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Results for "Steven Gallinger"

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Improving Prognostic Performance in Resectable Pancreatic Ductal Adenocarcinoma using Radiomics and Deep Learning Features Fusion in CT ImagesJul 10 2019As an analytic pipeline for quantitative imaging feature extraction and analysis, radiomics has grown rapidly in the past a few years. Recent studies in radiomics aim to investigate the relationship between tumors imaging features and clinical outcomes. ... More
Improving Prognostic Value of CT Deep Radiomic Features in Pancreatic Ductal Adenocarcinoma Using Transfer LearningMay 23 2019Pancreatic ductal adenocarcinoma (PDAC) is one of the most aggressive cancers with an extremely poor prognosis. Radiomics has shown prognostic ability in multiple types of cancer including PDAC. However, the prognostic value of traditional radiomics pipelines, ... More
CNN-based Survival Model for Pancreatic Ductal Adenocarcinoma in Medical ImagingJun 25 2019Cox proportional hazard model (CPH) is commonly used in clinical research for survival analysis. In quantitative medical imaging (radiomics) studies, CPH plays an important role in feature reduction and modeling. However, the underlying linear assumption ... More
Reliability of swarming algorithms for mobile sensor network applicationsSep 24 2012There are many well-studied swarming algorithms which are often suited to very specific purposes. As mobile sensor networks become increasingly complex, and are comprised of more and more agents, it makes sense to consider swarming algorithms for movement ... More
Supermatrix Representations of Semigroup BandsSep 19 1996Various semigroups of noninvertible supermatrices of the special (antitriangle) shape having nilpotent Berezinian which appear in supersymmetric theories are defined and investigated. A subset of them continuously represents left and right zero semigroups ... More
Six-dimensional Methods for Four-dimensional Conformal Field Theories II: Irreducible FieldsSep 20 2012Sep 29 2012This note supplements an earlier paper on conformal field theories. There it was shown how to construct tensor, spinor, and spinor-tensor primary fields in four dimensions from their counterparts in six dimensions, where conformal transformations act ... More
Effective Field Theories in the Large $N$ LimitJun 06 1997Various effective field theories in four dimensions are shown to have exact non-trivial solutions in the limit as the number $N$ of fields of some type becomes large. These include extended versions of the U(N) Gross-Neveu model, the non-linear O(N) $\sigma$-model, ... More
Theories of the Cosmological ConstantOct 07 1996This is a talk given at the conference ``Critical Dialogues in Cosmology'' at Princeton University, June 24-- 27, 1996. It gives a brief summary of our present theoretical understanding regarding the value of the cosmological constant, and describes how ... More
Effective Action and Renormalization Group Flow of Anisotropic SuperconductorsJun 27 1993We calculate the effective action of a superconductor, without assuming that either the electron-electron potential or the Fermi surface obey rotational invariance. This approach leads to the same gap equation and equilibrium free energy as more conventional ... More
Pions in Large-$N$ Quantum ChromodynamicsSep 08 2010Dec 14 2010An effective field theory of quarks, gluons, and pions, with the number $N$ of colors treated as large, is proposed as a basis for calculations of hadronic phenomena at moderate energies. The qualitative consequences of the large $N$ limit are similar ... More
Living with InfinitiesMar 03 2009Apr 21 2009This is the written version of a talk given in memory of Gunnar K\"{a}ll\'{e}n, at the Departments of Theoretical Physics, Physics, and Astronomy of Lund University on February 13, 2009. It will be published in a collection of the papers of Gunnar K\"{a}ll\'{e}n, ... More
Quantum Contributions to Cosmological Correlations II: Can These Corrections Become Large?May 24 2006Jun 22 2006This is a sequel to a previous detailed study of quantum corrections to cosmological correlations. It was found there that except in special cases these corrections depend on the whole history of inflation, not just on the behavior of fields at horizon ... More
