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On the Computation and Applications of Large Dense Partial Correlation NetworksMar 17 2019While sparse inverse covariance matrices are very popular for modeling network connectivity, the value of the dense solution is often overlooked. In fact the L2-regularized solution has deep connections to a number of important applications to spectral ... More

High-contrast imager for complex aperture telescopes (HiCAT): 5. first results with segmented-aperture coronagraph and wavefront controlMar 13 2019Segmented telescopes are a possibility to enable large-aperture space telescopes for the direct imaging and spectroscopy of habitable worlds. However, the complexity of their aperture geometry, due to the central obstruction, support structures and segment ... More

Science with an ngVLA: Radio Continuum Emission from Galaxies: An Accounting of Energetic ProcessesOct 15 2018Radio continuum observations have proven to be a workhorse in our understanding of the star formation process (i.e., stellar birth and death) from galaxies both in the nearby universe and out to the highest redshifts. In this article we focus on how the ... More

Redundant Array Configurations for 21 cm CosmologyFeb 19 2016Jul 06 2016Realizing the potential of 21 cm tomography to statistically probe the intergalactic medium before and during the Epoch of Reionization requires large telescopes and precise control of systematics. Next-generation telescopes are now being designed and ... More

A Fast Method for Power Spectrum and Foreground Analysis for 21 cm CosmologyNov 09 2012Feb 01 2013We develop and demonstrate an acceleration of the Liu & Tegmark quadratic estimator formalism for inverse variance foreground subtraction and power spectrum estimation in 21 cm tomography from O(N^3) to O(N log N), where N is the number of voxels of data. ... More

Structure of Cubic Lehman MatricesMay 19 2018A pair $(A,B)$ of square $(0,1)$-matrices is called a Lehman pair if $AB^T=J+kI$ for some integer $k\in\{-1,1,2,3,\ldots\}$, and the matrices $A$ and $B$ are called Lehman pair. This terminology arises because Lehman showed that the rows of minimum weight ... More

A Bayesian Approach to Constraint Based Causal InferenceOct 16 2012We target the problem of accuracy and robustness in causal inference from finite data sets. Some state-of-the-art algorithms produce clear output complete with solid theoretical guarantees but are susceptible to propagating erroneous decisions, while ... More

K-shell Core Electron Excitations in the Electronic Stopping of Protons in WaterMar 07 2019Developing a detailed understanding for the role of core electron excitation in liquid water under proton irradiation has become important due to the growing use of proton beams in radiation oncology. Using a first-principles, non-equilibrium simulation ... More

A Logical Characterization of Constraint-Based Causal DiscoveryFeb 14 2012We present a novel approach to constraint-based causal discovery, that takes the form of straightforward logical inference, applied to a list of simple, logical statements about causal relations that are derived directly from observed (in)dependencies. ... More

The Euler characteristic of a category as the sum of a divergent seriesJul 05 2007The Euler characteristic of a cell complex is often thought of as the alternating sum of the number of cells of each dimension. When the complex is infinite, the sum diverges. Nevertheless, it can sometimes be evaluated; in particular, this is possible ... More

Perfect numbers and groupsApr 01 2001A number is perfect if it is the sum of its proper divisors; here we call a finite group `perfect' if its order is the sum of the orders of its proper normal subgroups. (This conflicts with standard terminology but confusion should not arise.) The notion ... More

Up-to-Homotopy MonoidsDec 10 1999Feb 22 2000Informally, a homotopy monoid is a monoid-like structure in which properties such as associativity only hold `up to homotopy' in some consistent way. This short paper comprises a rigorous definition of homotopy monoid and a brief analysis of some examples. ... More

A general theory of self-similarityOct 21 2010Nov 09 2010A little-known and highly economical characterization of the real interval [0, 1], essentially due to Freyd, states that the interval is homeomorphic to two copies of itself glued end to end, and, in a precise sense, is universal as such. Other familiar ... More

Higher Operads, Higher CategoriesMay 02 2003Higher-dimensional category theory is the study of n-categories, operads, braided monoidal categories, and other such exotic structures. It draws its inspiration from areas as diverse as topology, quantum algebra, mathematical physics, logic, and theoretical ... More

