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Steiner triangular drop dynamicsJun 11 2019Steiner's circumellipse is the unique regularization of any triangle to a circumscribed ellipse with the same centroid, a regularization that motivates our introduction of the Steiner triangle as a minimal model of a liquid droplet. The center of mass ... More

On the free Gamma distributionsFeb 15 2013For each positive number $\alpha$ we study the analog $\nu_alpha$ in free probability of the classical Gamma distribution with parameter $\alpha$. We prove that $\nu_\alpha$ is absolutely continuous and establish the main properties of the density, including ... More

Can Planck-scale physics be seen in the cosmic microwave background ?Jul 01 2003We investigate the potential of observations of anisotropies in the cosmic microwave background (CMB) and large-scale structure in the Universe to detect possible modifications of standard inflationary models by physics beyond the Planck scale. A generic ... More

Volume Scavenging of Networked DropletsAug 13 2018A system of N spherical-cap fluid droplets protruding from circular openings on a plane is connected through channels. This system is governed by surface tension acting on the droplets and viscous stresses inside the fluid channels. The fluid rheology ... More

The winner takes all: Volume-scavenging populations of networked dropletsAug 13 2018Feb 15 2019In this work we present and analyze a fluid-mechanical model of competition (scavenging) amongst $N$ liquid droplets (individual competitors). The eventual outcome of this competition depends sensitively on the average resource (volume) per individual ... More

Dynamics of sessile drops. Part 3. Theory of forced oscillationsMay 17 2016A partially-wetting sessile drop is driven by a sinusoidal pressure field that produces capillary waves on the liquid/gas interface. The analysis presented in Part 1 of this series (Bostwick & Steen 2014) is extended by computing response diagrams and ... More

Assessing the consistency of community structure in complex networksMay 31 2011Aug 02 2011In recent years, community structure has emerged as a key component of complex network analysis. As more data has been collected, researchers have begun investigating changing community structure across multiple networks. Several methods exist to analyze ... More

Excited Sessile Drops Dance HarmonicallyOct 10 2013Oct 16 2013In our fluid dynamics video, we demonstrate our method of visualizing and identifying various mode shapes of mechanically oscillated sessile drops. By placing metal mesh under an oscillating drop and projecting light from below, the drop's shape is visualized ... More

Restrictions and extensions of semibounded operatorsMar 06 2012We study restriction and extension theory for semibounded Hermitian operators in the Hardy space of analytic functions on the disk D. Starting with the operator zd/dz, we show that, for every choice of a closed subset F in T=bd(D) of measure zero, there ... More

Comparison of exit moment spectra for extrinsic metric ballsSep 07 2010We prove explicit upper and lower bounds for the $L^1$-moment spectra for the Brownian motion exit time from extrinsic metric balls of submanifolds $P^m$ in ambient Riemannian spaces $N^{n}$. We assume that $P$ and $N$ both have controlled radial curvatures ... More

p-Capacity and p-hyperbolicity of submanifoldsOct 31 2006We use drifted Brownian motion in warped product model spaces as comparison constructions to show $p$-hyperbolicity of a large class of submanifolds for $p\ge 2$. The condition for $p$-hyperbolicity is expressed in terms of upper support functions for ... More

Winning Cores in Parity GamesFeb 05 2016We introduce the novel notion of winning cores in parity games and develop a deterministic polynomial-time under-approximation algorithm for solving parity games based on winning core approximation. Underlying this algorithm are a number properties about ... More

Local Operator Multipliers and PositivityJun 18 2012We establish an unbounded version of Stinespring's Theorem and a lifting result for Stinespring representations of completely positive modular maps defined on the space of all compact operators. We apply these results to study positivity for Schur multipliers. ... More

Cotorsion torsion triples and the representation theory of filtered hierarchical clusteringApr 15 2019We give a full classification of representation types of the subcategories of representations of an $m \times n$ rectangular grid with monomorphisms (dually, epimorphisms) in one or both directions, which appear naturally in the context of clustering ... More

The Modular X- and Gamma-Ray Sensor (MXGS)of the ASIM Payload on the International Space StationJun 25 2019The Modular X- and Gamma-ray Sensor (MXGS) is an imaging and spectral X- and Gamma-ray instrument mounted on the starboard side of the Columbus module on the International Space Station. Together with the Modular Multi-Spectral Imaging Assembly (MMIA) ... More

