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From tokamaks to stellarators: understanding the role of 3D shapingMay 01 2017Jul 11 2017In this work, the role which three-dimensional shaping plays in the generation of rotational transform in toroidal magnetically confinement devices is explored. The susceptance matrix as defined by Strand & Houlberg (2001) is presented and compared to ... More

Verification of the global gyrokinetic stellarator code XGC-S for linear ion temperature gradient driven modesMay 14 2019XGC (X-point Gyrokinetic Code) is a whole-volume, total-f gyrokinetic particle-in-cell code developed for modelling tokamaks. In recent work, XGC has been extended to model more general 3D toroidal magnetic configurations, such as stellarators. These ... More

A special case of the $Γ_{00}$ conjectureApr 03 2008Sep 02 2010In this paper we prove the $\Gamma_{00}$ conjecture of van Geemen and van der Geer, under the additional assumption that the matrix of coefficients of the tangent has rank at most 2. This assumption is satisfied by Jacobians, and thus our result gives ... More

On Improved Bounds on Bounded Degree Spanning Trees for Points in Arbitrary DimensionMay 13 2013Jan 05 2014Given points in Euclidean space of arbitrary dimension, we prove that there exists a spanning tree having no vertices of degree greater than 3 with weight at most 1.559 times the weight of the minimum spanning tree. We also prove that there is a set of ... More

Exploratory topic modeling with distributional semanticsJul 16 2015As we continue to collect and store textual data in a multitude of domains, we are regularly confronted with material whose largely unknown thematic structure we want to uncover. With unsupervised, exploratory analysis, no prior knowledge about the content ... More

On Quantum NoncompressionNov 16 2015This article presents a quantum transmission problem, in which Alice is trying to send a number of qbits to Bob. Alice has access to two channels, one that sends classical bits and another that sends quantum bits. We show that under certain error terms, ... More

Canonical Cartan connection for $4$-dimensional CR-manifolds belonging to general class ${\sf II}$May 05 2014We study the equivalence problem for $4$-dimensional CR-manifolds of CR-dimension $1$ and codimension $2$ which are referred to as Engel CR-manifolds. We construct a canonical Cartan connection on such CR-manifolds through Cartan equivalence's method. ... More

Towards 3-Dimensional Rewriting TheoryMar 17 2014Apr 02 2014String rewriting systems have proved very useful to study monoids. In good cases, they give finite presentations of monoids, allowing computations on those and their manipulation by a computer. Even better, when the presentation is confluent and terminating, ... More

Convergence of the Yang-Mills-Higgs flow on gauged holomorphic maps and applicationsOct 07 2016The symplectic vortex equations admit a variational description as global minimum of the Yang--Mills--Higgs functional. We study its negative gradient flow on holomorphic pairs $(A,u)$ where $A$ is a connection on a principal $G$-bundle $P$ over a closed ... More

Extraction of Cosmological Information from WiggleZApr 06 2016In this thesis, I analyse the 2D anisotropic Baryon Acoustic Oscillation (BAO) signal present in the final WiggleZ dataset. I utilise newly released covariance matrices from the WizCOLA simulations and follow well tested methodologies used in prior analyses ... More

On Certain Tilting Modules for SL2May 19 2017Sep 19 2017We give a complete picture of when the tensor product of an induced module and a Weyl module is a tilting module for the algebraic group $SL_2$ over an algebraically closed field of characteristic $p$. Whilst the result is recursive by nature, we give ... More

The global gravitational anomaly of the self-dual field theoryOct 20 2011May 10 2013We derive a formula for the global gravitational anomaly of the self-dual field theory on an arbitrary compact oriented Riemannian manifold. Along the way, we uncover interesting links between the theory of determinant line bundles of Dirac operators, ... More

A Dichotomy in Machine KnowledgeAug 04 2011We show that a machine, which knows basic logic and arithmetic and basic axioms of knowledge, and which is factive (knows nothing false), can either know that it is factive, or know its own Goedel number, but not both.

