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Unit Tests for Stochastic OptimizationDec 20 2013Feb 25 2014Optimization by stochastic gradient descent is an important component of many large-scale machine learning algorithms. A wide variety of such optimization algorithms have been devised; however, it is unclear whether these algorithms are robust and widely ... More

Successor Features for Transfer in Reinforcement LearningJun 16 2016Transfer in reinforcement learning refers to the notion that generalization should occur not only within a task but also across tasks. Our focus is on transfer where the reward functions vary across tasks while the environment's dynamics remain the same. ... More

Residual Policy LearningDec 15 2018Jan 03 2019We present Residual Policy Learning (RPL): a simple method for improving nondifferentiable policies using model-free deep reinforcement learning. RPL thrives in complex robotic manipulation tasks where good but imperfect controllers are available. In ... More

Prioritized Experience ReplayNov 18 2015Feb 25 2016Experience replay lets online reinforcement learning agents remember and reuse experiences from the past. In prior work, experience transitions were uniformly sampled from a replay memory. However, this approach simply replays transitions at the same ... More

Twisted Alexander Invariants of Twisted LinksFeb 07 2012Let L be an oriented (d+1)-component link in the 3-sphere, and let L(q) be the d-component link in a homology 3-sphere that results from performing 1/q-surgery on the last component. Results about the Alexander polynomial and twisted Alexander polynomials ... More

Alexander groups of long virtual knotsMay 24 2004Alexander group systems for virtual long knots are defined and used to show that any virtual knot is the closure of infinitely many long virtual knots. Manturov's result that there exists a pair of long virtual knots that do not commute is reproved.

An invariant for open virtual stringsSep 10 2004Dec 28 2004Extended Alexander groups are used to define an invariant for open virtual strings. Examples of non-commuting open strings and a ribbon-concordance obstruction are given. An example is given of a slice virtual open string that is not ribbon. Definitions ... More

Few-Shot Bayesian Imitation Learning with Logic over ProgramsApr 12 2019We describe an expressive class of policies that can be efficiently learned from a few demonstrations. Policies are represented as logical combinations of programs drawn from a small domain-specific language (DSL). We define a prior over policies with ... More

Learning Continuous Control Policies by Stochastic Value GradientsOct 30 2015We present a unified framework for learning continuous control policies using backpropagation. It supports stochastic control by treating stochasticity in the Bellman equation as a deterministic function of exogenous noise. The product is a spectrum of ... More

FeUdal Networks for Hierarchical Reinforcement LearningMar 03 2017Mar 06 2017We introduce FeUdal Networks (FuNs): a novel architecture for hierarchical reinforcement learning. Our approach is inspired by the feudal reinforcement learning proposal of Dayan and Hinton, and gains power and efficacy by decoupling end-to-end learning ... More

Successor Features for Transfer in Reinforcement LearningJun 16 2016Apr 12 2018Transfer in reinforcement learning refers to the notion that generalization should occur not only within a task but also across tasks. We propose a transfer framework for the scenario where the reward function changes between tasks but the environment's ... More

Knot Invariants from Laplacian MatricesSep 18 2018Nov 12 2018A checkerboard graph of a special diagram of an oriented link is made a directed, edge-weighted graph in a natural way so that a principal minor of its Laplacian matrix is a Seifert matrix of the link. Doubling and weighting the edges of the graph produces ... More

On Eigenvalues of Free Group EndomorphismsJun 21 2012Jun 25 2012Let \phi be an endomorphism of a finitely generated free group F, and let H be a finite-index subgroup of F that is invariant under \phi. The nonzero eigenvalues of \phi are contained in the eigenvalues of \phi restricted to H.

Twisting Alexander Invariants with Periodic RepresentationsJun 21 2010Dec 21 2010Twisted Alexander invariants have been defined for any knot and linear representation of its group. The invariants are generalized for any periodic representation of the commutator subgroup of the knot group. Properties of the new twisted invariants are ... More

Reinforcement Learning with Unsupervised Auxiliary TasksNov 16 2016Deep reinforcement learning agents have achieved state-of-the-art results by directly maximising cumulative reward. However, environments contain a much wider variety of possible training signals. In this paper, we introduce an agent that also maximises ... 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

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

Universal Successor Features ApproximatorsDec 18 2018The ability of a reinforcement learning (RL) agent to learn about many reward functions at the same time has many potential benefits, such as the decomposition of complex tasks into simpler ones, the exchange of information between tasks, and the reuse ... More

