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A Simple Hash Class with Strong Randomness Properties in Graphs and HypergraphsOct 31 2016We study randomness properties of graphs and hypergraphs generated by simple hash functions. Several hashing applications can be analyzed by studying the structure of $d$-uniform random ($d$-partite) hypergraphs obtained from a set $S$ of $n$ keys and ... More

Counting Zeros in Random Walks on the Integers and Analysis of Optimal Dual-Pivot QuicksortFeb 12 2016May 11 2016We present an average case analysis of two variants of dual-pivot quicksort, one with a non-algorithmic comparison-optimal partitioning strategy, the other with a closely related algorithmic strategy. For both we calculate the expected number of comparisons ... More

Dual-Pivot Quicksort: Optimality, Analysis and Zeros of Associated Lattice PathsNov 01 2016Nov 27 2017We present an average case analysis of a variant of dual-pivot quicksort. We show that the used algorithmic partitioning strategy is optimal, i.e., it minimizes the expected number of key comparisons. For the analysis, we calculate the expected number ... More

Optimal Partitioning for Dual-Pivot QuicksortMar 21 2013Oct 13 2015Dual-pivot quicksort refers to variants of classical quicksort where in the partitioning step two pivots are used to split the input into three segments. This can be done in different ways, giving rise to different algorithms. Recently, a dual-pivot algorithm ... More

Efficient Gauss Elimination for Near-Quadratic Matrices with One Short Random Block per Row, with ApplicationsJul 10 2019In this paper we identify a new class of sparse near-quadratic random Boolean matrices that have full row rank over $\mathbb{F}_2=\{0,1\}$ with high probability and can be transformed into echelon form in almost linear time by a simple version of Gauss ... More

Tight Lower Bounds for Greedy Routing in Higher-Dimensional Small-World GridsMay 06 2013We consider Kleinberg's celebrated small world graph model (Kleinberg, 2000), in which a D-dimensional grid {0,...,n-1}^D is augmented with a constant number of additional unidirectional edges leaving each node. These long range edges are determined at ... More

Succinct Data Structures for Retrieval and Approximate MembershipMar 26 2008The retrieval problem is the problem of associating data with keys in a set. Formally, the data structure must store a function f: U ->{0,1}^r that has specified values on the elements of a given set S, a subset of U, |S|=n, but may have any value on ... More

Towards Optimal Degree-distributions for Left-perfect Matchings in Random Bipartite GraphsMar 07 2012Apr 27 2012Consider a random bipartite multigraph $G$ with $n$ left nodes and $m \geq n \geq 2$ right nodes. Each left node $x$ has $d_x \geq 1$ random right neighbors. The average left degree $\Delta$ is fixed, $\Delta \geq 2$. We ask whether for the probability ... More

Dense Peelable Random Uniform HypergraphsJul 10 2019We describe a new family of $k$-uniform hypergraphs with independent random edges. The hypergraphs have a high probability of being peelable, i.e. to admit no sub-hypergraph of minimum degree $2$, even when the edge density (number of edges over vertices) ... More

On testing single connectedness in directed graphs and some related problemsDec 04 2014Mar 02 2015Let $G=(V,E)$ be a directed graph with $n$ vertices and $m$ edges. The graph $G$ is called singly-connected if for each pair of vertices $v,w \in V$ there is at most one simple path from $v$ to $w$ in $G$. Buchsbaum and Carlisle (1993) gave an algorithm ... More

How Good is Multi-Pivot Quicksort?Oct 15 2015May 31 2016Multi-Pivot Quicksort refers to variants of classical quicksort where in the partitioning step $k$ pivots are used to split the input into $k + 1$ segments. For many years, multi-pivot quicksort was regarded as impractical, but in 2009 a 2-pivot approach ... More

Explicit and Efficient Hash Families Suffice for Cuckoo Hashing with a StashApr 19 2012It is shown that for cuckoo hashing with a stash as proposed by Kirsch, Mitzenmacher, and Wieder (2008) families of very simple hash functions can be used, maintaining the favorable performance guarantees: with stash size $s$ the probability of a rehash ... More

A More Reliable Greedy Heuristic for Maximum Matchings in Sparse Random GraphsMar 19 2012We propose a new greedy algorithm for the maximum cardinality matching problem. We give experimental evidence that this algorithm is likely to find a maximum matching in random graphs with constant expected degree c>0, independent of the value of c. This ... More