Cosmological mass limits on neutrinos, axions, and other light particlesDec 11 2003Apr 16 2004The small-scale power spectrum of the cosmological matter distribution together with other cosmological data provides a sensitive measure of the hot dark matter fraction, leading to restrictive neutrino mass limits. We extend this argument to generic ... More

Imprint of Sterile Neutrinos in the Cosmic Microwave Background RadiationMay 17 1998Nov 04 1998The existence of low-mass sterile neutrinos is suggested by the current status of solar and atmospheric neutrinos together with the LSND experiment. In typical four-flavor scenarios, neutrinos would contribute to a cosmic hot dark matter component and ... More

Control of ribosome traffic by position-dependent choice of synonymous codonsSep 04 2013Messenger RNA encodes a sequence of amino acids by using codons. For most amino acids there are multiple synonymous codons that can encode the amino acid. The translation speed can vary from one codon to another, thus there is room for changing the ribosome ... More

How large are the spectral gaps?Apr 08 2001Let $D$ be a bounded domain in ${\Bbb R}^n$ whose boundary has a Minkowski dimension $\alpha<n$. Suppose that $E_{\Lambda}= {\{e^{2 \pi i x \cdot \lambda}\}}_{\lambda \in \Lambda}$, $\Lambda$ an infinite discrete subset of ${\Bbb R}^n$, is a frame of ... More

Nucleosynthesis and the mass of the tau neutrinoMar 01 1996The primordial abundance of long-lived heavy Majorana neutrinos is calculated from the full Boltzmann equation. Inclusion of scattering reactions drastically change the predicted abundance of a heavy neutrino species. This loosens the well known mass ... More

Elements of a Theory of SimulationApr 10 1995Unlike computation or the numerical analysis of differential equations, simulation does not have a well established conceptual and mathematical foundation. Simulation is an arguable unique union of modeling and computation. However, simulation also qualifies ... More

Cosmological constraints on the dark energy equation of state and its evolutionJul 13 2004Jul 19 2004We have calculated constraints on the evolution of the equation of state of the dark energy, w(z), from a joint analysis of data from the cosmic microwave background, large scale structure and type-Ia supernovae. In order to probe the time-evolution of ... More

Probing the dark side: Constraints on the dark energy equation of state from CMB, large scale structure and Type Ia supernovaeMay 07 2002Aug 31 2002We have reanalysed constraints on the equation of state parameter, w_Q = P/rho, of the dark energy, using several cosmological data sets and relaxing the usual constraint w_Q > -1. We find that combining Cosmic Microwave Background, large scale structure ... More

On the denominators of Young's seminormal basisApr 27 2009Feb 16 2010We study the seminormal basis ${f\_t}$ for the Specht modules of the Iwahori-Hecke algebra $\cal H\_{q,n}$ of type $A_{n-1}$. We focus on the base change coefficients between the seminormal basis ${f\_t}$ and Young's natural basis ${e\_t}$ with emphasis ... More

Dark matter density profiles from the Jeans equationMay 19 2004Jul 12 2004We make a simple analytical study of radial profiles of dark matter structures, with special attention to the question of the central radial density profile. We let our theoretical assumptions be guided by results from numerical simulations, and show ... More

The Higher-Order Prover Leo-III (Extended Version)Feb 08 2018Apr 19 2018The automated theorem prover Leo-III for classical higher-order logic with Henkin semantics and choice is presented. Leo-III is based on extensional higher-order paramodulation and accepts every common TPTP dialect (FOF, TFF, THF), including their recent ... More

Grid Based Linear Neutrino Perturbations in Cosmological N-body SimulationsDec 17 2008We present a novel, fast and precise method for including the effect of light neutrinos in cosmological N-body simulations. The effect of the neutrino component is included by using the linear theory neutrino perturbations in the calculation of the gravitational ... More

Supernova Neutrino Opacity from Nucleon-Nucleon Bremsstrahlung and Related ProcessesNov 12 1997May 26 1998Elastic scattering on nucleons, \nu N -> N \nu, is the dominant supernova (SN) opacity source for \mu and \tau neutrinos. The dominant energy- and number-changing processes were thought to be \nu e^- -> e^- \nu and \nu\bar \nu <-> e^+ e^- until Suzuki ... More