Cosmological Fluctuations of Short WavelengthJul 18 2002This paper presents a completely analytic treatment of cosmological fluctuations whose wavelength is small enough to come within the horizon well before the energy densities of matter and radiation become equal. This analysis yields a simple formula for ... More
Making High T$_c$ Higher: A Theoretical ProposalSep 09 2001There is considerable evidence that the highest $T_c$ obtainable in a copper-oxide plane is limitted by the competition between two effects: On the one hand, as the concentration of doped-holes, $ x$, is increased, the pairing scale, which is related ... More
Using the D1D5 CFT to Understand Black HolesDec 01 2010In this dissertation, we review work presented in arXiv:0906.2015, arXiv:0907.1663, arXiv:1002.3132, arXiv:1003.2746, and arXiv:1007.2202 on the D1D5 system. We begin with some motivational material for black holes in string theory. In Chapter 2, we review ... More
Elementary development of the gravitational self-forceAug 31 2009The gravitational field of a particle of small mass $\mu$ moving through curved spacetime, with metric $g_{ab}$, is naturally and easily decomposed into two parts each of which satisfies the perturbed Einstein equations through $O(\mu)$. One part is an ... More
ProofPeer - A Cloud-based Interactive Theorem Proving SystemJan 02 2012ProofPeer strives to be a system for cloud-based interactive theorem proving. After illustrating why such a system is needed, the paper presents some of the design challenges that ProofPeer needs to meet to succeed. Contexts are presented as a solution ... More
Idempotents and Nilpotents Modulo nMay 01 2006We study asymptotic properties of periods and transient phases associated with modular power sequences. The latter are simple; the former are vaguely related to the reciprocal sum of square-free integer kernels.
Lectures in (2+1)-Dimensional GravityMar 14 1995Mar 18 1995These lectures briefly review our current understanding of classical and quantum gravity in three spacetime dimensions, concentrating on the quantum mechanics of closed universes and the (2+1)-dimensional black hole. Three formulations of the classical ... More
PhonologyApr 11 2002Phonology is the systematic study of the sounds used in language, their internal structure, and their composition into syllables, words and phrases. Computational phonology is the application of formal and computational techniques to the representation ... More
A Mass Partition Problem Related to Equivariant Sections of Stiefel BundlesNov 08 2010Jun 19 2012We consider a geometric combinatorial problem naturally associated to the geometric topology of certain spherical space forms. Given a collection of m mass distributions on R^n, the existence of k linearly independent regular q-fans, each of which equipartitions ... More
Gauge theory of gravity and matterAug 08 2014It is shown how to write the first order action for gravity in a gauge theoretic formalism where the spin connection and frame field degrees of freedom are assimilated together into a gauge connection. It is then shown how to couple the theory to spin-0, ... More
Necessary and Sufficient Condition on the Lindblad Equation to Prevent Entropy IncreaseNov 18 2015Nov 23 2015It is shown that in order for the solutions of the Lindblad equation never to give a decreasing von Neumann entropy, it is necessary and sufficient that the operators appearing in this equation should be unitary linear combinations of their adjoints. ... More
Philosophical Solution to P=?NP: P is Equal to NPMar 19 2016The P=?NP problem is philosophically solved by showing P is equal to NP in the random access with unit multiply (MRAM) model. It is shown that the MRAM model empirically best models computation hardness. The P=?NP problem is shown to be a scientific rather ... More
Measure Partitions via Fourier Analysis II: Center Transversality in the $L^2$-norm for Complex HyperplanesJun 22 2015Sep 13 2015Applications of harmonic analysis on finite groups were recently introduced to measure partition problems, with a variety of equipartition types by convex fundamental domains obtained as the vanishing of prescribed Fourier transforms. Considering the ... More