Cuckoo Hashing with PagesApr 27 2011Although cuckoo hashing has significant applications in both theoretical and practical settings, a relevant downside is that it requires lookups to multiple locations. In many settings, where lookups are expensive, cuckoo hashing becomes a less compelling ... More

A Subquadratic Algorithm for 3XORApr 30 2018Given a set $X$ of $n$ binary words of equal length $w$, the 3XOR problem asks for three elements $a, b, c \in X$ such that $a \oplus b=c$, where $ \oplus$ denotes the bitwise XOR operation. The problem can be easily solved on a word RAM with word length ... More

Dual-Pivot Quicksort: Optimality, Analysis and Zeros of Associated Lattice PathsNov 01 2016We present an average case analysis of a variant of dual-pivot quicksort. We show that the used algorithmic partitioning strategy is optimal, i.e., it minimizes the expected number of key comparisons. For the analysis, we calculate the expected number ... More

Tight Bounds for Blind Search on the IntegersFeb 20 2008We analyze a simple random process in which a token is moved in the interval $A=\{0,...,n\$: Fix a probability distribution $\mu$ over $\{1,...,n\$. Initially, the token is placed in a random position in $A$. In round $t$, a random value $d$ is chosen ... More

Tight Thresholds for Cuckoo Hashing via XORSATDec 01 2009Dec 21 2010We settle the question of tight thresholds for offline cuckoo hashing. The problem can be stated as follows: we have n keys to be hashed into m buckets each capable of holding a single key. Each key has k >= 3 (distinct) associated buckets chosen uniformly ... More

A New Riemannian Setting for Surface RegistrationJun 03 2011Sep 19 2014We present a new approach for matching regular surfaces in a Riemannian setting. We use a Sobolev type metric on deformation vector fields which form the tangent bundle to the space of surfaces. In this article we compare our approach with the diffeomorphic ... More

Cosmologically inspired Kastor-Traschen solutionJul 29 2013Jan 25 2014Kastor-Traschen (KT) type solution in a cosmological set up is studied in this article. We examine a hybrid of a KT metric and a Friedmann-Robertson-Walker-Lemaitre (FRWL) solution. The problem is treated in a general number of dimensions D>=4 and we ... More

Thin static charged dust Majumdar-Papapetrou shells with high symmetry in D >= 4Feb 28 2012Apr 27 2012We present a systematical study of static D >= 4 space-times of high symmetry with the matter source being a thin charged dust hypersurface shell. The shell manifold is assumed to have the following structure S_(beta) X R^(D-2-beta), beta (in the interval ... More

On a generalization of Matérn hard-core processes with applications to max-stable processesSep 18 2017The Mat\'ern hard-core processes are classical examples for point process models obtained from (marked) Poisson point processes. Points of the original Poisson process are deleted according to a dependent thinning rule, resulting in a process whose points ... More

Quantum integrable Toda like systemsOct 14 1998Using deformation quantization and suitable 2 by 2 quantum $R$-matrices we show that a list of Toda like classical integrable systems given by Y.B.Suris is quantum integrable in the sense that the classical conserved quantities (which are already in involution ... More

Algorithmic Optimisations for Iterative Deconvolution MethodsApr 26 2013We investigate possibilities to speed up iterative algorithms for non-blind image deconvolution. We focus on algorithms in which convolution with the point-spread function to be deconvolved is used in each iteration, and aim at accelerating these convolution ... More

Open-closed modular operads, Cardy condition and string field theoryNov 26 2016We prove that the modular operad of diffeomorphism classes of Riemann surfaces with both `open' and `closed' boundary components, in the sense of string field theory, is the modular completion of its genus 0 part quotiented by the Cardy condition. We ... More

Neutralino Dark Matter and the CurvatonNov 30 2006Mar 09 2007We build a realistic model of curvaton cosmology, in which the energy content is described by radiation, WIMP dark matter and a curvaton component. We calculate the curvature and isocurvature perturbations, allowing for arbitrary initial density perturbations ... More

Ground States and Singular Vectors of Convex Variational Regularization MethodsNov 09 2012Singular value decomposition is the key tool in the analysis and understanding of linear regularization methods. In the last decade nonlinear variational approaches such as $\ell^1$ or total variation regularizations became quite prominent regularization ... More

