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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

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

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

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

Randomness Conservation over AlgorithmsJul 11 2013Oct 14 2013Current discrete randomness and information conservation inequalities are over total recursive functions, i.e. restricted to deterministic processing. This restriction implies that an algorithm can break algorithmic randomness conservation inequalities. ... 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

Sets Have Simple MembersJul 07 2011Mar 20 2014The combined Universal Probability M(D) of strings x in sets D is close to max M({x}) over x in D: their ~logs differ by at most D's information j=I(D:H) about the halting sequence H. Thus if all x have complexity K(x) >k, D carries >i bits of information ... More

Morse theory for the uniform energySep 29 2016In this paper we develop a Morse theory for the uniform energy. We use the one-sided directional derivative of the distance function to study the minimizing properties of variations through closed geodesics. This derivative is then used to define a one-sided ... More

Analytical Design of Printed-Circuit-Board (PCB) Metagratings for Perfect Anomalous ReflectionJan 14 2018We present an analytical scheme for the design of realistic metagratings for wide-angle engineered reflection. These recently proposed planar structures can reflect an incident plane wave into a prescribed (generally non-specular) angle with very high ... More

Subelliptic Spin_c Dirac operators, III The Atiyah-Weinstein conjectureJul 26 2005May 11 2007In this paper we show that there is a well defined modified dbar-Neumann problem for a spin_c manifold with a strictly pseudoconvex boundary (in the contact geometry sense). We show that the index of the associated boundary value problem can be computed ... More

Subelliptic SpinC Dirac Operators, IV Proof of the Relative Index ConjectureMar 25 2012We prove the relative index conjecture, which in turn implies that the set of embeddable deformations of a strictly pseudoconvex CR-structure on a compact 3-manifold is closed in the C\infty-topology.

Hilbert-Kunz multiplicity of products of idealsDec 31 2015Feb 26 2016We give bounds for the Hilbert-Kunz multiplicity of the product of two ideals, and we characterize the equality in terms of the tight closures of the ideals. Connections are drawn with $*$-spread and with ordinary length calculations.

Algorithmic Problems in Amalgams of Finite Groups: Conjugacy and Intersection PropertiesJul 02 2007Geometric methods proposed by Stallings for treating finitely generated subgroups of free groups were successfully used to solve a wide collection of decision problems for free groups and their subgroups. In the present paper we employ the generalized ... More

Stallings' Foldings and Subgroups of Amalgams of Finite GroupsMay 05 2007In the 1980's Stallings showed that every finitely generated subgroup of a free group is canonically represented by a finite minimal immersion of a bouquet of circles. In terms of the theory of automata, this is a minimal finite inverse automaton. This ... More

Generalized selfish bin packingFeb 18 2012Standard bin packing is the problem of partitioning a set of items with positive sizes no larger than 1 into a minimum number of subsets (called bins) each having a total size of at most 1. In bin packing games, an item has a positive weight, and given ... More

Reading Off Kurosh DecompositionsJun 01 2007Jul 04 2007Geometric methods proposed by Stallings for treating finitely generated subgroups of free groups were successfully used by many authors to solve a wide collection of decision problems for free groups and their subgroups. In the present paper we employ ... More

Algorithmic Problems in Amalgams of Finite GroupsMay 05 2007Jul 02 2007Geometric methods proposed by Stallings for treating finitely generated subgroups of free groups were successfully used to solve a wide collection of decision problems for free groups and their subgroups. It turns out that Stallings' methods can be effectively ... More

Starquake-Induced Glitches in PulsarsJan 21 2000The neutron star crust is rigid material floating on a neutron-proton liquid core. As the star's spin rate slows, the changing stellar shape stresses the crust and causes fractures. These starquakes may trigger pulsar glitches as well as the jumps in ... More

Parametric packing of selfish items and the subset sum algorithmJul 24 2009The subset sum algorithm is a natural heuristic for the classical Bin Packing problem: In each iteration, the algorithm finds among the unpacked items, a maximum size set of items that fits into a new bin. More than 35 years after its first mention in ... More

On the convergence of local expansions of layer potentialsDec 17 2012Apr 22 2013In a recently developed quadrature method (quadrature by expansion or QBX), it was demonstrated that weakly singular or singular layer potentials can be evaluated rapidly and accurately on surface by making use of local expansions about carefully chosen ... More

Frictional Heating and Neutron Star Thermal EvolutionApr 24 1994Feb 04 1995Differential rotation between the neutron star crust and a more rapidly rotating interior superfluid leads to frictional heating that affects the star's long-term thermal evolution and resulting surface emission. Here we present the results of thermal ... More

Social Conformity Despite Individual Preferences for DistinctivenessJul 29 2014Feb 11 2015We demonstrate that individual behaviors directed at the attainment of distinctiveness can in fact produce complete social conformity. We thus offer an unexpected generative mechanism for this central social phenomenon. Specifically, we establish that ... More

Superstring scattering amplitudes in higher genusMar 24 2008May 20 2008In this paper we continue the program pioneered by D'Hoker and Phong, and recently advanced by Cacciatori, Dalla Piazza, and van Geemen, of finding the chiral superstring measure by constructing modular forms satisfying certain factorization constraints. ... More

The defect recollement, the MacPherson-Vilonen construction, and pp formulasAug 19 2018Dec 23 2018For 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

A Contractive Approach to Separable Lyapunov Functions for Monotone SystemsApr 13 2017Oct 24 2017Monotone systems preserve a partial ordering of states along system trajectories and are often amenable to separable Lyapunov functions that are either the sum or the maximum of a collection of functions of a scalar argument. In this paper, we consider ... More