Structures in higher-dimensional category theorySep 04 2001This paper, written in 1998, aims to clarify various higher categorical structures, mostly through the theory of generalized operads and multicategories. Chapters I and II, which cover this theory and its application to give a definition of weak n-category, ... More

The triangle-free processJun 26 2008Consider the following stochastic graph process. We begin with the empty graph on n vertices and add edges one at a time, where each edge is chosen uniformly at random from the collection of potential edges that do not form triangles when added to the ... More

TASI Lectures on Holographic Space-Time, SUSY and Gravitational Effective Field TheoryJul 22 2010Sep 23 2010I argue that the conventional field theoretic notion of vacuum state is not valid in quantum gravity. The arguments use gravitational effective field theory, as well as results from string theory, particularly the AdS/CFT correspondence. Different solutions ... More

M Theory and CosmologyNov 10 1999This is a series of lectures on M Theory for cosmologists. After summarizing some of the main properties of M Theory and its dualities I show how it can be used to address various fundamental and phenomenological issues in cosmology.

Quantum Hair on D-branes and Black Hole Information in String TheoryJun 05 1996Jun 07 1996We introduce a notion of quantum hair which completely characterizes the state of a D-brane in perturbative string theory. The hair manifests itself as a phase (more generally a unitary matrix in subspaces of degenerate string eigenstates) in the scattering ... More

Orders of elements and zeros and heights of characters in a finite groupApr 14 2006Let \chi be an irreducible character of the finite group G. If g is an element of G and \chi(g) is not zero, then we conjecture that the order of g divides |G|/\chi(1). The conjecture is a generalization of the classical fact that irreducible p-projective ... More

Numerical simulations of quasar absorbersJul 25 2005The physical state of the intergalactic medium can be probed in great detail with the intervening absorption systems seen in quasar spectra. The properties of the Hydrogen absorbers depend on many cosmological parameters, such as the matter-power spectrum, ... More

Numerical study of energy diffusion in King modelsNov 07 1995The energy diffusion coefficients D_n(E) (n=1,2) for a system of equal mass particles moving self-consistently in an N-body realisation of a King model are computed from the probability per unit time, P(E, Delta E), that a star with initial energy E will ... More

Majority Rule at Low Temperatures on the Square and Triangular LatticesMay 16 1996We consider the majority rule renormalization group transformation applied to nearest neighbor Ising models. For the square lattice with 2 by 2 blocks we prove that if the temperature is sufficiently low, then the transformation is not defined. We use ... More

Conformal Invariance and Stochastic Loewner Evolution Predictions for the 2D Self-Avoiding Walk - Monte Carlo TestsJul 25 2002Feb 05 2003Simulations of the self-avoiding walk (SAW) are performed in a half-plane and a cut-plane (the complex plane with the positive real axis removed) using the pivot algorithm. We test the conjecture of Lawler, Schramm and Werner that the scaling limit of ... More

Getting more flavour out of one-flavour QCDDec 02 2013We argue that no notion of flavour is necessary when performing amplitude calculations in perturbative QCD with massless quarks. We show this explicitly at tree-level, using a flavour recursion relation to obtain multi-flavoured QCD from one-flavour QCD. ... More

Cartesian closed 2-categories and permutation equivalence in higher-order rewritingJul 24 2013Sep 20 2013We propose a semantics for permutation equivalence in higher-order rewriting. This semantics takes place in cartesian closed 2-categories, and is proved sound and complete.

Natural coordinate descent algorithm for L1-penalised regression in generalised linear modelsMay 16 2014Aug 25 2015The problem of finding the maximum likelihood estimates for the regression coefficients in generalised linear models with an L1 sparsity penalty is shown to be equivalent to minimising the unpenalised maximum log-likelihood function over a box with boundary ... More

Full abstraction for fair testing in CCSMay 27 2013In previous work with Pous, we defined a semantics for CCS which may both be viewed as an innocent presheaf semantics and as a concurrent game semantics. It is here proved that a behavioural equivalence induced by this semantics on CCS processes is fully ... More

Full abstraction for fair testing in CCS (expanded version)Sep 29 2014Nov 02 2014In previous work with Pous, we defined a semantics for CCS which may both be viewed as an innocent form of presheaf semantics and as a concurrent form of game semantics. We define in this setting an analogue of fair testing equivalence, which we prove ... More