A tight bound on the speed-up through storage for quickest multi-commodity flowsJun 18 2014Multi-commodity flows over time exhibit the non-intuitive property that letting flow wait can allow us to send flow faster overall. Fleischer and Skutella (IPCO~2002) show that the speed-up through storage is at most a factor of~$2$, and that there are ... More

On the representation of polyhedra by polynomial inequalitiesMar 26 2002Oct 24 2002A beautiful result of Br\"ocker and Scheiderer on the stability index of basic closed semi-algebraic sets implies, as a very special case, that every $d$-dimensional polyhedron admits a representation as the set of solutions of at most $d(d+1)/2$ polynomial ... More

Pebble Games and Linear EquationsApr 09 2012Mar 24 2015We give a new, simplified and detailed account of the correspondence between levels of the Sherali-Adams relaxation of graph isomorphism and levels of pebble-game equivalence with counting (higher-dimensional Weisfeiler-Lehman colour refinement). The ... More

I^K-convergenceSep 13 2011In this paper we introduce I^K-convergence which is a common generalization of the I^K-convergence of sequences, double sequences and nets. We show that many results that were shown before for these special cases are true for the I^K-convergence, too

Modern Regularization Methods for Inverse ProblemsJan 30 2018Regularization methods are a key tool in the solution of inverse problems. They are used to introduce prior knowledge and make the approximation of ill-posed (pseudo-)inverses feasible. In the last two decades interest has shifted from linear towards ... More

The asymptotics of an eigenfunction-correlation determinant for Dirac-$δ$ perturbationsMar 12 2015We prove the exact asymptotics of the scalar product of the ground states of two non-interacting Fermi gases confined to a $3$-dimensional ball $B_L$ of radius $L$ in the thermodynamic limit, where the underlying one-particle operators differ by a Dirac-$\delta$ ... More

Finite-size energy of non-interacting Fermi gasesJun 14 2014Feb 23 2016We prove the asymptotics of the difference of the ground-state energies of two non-interacting $N$-particle Fermi gases on the half line of length $L$ in the thermodynamic limit up to order $1/L$. We are particularly interested in subdominant terms proportional ... More

Target echo strength modelling at FOI, including results from the BeTSSi II workshopApr 08 2016An overview of the target echo strength (TS) modelling capacity at the Swedish Defense Research Agency (FOI) is presented. The modelling methods described range from approximate ones, such as raytracing and Kirchhoff approximation codes, to high accuracy ... More

Confluence of singularities in hypergeometric systemsNov 03 2015A system in a Birkhoff normal form with an irregular singularity of Poincare rank 1 at the origin and a regular singularity at infinity is through the Borel-Laplace transform dual to a system in an Okubo form. Schafke has showed that the Birkhoff system ... More

Necrotic tumor growth: an analytic approachApr 13 2011Apr 11 2012The present paper deals with a free boundary problem modeling the growth process of necrotic multi-layer tumors. We prove the existence of flat stationary solutions and determine the linearization of our model at such an equilibrium. Finally, we compute ... More

Software that Learns from its Own FailuresFeb 03 2015All non-trivial software systems suffer from unanticipated production failures. However, those systems are passive with respect to failures and do not take advantage of them in order to improve their future behavior: they simply wait for them to happen ... More

Was ist Unendlichkeit - und wenn ja, wie viele?Oct 17 2013This article, written in German language, gives a very elementary introduction to infinite sets. It is meant for interested non-mathematicians.

Non-Zeeman Circular Polarization of Molecular Maser Spectral LinesSep 04 2014We apply the anisotropic resonant scattering model developed to explain the presence of non-Zeeman circular polarization signals recently detected in the $^{12}\mathrm{CO}\;\left(J=2\rightarrow1\right)$ and $\left(J=1\rightarrow0\right)$ transitions in ... More

AdS twistors for higher spin theoryDec 19 2004We construct spectra of supersymmetric higher spin theories in D=4, 5 and 7 from twistors describing massless (super-)particles on AdS spaces. A massless twistor transform is derived in a geometric way from classical kinematics. Relaxing the spin-shell ... More

A Center-Symmetric 1/N ExpansionOct 26 2004Dec 13 2004The free energy of U(N) gauge theory is expanded about a center-symmetric topological background configuration with vanishing action and vanishing Polyakov loops. We construct this background for SU(N) lattice gauge theory and show that it uniquely describes ... More