Neutrinos secretly converting to lighter particles to please both KATRIN and the cosmosOct 08 2015Within the framework of the Standard Model of particle physics and standard cosmology, observations of the Cosmic Microwave Background (CMB) and Baryon Acoustic Oscillations (BAO) set stringent bounds on the sum of the masses of neutrinos. If these bounds ... More

Cosmological N-body simulations with generic hot dark matterMay 31 2017We have calculated the non-linear effects of generic fermionic and bosonic hot dark matter components in cosmological N-body simulations. For sub-eV masses, the non-linear power spectrum suppression caused by thermal free-streaming resembles the one seen ... More

Strong generators in tensor triangulated categoriesSep 02 2014We show that in an essentially small rigid tensor triangulated category with connected Balmer spectrum there are no proper non-zero thick tensor ideals admitting strong generators. This proves, for instance, that the category of perfect complexes over ... More

Some remarks on Ext groupsMay 25 2009May 27 2009We calculate certain ext-groups between modules for a linear algebraic group. The results are in agreement with the Lusztig conjecture.

Optimal prior for Bayesian inference in a constrained parameter spaceOct 24 2017Feb 22 2019Bayesian parameter inference depends on a choice of prior probability distribution for the parameters in question. The prior which makes the posterior distribution maximally sensitive to data is called the Jeffreys prior, and it is completely determined ... More

A q-Analogue of Kempf's vanishing theoremMay 03 2009We use deep properties of Kashiwara's crystal basis to show that the induction functor $ {H}^0 (-) $ introduced by Andersen, Polo and Wen satisfies an analogon of Kempf's vanishing Theorem.

Extrinsic Isoperimetric Analysis on Submanifolds with Curvatures Bounded from BelowAug 31 2007We obtain upper bounds for the isoperimetric quotients of extrinsic balls of submanifolds in ambient spaces which have a lower bound on their radial sectional curvatures. The submanifolds are themselves only assumed to have lower bounds on the radial ... More

Curvature, triameter, and beyondOct 01 1992In its most general form, the recognition problem in Riemannian geometry asks for the identification of an unknown Riemannian manifold via measurements of metric invariants on the manifold. We introduce a new infinite sequence of invariants, the first ... More

Unimodality of the freely selfdecomposable probability lawsSep 26 2013Jan 07 2015We show that any freely selfdecomposable probability law is unimodal. This is the free probabilistic analog of Yamazato's result in [Ann. Probab. 6 (1978), 523-531].

Extraction of cluster parameters from Sunyaev-Zeldovich effect observations with simulated annealing optimizationOct 06 2003We present a user-friendly tool for the analysis of data from Sunyaev-Zeldovich effect observations. The tool is based on the stochastic method of simulated annealing, and allows the extraction of the central values and error-bars of the 3 SZ parameters, ... More

A new application of Random Matrices: Ext(C*_{red}(F_2)) is not a groupDec 19 2002Jun 21 2007In the process of developing the theory of free probability and free entropy, Voiculescu introduced in 1991 a random matrix model for a free semicircular system. Since then, random matrices have played a key role in von Neumann algebra theory (cf. [V8], ... More

Measuring the velocity field from type Ia supernovae in an LSST-like sky surveyAug 16 2016Aug 17 2016With the upcoming sky survey with the Large Synoptic Survey Telescope a great sample of type Ia supernovae will be observed, allowing for a precise mapping of the velocity structure of the universe. Since the source of peculiar velocities is variations ... More

Updated constraints on non-standard neutrino interactions from PlanckNov 15 2013Aug 12 2014We provide updated bounds on non-standard neutrino interactions based on data from the Planck satellite as well as auxiliary cosmological measurements. Two types of models are studied - A Fermi-like 4-point interaction and an interaction mediated by a ... More

Nucleosynthesis and the mass of the tau neutrino---ERRATUMJun 27 1996Our results for the primordial abundance of a massive Majorana tau neutrino (hep-ph/9603201) published in PRL76, 2848 (1996) were incorrect due to a trivial (but annoying) error in the numerical code. In this ERRATUM we present the corrected results.