A Ham Sandwich Analogue for Quaternionic Measures and Finite Subgroups of S^3Sep 29 2010Sep 03 2011A "ham sandwich" theorem is established for n quaternionic Borel measures on quaternionic space H^n. For each finite subgroup G of S^3, it is shown that there is a quaternionic hyperplane H and a corresponding tiling of H^n into |G| fundamental regions ... More
From the Ham Sandwich to the Pizza Pie: A Simultaneous Z_m Equipartition of Complex MeasuresJun 23 2010Sep 03 2011A "ham sandwich" theorem is derived for n complex Borel measures on C^n. For each integer m>=2, it shown that there exists a regular m-fan centered about a complex hyperplane, satisfying the condition that for each complex measure, the "Z_m rotational ... More
A review of Dan's reduction method for multiple polylogarithmsMar 11 2017In this paper we will give an account of Dan's reduction method for reducing the weight $ n $ multiple logarithm $ I_{1,1,\ldots,1}(x_1, x_2, \ldots, x_n) $ to an explicit sum of lower depth multiple polylogarithms in $ \leq n - 2 $ variables. We provide ... More
Neutrino Mass Ordering Studies with PINGU and IceCube/DeepCoreApr 29 2016The Precision IceCube Next Generation Upgrade (PINGU) is a proposed extension to the IceCube detector. The design of PINGU would augment the existing 86 strings with an additional 40 with the main goal of determining the neutrino mass ordering (NMO). ... More
Particle propagators on discrete spacetimeJun 19 2008Oct 01 2008A quantum mechanical description of particle propagation on the discrete spacetime of a causal set is presented. The model involves a discrete path integral in which trajectories within the causal set are summed over to obtain a particle propagator. The ... More
Explicit examples of equivalence relations and factors with prescribed fundamental group and outer automorphism groupOct 18 2010Mar 13 2012In this paper we give a number of explicit constructions for II$_1$ factors and II$_1$ equivalence relations that have prescribed fundamental group and outer automorphism group. We construct factors and relations that have uncountable fundamental group ... More
On Arthur's Φ-FunctionMar 24 2005Write $\Theta^E$ for the stable character associated to a finite dimensional representation $E$ of a connected real reductive group $G$. Let $M$ be the centralizer of a maximal torus $T$, and denote by $\Phi_M(\gm,\Theta^E)$ Arthur's extension of $ |D_M^G(\gm)|^{\half} ... More
Quartic and Octic Characters Modulo nJul 28 2009Mar 25 2016The average number of primitive quadratic Dirichlet characters of modulus n tends to a constant as n->infty. The same is true for primitive cubic characters. It is therefore surprising that, as n->infty, the average number of primitive quartic characters ... More
Idempotents and Nilpotents Modulo nMay 01 2006Nov 18 2017We study asymptotic properties of periods and transient phases associated with modular power sequences. The latter are simple; the former are vaguely related to the reciprocal sum of square-free integer kernels.
Stably Newton non-degenerate singularitiesJun 02 2014Jan 28 2015We discuss a problem of Arnold, whether every function is stably equivalent to one which is non-degenerate for its Newton diagram. The answer is negative. The easiest example can be given in characteristic $p$: the function $x^p$ is not stably equivalent ... More
On the Descending Central Series of Higher Commutators for Simple AlgebrasDec 12 2018This paper characterizes the potential behaviors of higher commutators in a simple algebra.
No Quantum Brooks' TheoremNov 27 2014First, I introduce quantum graph theory. I also discuss a known lower bound on the independence numbers and derive from it an upper bound on the chromatic numbers of quantum graphs. Then, I construct a family of quantum graphs that can be described as ... More
Donaldson invariants of symplectic manifoldsJan 03 2013Jan 07 2013We prove that symplectic 4-manifolds with $b_1 = 0$ and $b^+ > 1$ have nonvanishing Donaldson invariants, and that the canonical class is always a basic class. We also characterize in many situations the basic classes of a Lefschetz fibration over the ... More
The contact homology of Legendrian knots with maximal Thurston-Bennequin invariantDec 22 2010We show that there exists a Legendrian knot with maximal Thurston-Bennequin invariant whose contact homology is trivial. We also provide another Legendrian knot which has the same knot type and classical invariants but nonvanishing contact homology.