Local Measure of Convex Surfaces induced by the Wiener Measure of PathsNov 10 2009The Wiener measure induces a measure of closed, convex, (d-1)-dimensional, Euclidean (hyper-)surfaces that are the convex hulls of closed d-dimensional Brownian bridges. I present arguments and numerical evidence that this measure, for odd d, is generated ... More

Pricing European Options in Realistic MarketsOct 06 2002We investigate the relation between the fair price for European-style vanilla options and the distribution of short-term returns on the underlying asset ignoring transaction and other costs. We compute the risk-neutral probability density conditional ... More

Influence of Tissue Geometry on Transversal RelaxationMay 27 2013With today's NMR techniques some microscopic geometry of tissue can still not be resolved directly. Often, there is also a specific off resonance field related to this geometry. In this work the impact of these off resonances on the transverse relaxation ... More

An interpolation theorem in toric varietiesDec 13 2006In the spirit of a theorem of Wood, we give necessary and sufficient conditions for a family of germs of analytic hypersurfaces in a smooth projective toric variety X to be interpolated by an algebraic hypersurface with a fixed class in the Picard group ... More

Pair production in classical Stueckelberg-Horwitz-Piron electrodynamicsApr 06 2016In this paper we calculate pair production from bremsstrahlung as a classical effect in Stueckelberg-Horwitz-Piron electrodynamics. In this framework, worldlines are traced out dynamically through the evolution of events $x^\mu(\tau)$ parameterized by ... More

A 2.542-Approximation for Precedence Constrained Single Machine Scheduling with Release Dates and Total Weighted Completion Time ObjectiveMar 15 2016Apr 21 2016We present a $\sqrt{e}/(\sqrt{e}-1)$-approximation algorithm for the nonpreemptive scheduling problem to minimize the total weighted completion time of jobs on a single machine subject to release dates and precedence constraints. The previously best known ... More

Thick domain walls and singular spacesFeb 05 2000Jul 17 2000We discuss thick domain walls interpolating between spaces with naked singularities and give arguments based on the $AdS$/CFT correspondence why such singularities may be physically meaningful. Our examples include thick domain walls with Minkowski, de ... More

Connected component identification and cluster update on GPUMay 29 2011Jun 12 2011Cluster identification tasks occur in a multitude of contexts in physics and engineering such as, for instance, cluster algorithms for simulating spin models, percolation simulations, segmentation problems in image processing, or network analysis. While ... More

Simulating spin models on GPUJun 19 2010Jun 07 2011Over the last couple of years it has been realized that the vast computational power of graphics processing units (GPUs) could be harvested for purposes other than the video game industry. This power, which at least nominally exceeds that of current CPUs ... More

Overconvergent subanalytic subsets in the framework of Berkovich spacesNov 28 2012Oct 29 2013We study the class of overconvergent subanalytic subsets of a $k$-affinoid space $X$ when $k$ is a non-archimedean field. These are the images along the projection $X \times B^n \to X$ of subsets defined with inequalities between functions of $X\times ... More

A Momentous Arrow of TimeOct 16 2009Quantum cosmology offers a unique stage to address questions of time related to its underlying (and perhaps truly quantum dynamical) meaning as well as its origin. Some of these issues can be analyzed with a general scheme of quantum cosmology, others ... More

Large scale effective theory for cosmological bouncesAug 21 2006Mar 27 2007An exactly solvable bounce model in loop quantum cosmology is identified which serves as a perturbative basis for realistic bounce scenarios. Its bouncing solutions are derived analytically, demonstrating why recent numerical simulations robustly led ... More

Quantum CosmologyMar 28 2006Quantum cosmology in general denotes the application of quantum physics to the whole universe and thus gives rise to many realizations and examples, covering problems at different mathematical and conceptual levels. It is related to quantum gravity and ... More

Loop Quantum CosmologyJan 20 2006Quantum gravity is expected to be necessary in order to understand situations where classical general relativity breaks down. In particular in cosmology one has to deal with initial singularities, i.e. the fact that the backward evolution of a classical ... More

(Loop) quantum gravity and the inflationary scenarioSep 06 2015Quantum gravity, as a fundamental theory of space-time, is expected to reveal how the universe may have started, perhaps during or before an inflationary epoch. It may then leave a potentially observable (but probably minuscule) trace in cosmic large-scale ... More