Fourier imaging of non-linear structure formationJan 23 2017Apr 19 2017We perform a Fourier space decomposition of the dynamics of non-linear cosmological structure formation in LCDM models. From N-body simulations involving only cold dark matter we calculate 3-dimensional non-linear density, velocity divergence and vorticity ... More

Intersections of certain deleted digits setsMay 17 2011We consider some properties of the intersection of deleted digits Cantor sets with their translates. We investigate conditions on the set of digits such that, for any t between zero and the dimension of the deleted digits Cantor set itself, the set of ... More

On the Growth Rate of Non-Enzymatic Molecular ReplicatorsMar 28 2011Sep 01 2011It is well known that non-enzymatic template directed molecular replicators X + nO ---> 2X exhibit parabolic growth d[X]/dt = k [X]^{1/2}. Here, we analyze the dependence of the effective replication rate constant k on hybridization energies, temperature, ... More

New Supernova Limit on Large Extra DimensionsMar 19 2001Jun 06 2001If large extra dimensions exist in nature, supernova (SN) cores will emit large fluxes of Kaluza-Klein gravitons, producing a cosmic background of these particles with energies and masses up to about 100 MeV. Radiative decays then give rise to a diffuse ... More

Cosmology and the neutrino mass orderingJun 15 2016We propose a simple method to quantify a possible exclusion of the inverted neutrino mass ordering from cosmological bounds on the sum of the neutrino masses. The method is based on Bayesian inference and allows for a calculation of the posterior odds ... More

Ultra-high energy Neutrinos from Centaurus A and the Auger hot spotDec 11 2007Jul 25 2008The Pierre Auger collaboration has reported a correlation between Ultra-High Energy Cosmic Rays (UHECR) and nearby Active Galactic Nuclei (AGNs) within 75 Mpc. Two of these events fall within 3 degrees from Centaurus A, the nearest AGN, clearly suggesting ... More

Spectral and Tiling properties of the Unit CubeApr 08 2001Let $\Q=[0,1)^d$ denote the unit cube in $d$-dimensional Euclidean space \Rd and let \T be a discrete subset of \Rd. We show that the exponentials $e_t(x):=exp(i2\pi tx)$, $t\in\T$ form an othonormal basis for $L^2(\Q)$ if and only if the translates $\Q+t$, ... More

Efficient calculation of cosmological neutrino clustering with both linear and non-linear gravityOct 10 2015We study in detail how neutrino perturbations can be followed in linear theory by using only terms up to $l=2$ in the Boltzmann hierarchy. We provide a new approximation to the third moment and demonstrate that the neutrino power spectrum can be calculated ... More

Momentum Operators in The Unit SquareJan 13 2013We investigate the skew-adjoint extensions of a partial derivative operator acting in the direction of one of the sides a unit square. We investigate the unitary equivalence of such extensions and the spectra of such extensions. It follows from our results, ... More

Enrichment and representability for triangulated categoriesApr 04 2016Given a fixed tensor triangulated category S we consider triangulated categories T together with an S-enrichment which is compatible with the triangulated structure of T. It is shown that, in this setting, an enriched analogue of Brown representability ... More

Ends, fundamental tones, and capacities of minimal submanifolds via extrinsic comparison theoryJan 07 2014We study the volume of extrinsic balls and the capacity of extrinsic annuli in minimal submanifolds which are properly immersed with controlled radial sectional curvatures into an ambient manifold with a pole. The key results are concerned with the comparison ... More

Accelerated expansion and the virial theoremMar 31 2012When dark matter structures form and equilibrate they have to release a significant amount of energy in order to obey the virial theorem. Since dark matter is believed to be unable to radiate, this implies that some of the accreted dark matter particles ... More

Interfacial free energy of the structure II cyclopentane hydrate in cyclopentane liquid from the capillary wave fluctuation methodJan 18 2016The interfacial stiffness of structure II cyclopentane hydrate in cyclopentane liquid has been measured by the Capillary Wave Fluctuation (CWF) method for an equilibrated system with temperature of T=280K and pressure of P~20bar, close to the upper (L$_w$-Hyd-Vap-L$_{HC}$) ... More

Constraining invisible neutrino decays with the cosmic microwave backgroundSep 26 2005Precision measurements of the acoustic peaks of the cosmic microwave background indicate that neutrinos must be freely streaming at the photon decoupling epoch when T ~ 0.3 eV. This requirement implies restrictive limits on ``secret neutrino interactions,'' ... More

Neutrino decoupling in the early UniverseJun 02 1995A calculation of neutrino decoupling in the early Universe, including full Fermi-Dirac statistics and electron mass dependence in the weak reaction rates, is presented. We find that after decoupling, the electron neutrinos contribute 0.83\% more to the ... More