Proof of a new colour decomposition for QCD amplitudesSep 10 2015Nov 15 2015Recently, Johansson and Ochirov conjectured the form of a new colour decomposition for QCD tree-level amplitudes. This note provides a proof of that conjecture. The proof is based on "Mario World" Feynman diagrams, which exhibit the hierarchical Dyck ... More

On the Possibility of Large Axion Moduli SpacesSep 19 2014May 23 2015We study the diameters of axion moduli spaces, focusing primarily on type IIB compactifications on Calabi-Yau three-folds. In this case, we derive a stringent bound on the diameter in the large volume region of parameter space for Calabi-Yaus with simplicial ... More

Filtered ends of infinite covers and groupsDec 04 2005Nov 17 2006Let f:A-->B be a covering map. We say A has e filtered ends with respect to f (or B) if for some filtration {K_n} of B by compact subsets, A - f^{-1}(K_n) "eventually" has e components. The main theorem states that if Y is a (suitable) free H-space, if ... More

The Riemann-Hilbert approach to obtain critical asymptotics for Hamiltonian perturbations of hyperbolic and elliptic systemsNov 15 2011The present paper gives an overview of the recent developments in the description of critical behavior for Hamiltonian perturbations of hyperbolic and elliptic systems of partial differential equations. It was conjectured that this behavior can be described ... More

A stability result for the union-closed size problemNov 10 2013A family of sets is called union-closed if whenever $A$ and $B$ are sets of the family, so is $A\cup B$. The long-standing union-closed conjecture states that if a family of subsets of $[n]$ is union-closed, some element appears in at least half the sets ... More

H3+ and UKIRT: a saga of discoveryApr 24 2009This paper relates the history of attempts to detect H3+ in the dense interstellar medium, from the early 1980's to the successful detection in 1996.

Approximate (Abelian) groupsDec 03 2012ECM survey article discussing the structure of subsets of Abelian groups which behave `a bit like' cosets (of subgroups).

A quantitative version of the non-abelian idempotent theoremDec 02 2009Dec 10 2010Suppose that G is a finite group and A is a subset of G such that 1_A has algebra norm at most M. Then 1_A is a plus/minus sum of at most L cosets of subgroups of G, and L can be taken to be triply tower in O(M). This is a quantitative version of the ... More

Chowla's cosine problemJul 31 2008Oct 14 2010Suppose that G is a discrete abelian group and A is a finite symmetric subset of G. We show two main results. i) Either there is a set H of O(log^c|A|) subgroups of G with |A \triangle \bigcup H| = o(|A|), or there is a character X on G such that -wh{1_A}(X) ... More

Stability conditions and Kleinian singularitiesAug 15 2005Sep 23 2005We describe the spaces of stability conditions on certain triangulated categories associated to Dynkin diagrams. These categories can be defined either algebraically via module categories of preprojective algebras, or geometrically via coherent sheaves ... More

Kähler structures on spaces of framed curvesJan 11 2017We consider the space $\mathcal{M}$ of Euclidean similarity classes of framed loops in $\mathbb{R}^3$. Framed loop space is shown to be an infinite-dimensional K\"{a}hler manifold by identifying it with a complex Grassmannian. We show that the space of ... More

On families of 9-congruent elliptic curvesApr 29 2015We compute equations for the families of elliptic curves 9-congruent to a given elliptic curve. We use these to find infinitely many non-trivial pairs of 9-congruent elliptic curves over Q, i.e. pairs of non-isogenous elliptic curves over Q whose 9-torsion ... More

Supports of irreducible characters of p-groupsJul 22 2013If chi is an irreducible character of a finite group G then the support of chi is the subset of G on which chi does not vanish. In this note, we study the supports of characters of certain classes of p-groups (a p-group is a finite group of prime power ... More

The distribution of the number of parts of $m$-ary partitions modulo $m$Feb 29 2016We investigate the number of parts modulo $m$ of $m$-ary partitions of a positive integer $n$. We prove that the number of parts is equidistributed modulo $m$ on a special subset of $m$-ary partitions. As consequences, we explain when the number of parts ... More