Mathematical Structure of Loop Quantum Cosmology: Homogeneous ModelsJun 26 2012Dec 30 2013The mathematical structure of homogeneous loop quantum cosmology is analyzed, starting with and taking into account the general classification of homogeneous connections not restricted to be Abelian. As a first consequence, it is seen that the usual approach ... More

Quantum nature of cosmological bouncesJan 25 2008Several examples are known where quantum gravity effects resolve the classical big bang singularity by a bounce. The most detailed analysis has probably occurred for loop quantum cosmology of isotropic models sourced by a free, massless scalar. Once a ... More

Quantum gravity and cosmological observationsJan 26 2007Quantum gravity places entirely new challenges on the formulation of a consistent theory as well as on an extraction of potentially observable effects. Quantum corrections due to the gravitational field are commonly expected to be tiny because of the ... More

Quantum Geometry and its Implications for Black HolesJul 28 2006General relativity successfully describes space-times at scales that we can observe and probe today, but it cannot be complete as a consequence of singularity theorems. For a long time there have been indications that quantum gravity will provide a more ... More

Inflation from Quantum GeometryJun 18 2002Quantum geometry predicts that a universe evolves through an inflationary phase at small volume before exiting gracefully into a standard Friedmann phase. This does not require the introduction of additional matter fields with ad hoc potentials; rather, ... More

Isotropic Loop Quantum CosmologyFeb 21 2002Isotropic models in loop quantum cosmology allow explicit calculations, thanks largely to a completely known volume spectrum, which is exploited in order to write down the evolution equation in a discrete internal time. Because of genuinely quantum geometrical ... More

Loop Quantum Cosmology III: Wheeler-DeWitt OperatorsAug 22 2000In the framework of loop quantum cosmology anomaly free quantizations of the Hamiltonian constraint for Bianchi class A, locally rotationally symmetric and isotropic models are given. Basic ideas of the construction in (non-symmetric) loop quantum gravity ... More

Loop Quantum Cosmology I: KinematicsOct 28 1999The framework of quantum symmetry reduction is applied to loop quantum gravity with respect to transitively acting symmetry groups. This allows to test loop quantum gravity in a large class of minisuperspaces and to investigate its features - e.g. the ... More

Bounds for the Hilbert function of polynomial ideals and for the degrees in the NullstellensatzOct 04 1996We present a new effective Nullstellensatz with bounds for the degrees which depend not only on the number of variables and on the degrees of the input polynomials but also on an additional parameter called the {\it geometric degree of the system of equations}. ... More

Spin chains and string theoryNov 23 2003Apr 14 2004Recently, an impressive agreement was found between anomalous dimensions of certain operators in N=4 SYM and rotating strings with two angular momenta in the bulk of AdS5xS5. A one-loop field theory computation, which involves solving a Heisenberg chain ... More

Planar diagrams in light-cone gaugeMar 27 2006Oct 20 2006We consider the open string vacuum amplitude determining the interaction between a stack of N D3-branes and a single probe brane. When using light cone gauge, it is clear that the sum of planar diagrams (relevant in the large-N limit) is described by ... More

Supergravity backgrounds corresponding to D7 branes wrapped on Kahler manifoldsOct 24 2003Nov 05 2003We consider supergravity solutions corresponding to D7 branes wrapped on Kahler manifolds with a U(1)_R twist such that some supersymmetry is preserved. We find a class of 1/4-BPS backgrounds where a D7-brane is wrapped on a T^2 torus with a metric of ... More

Compressing Word EmbeddingsNov 19 2015May 16 2016Recent methods for learning vector space representations of words have succeeded in capturing fine-grained semantic and syntactic regularities using vector arithmetic. However, these vector space representations (created through large-scale text analysis) ... More

The stability of late-type stars close to the Eddington limitOct 15 1997Super-Eddington luminosities in hydrostatic model atmospheres manifest themselves by the presence of gas pressure inversions. Such inversions are not an artifact of the assumption of hydrostatic equilibrium but can also be present in hydrodynamical model ... More

Scalar mesons and polarizability of the nucleonMar 07 2008It is shown that the scalar mesons $\sigma$, $f_0(980)$ and $a_0(980)$ as $t$-channel exchanges quantitatively solve the problem of diamagnetism and give an explanation of the large missing part of the electric polarizability $\alpha$ showing up when ... More