Gravity and decoherence: the double slit experiment revisitedJun 14 2017Jan 29 2018The double slit experiment is iconic and widely used in classrooms to demonstrate the fundamental mystery of quantum physics. The puzzling feature is that the probability of an electron arriving at the detector when both slits are open is not the sum ... More

On Contact Numbers of Finite Lattice Sphere Packings and the Maximal Coordination of Monatomic CrystalsFeb 06 2016We algorithmically characterize the maximal contact number problem for finite congruent lattice sphere packings in $\mathbb{R}^d$ and show that in $\mathbb{R}^3$ this problem is equivalent to determining the maximal coordination of a monatomic crystal. ... More

Higher abelian Dijkgraaf-Witten theoryFeb 16 2015Jul 06 2016Dijkgraaf-Witten theories are quantum field theories based on (form degree 1) gauge fields valued in finite groups. We describe their generalization based on $p$-form gauge fields valued in finite abelian groups, as field theories extended to codimension ... More

The classification of torsion-free abelian groups of finite rank up to isomorphism and up to quasi-isomorphismFeb 07 2009The isomorphism and quasi-isomorphism relations on the $p$-local torsion-free abelian groups of rank $n\geq3$ are incomparable with respect to Borel reducibility.

Some Notes on Temporal Justification LogicOct 25 2015Justification logics are modal-like logics with the additional capability of recording the reason, or justification, for modalities in syntactic structures, called justification terms. Justification logics can be seen as explicit counterparts to modal ... More

Graphes, moyennabilité et bas du spectre de variétés topologiquement infiniesJan 14 2010From a graph $G$ with constant valency $v$ and a (non-compact) manifold $C$ with $v$ boundary components, we build a $G$-periodic manifold $M$. This process gives a class of topologically infinite manifolds which generalizes periodic manifolds and includes ... More

Generic metrics, eigenfunctions and riemannian coverings of non compact manifoldsJan 14 2010Let $(M,g)$ be a non-compact riemannian $n$-manifold with bounded geometry at order $k\geq\frac{n}{2}$. We show that if the spectrum of the Laplacian starts with $q+1$ discrete eigenvalues isolated from the essential spectrum, and if the metric is generic ... More

A type of simulation which some experimental evidence suggests we don't live inJul 03 2018Do we live in a computer simulation? I will present an argument that the results of a certain experiment constitute empirical evidence that we do not live in, at least, one type of simulation. The type of simulation ruled out is very specific. Perhaps ... More

Global gravitational anomaly cancellation for five-branesOct 08 2013Nov 07 2014We show that the global mixed gauge-gravitational anomaly of the worldvolume theory of the M5-brane vanishes, when the anomaly inflow from the bulk is taken into account. This result extends to the type IIA and heterotic $E_8 \times E_8$ five-branes. ... More

Some criteria for the symmetry of stratified water wavesMar 05 2009This paper considers two-dimensional stably stratified steady periodic gravity water waves with surface profiles monotonic between crests and troughs. We provide sufficient conditions under which such waves are necessarily symmetric. This is done by first ... More

Modified algebraic Bethe ansatz for XXZ chain on the segment - I - triangular casesAug 20 2014Jan 16 2015The modified algebraic Bethe ansatz, introduced by Cramp\'e and the author [8], is used to characterize the spectral problem of the Heisenberg XXZ spin-$\frac{1}{2}$ chain on the segment with lower and upper triangular boundaries. The eigenvalues and ... More

Construction of solutions of the defocusing nonlinear Schrödinger equation with asymptotically time-periodic boundary valuesJul 03 2019We study the defocusing nonlinear Schr\"odinger equation in the quarter plane with asymptotically periodic boundary values. By studying an associated Riemann-Hilbert problem and employing nonlinear steepest descent arguments, we construct solutions in ... More

Regular Totally Separable Sphere PackingsJun 06 2015The topic of totally separable sphere packings is surveyed with a focus on regular constructions, uniform tilings, and contact number problems. An enumeration of all regular totally separable sphere packings in $\mathbb{R}^2$, $\mathbb{R}^3$, and $\mathbb{R}^4$ ... More

A Small Model for the Cohomology of Some Principal BundlesSep 25 2013Let G be a compact, connected and simply connected Lie group, and {\Omega}G the space of the loops in G based at the identity. This note shows a way to compute the cohomology of the total space of a principal {\Omega}G-bundle over a manifold M, from the ... More

Duality and contravariant functors in the representation theory of artin algebrasMar 18 2016Feb 23 2017We know that the 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 $R\textbf{-Mod}\to\textbf{Ab}$ ... More

Hamiltonian anomalies from extended field theoriesOct 27 2014Jan 10 2019We 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

On Generalizing a Temporal Formalism for Game Theory to the Asymptotic Combinatorics of S5 Modal FramesMay 01 2013A temporal-theoretic formalism for understanding game theory is described where a strict ordering relation on a set of time points $T$ defines a game on $T$. Using this formalism, a proof of Zermelo's Theorem, which states that every finite 2-player zero-sum ... More

A gluing theorem for negatively curved complexesOct 09 2015Jul 09 2016A simplicial complex is called negatively curved if all its simplices are isometric to simplices in hyperbolic space, and it satisfies Gromov's Link Condition. We prove that, subject to certain conditions, a compact graph of spaces whose vertex spaces ... More

Dynamics on dendrites with closed endpoint setsJul 03 2019We construct dendrites with endpoint sets isometric to any totally disconnected compact metric space. This allows us to embed zero-dimensional dynamical systems into dendrites and solve a problem regarding Li-Yorke and distributional chaos.

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

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

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

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

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

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 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

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

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 $d>2$.

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

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

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

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

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.

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

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