Bell's Experiment in Quantum Mechanics and Classical PhysicsAug 21 2013Both the quantum mechanical and classical Bells experiment are within the focus of this paper. The fact that one measures different probabilities in both experiments is traced back to the superposition of two orthogonal but nonentangled substates in the ... More

Iwasawa invariants of Galois deformationsMay 26 2004We study the behavior of Iwasawa invariants among ordinary deformations of a fixed residual Galois representation taking values in a reductive algebraic group G. In particular, under the assumption that these Selmer groups are cotorsion modules over the ... More

A formula for the Jacobian of a genus one curve of arbitrary degreeOct 14 2015We extend the formulae of classical invariant theory for the Jacobian of a genus one curve of degree $n \le 4$ to curves of arbitrary degree. To do this, we associate to each genus one normal curve of degree $n$, an $n \times n$ alternating matrix of ... More

Topologizing Rings of Map Germs: An Order Theoretic Analysis of Germs via Nonstandard MethodsJun 03 2012Using nonstandard analysis we define a topology on the ring of germs of functions: $(mathbb R^n,0)\rightarrow(mathbb R,0)$. We prove that this topology is absolutely convex, Hausdorff, that convergent nets of continuous germs have continuous germs as ... More

Water alignment, dipolar interactions, and multiple proton occupancy during water-wire proton transportOct 29 2003A discrete multistate kinetic model for water-wire proton transport is constructed and analyzed using Monte-Carlo simulations. The model allows for each water molecule to be in one of three states: oxygen lone pairs pointing leftward, pointing rightward, ... More

Enhancement of charged macromolecule capture by nanopores in a salt gradientMay 08 2009Nanopores spanning synthetic membranes have been used as key components in proof-of-principle nanofluidic applications, particularly those involving manipulation of biomolecules or sequencing of DNA. The only practical way of manipulating charged macromolecules ... More

Kelvin-Helmholtz instabilities across periodic platesSep 14 2006We consider the linear stability of two inviscid fluids, in the presence of gravity, sheared past each other and separated by an flexible plate. Conditions for exponential growth of velocity perturbations are found as functions of the flexural rigidity ... More

Kinetics of nanopore transportJan 31 1998A nonlinear kinetic exclusion model is used to study osmosis and pressure driven flows through nearly single file pores such as antibiotic channels, aquaporins, zeolites and nanotubules. Two possible maxima in the steady state flux as a function of pore-solvent ... More

Growth-type invariants for $\mathbb{Z}^d$ subshifts of finite type and classes arithmetical of real numbersFeb 02 2009We discuss some numerical invariants of multidimensional shifts of finite type (SFTs) which are associated with the growth rates of the number of admissible finite configurations. Extending an unpublished example of Tsirelson, we show that growth complexities ... More

Givental's Lagrangian Cone and S^1-Equivariant Gromov-Witten TheoryJul 31 2006Oct 25 2007In the approach to Gromov-Witten theory developed by Givental, genus-zero Gromov-Witten invariants of a manifold X are encoded by a Lagrangian cone in a certain infinite-dimensional symplectic vector space. We give a construction of this cone, in the ... More

A shorter proof of Lemma A.6 (arXiv:1005.0768)Jun 21 2012For the convenience of readers of the article {\em No-arbitrage pricing under systemic risk: accounting for cross-ownership} (Fischer, 2012, arXiv:1005.0768), a full proof of Lemma A.5 and a shorter proof of Lemma A.6 of that paper are provided.

Constructing Q-Fano 3-folds à la Prokhorov & ReidOct 06 2016We generalise a construction by Prokhorov & Reid of two families of Q-Fano 3-folds of index 2 to obtain five more families of Q-Fano 3-folds; four of index 2 and one of index 3. Two of the families constructed have the same Hilbert series and we study ... More

The structure theory of set addition revisitedDec 03 2012In this article we survey some of the recent developments in the structure theory of set addition.

Green's sumset problem at density one halfMar 29 2010Dec 02 2010We investigate the size of subspaces in sumsets and show two main results. First, if A is a subset of F_2^n with density at least 1/2 - o(n^{-1/2}) then A+A contains a subspace of co-dimension 1. Secondly, if A is a subset of F_2^n with density at least ... More

Three-term arithmetic progressions and sumsetsNov 10 2006Apr 01 2010Suppose that G is an abelian group and A is a finite subset of G containing no three-term arithmetic progressions. We show that |A+A| >> |A|(log |A|)^{1/3-\epsilon} for all \epsilon>0.