Characterisations of purity in a locally finitely presented additive category: A short functorial proofFeb 23 2017In this short note, we will give an efficient functorial proof of the equivalence of various characterisations of purity in a locally finitely presented additive category $C$. The complications of the proofs for specific choices of $C$ (e.g. $C=A\text{-Mod}$ ... More

Ioana's superrigidity theorem and orbit equivalence relationsOct 09 2013Dec 31 2013In this expository article, we give a survey of Adrian Ioana's cocycle superrigidity theorem for profinite actions of Property (T) groups, and its applications to ergodic theory and set theory. In addition to a statement and proof of Ioana's theorem, ... More

A theoretical framework for retinal computations: insights from textbook knowledgeJun 07 2018Neural circuits in the retina divide the incoming visual scene into more than a dozen distinct representations that are sent on to central brain areas, such as the lateral geniculate nucleus and the superior colliculus. The retina can be viewed as a parallel ... More

A quantum point contact as a (near) perfect spin polariserNov 28 2018In this paper, I present a simple method of obtaining spin-polarised current from a QPC with a large Rashba interaction. The origin of this spin polarisation is the adiabatic evolution of spin "up" of the first QPC sub-band, into spin "down" of the second ... More

Propagation in media as a probe for topological propertiesSep 23 2017The central goal of this thesis is to develop methods to experimentally study topological phases. We do so by applying the powerful toolbox of quantum simulation techniques with cold atoms in optical lattices. To this day, a complete classification of ... More

A Sequent Calculus for Dynamic Topological LogicJul 25 2014Aug 03 2014We introduce a sequent calculus for the temporal-over-topological fragment $\textbf{DTL}_{0}^{\circ * \slash \Box}$ of dynamic topological logic $\textbf{DTL}$, prove soundness semantically, and prove completeness syntactically using the axiomatization ... More

Asymptotically faster algorithm for counting self-avoiding walks and self-avoiding polygonsMar 10 2019May 06 2019We give an algorithm for counting self-avoiding walks or self-avoiding polygons that runs in time $\exp(C\sqrt{n\log n})$ on 2-dimensional lattices and time $\exp(C_dn^{(d-1)/d}\log n)$ on $d$-dimensional lattices for $d>2$.

Escaping the Tragedy of the Commons through Targeted PunishmentJun 04 2015Failures of cooperation cause many of society's gravest problems. It is well known that cooperation among many players faced with a social dilemma can be maintained thanks to the possibility of punishment, but achieving the initial state of widespread ... More

Interplay between Network Topology and Dynamics in Neural SystemsFeb 16 2013This thesis is a compendium of research which brings together ideas from the fields of Complex Networks and Computational Neuroscience to address two questions regarding neural systems: 1) How the activity of neurons, via synaptic changes, can shape the ... More

On weighted optimality of experimental designsOct 20 2016When the experimental objective is expressed by a set of estimable functions, and any eigenvalue-based optimality criterion is selected, we prove the equivalence of the recently introduced weighted optimality and the 'standard' optimality criteria for ... More

Real-Time Multiple Object Tracking - A Study on the Importance of SpeedSep 11 2017Oct 02 2017In this project, we implement a multiple object tracker, following the tracking-by-detection paradigm, as an extension of an existing method. It works by modelling the movement of objects by solving the filtering problem, and associating detections with ... More

Simple fixed-brane gauges in $S_1/Z_2$ braneworldsApr 07 2006For five-dimensional braneworlds with an $S_1/\mathbb{Z}_2$ orbifold topology for the extra dimension $x^5$, we discuss the validity of recent claims that a gauge exists where the two boundary branes lie at fixed positions and the metric satisfies $g_{\mu ... More

Twisted Spin in Quantum MechanicsJul 01 2019In quantum mechanics, spin is quantized. It is often thought that the spin of an object points in a fixed direction at any point in time. For example, after selecting the z-direction as the axis of quantization, a spin 1/2 object (such as an electron) ... More

The number of points from a random lattice that lie inside a ballNov 12 2013We prove a sharp bound for the remainder term of the number of lattice points inside a ball, when averaging over a compact set of (not necessarily unimodular) lattices, in dimensions two and three. We also prove that such a bound cannot hold if one averages ... More

Infinitesimal thickenings of Morava K-theoriesJul 05 2006Mar 06 2008A. Baker has constructed certain sequences of cohomology theories which interpolate between the Johnson-Wilson and the Morava K-theories. We realize the representing sequences of spectra as sequences of MU-algebras. Starting with the fact that the spectra ... More

I-adic towers in topologyNov 18 2004Nov 30 2005A large variety of cohomology theories is derived from complex cobordism MU^*(-) by localizing with respect to certain elements or by killing regular sequences in MU_*. We study the relationship between certain pairs of such theories which differ by a ... More