Lower Bounds for Cubical PseudomanifoldsSep 30 2009Apr 02 2011It is verified that the number of vertices in a $d$-dimensional cubical pseudomanifold is at least $2^{d+1}$. Using Adin's cubical $h$-vector, the generalized lower bound conjecture is established for all cubical 4-spheres, as well as for some special ... More
The 21 Centimeter ForestApr 10 2006We examine the prospects for studying the pre-reionization intergalactic medium (IGM) through the so-called 21 cm forest in spectra of bright high-redshift radio sources. We first compute the evolution of the mean optical depth for models that include ... More
Non-embeddable 1-convex manifoldsSep 27 2012Nov 11 2013We show that every small resolution of a three-dimensional terminal hypersurface singularity can occur on a non-embeddable 1-convex manifold. We give an explicit example of a non-embeddable manifold containing an irreducible exceptional rational curve ... More
Degenerations of elliptic curves and cusp singularitiesDec 21 1995We give more or less explicit equations for all two-dimensional cusp singularities of embedding dimension at least 4. They are closely related to Felix Klein's equations for universal curves with level n structure. The main technical result is a description ... More
Initial Blow-up of Solutions of Semilinear Parabolic InequalitiesNov 19 2009We obtain an upper bound on the initial blow-up of nonnegative solutions of second order semilinear parabolic inequalities when a superlinear exponent in the inequalities is not too large.
Non-uniform covering array with symmetric forbidden edge constraintsJan 08 2019It has been conjectured that whenever an optimal covering array exists there is also a uniform covering array with the same parameters and this is true for all known optimal covering arrays. When used as a test suite, the application context may have ... More
Topological complexity of n points on a treeJul 27 2016Jan 24 2018The topological complexity of a path-connected space $X,$ denoted $TC(X),$ can be thought of as the minimum number of continuous rules needed to describe how to move from one point in $X$ to another. The space $X$ is often interpreted as a configuration ... More
Polyadic Hopf algebras and quantum groupsNov 07 2018Apr 04 2019This article continues the study of concrete algebra-like structures in our polyadic approach, where the arities of all operations are initially taken as arbitrary, but the relations between them, the arity shapes, are to be found from some natural conditions ... More
Polyadic integer numbers and finite (m,n)-fieldsJul 03 2017Jul 13 2017The polyadic integer numbers, which form a polyadic ring, are representatives of a fixed congruence class. The basics of polyadic arithmetic are presented: prime polyadic numbers, the polyadic Euler function, polyadic division with a remainder, etc. are ... More
Random Cyclic QuadrilateralsOct 03 2016The circumcircle of a planar convex polygon P is a circle C that passes through all vertices of P. If such a C exists, then P is said to be cyclic. Fix C to have unit radius. While any two angles of a uniform cyclic triangle are negatively correlated, ... More
Random Gaussian TetrahedraMay 06 2010Dec 17 2015Given independent normally distributed points A,B,C,D in Euclidean 3-space, let Q denote the plane determined by A,B,C and D^ denote the orthogonal projection of D onto Q. The probability that the tetrahedron ABCD is acute remains intractible. We make ... More
Flavour Democracy in Strong UnificationApr 29 1998We show that the fermion mass spectrum may naturally be understood in terms of flavour democratic fixed points in supersymmetric theories which have a large domain of attraction in the presence of "strong unification". Our approach provides an alternative ... More
Second N=1 Superanalog of Complex StructureOct 19 1995We found another N=1 odd superanalog of complex structure (the even one is widely used in the theory of super Riemann surfaces). New N=1 superconformal-like transformations are similar to anti-holomorphic ones of nonsupersymmetric complex function theory. ... More
Stochastic Attribute-Value GrammarsOct 23 1996Probabilistic analogues of regular and context-free grammars are well-known in computational linguistics, and currently the subject of intensive research. To date, however, no satisfactory probabilistic analogue of attribute-value grammars has been proposed: ... More
An Incidence Bound Over FieldsSep 20 2016We prove an upper bound on incidences between points and lines in the plane over a field $\mathbb{F}$. In particular, given $n$ points and $m$ lines in $\mathbb{F}^2$ (where $n\leq m$, and if $\text{char}(\mathbb{F})=p>0$, then $n\leq p^{4/3}$), we prove ... More
Tetraquark Mesons in Large $N$ Quantum ChromodynamicsMar 02 2013It is argued that exotic mesons consisting of two quarks and two antiquarks are not ruled out in quantum chromodynamics with a large number $N$ of colors, as generally thought. They can come in two varieties: short-lived tetraquarks with decay rates proportional ... More
Asymptotically Safe InflationNov 16 2009Mar 30 2010Inflation is studied in the context of asymptotically safe theories of gravitation. Conditions are explored under which it is possible to have a long period of nearly exponential expansion that eventually comes to an end.