Additive structures in sumsetsMay 18 2006Apr 01 2010Suppose that A is a subset of the integers {1,...,N} of density a. We provide a new proof of a result of Green which shows that A+A contains an arithmetic progression of length exp(ca(log N)^{1/2}) for some absolute c>0. Furthermore we improve the length ... More

A statistical approach to covering lemmasOct 22 2016We discuss a statistical variant of Ruzsa's covering lemma and use it to show that if G is an Abelian group of bounded exponent and A in G has |A+A| < K|A| then the subgroup generated by A has size at most exp(O(K log^22K))|A|, where the constant in the ... More

An analytic approach to a weak non-Abelian Kneser-type theoremDec 03 2012We prove the following result due to Hamidoune using an analytic approach. Suppose that A is a subset of a finite group G with |AA^{-1}| \leq (2-\varepsilon)|A|. Then there is a subgroup H of G and a set X of size O_\varepsilon(1) such that A \subset ... More

Algebraicity and Asymptotics: An explosion of BPS indices from algebraic generating seriesJun 08 2016It is an observation of Kontsevich and Soibelman that generating series that produce certain (generalized) Donaldson Thomas invariants are secretly algebraic functions over the rationals. From a physical perspective this observation arises naturally for ... More

Pole-free solutions of the first Painlevé hierarchy and non-generic critical behavior for the KdV equationJul 01 2011We establish the existence of real pole-free solutions to all even members of the Painlev\'e I hierarchy. We also obtain asymptotics for those solutions and describe their relevance in the description of critical asymptotic behavior of solutions to the ... More

Sampling Generative Networks: Notes on a Few Effective TechniquesSep 14 2016Sep 16 2016We introduce several techniques for sampling and visualizing the latent spaces of generative models. Replacing linear interpolation with spherical linear interpolation prevents diverging from a model's prior distribution and produces sharper samples. ... More

Continuous Disintegrations of Gaussian ProcessesMar 04 2010Mar 28 2011The goal of this paper is to understand the conditional law of a stochastic process once it has been observed over an interval. To make this precise, we introduce the notion of a continuous disintegration: a regular conditional probability measure which ... More

Scattering diagrams, Hall algebras and stability conditionsMar 01 2016Nov 11 2016To any quiver with relations we associate a consistent scattering diagram taking values in the motivic Hall algebra of its category of representations. We show that the chamber structure of this scattering diagram coincides with the natural chamber structure ... More

A new strain energy function for the hyperelastic modelling of ligaments and tendons based on fascicle microstructureOct 02 2015A new strain energy function for the hyperelastic modelling of ligaments and tendons based on the geometrical arrangement of their fibrils is derived. The distribution of the crimp angles of the fibrils is used to determine the stress-strain response ... More

Interlacements and the Wired Uniform Spanning ForestDec 28 2015Oct 18 2016We extend the Aldous-Broder algorithm to generate the wired uniform spanning forests (WUSFs) of infinite, transient graphs. We do this by replacing the simple random walk in the classical algorithm with Sznitman's random interlacement process. We then ... More

General Graph Identification By HashingDec 22 2015A method for identifying graphs using MD5 hashing is presented. This allows fast graph equality comparisons and can also be used to facilitate graph isomorphism testing. The graphs can be labeled or unlabeled. The method identifies vertices by hashing ... More

The bijection between projective indecomposable and simple modulesOct 14 2014For modules over a finite-dimensional algebra, there is a canonical one-to-one correspondence between the projective indecomposable modules and the simple modules. In this purely expository note, we take a straight-line path from the definitions to this ... More

Conformal invariance of the 3D self-avoiding walkOct 25 2013We show that if the three dimensional self-avoiding walk (SAW) is conformally invariant, then one can compute the hitting densities for the SAW in a half space and in a sphere. We test these predictions by Monte Carlo simulations and find excellent agreement, ... More