Transfer in Deep Reinforcement Learning Using Successor Features and Generalised Policy ImprovementJan 30 2019The ability to transfer skills across tasks has the potential to scale up reinforcement learning (RL) agents to environments currently out of reach. Recently, a framework based on two ideas, successor features (SFs) and generalised policy improvement ... More

Continuous control with deep reinforcement learningSep 09 2015Feb 29 2016We adapt the ideas underlying the success of Deep Q-Learning to the continuous action domain. We present an actor-critic, model-free algorithm based on the deterministic policy gradient that can operate over continuous action spaces. Using the same learning ... More

Invariants of Links in Thickened SurfacesApr 17 2013A group invariant for links in thickened closed orientable surfaces is studied. Associated polynomial invariants are defined. The group detects nontriviality of a virtual link and determines its virtual genus.

Twisted magnetic structures emerging from buoyancy instabilitiesOct 30 2012We here report calculations of magnetic buoyancy instabilities of a sheared magnetic layer where two separate zones are unstable. The idea is to study the possible generation of large-scale helical structures which could then rise through a stellar convection ... 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

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

On the Bogolyubov-Ruzsa lemmaOct 30 2010Dec 03 2012Our main result is that if A is a finite subset of an abelian group with |A+A| < K|A|, then 2A-2A contains an O(log^{O(1)} K)-dimensional coset progression M of size at least exp(-O(log^{O(1)} K))|A|.

Roth's theorem in Z_4^nJul 31 2008Apr 01 2010We show that if A is a subset of Z_4^n containing no three-term arithmetic progression in which all the elements are distinct then |A|=o(4^n/n).

A Freiman-type theorem for locally compact abelian groupsOct 12 2007Apr 01 2010We prove a Freiman-type theorem for locally compact abelian groups. If A is a subset of a locally compact abelian group with Haar measure m and m(nA) < n^dm(A) for all n>d log d then we describe A in a way which is tight up to logarithmic factors in d. ... More

A note on Freiman's theorem in vector spacesMay 18 2006Apr 01 2010We show that if A is a subset of F_2^n and |A+A| < K|A| then A is contained in a subspace of size at most 2^{O(K^{3/2}log K)}|A|. This improves on the previous best of 2^{O(K^2)}.

The Littlewood-Gowers problemMay 18 2006Apr 01 2010We show that if A is a subset of Z/pZ (p a prime) of density bounded away from 0 and 1 then the A(Z/pZ)-norm (that is the l^1-norm of the Fourier transform) of the characterstic function of A is bounded below by an absolute constant times (log p)^{1/2 ... More

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

Affine Grassmannians in A^1-algebraic topologyJan 25 2018Let k be a field. Denote by Spc(k)_* the unstable, pointed motivic homotopy category and by Omega_Gm: Spc(k)_* \to Spc(k)_* the Gm-loops functor. For a k-group G, denote by Gr_G the affine Grassmannian of G. If k is infinite and G is split reductive, ... More

Riemann-Hilbert problems from Donaldson-Thomas theoryNov 11 2016We study a class of Riemann-Hilbert problems arising naturally in Donaldson-Thomas theory. In certain special cases we show that these problems have unique solutions which can be written explicitly as products of gamma functions. We briefly explain connections ... More

Note on a Paper by Ooguri and VafaNov 28 2016Nov 30 2016In a recent paper, Ooguri and Vafa [arXiv:1610.04564] argued that a mild extension of the Weak Gravity conjecture\cite{weakgrav} led to the conclusion that the only models of quantum gravity in AdS space with "radius large compared to the string scale" ... 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

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

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

Bootstrapping partition regularity of linear systemsApr 16 2019Suppose that $A$ is a $k \times d$ matrix of integers and write $\mathfrak{R}_A:\mathbb{N} \rightarrow \mathbb{N}\cup \{ \infty\}$ for the function taking $r$ to the largest $N$ such that there is an $r$-colouring $\mathcal{C}$ of $[N]$ with $\bigcup_{C ... 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

Generalized solutions of nonlinear differential equations A nonstandard jets approachMay 02 2012Using the rudiments of pde jets theory in a nonstandard setting, we first deepen and extend previous nonstandard existence results for generalized solutions of linear differential equations and second extend the previous results for linear differential ... 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

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

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

On some algebras associated to genus one curvesJul 26 2017Haile, Han and Kuo have studied certain non-commutative algebras associated to a binary quartic or ternary cubic form. We extend their construction to pairs of quadratic forms in four variables, and conjecture a further generalisation to genus one curves ... More