Non-Gaussian Correlations Outside the Horizon II: The General CaseOct 16 2008The results of a recent paper [0808.2909] are generalized. A more detailed proof is presented that under essentially all conditions, the non-linear classical equations governing matter and gravitation in cosmology have ``adiabatic'' solutions in which, ... More
A Tree Theorem for InflationMay 24 2008Aug 13 2008It is shown that the generating function for tree graphs in the "in-in" formalism may be calculated by solving the classical equations of motion subject to certain constraints. This theorem is illustrated by application to the evolution of a single inflaton ... More
Living in the MultiverseNov 03 2005This is the written version of the opening talk at the symposium "Expectations of a Final Theory," at Trinity College, Cambridge, on September 2, 2005. It is to be published in Universe or Multiverse?, ed. B. Carr (Cambridge University Press).
What is Quantum Field Theory, and What Did We Think It Is?Feb 04 1997This is a talk presented at the conference ``Historical and Philosophical Reflections on the Foundations of Quantum Field Theory,'' at Boston University, March 1996. It will be published in the proceedings of this conference.
Effective Field Theory, Past and FutureAug 13 2009Sep 26 2009This is a written version of the opening talk at the 6th International Workshop on Chiral Dynamics, at the University of Bern, Switzerland, July 6, 2009, to be published in the proceedings of the Workshop. In it, I reminisce about the early development ... More
Can Non-Adiabatic Perturbations Arise After Single-Field Inflation?Jan 15 2004May 18 2004It is shown that non-adiabatic cosmological perturbations cannot arise during the period of reheating following inflation with a single scalar inflaton field.
Fluctuations in the Cosmic Microwave Background II: $C_\ell$ at Large and Small $\ell$Mar 19 2001Aug 16 2001General asymptotic formulas are given for the coefficient $C_\ell$ of the term of multipole number $\ell$ in the temperature correlation function of the cosmic microwave background, in terms of scalar and dipole form factors introduced in a companion ... More
Imitating quantum mechanics: qubit-based model for simulationJun 29 2009We present an approach to simulating quantum computation based on a classical model that directly imitates discrete quantum systems. Qubits are represented as harmonic functions in a 2D vector space. Multiplication of qubit representations of different ... More
Radiation reaction and the self-force for a point mass in general relativityNov 11 2000A point particle of mass m moving on a geodesic creates a perturbation h, of the spacetime metric g, that diverges at the particle. Simple expressions are given for the singular m/r part of h and its quadrupole distortion caused by the spacetime. Subtracting ... More
Perspective on gravitational self-force analysesJan 03 2005May 24 2005A point particle of mass $\mu$ moving on a geodesic creates a perturbation $h_{ab}$, of the spacetime metric $g_{ab}$, that diverges at the particle. Simple expressions are given for the singular $\mu/r$ part of $h_{ab}$ and its distortion caused by the ... More
Permutation Complexity Related to the Letter Doubling MapAug 18 2011Given a countable set X (usually taken to be the natural numbers or integers), an infinite permutation, \pi, of X is a linear ordering of X. This paper investigates the combinatorial complexity of infinite permutations on the natural numbers associated ... More
Permutation Complexity of the Thue-Morse WordMar 31 2010Apr 05 2010Given a countable set X (usually taken to be the natural numbers or the integers), an infinite permutation \pi of X is a linear ordering of X. This paper investigates the combinatorial complexity of the infinite permutation on the natural numbers associated ... More
Spontaneous Dimensional Reduction in Short-Distance Quantum Gravity?Sep 17 2009Several lines of evidence suggest that quantum gravity at very short distances may behave effectively as a two-dimensional theory. I summarize these hints, and offer an additional argument based on the strong-coupling limit of the Wheeler-DeWitt equation. ... More
The Statistical Mechanics of the Three-Dimensional Euclidean Black HoleJun 17 1996Oct 08 1996In its formulation as a Chern-Simons theory, three-dimensional general relativity induces a Wess-Zumino-Witten action on spatial boundaries. Treating the horizon of the three-dimensional Euclidean black hole as a boundary, I count the states of the resulting ... More
Computational PhonologyApr 10 2002Phonology, as it is practiced, is deeply computational. Phonological analysis is data-intensive and the resulting models are nothing other than specialized data structures and algorithms. In the past, phonological computation - managing data and developing ... More