Dyck Words and Multi-Quark Primitive AmplitudesApr 29 2013I study group theory (Kleiss-Kuijf) relations between purely multi-quark primitive amplitudes at tree level, and prove that they reduce the number of independent primitives to (n-2)!/(n/2)!, where n is the number of quarks plus antiquarks, in the case ... More

Sets of beta-expansions and the Hausdorff Measure of Slices through FractalsJul 08 2013We study natural measures on sets of beta-expansions and on slices through self similar sets. In the setting of beta-expansions, these allow us to better understand the measure of maximal entropy for the random beta-transformation and to reinterpret a ... More

On the Conservativity of Some Functors in Motivic Homotopy TheoryJun 24 2015Feb 23 2016Given a 0-connective motivic spectrum $E \in SH(k)$ over a perfect field k, we determine $h_0$ of the associated motive $M E \in DM(k)$ in terms of $\pi_0 (E)$. Using this we show that if k has finite 2-\'etale cohomological dimension, then the functor ... More

The Scenery Flow for Self-Affine MeasuresMay 07 2015We describe the scaling scenery associated to Bernoulli measures supported on separated self-affine sets under the condition that certain projections of the measure are absolutely continuous.

The Generalized Slices of Hermitian K-TheoryOct 05 2016We compute the generalized slices (as defined by Spitzweck-{\O}stv{\ae}r) of the motivic spectrum KO (representing hermitian K-theory) in terms of motivic cohomology and (a version of) generalized motivic cohomology, obtaining good agreement with the ... More

Notions of Möbius inversionJan 02 2012Oct 07 2012M\"obius inversion, originally a tool in number theory, was generalized to posets for use in group theory and combinatorics. It was later generalized to categories in two different ways, both of which are useful. We provide a unifying abstract framework. ... More

Generalized Enrichment for Categories and MulticategoriesJan 29 1999In this paper we answer the question: `what kind of a structure can a general multicategory be enriched in?' The answer is, in a sense to be made precise, that a multicategory of one type can be enriched in a multicategory of the type one level up. In ... More

Basic BicategoriesOct 04 1998A concise guide to very basic bicategory theory, from the definition of a bicategory to the coherence theorem.

General Operads and MulticategoriesOct 08 1998Notions of `operad' and `multicategory' abound. This work provides a single framework in which many of these various notions can be expressed. Explicitly: given a monad * on a category S, we define the term `(S,*)-multicategory', subject to certain conditions ... More

Stability conditions on a non-compact Calabi-Yau threefoldSep 02 2005Feb 28 2006We study the space of stability conditions $\Stab(X)$ on the non-compact Calabi-Yau threefold $X$ which is the total space of the canonical bundle of $\PP^2$. We give a combinatorial description of an open subset of $\Stab(X)$ and state a conjecture relating ... More

Flops and derived categoriesSep 06 2000This paper contains some applications of Fourier-Mukai techniques to the birational geometry of threefolds. In particular, we prove that birational Calabi-Yau threefolds have equivalent derived categories. To do this we show how flops arise naturally ... More

Algebraic and Affine Pattern AvoidanceMar 15 2013We investigate various connections between the 0-Hecke monoid, Catalan monoid, and pattern avoidance in permutations, providing new tools for approaching pattern avoidance in an algebraic framework. In particular, we characterize containment of a class ... More

Hall algebras and curve-counting invariantsFeb 23 2010We use Joyce's theory of motivic Hall algebras to prove that reduced Donaldson-Thomas curve-counting invariants on Calabi-Yau threefolds coincide with stable pair invariants, and that the generating functions for these invariants are Laurent expansions ... More

Diffusions in random environment and ballistic behaviorSep 23 2005Sep 26 2005This article is accepted for publication in the "Annals I.H.P. Prob. & Stat.". We investigate the ballistic behavior of diffusions in random environment. We introduce conditions in the spirit of (T) and (T') of the discrete setting, cf. Sznitman \cite{szn01}, ... More

Monte Carlo Tests of SLE Predictions for the 2D Self-Avoiding WalkDec 21 2001The conjecture that the scaling limit of the two-dimensional self-avoiding walk (SAW) in a half plane is given by the stochastic Loewner evolution (SLE) with $\kappa=8/3$ leads to explicit predictions about the SAW. A remarkable feature of these predictions ... More