Infinite graphs in systematic biology, with an application to the species problemJan 13 2012Dec 13 2012We argue that C. Darwin and more recently W. Hennig worked at times under the simplifying assumption of an eternal biosphere. So motivated, we explicitly consider the consequences which follow mathematically from this assumption, and the infinite graphs ... More

Highly lopsided information and the Borel hierarchyJun 01 2011In a game where both contestants have perfect information, there is a strict limit on how perfect that information can be. By contrast, when one player is deprived of all information, the limit on the other player's information disappears, admitting a ... More

Almost prime values of the order of abelian varieties over finite fieldsMar 09 2018Let $E/\mathbb Q$ be an elliptic curve, and denote by $N(p)$ the number of $\mathbb{F}_p$-points of the reduction modulo $p$ of $E$. A conjecture of Koblitz, refined by Zywina, states that the number of primes $p \leq X$ at which $N(p)$ is also prime ... More

New classes of null hypersurfaces in indefinite Sasakian space-formsJul 10 2019We introduce two classes of null hypersurfaces of an indefinite Sasakian manifold, $(\overline{M}, \overline{\phi},\zeta, \eta)$, tangent to the characteristic vector field $\zeta$, called; {\it contact screen conformal} and {\it contact screen umbilic} ... More

Complexity of comparing monomials and two improvements of the BM-algorithmJul 15 2008Aug 27 2008We give a new algorithm for merging sorted lists of monomials. Together with a projection technique we obtain a new complexity bound for the BM-algorithm.

Context-Independent Polyphonic Piano Onset Transcription with an Infinite Training DatasetJul 26 2017Many of the recent approaches to polyphonic piano note onset transcription require training a machine learning model on a large piano database. However, such approaches are limited by dataset availability; additional training data is difficult to produce, ... More

Chern classes of the tangent bundle on the Hilbert scheme of points on the affine planeOct 21 2004Mar 31 2005The cohomology of the Hilbert schemes of points on smooth projective surfaces can be approached both with vertex algebra tools and equivariant tools. Using the first tool, we study the existence and the structure of universal formulas for the Chern classes ... More

Polar actions on Hermitian and quaternion-Kähler symmetric spacesDec 18 2006Jan 17 2007We analyze polar actions on Hermitian and quaternion-K\"ahler symmetric spaces of compact type. For complex integrable polar actions on Hermitian symmetric spaces of compact type we prove a reduction theorem and several corollaries concerning the geometry ... More

Canonical Cartan connection for $5$-dimensional CR-manifolds belonging to general class ${\sf III_2}$May 05 2014We study the equivalence problem for CR-manifolds belonging to general class III_2, i.e. the 5-dimensional CR-manifolds of CR-dimension 1 and codimension 3 whose CR-bundle satisfies a certain degeneracy condition. For such a CR-manifold M, we construct ... More

Properties of the thermal two-point functions in curved spacetimes for a self-interacting scalar fieldJan 21 2016We will present a method for building a consistent AQFT on Schwarzschild spacetime for a thermal system ruled by an interacting and massive scalar field, extending the methods and the results of K. Fredenhagen and F. Lindner valid for the flat case. In ... More

Wick Rotation in the Tangent SpaceOct 26 2015Wick rotation is usually performed by rotating the time coordinate to imaginary values. In a general curved spacetime, the notion of a time coordinate is ambiguous. We note here, that within the tetrad formalism of general relativity, it is possible to ... More

On the rate of equidistribution of expanding horospheres in finite-volume quotients of $\mathrm{SL}(2,\mathbb{C})$Dec 08 2015Let $\Gamma$ be a lattice in $G=\mathrm{SL}(2,\mathbb{C})$. We give an effective equidistribution result with precise error terms for expanding translates of pieces of horospherical orbits in $\Gamma\backslash G$. Our method of proof relies on the theory ... More

Hamiltonian anomalies from extended field theoriesOct 27 2014Apr 22 2015We develop a proposal by Freed to see anomalous field theories as relative field theories, namely field theories taking value in a field theory in one dimension higher, the anomaly field theory. We show that when the anomaly field theory is extended down ... More

Fast-collapsing theoriesNov 13 2013Nov 14 2013Reinhardt's conjecture, a formalization of the statement that a truthful knowing machine can know its own truthfulness and mechanicalness, was proved by Carlson using sophisticated structural results about the ordinals and transfinite induction just beyond ... More

Asymptotically faster algorithm for counting self-avoiding walks and self-avoiding polygonsMar 10 2019We give an algorithm for counting self-avoiding walks or self-avoiding polygons that runs in time $\exp(C\sqrt{n\log n})$ on 2-dimensional lattices and time $\exp(C_dn^{(d-1)/d}\log n)$ on $d$-dimensional lattices for $d>2$.