Dispersion theory of nucleon polarizabilities and outlook on chiral effective field theoryJul 08 2013Jul 10 2014Based on Compton scattering and meson photoproduction data the polarizabilities of the nucleon are precisely studied and well understood due to recent experimental and theoretical work based on nonsubtracted dispersion relations. The {\it recommended} ... More

Constraints on variations of m$_\mathrm{p}$/m$_\mathrm{e}$ based on UVES observations of H$_2$Oct 30 2013This article summarizes the latest results on the proton-to-electron mass ratio $\mu$ derived from H$_2$ observations at high redshift in the light of possible variations of fundamental physical constants. The focus lies on UVES observations of the past ... More

Symmetric orthogonality and contractive projections in metric spacesApr 07 2016In this paper known result of symmetric orthogonality, as introduced by G. Birkhoff, and contractive nearest point projections from the linear are extended to the metric setting. If the space has non-positive curvature in the sense Pedersen or Busemann ... More

A Note on Lipschitz Continuity of Solutions of Poisson Equations in Metric Measure SpacesJul 08 2013Jul 17 2013In this note we show how to adjust some proofs of Koskela et. al 2003 and Jiang 2011 in order to show that in certain spaces $(X,d,\mu)$, like $RCD(K,N)$-spaces, every Sobolev function with local $L^{p}$-Laplacian and $p>\dim\mu$ is locally Lipschitz ... More

q-heat flow and the gradient flow of the Renyi entropy in the p-Wasserstein spaceJan 04 2014Based on the idea of a recent paper by Ambrosio-Gigli-Savar\'e in Invent. Math. (2013), we show that flow of the $q$-Cheeger energy, called $q$-heat flow, solves the gradient flow problem of the Renyi entropy functional in the $p$-Wasserstein. For that, ... More

Symplectic quotients by a nonabelian group and by its maximal torusJan 01 2000This paper examines the relationship between the symplectic quotient X//G of a Hamiltonian G-manifold X, and the associated symplectic quotient X//T, where T is a maximal torus, in the case in which X//G is a compact manifold or orbifold. The three main ... More

Observing the molecular composition of galaxiesAug 20 2009The recent availability of wideband receivers and high sensitivity instruments in the mm and submm wavelengths has opened the possibility of studying in detail the chemistry of the interstellar medium in extragalactic objects. Within the central few hundred ... More

Semiclassical Transition from an Elliptical to an Oval BilliardNov 14 1996Semiclassical approximations often involve the use of stationary phase approximations. This method can be applied when $\hbar$ is small in comparison to relevant actions or action differences in the corresponding classical system. In many situations, ... More

Random sets and exact confidence regionsFeb 08 2013Oct 15 2013An important problem in statistics is the construction of confidence regions for unknown parameters. In most cases, asymptotic distribution theory is used to construct confidence regions, so any coverage probability claims only hold approximately, for ... More

Design of a technique to measure the density of ultracold atoms in a short-period optical lattice in three dimensions with single atom sensitivityNov 25 2010Mar 22 2011A measurement technique is described which has the potential to map the atomic site occupancies of ultracold atoms in a short-period three-dimensional optical lattice. The method uses accordion and pinning lattices, together with polarization gradient ... More

Real Computation with Least Discrete Advice: A Complexity Theory of Nonuniform ComputabilityNov 24 2008Sep 02 2009It is folklore particularly in numerical and computer sciences that, instead of solving some general problem f:A->B, additional structural information about the input x in A (that is any kind of promise that x belongs to a certain subset A' of A) should ... More

Effectively Open Real FunctionsJan 12 2005Jun 17 2005A function f is continuous iff the PRE-image f^{-1}[V] of any open set V is open again. Dual to this topological property, f is called OPEN iff the IMAGE f[U] of any open set U is open again. Several classical Open Mapping Theorems in Analysis provide ... More

Physically-Relativized Church-Turing HypothesesMay 09 2008We turn `the' Church-Turing Hypothesis from an ambiguous source of sensational speculations into a (collection of) sound and well-defined scientific problem(s): Examining recent controversies, and causes for misunderstanding, concerning the state of the ... More

Finiteness results for Teichmueller curvesSep 04 2005We show that for each genus there are only finitely many algebraically primitive Teichmueller curves C, such that i) C lies in the hyperelliptic locus and ii) C is generated by an abelian differential with two zeros of order g-1. We prove moreover that ... More