Finding rational points on elliptic curves using 6-descent and 12-descentNov 23 2007We explain how recent work on 3-descent and 4-descent for elliptic curves over Q can be combined to search for generators of the Mordell-Weil group of large height. As an application we show that every elliptic curve of prime conductor in the Stein-Watkins ... More

Spaces of stability conditionsNov 16 2006Stability conditions are a mathematical way to understand $\Pi$-stability for D-branes in string theory. Spaces of stability conditions seem to be related to moduli spaces of conformal field theories. This is a survey article describing what is currently ... More

On Multiple and Polynomial Recurrent extensions of infinite measure preserving transformationsMar 30 2007Mar 11 2009We prove that multiple-recurrence and polynomial-recurrence of invertible infinite measure preserving transformations are both properties which pass to extensions.

A Fast Algorithm for Simulating the Chordal Schramm-Loewner EvolutionJul 29 2005Apr 24 2007The Schramm-Loewner evolution (SLE) can be simulated by dividing the time interval into N subintervals and approximating the random conformal map of the SLE by the composition of N random, but relatively simple, conformal maps. In the usual implementation ... More

Testing the Boundary Conditions of General Relativity Near the Earth-Sun Saddle PointJun 07 1998Jun 03 1999We suggest that a satellite with a stable atomic clock on board be sent through the Earth-Sun gravitational saddle point to experimentally determine whether Nature prefers static solutions of the field equations of General Relativity, such as the standard ... More

Explicit moduli spaces for congruences of elliptic curvesApr 26 2018We determine explicit birational models over Q for the modular surfaces parametrising pairs of N-congruent elliptic curves in all cases where this surface is an elliptic surface. In each case we also determine the rank of the Mordell-Weil lattice and ... More

Minimal elements of stopping time $σ$-algebrasDec 12 2011Jun 19 2012We show how minimal elements of a stopping time $\sigma$-algebra can be expressed in terms of the minimal elements of the $\sigma$-algebra of the underlying filtration. This facilitates an intuitive interpretation of stopping time $\sigma$-algebras. An ... More

Stopping times are hitting times: a natural representationDec 07 2011Jun 19 2012There exists a simple, didactically useful one-to-one relationship between stopping times and adapted c\`agl\`ad (LCRL) processes that are non-increasing and take the values 0 and 1 only. As a consequence, stopping times are always hitting times.

Clifford correspondences and irreducible restrictions of charactersJun 09 2018For a finite group $G$ and complex character $\chi\in\mathrm{Irr}(G)$ that restricts irreducibly to a normal subgroup $N\vartriangleleft G,$ we prove a theorem about Clifford correspondences between the characters of subgroups of $G$ that induce $\chi.$ ... More

Magnification Spaces: A nonstandard approach to inverse mapping theoremsJul 20 2012This paper develops an infinitesimal order of magnitude coupled with overflow technique that allows nonnumerical proofs of nondegenerate and degenerate inverse mapping theorems for mappings minimally regular at a point. This approach is used first to ... More

Regularity and nearness theorems for families of local Lie groupsJun 14 2012In this work, we prove three types of results with the strategy that, together, the author believes these should imply the local version of Hilbert's Fifth problem. In a separate development, we construct a nontrivial topology for rings of map germs on ... More

Minimisation and reduction of 5-coverings of elliptic curvesDec 21 2011We consider models for genus one curves of degree 5, which arise in explicit 5-descent on elliptic curves. We prove a theorem on the existence of minimal models with the same invariants as the minimal model of the Jacobian elliptic curve and give an algorithm ... More

Monte Carlo comparisons of the self-avoiding walk and SLE as parameterized curvesOct 27 2005The scaling limit of the two-dimensional self-avoiding walk (SAW) is believed to be given by the Schramm-Loewner evolution (SLE) with the parameter kappa equal to 8/3. The scaling limit of the SAW has a natural parameterization and SLE has a standard ... More

Conformal invariance predictions for the three-dimensional self-avoiding walkAug 20 2014Dec 23 2014If the three dimensional self-avoiding walk (SAW) is conformally invariant, then one can compute the hitting densities for the SAW in a half-space and in a sphere. The ensembles of SAW's used to define these hitting densities involve walks of arbitrary ... More