On Guessing Whether A Sequence Has A Certain PropertyNov 30 2010Jan 23 2012A concept of "guessability" is defined for sets of sequences of naturals. Eventually, these sets are thoroughly characterized. To do this, a nonstandard logic is developed, a logic containing symbols for the ellipsis as well as for functions without fixed ... More

Homogeneous 3-dimensional permutation structuresOct 14 2017We provide a classification of the homogeneous 3-dimensional permutation structures, i.e. homogeneous structures in a language of 3 linear orders, partially answering a question of Cameron. We also arrive at a natural description of all known homogeneous ... More

A Modern Point of View on AnomaliesMar 07 2019We review the concept of anomaly field theory, namely the fact that the anomalies of a $d$-dimensional field theory can be encoded in a $d+1$-dimensional field theory functor. We give numerous examples of anomaly field theories, explain how classical ... More

Monte Carlo simulation of 192Ir radioactive source in a phantom designed for brachytherapy dosimetry and source position evaluationNov 25 2018In this report simulations of 192Ir source located inside a phantom designed for measuring the absorbed dose and radioactive source position are presented. Monte Carlo simulations were performed and results were compared with a theoretical model that ... More

Borel reductions of profinite actions of SL(n,Z)Sep 03 2009Sep 30 2010Greg Hjorth and Simon Thomas proved that the classification problem for torsion-free abelian groups of finite rank \emph{strictly increases} in complexity with the rank. Subsequently, Thomas proved that the complexity of the classification problems for ... More

A Flexible Thread Scheduler for Hierarchical Multiprocessor MachinesJun 27 2005With the current trend of multiprocessor machines towards more and more hierarchical architectures, exploiting the full computational power requires careful distribution of execution threads and data so as to limit expensive remote memory accesses. Existing ... More

On the McKay correspondences for the Hilbert scheme of points on the affine planeOct 11 2004The quotient of a finite-dimensional vector space by the action of a finite subgroup of automorphisms is usually a singular variety. Under appropriate assumptions, the McKay correspondence relates the geometry of nice resolutions of singularities and ... More

Towards the multiplicative behavior of the K-theoretical McKay correspondenceJan 24 2005May 01 2005When the quotient of a symplectic vector space by the action of a finite subgroup of symplectic automorphisms admits as a crepant projective resolution of singularities the Hilbert scheme of regular orbits of Nakamura, then there is a natural isomorphism ... More

Optimal designs for treatment comparisons represented by graphsDec 20 2016Consider an experiment consisting of a set of independent trials for comparing a set of treatments. In each trial, one treatment is chosen and the mean response of the trial is equal to the effect of the chosen treatment. We examine the optimal approximate ... More

Biologically Unavoidable SequencesDec 02 2012Feb 05 2013A biologically unavoidable sequence is an infinite gender sequence which occurs in every gendered, infinite genealogical network satisfying certain tame conditions. We show that every eventually periodic sequence is biologically unavoidable (this generalizes ... More

Rectifications of Convex PolyhedraApr 03 2016A convex polyhedron, that is, a compact convex subset of $\mathbb{R}^3$ which is the intersection of finitely many closed half-spaces, can be rectified by taking the convex hull of the midpoints of the edges of the polyhedron. We derive expressions for ... More

Finite higher spin transformations from exponentiationFeb 18 2014Mar 19 2015We study the exponentiation of elements of the gauge Lie algebras ${\rm hs}(\lambda)$ of three-dimensional higher spin theories. Exponentiable elements generate one-parameter groups of finite higher spin symmetries. We show that elements of ${\rm hs}(\lambda)$ ... More

The defect recollement, the MacPherson-Vilonen construction, and pp formulasAug 19 2018May 29 2019For any abelian category $\mathcal{A}$, Auslander constructed a localisation $w:\mathrm{fp}(\mathcal{A}^{\mathrm{op}},\mathrm{Ab})\to \mathcal{A}$ called the defect, which is the left adjoint to the Yoneda embedding $Y:\mathcal{A}\to\mathrm{fp}(\mathcal{A}^{\mathrm{op}},\mathrm{Ab})$. ... More

