity analysis for matched observational studies with application to the effect of second-hand smoke exposure on blood lead levels in U.S. childrenDec 01 2018Matched observational studies are commonly used to study treatment effects in non-randomized data. After matching for observed confounders, there could remain bias from unobserved confounders. A standard way to address this problem is to do a sensitivity ... More
Grid Diagrams, Braids, and Contact GeometryDec 19 2008Feb 16 2009We use grid diagrams to present a unified picture of braids, Legendrian knots, and transverse knots.
On the Hausdorff dimension of some sets of numbers defined through the digits of their $Q$-Cantor series expansionsJul 03 2014Jul 15 2014Following in the footsteps of P. Erd\H{o}s and A. R\'enyi we compute the Hausdorff dimension of sets of numbers whose digits with respect to their $Q$-Cantor series expansions satisfy various statistical properties. In particular, we consider difference ... More
From rubber bands to rational maps: A research reportFeb 09 2015May 19 2016This research report outlines work, partially joint with Jeremy Kahn and Kevin Pilgrim, which gives parallel theories of elastic graphs and conformal surfaces with boundary. One one hand, this lets us tell when one rubber band network is looser than another, ... More
Cyclic vs mixed homologyJul 07 2016The spectral theory of the Karoubi operator due to Cuntz and Quillen is extended to general mixed (duchain) complexes, that is, chain complexes which are simultaneously cochain complexes. Connes' coboundary map B can be viewed as a perturbation of the ... More
Relativistic SpringsMay 13 2012May 15 2012Here we develop a model for the relativistic spring. We examine the effects of revising the simple harmonic oscillator to include relativistic momentum and a delayed force law. These corrections alter two of the most significant features of the simple ... More
Elastic GraphsJul 01 2016An elastic graph is a graph with an elasticity associated to each edge, which may be viewed as a network made out of ideal rubber bands. The rubber bands may be stretched on a target space, giving an elastic energy. We characterize when a homotopy class ... More
General indifference pricing with small transaction costsJan 14 2014Apr 04 2015We study the utility indifference price of a European option in the context of small transaction costs. Considering the general setup allowing consumption and a general utility function at final time T, we obtain an asymptotic expansion of the utility ... More
Comparing Covariate Prioritization via Matching to Machine Learning Methods for Causal Inference using Five Empirical ApplicationsMay 09 2018Jan 08 2019When investigators seek to estimate causal effects, they often assume that selection into treatment is based only on observed covariates. Under this identification strategy, analysts must adjust for observed confounders. While basic regression models ... More
Mediation Analysis Without Sequential Ignorability: Using Baseline Covariates Interacted with Random Assignment as Instrumental VariablesSep 06 2011Dec 31 2012In randomized trials, researchers are often interested in mediation analysis to understand how a treatment works, in particular how much of a treatment's effect is mediated by an intermediated variable and how much the treatment directly affects the outcome ... More
A positive basis for surface skein algebrasOct 07 2013Feb 16 2015We show that the twisted SL(2) skein algebra of a surface has a natural basis (the bracelets basis) that is positive, in the sense that the structure constants for multiplication are positive integers.
Control Function Instrumental Variable Estimation of Nonlinear Causal Effect ModelsFeb 02 2016The instrumental variable method consistently estimates the effect of a treatment when there is unmeasured confounding and a valid instrumental variable. A valid instrumental variable is a variable that is independent of unmeasured confounders and affects ... More
From Dominoes to HexagonsMay 25 2004Sep 12 2016There is a natural generalization of domino tilings to tilings of a polygon by hexagons, or, dually, configurations of oriented curves that meet in triples. We show exactly when two such tilings can be connected by a series of moves analogous to the domino ... More
Uniqueness for Some Higher-Order Geometric FlowsJul 16 2014We show that solutions to certain higher-order intrinsic geometric flows on a compact manifold, including some flows generated by the ambient obstruction tensor, are unique. With the goal of providing a complete self-contained proof, details surrounding ... More
GOGMA: Globally-Optimal Gaussian Mixture AlignmentMar 01 2016Gaussian mixture alignment is a family of approaches that are frequently used for robustly solving the point-set registration problem. However, since they use local optimisation, they are susceptible to local minima and can only guarantee local optimality. ... More
Local Smoothing Estimates near a Trapped Set with Infinitely Many Connected ComponentsDec 19 2014Feb 09 2018We prove a local smoothing result for the Schr\"odinger equation on a class of surfaces of revolution which have infinitely many trapped geodesics. Our main result is a local smoothing estimate with loss (compared to \cite{ChMe-lsm}) depending on the ... More
Contracting theory with competitive interacting agentsMay 25 2016In a framework close to the one developed by Holmstr\"om and Milgrom [44], we study the optimal contracting scheme between a Principal and several Agents. Each hired Agent is in charge of one project, and can make efforts towards managing his own project, ... More
Laminations from the symplectic doubleOct 11 2014Jun 24 2016Let $S$ be a compact oriented surface with boundary together with finitely many marked points on the boundary, and let $S^\circ$ be the same surface equipped with the opposite orientation. We consider the double $S_\mathcal{D}$ obtained by gluing the ... More
Normality of different orders for Cantor series expansionsJul 25 2016Let $S \subseteq \mathbb{N}$ have the property that for each $k \in S$ the set $(S - k) \cap \mathbb{N} \setminus S$ has asymptotic density $0$. We prove that there exists a basic sequence $Q$ where the set of numbers $Q$-normal of all orders in $S$ but ... More
A breakpoint detection error function for segmentation model selection and evaluationSep 01 2015We consider the multiple breakpoint detection problem, which is concerned with detecting the locations of several distinct changes in a one-dimensional noisy data series. We propose the breakpointError, a function that can be used to evaluate estimated ... More
Cluster algebras and triangulated surfaces. Part II: Lambda lengthsOct 20 2012For any cluster algebra whose underlying combinatorial data can be encoded by a bordered surface with marked points, we construct a geometric realization in terms of suitable decorated Teichmueller space of the surface. On the geometric side, this requires ... More
Short-time existence for some higher-order geometric flowsOct 20 2010We establish short-time existence and regularity for higher-order flows generated by a class of polynomial natural tensors that, after an adjustment by the Lie derivative of the metric with respect to a suitable vector field, have strongly parabolic linearizations. ... More
An Adaptive Data Representation for Robust Point-Set Registration and MergingNov 13 2015This paper presents a framework for rigid point-set registration and merging using a robust continuous data representation. Our point-set representation is constructed by training a one-class support vector machine with a Gaussian radial basis function ... More
Symplectic groupoids for cluster manifoldsJul 10 2018We construct symplectic groupoids integrating log-canonical Poisson structures on cluster varieties of type $\mathcal{A}$ and $\mathcal{X}$ over both the real and complex numbers. Extensions of these groupoids to the completions of the cluster varieties ... More
Normal equivalencies for eventually periodic basic sequencesAug 26 2014W. M. Schmidt, A. D. Pollington, and F. Schweiger have studied when normality with respect to one expansion is equivalent to normality with respect to another expansion. Following in their footsteps, we show that when $Q$ is an eventually periodic basic ... More