l --> l' gamma in the Lepton Number Violating MSSMOct 30 2006A minimal particle content supersymmetric model with a discrete Z_3 symmetry, allowing lepton number violating terms, is studied. Within this model, the neutrino masses and mixing can be generated by lepton number violating couplings. Choosing parameters ... More
On the classification of rational surface singularitiesApr 01 2012A general strategy is given for the classification of graphs of rational surface singularities. For each maximal rational double point configuration we investigate the possible multiplicities in the fundamental cycle. We classify completely certain types ... More
Partial Hamiltonian formalism, multi-time dynamics and singular theoriesJul 22 2013We formulate singular classical theories without involving constraints. Applying the action principle for the action (27) we develop a partial (in the sense that not all velocities are transformed to momenta) Hamiltonian formalism in the initially reduced ... More
The localic compact interval is an Escardó-Simpson interval objectJun 26 2015The locale corresponding to the real interval [-1,1] is an interval object, in the sense of Escard\'o and Simpson, in the category of locales. The map c from 2^\omega to [-1,1], mapping a stream s of signs +1 or -1 to \Sum_{i=1}^\infty s_i 2^{-i}, is ... More
Hamiltonian analysis of self-dual gauge gravityApr 15 2015The Hamiltonian analysis of the self-dual gauge gravity theory is carried out. The resulting canonical structure is equivalent to that of self-dual gravity.
A semiclassical reversibility paradox in simple chaotic systemsSep 27 2015Using semiclassical methods, it is possible to construct very accurate approximations in the short wavelength limit of quantum dynamics that rely exclusively on classical dynamical input. For systems whose classical realization is strongly chaotic, there ... More
Algebroids and Twistor SpacesDec 14 2015We introduce a plethora of skew algebroids on twistor spaces and describe the corresponding foliations. In a forthcoming paper, we use these algebroids to derive results about bihermitian manifolds, also known as generalized Kahler manifolds.
Polyadic Hopf algebras and quantum groupsNov 07 2018This article continues the study of concrete algebra-like structures in our polyadic approach, when the arities of all operations are initially taken as arbitrary, but the relations between them, the arity shapes, are to be found from some natural conditions. ... More
Selling train tickets by SMSJul 06 2011Selling train tickets has evolved in the last ten years from queuing in the railway station, to buying tickets on the internet and printing them. Both alternatives are still viable options, though they are time consuming or need printing devices. Nowadays ... More
A Popperian Falsification of Artificial Intelligence - Lighthill DefendedApr 23 2017Apr 18 2018The area of computation called artificial intelligence (AI) is falsified by describing a previous 1972 falsification of AI by British applied mathematician James Lighthill. It is explained how Lighthill's arguments continue to apply to current AI. It ... More
Chern-Weil theory for certain infinite-dimensional Lie groupsJun 18 2013Chern-Weil and Chern-Simons theory extend to certain infinite-rank bundles that appear in mathematical physics. We discuss what is known of the invariant theory of the corresponding infinite-dimensional Lie groups. We use these techniques to detect cohomology ... More
A Dynamical Mechanism for Large Volumes with Consistent CouplingsSep 05 2016A mechanism for addressing the 'decompactification problem' is proposed, which consists of balancing the vacuum energy in Scherk-Schwarzed theories against contributions coming from non- perturbative physics. Universality of threshold corrections ensures ... More
A "q-deformed" generalization of the Hosszu-Gluskin theoremSep 04 2013Sep 08 2014In this paper a new form of the Hossz\'u-Gluskin theorem is presented in terms of polyadic powers and using the language of diagrams. It is shown that the Hossz\'u-Gluskin chain formula is not unique and can be generalized ("deformed") using a parameter ... More
Cosets, Voltages, and Derived EmbeddingsNov 17 2014Nov 09 2016An ordinary voltage graph embedding of a graph in a surface encodes a certain kind of highly symmetric covering space of that surface. Given an ordinary voltage graph embedding of a graph $G$ in a surface with voltage group $A$ and a connected subgraph ... More