Remarks on screen integrable null hypersurfaces in Lorentzian manifoldsJun 12 2019In the present paper, we show that the geometry of a screen integrable null hypersurface can be generated from an isometric immersion of a leaf of its screen distribution into the ambient space. We prove, under certain geometric conditions, that such ... More

Siegel-Veech constants in H(2)Mar 30 2005Mar 16 2009Abelian differentials on Riemann surfaces can be seen as translation surfaces, which are flat surfaces with cone-type singularities. Closed geodesics for the associated flat metrics form cylinders whose number under a given maximal length generically ... More

Multiplication matrices and ideals of projective dimension zeroMar 11 2009Mar 12 2009We introduce the concept of multiplication matrices for ideals of projective dimension zero. We discuss various applications and in particular, we give a new algorithm to compute the variety of an ideal of projective dimension zero.

Upper Bounds for Non-Congruent Sphere PackingsSep 28 2015We prove upper bounds on the average kissing number $k(\mathcal{P})$ and contact number $C(\mathcal{P})$ of an arbitrary finite non-congruent sphere packing $\mathcal{P}$, and prove an upper bound on the packing density $\delta(\mathcal{P})$ of an arbitrary ... More

CAT(-1) metrics on small cancellation groupsJul 09 2016Jul 12 2016We give a proof that groups satisfying the "uniform C'(1/6)" small cancellation condition admit a geometric action on a CAT(-1) space. It follows that random groups at density <1/12 are CAT(-1). The proof consists of a direct construction of a piecewise ... More

Information KernelsJul 01 2019Given a set X of finite strings, one interesting question to ask is whether there exists a member of X which is simple conditional to all other members of X. Conditional simplicity is measured by low conditional Kolmogorov complexity. We prove the affirmative ... More

On the Complexity of Completing Binary PredicatesJul 10 2019Given a binary predicate P, the length of the smallest program that computes a complete extension of P is less than the size of the domain of P plus the amount of information that P has with the halting sequence. This result is derived from a theorem ... More

Veech surfaces associated with rational billiardsMay 23 2002A nice trick for studying the billiard flow in a rational polygon is to unfold the polygon along the trajectories. This gives rise to a translation or half-translation surface tiled by the original polygon, or equivalently an Abelian or quadratic differential. ... More

Cubic equations for the hyperelliptic locusMar 02 2005We discuss the conjecture of Buchstaber and Krichever that their multi-dimensional vector addition formula for Baker-Akhiezer functions characterizes Jacobians among principally polarized abelian varieties, and prove that it is indeed a weak characterization, ... More

Multiplier ideals in algebraic geometryFeb 17 2005Mar 28 2005In this expository introductory text we discuss the multiplier ideals in algebraic geometry. We state Kawamata-Viehweg's and Nadel's vanishing theorems, give a proof (following Ein and Lazarsfeld) of Koll\'ar's bound on the maximal multiplicity of the ... More

The Schottky ProblemSep 02 2010Sep 30 2010In this survey we discuss some of the classical and modern methods in studying the (Riemann-)Schottky problem, the problem of characterizing Jacobians of curves among principally polarized abelian varieties. We present many of the recent results in this ... More

Duality and contravariant functors in the representation theory of artin algebrasMar 18 2016May 22 2016The model theory of modules leads to a way of obtaining definable categories of modules over a ring $R$ as the kernels of certain functors $(R\textbf{-Mod})^{\text{op}}\to\textbf{Ab}$ rather than of functors $R\textbf{-Mod}\to\textbf{Ab}$ which are given ... More

Geometric ergodicity of the Random Walk Metropolis with position-dependent proposal covarianceJul 21 2015Jul 29 2015We consider a Metropolis-Hastings method with proposal kernel $\mathcal{N}(x,hG^{-1}(x))$, where $x$ is the current state. After discussing specific cases from the literature, we analyse the ergodicity properties of the resulting Markov chains. In one ... More

Lie algebras of infinitesimal automorphisms for the model manifolds of general classes ${\sf II}$, ${\sf III_2}$ and ${\sf IV_2}$Apr 22 2014May 05 2014We determine the Lie algebras of infinitesimal automorphisms for the models of the CR-manifolds belonging to general classes ${\sf II}$, ${\sf III_2}$ and ${\sf IV_2}$ through Cartan's equivalence method.