The birth of a cut in unitary random matrix ensemblesNov 16 2007We study unitary random matrix ensembles in the critical regime where a new cut arises away from the original spectrum. We perform a double scaling limit where the size of the matrices tends to infinity, but in such a way that only a bounded number of ... More

A non-intersecting random walk on the Manhattan lattice and SLE_6Mar 18 2018May 18 2018We consider a random walk on the Manhattan lattice. The walker must follow the orientations of the bonds in this lattice, and the walker is not allowed to visit a site more than once. When both possible steps are allowed, the walker chooses between them ... 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

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

Invariant theory for the elliptic normal quintic, I. Twists of X(5)Oct 16 2011A genus one curve of degree 5 is defined by the 4 x 4 Pfaffians of a 5 x 5 alternating matrix of linear forms on P^4. We describe a general method for investigating the invariant theory of such models. We use it to explain how we found our algorithm for ... 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

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

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

Gibbs and equilibrium measures for some families of subshiftsMar 08 2009For SFTs, any equilibrium measure is Gibbs, as long a $f$ has $d$-summable variation. This is a theorem of Lanford and Ruelle. Conversely, a theorem of Dobru{\v{s}}in states that for strongly-irreducible subshifts, shift-invariant Gibbs-measures are equilibrium ... More

Pseudo-Orbit Tracing and Algebraic actions of countable amenable groupsJan 05 2017Feb 06 2017Consider a countable amenable group acting by homeomorphisms on a compact metrizable space. Chung and Li asked if expansiveness and positive entropy of the action imply existence of an off-diagonal asymptotic pair. For algebraic actions of polycyclic-by-finite ... More

rpSPH: a novel Smoothed Particle Hydrodynamics AlgorithmMar 04 2010Dec 01 2010We suggest a novel discretisation of the momentum equation for Smoothed Particle Hydrodynamics (SPH) and show that it significantly improves the accuracy of the obtained solutions. Our new formulation which we refer to as relative pressure SPH, rpSPH, ... More

Graphs of large linear size are antimagicSep 12 2014Given a graph $G=(V,E)$ and a colouring $f:E\mapsto \mathbb N$, the induced colour of a vertex $v$ is the sum of the colours at the edges incident with $v$. If all the induced colours of vertices of $G$ are distinct, the colouring is called antimagic. ... More

Rethinking set theoryDec 28 2012Mathematicians manipulate sets with confidence almost every day, rarely making mistakes. Few of us, however, could accurately quote what are often referred to as "the" axioms of set theory. This suggests that we all carry around with us, perhaps subconsciously, ... More

Codensity and the ultrafilter monadSep 17 2012Jul 10 2013Even a functor without an adjoint induces a monad, namely, its codensity monad; this is subject only to the existence of certain limits. We clarify the sense in which codensity monads act as substitutes for monads induced by adjunctions. We also expand ... More

Integral geometry for the 1-normDec 29 2010Mar 04 2012Classical integral geometry takes place in Euclidean space, but one can attempt to imitate it in any other metric space. In particular, one can attempt this in R^n equipped with the metric derived from the p-norm. This has, in effect, been investigated ... More

The magnitude of metric spacesDec 29 2010Jan 22 2011Magnitude is a real-valued invariant of metric spaces, analogous to the Euler characteristic of topological spaces and the cardinality of sets. The definition of magnitude is a special case of a general categorical definition that clarifies the analogies ... More

A general theory of self-similarity INov 15 2004Consider a self-similar space X. A typical situation is that X looks like several copies of itself glued to several copies of another space Y, and Y looks like several copies of itself glued to several copies of X, or the same kind of thing with more ... More

Operads in Higher-Dimensional Category TheoryNov 16 2000The purpose of this dissertation is to set up a theory of generalized operads and multicategories, and to use it as a language in which to propose a definition of weak n-category. Included is a full explanation of why the proposed definition of n-category ... More

fc-multicategoriesFeb 28 1999fc-multicategories are a very general kind of two-dimensional structure, encompassing bicategories, monoidal categories, double categories and ordinary multicategories. We define them and explain how they provide a natural setting for two familiar categorical ... More

Quantum groups via Hall algebras of complexesNov 03 2011We describe quantum enveloping algebras of symmetric Kac-Moody Lie algebras via a finite field Hall algebra construction involving Z_2-graded complexes of quiver representations.