Applications Of Ordinary Voltage Graph Theory To Graph Embeddability, Part 1Jan 06 2015We study embeddings of a graph $G$ in a surface $S$ by considering representatives of different classes of $H_1(S)$ and their intersections. We construct a matrix invariant that can be used to detect homological invariance of elements of the cycle space ... More
Simple surface singularitiesMar 04 2013By the famous ADE classification rational double points are simple. Rational triple points are also simple. We conjecture that the simple normal surface singularities are exactly those rational singularities, whose resolution graph can be obtained from ... More
The versal deformation of cyclic quotient singularitiesJun 08 2009We describe the versal deformation of two-dimensional cyclic quotient singularities in terms of equations, following Arndt, Brohme and Hamm. For the reduced components the equations are determined by certain systems of dots in a triangle. The equations ... More
Classifying foliationsApr 08 2008Oct 28 2008We give a survey of the approaches to classifying foliations, starting with the Haefliger classifying spaces and the various results and examples about the secondary classes of foliations. Various dynamical properties of foliations are introduced and ... More
Ptolemy Constants as Described by EccentricityAug 12 2016Let J denote a simple closed curve in the plane. Let points a, b, c, d \in J occur in this order when traversing J in a counterclockwise direction. Define p(a,b,c,d) to be the ratio of ab*cd+ad*bc to ac*bd, where zw denotes distance between z and w. Define ... More
On the depth overhead incurred when running quantum algorithms on near-term quantum computers with limited qubit connectivityMay 31 2018Sep 25 2018This paper addresses the problem of finding the depth overhead that will be incurred when running quantum algorithms on near-term quantum computers. Specifically, it is envisaged that near-term quantum computers will have low qubit connectivity: each ... More
Aspects of the topology and combinatorics of Higgs bundle moduli spacesSep 15 2018Dec 08 2018This survey provides an introduction to basic questions and techniques surrounding the topology of the moduli space of stable Higgs bundles on a Riemann surface. Through examples, we demonstrate how the structure of the cohomology ring of the moduli space ... More
Kulikov singularitiesDec 11 2018In the study of normal surface singularities the relation between analytical and topological properties and invariants of the singularity is a very rich problem. This relation is particularly close for surface singularities constructed from families of ... More
Two Sample Covariances from a Trivariate Normal DistributionMay 07 2010Dec 17 2015The joint distribution of two off-diagonal Wishart matrix elements was useful in recent work on geometric probability [Finch 2010]. Not finding such formulas in the literature, we report these here.
Permutation Complexity and the Letter Doubling MapFeb 27 2011Given a countable set X (usually taken to be N or Z), an infinite permutation $\pi$ of X is a linear ordering $<_\pi$ of X. This paper investigates the combinatorial complexity of infinite permutations on N associated with the image of uniformly recurrent ... More
On Alternative Supermatrix ReductionJun 02 1995Jun 16 1995We consider a nonstandard odd reduction of supermatrices (as compared with the standard even one) which arises in connection with possible extension of manifold structure group reductions. The study was initiated by consideration of the generalized noninvertible ... More
Six-dimensional Methods for Four-dimensional Conformal Field TheoriesJun 17 2010Aug 02 2010The calculation of both spinor and tensor Green's functions in four-dimensional conformally invariant field theories can be greatly simplified by six-dimensional methods. For this purpose, four-dimensional fields are constructed as projections of fields ... More
A No-Truncation Approach to Cosmic Microwave Background AnisotropiesJul 05 2006Sep 12 2006We offer a method of calculating the source term in the line-of-sight integral for cosmic microwave background anisotropies without using a truncated partial-wave expansion in the Boltzmann hierarchy.
Damping of Tensor Modes in CosmologyJun 16 2003Oct 05 2003An analytic formula is given for the traceless transverse part of the anisotropic stress tensor due to free streaming neutrinos, and used to derive an integro-differential equation for the propagation of cosmological gravitational waves. The solution ... More
The Cosmological Constant Problems (Talk given at Dark Matter 2000, February, 2000)May 12 2000The old cosmological constant problem is to understand why the vacuum energy is so small; the new problem is to understand why it is comparable to the present mass density. Several approaches to these problems are reviewed. Quintessence does not help ... More