All Sampling Methods Produce OutliersApr 14 2013May 10 2013Given a computable probability measure P over natural numbers or infinite binary sequences, there is no method that can produce an arbitrarily large sample such that all its members are typical of P. This paper also contains upper bounds on the minimal ... More

On Ruby's solid angle formula and some of its generalizationsOct 15 2014Using the Mellin-Barnes representation, we show that Ruby's solid angle formula and some of its generalizations may be expressed in a compact way in terms of the Appell F4 and Lauricella Fc functions.

Distributed delays stabilize negative feedback loopsOct 23 2009Linear scalar differential equations with distributed delays appear in the study of the local stability of nonlinear differential equations with feedback, which are common in biology and physics. Negative feedback loops tend to promote oscillation around ... More

Quantum Deformations from Toric GeometryNov 03 2005Feb 23 2006We will demonstrate how calculations in toric geometry can be used to compute quantum corrections to the relations in the chiral ring for certain gauge theories. We focus on the gauge theory of the del Pezzo 2, and derive the chiral ring relations and ... More

Topological field theories on manifolds with Wu structuresJul 05 2016We construct invertible field theories generalizing abelian prequantum spin Chern-Simons theory to manifolds of dimension 4k+3 endowed with a Wu structure of degree 2k+2. After analysing the anomalies of a certain discrete symmetry, we gauge it, producing ... More

A quantum lower bound for the collision problemApr 24 2003We extend Shi's 2002 quantum lower bound for collision in $r$-to-one functions with $n$ inputs. Shi's bound of $\Omega((n/r)^{1/3})$ is tight, but his proof applies only in the case where the range has size at least $3n/2$. We give a modified version ... More

Separability of Lyapunov Functions for Contractive Monotone SystemsSep 20 2016We consider constructing Lyapunov functions for systems that are both monotone and contractive with respect to a weighted one norm or infinity norm. This class of systems admits separable Lyapunov functions that are either the sum or the maximum of a ... More

A machine that knows its own codeMay 27 2013We construct a machine that knows its own code, at the price of not knowing its own factivity.

A Simple Proof of Vitali's Theorem for Signed MeasuresFeb 09 2012May 14 2012There are several theorems named after the Italian mathematician Vitali. In this note we provide a simple proof of an extension of Vitali's Theorem on the existence of non-measurable sets. Specifically, we show, without using any decomposition theorems, ... More

$Λ$-ultrametric spaces and lattices of equivalence relationsNov 27 2018For a finite lattice $\Lambda$, $\Lambda$-ultrametric spaces have, among other reasons, appeared as a means of constructing structures with lattices of equivalence relations embedding $\Lambda$. This makes use of an isomorphism of categories between $\Lambda$-ultrametric ... More

Analytic Combinatorics of Planar Lattice PathsApr 23 2013Lattice paths effectively model phenomena in chemistry, physics and probability theory. Asymptotic enumeration of lattice paths is linked with entropy in the physical systems being modeled. Lattice paths restricted to different regions of the plane are ... More

Counting nonsingular matrices with primitive row vectorsNov 12 2012May 02 2013We give an asymptotic expression for the number of nonsingular integer n-by-n-matrices with primitive row vectors, determinant k, and Euclidean matrix norm less than T, for large T. We also investigate the density of matrices with primitive rows in the ... More

A Discrete Inverse Scattering Transform for Q3$_δ$Oct 05 2012We derive a fully discrete Inverse Scattering Transform as a method for solving the initial-value problem for the Q3$_\delta$ lattice (difference-difference) equation for real-valued solutions. The initial condition is given on an infinite staircase within ... More

Algorithmic No-Cloning TheoremAug 09 2018We introduce the notions of algorithmic mutual information and rarity of quantum states. These definitions enjoy conservation inequalities over unitary transformations and partial traces. We show that a large majority of pure states have minute self algorithmic ... More

Constant Slope Models for Finitely Generated MapsJul 14 2017We study countably monotone and Markov interval maps. We establish sufficient conditions for uniqueness of a conjugate map of constant slope. We explain how global window perturbation can be used to generate a large class of maps satisfying these conditions. ... More

Homology of powers of regular idealsAug 27 2003For a commutative ring R with an ideal I, generated by a finite regular sequence, we construct differential graded algebras which provide R-free resolutions of I^s and of R/I^s for s>0 and which generalise the Koszul resolution. We derive these from a ... More