Fourier-Mukai transforms for elliptic surfacesMay 01 1997Jun 23 1998We compute a large number of moduli spaces of stable bundles on a general algebraic elliptic surface using a new class of Fourier-Mukai type transforms.

On the Invariant Density of the Random Beta-TransformationMar 05 2013We construct a Lebesgue measure preserving natural extension of the random beta-transformation. This allows us to give a formula for the density of the absolutely continuous invariant probability measure, answering a question of Dajani and de Vries, and ... More

TASI Lectures on Matrix TheoryNov 10 1999Dec 13 1999This is a summary of key issues in Matrix Theory and its compactifications. It is emphasized that Matrix Theory is a valid Discrete Light Cone Quantization of M Theory with at least 6 noncompact asymptotically flat dimensions and 16 or 32 Supersymmetry ... More

Remarks on M Theoretic CosmologyJun 16 1999I present cosmological arguments which point towards a Horava-Witten like picture of the universe, with the unification scale of order the fundamental gravitational scale. The SUSY breaking scale is determined by the dynamics of gauge fields which are ... More

Gravitational `Convergence' and Cluster MassesDec 01 1995Two colour photometry of the cluster A1689 reveals a `relative magnification-bias' between lensed blue and red background galaxies, arising from a dependence of the faint galaxy count-slope on colour. The colour distribution is skewed blueward of the ... More

Enumerative geometry of hyperelliptic plane curvesAug 18 1998We recursively compute the Gromov-Witten invariants of the Hilbert scheme of two points in the plane. By studying the space of stable maps and computing virtual contributions, we use these invariants to enumerate hyperelliptic plane curves of degree d ... More

Some Remarks on Extragalactic Globular ClustersDec 21 2005I comment (in a review fashion) on a few selected topics in the field of extragalactic globular clusters with strong emphasis on recent work. The topics are: bimodality in the colour distribution of cluster systems, young massive clusters, and the brightest ... More

A faster implementation of the pivot algorithm for self-avoiding walksSep 17 2001The pivot algorithm is a Markov Chain Monte Carlo algorithm for simulating the self-avoiding walk. At each iteration a pivot which produces a global change in the walk is proposed. If the resulting walk is self-avoiding, the new walk is accepted; otherwise, ... More

Integral Canonical Models for Automorphic Vector Bundles of Abelian TypeMay 09 2016We define and construct integral canonical models for automorphic vector bundles over Shimura varieties of abelian type. More precisely, we first build on Kisin's work to construct integral canonical models over rings of integers of number fields with ... More

Some results on change-point detection in cross-sectional dependence of multivariate data with changes in marginal distributionsJun 05 2015Mar 25 2016Tests for break points detection in the law of random vectors have been proposed in several papers. Nevertheless, they have often little powers for alternatives involving a change in the dependence between components of vectors. Specific tests for detection ... More

Note on a Paper by Ooguri and VafaNov 28 2016In a recent paper, Ooguri and Vafa [arXiv:1610.04564] argued that a mild extension of the Weak Gravity conjecture\cite{weakgrav} led to the conclusion that the only models of quantum gravity in AdS space with "radius large compared to the string scale" ... More

Research trends in structural software complexityAug 04 2016There are many dimensions of software complexity. In this article, we explore how structural complexity is measured and used to study and control evolving software systems. We also present the current research challenges and emerging trends in this domain ... More

Computing the Loewner driving process of random curves in the half planeFeb 03 2007Mar 03 2008We simulate several models of random curves in the half plane and numerically compute their stochastic driving process (as given by the Loewner equation). Our models include models whose scaling limit is the Schramm-Loewner evolution (SLE) and models ... More

An introduction to motivic Hall algebrasFeb 23 2010We give an introduction to Joyce's construction of the motivic Hall algebra of coherent sheaves on a variety M. When M is a Calabi-Yau threefold we define a semi-classical integration map from a Poisson subalgebra of this Hall algebra to the ring of functions ... More

Kummer theory of abelian varieties and reductions of Mordell-Weil groupsAug 14 2002Let A be an abelian variety over a number field F with End(A/F) commutative. Let S be a subgroup of A(F) and let x be a point of A(F). Suppose that for almost all places v of F the reduction of x modulo v lies in the reduction of S modulo v. In this paper ... More

General Relativity and Spatial Flows: I. Absolute Relativistic DynamicsJun 08 2000Two complementary and equally important approaches to relativistic physics are explained. One is the standard approach, and the other is based on a study of the flows of an underlying physical substratum. Previous results concerning the substratum flow ... More