Prym covers, theta functions and Kobayashi curves in Hilbert modular surfacesNov 10 2011Algebraic curves in Hilbert modular surfaces that are totally geodesic for the Kobayashi metric have very interesting geometric and arithmetic properties, e.g. they are rigid. There are very few methods known to construct such algebraic geodesics that ... More

Quasar Structure Emerges from the Three Forms of Radiation PressureJan 17 2012All quasar spectra show the same atomic features in the optical, UV, near-IR and soft X-rays over all of cosmic time, luminosity black hole mass and accretion rate. This is a puzzle. Here I show that it is possible that all of these atomic features can ... More

Type 1 AGN UnificationSep 27 2001The model I recently proposed for the structure of quasars offers to unify the many aspects of Type 1 AGN: emission lines, absorption lines and reflection features. This makes the model heavily overconstrained by observation and readily tested. Here I ... More

Hypermodular Self-Assembling Space Solar Power -- Design Option for Mid-Term GEO Utility-Scale Power PlantsNov 18 2013Nov 23 2013This paper presents a design for scaleable space solar power systems based on free-flying reflectors and module self-assembly. Lower system cost of utility-scale space solar power is achieved by design independence of yet-to-be-built in-space assembly ... More

An exact result concerning the $1/f$ noise contribution to the large-angle error in CMB temperature and polarization mapsFeb 26 2016Feb 29 2016We present an exact expression for the $1/f$ contribution to the noise of the CMB temperature and polarization maps for a survey in which the scan pattern is isotropic. The result for polarization applies likewise to surveys with and without a rotating ... More

Fluctuation Kinetics in a Multispecies Reaction-Diffusion SystemOct 11 1995We study fluctuation effects in a two species reaction-diffusion system, with three competing reactions $A+A\rightarrow\emptyset$, $B+B\rightarrow\emptyset$, and $A+B\rightarrow\emptyset$. Asymptotic density decay rates are calculated for $d\leq 2$ using ... More

UV, optical and near-IR diagnostics of massive starsOct 26 2010We present an overview of a few spectroscopic diagnostics of massive stars. We explore the following wavelength ranges: UV (1000 to 2000 A), optical (4000--7000 A) and near-infrared (mainly H and K bands). The diagnostics we highlight are available in ... More

Square root voting in the Council of the European Union: Rounding effects and the Jagiellonian CompromiseDec 17 2007May 19 2008In recent years, enlargement of the European Union has brought with it renewed discussion of voting arrangements in the Council of the EU. During these negotiations, the Polish government proposed a voting scheme that gives each country a voting weight ... More

Geometrical origins of contractility in disordered actomyosin networksJul 24 2014Movement within eukaryotic cells largely originates from localized forces exerted by myosin motors on scaffolds of actin filaments. Although individual motors locally exert both contractile and extensile forces, large actomyosin structures at the cellular ... More

Local Langlands Duality and a Duality of Conformal Field TheoriesJun 01 2015We show that the numerical local Langlands duality for GL_n and the T - duality of two-dimensional quantum gravity arise from one and the same symmetry principle. The unifying theme is that the local Fourier transform in both its l-adic and complex incarnation ... More

Duality of 2D gravity as a local Fourier dualityMay 22 2014May 07 2015The p - q duality is a relation between the (p,q) model and the (q,p) model of two-dimensional quantum gravity. Geometrically this duality corresponds to a relation between the two relevant points of the Sato Grassmannian. Kharchev and Marshakov have ... More

Constraints on the tachyon condensate from anomalous symmetriesNov 27 2000Using anomalous symmetries of the cubic string field theory vertex we derive set of relations between the coefficients of the tachyon condensate. They are in agreement with the results obtained from level truncation approximation.

Mapping of Parent Hamiltonians: from Abelian and non-Abelian Quantum Hall States to Exact Models of Critical Spin ChainsSep 28 2011This monograph introduces an exact model for a critical spin chain with arbitrary spin S, which includes the Haldane--Shastry model as the special case S=1/2. While spinons in the Haldane--Shastry model obey abelian half-fermi statistics, the spinons ... More

Confinement in a Quantum MagnetNov 24 2009The elementary excitations of a state of matter consisting of large collection of interacting particles can be very different from the original particles. In the most interesting examples, the particles effectively decompose into smaller constituent particles, ... More