Stable solutions of semilinear elliptic equations in unbounded domainsOct 19 2018This paper establishes some properties for stable solutions of a semilin-ear elliptic equation with homogeneous Neumann boundary conditions in unbounded domains. A seminal result of Casten, Holland [16] and Matano [23] states that, in convex bounded domains, ... More

The Maximum Number of Subset Divisors of a Given SizeJul 17 2014May 20 2015If $s$ is a positive integer and $A$ is a set of positive integers, we say that $B$ is an $s$-divisor of $A$ if $\sum_{b\in B} b\mid s\sum_{a\in A} a$. We study the maximal number of $k$-subsets of an $n$-element set that can be $s$-divisors. We provide ... More

Exact sequence between real and complex bivariant K theories and application to the Z2 pairingJul 16 2019We give some formulas for the ZZ pairing in KO theory using a long exact sequence for bivariant K theory which links real and complex theories. This is discussed under the framework of real structures given by antilinear operators verifying some symmetries. ... More

f-vectors of Simplicial Posets that are BallsSep 10 2010Results of R. Stanley and M. Masuda completely characterize the h-vectors of simplicial posets whose order complexes are spheres. In this paper we examine the corresponding question in the case where the order complex is a ball. Using the face rings of ... More

Minimising Hausdorff Dimension under Hölder EquivalenceJan 18 2019We study the infimal value of the Hausdorff dimension of spaces that are H\"older equivalent to a given metric space; we call this bi-H\"older-invariant "H\"older dimension". This definition and some of our methods are analogous to those used in the study ... More

The Square Sieve and a Lang-Trotter Question for Generic Abelian VarietiesFeb 09 2017Mar 02 2017Let $A$ be a $g$-dimensional abelian variety over $\mathbb{Q}$ whose adelic Galois representation has open image in $\text{GSp}_{2g} \widehat{\mathbb{Z}}$. We investigate the endomorphism algebras $\text{End}(A_p) \otimes \mathbb{Q} = \mathbb{Q}( \pi_p ... More

Boolean ideals and their varietiesNov 14 2012May 25 2015We consider ideals in the ring $\mathbb{Z}_2[x_1,\ldots, x_n]$ that contain the polynomials $x_i^2 - x_i$ for $i = 1, \ldots, n$ and give various results related to the one-to-one correspondence between these ideals and the subsets of $\mathbb{Z}_2^n$. ... More

Vector space bases associated to vanishing ideals of pointsAug 26 2008Apr 14 2009We discuss four different constructions of vector space bases associated to vanishing ideals of points. We show how to compute normal forms with respect to these bases and give new complexity bounds. As an application, we improve the computational algebra ... More

The Donaldson hyperkähler metric on the almost-Fuchsian moduli spaceSep 04 2018Donaldon constructed a hyperk\"ahler moduli space $\mathcal{M}$ associated to a closed oriented surface $\Sigma$ with $\textrm{genus}(\Sigma) \geq 2$. This embeds naturally into the cotangent bundle $T^*\mathcal{T}(\Sigma)$ of Teichm\"uller space or can ... More

Homology of I-adic towersNov 09 2004Nov 29 2005Let R be a commutative ring with unit and let I be an ideal generated by a regular sequence. Then it is known that the natural sequences 0-> Tor_*^R(R/I,I^s)-> Tor_*^R(R/I,I^s/I^{s+1})-> Tor_{*-1}^R(R/I,I^{s+1})-> 0 are short exact sequences of graded ... More

Lazy Transformation-Based LearningJun 03 1998We introduce a significant improvement for a relatively new machine learning method called Transformation-Based Learning. By applying a Monte Carlo strategy to randomly sample from the space of rules, rather than exhaustively analyzing all possible rules, ... More

Noncommutativity inspired Black Holes as Dark Matter CandidateApr 17 2015May 30 2016We study a black hole with a blurred mass density instead of a singular one, which could be caused by the noncommutativity of 3-space. Depending on its mass, such object has either none, one or two event horizons. It possesses new properties, which become ... More

The degree of the Jacobian locus and the Schottky problemFeb 29 2004We show that the degree of the images of the moduli space of (principally polarized) abelian varieties A_g and of the moduli space of curves M_g in the projective space under the theta constant embedding are equal to the top self-intersection numbers ... More