A Cosmological Three Level Neutrino LaserFeb 14 1997We present a calculation of a neutrino decay scenario in the early Universe. The specific decay is \nu_{2} \to \nu_{1} + \phi, where \phi is a boson. If there is a neutrino mass hierarchy, m_{\nu_{e}} < m_{\nu_{\mu}} < m_{\nu_{\tau}}, we show that it ... More

The Ariki-Terasoma-Yamada tensor space and the blob-algebraMay 12 2005Mar 11 2010We show that the Ariki-Terasoma-Yamada tensor module and its permutation submodules $ M(\lambda) $ are modules for the blob algebra when the Ariki-Koike algebra is a Hecke algebra of type $B$. We show that $ M(\lambda)$ and the standard modules $ \Delta(\lambda) ... More

Koszul duality of translation--and Zuckerman functorsMay 04 2009We review Koszul duality in representation theory of category $ \cal O $, especially we give a new presentation of the Koszul duality functor. Combining this with work of Backelin, we show that the translation and Zuckerman functors are Koszul dual to ... More

Asymptotic expansions for the Gaussian Unitary EnsembleApr 20 2010Sep 23 2010Let g:{\mathbb R} --> {\mathbb C} be a C^{\infty}-function with all derivatives bounded and let tr_n denote the normalized trace on the n x n matrices. In the paper [EM] Ercolani and McLaughlin established asymptotic expansions of the mean value E{tr_n(g(X_n))} ... More

Graphical models for mediation analysisJan 18 2018Mediation analysis seeks to infer how much of the effect of an exposure on an outcome can be attributed to specific pathways via intermediate variables or mediators. This requires identification of so-called path-specific effects. These express how a ... More

Might we eventually understand the origin of the dark matter velocity anisotropy?Dec 04 2008The density profile of simulated dark matter structures is fairly well-established, and several explanations for its characteristics have been put forward. In contrast, the radial variation of the velocity anisotropy has still not been explained. We suggest ... More

Cluster temperatures and non-extensive thermo-statisticsJan 18 2005We propose a novel component to the understanding of the temperature structure of galaxy clusters which does not rely on any heating or cooling mechanism. The new ingredient is the use of non-extensive thermo-statistics which is based on the natural generalization ... More

Cluster temperature profiles and Sunyaev-Zeldovich observationsJan 20 2004Apr 22 2004Galaxy clusters are not iso-thermal, and the radial temperature dependence will affect the cluster parameters derived through the observation of the Sunyaev-Zeldovich (SZ) effect. We show that the derived peculiar velocity will be systematically shifted ... More

Galactic hydraulic drop?Oct 10 2003Galaxies and galaxy clusters are observed to have a rather non-trivial radial behaviour. The observations show that the radial profiles change from one power-law profile near the centre to another power-law profile in the outer region. We present a simple ... More

On the possibility of distinguishing between Majorana and Dirac neutrinosAug 15 1997We clarify that one cannot distinguish between Majorana and Dirac neutrinos in the limit of vanishing neutrino mass. In particular we show, that the forward-backward asymmetry in the reaction e^+ e^- -> \nu \nu is the same for \nu_M and \nu_D, in contrast ... More

SZ cluster science with the Planck HFI experimentSep 30 2004In the near future the Planck satellite will gather impressive information about the anisotropies of the cosmic microwave background and about the galaxy clusters which perturb that signal. We will here review the ability of Planck to extract information ... More

Deep Learning Methods for Parallel Magnetic Resonance Image ReconstructionApr 01 2019Following the success of deep learning in a wide range of applications, neural network-based machine learning techniques have received interest as a means of accelerating magnetic resonance imaging (MRI). A number of ideas inspired by deep learning techniques ... More

The dynamics of domain wall SkyrmionsMay 13 2013It has recently been shown that Skyrmions with a fixed size can exist in theories without a Skyrme term, providing the Skyrmion is located on a domain wall. Here we numerically compute domain wall Skyrmions of this type, in a (2+1)-dimensional O(3) sigma ... More

Can Dust Segregation Mimic a Cosmological Constant?Sep 14 1999Recent measurements of type Ia supernovae indicate that distant supernovae are substantially fainter than expected from the standard flat cold dark matter model. One possible explanation is that the energy density in our universe is in fact dominated ... More

What it takes to measure a fundamental difference between dark matter and baryons: the halo velocity anisotropyApr 23 2007Jun 11 2007Numerous ongoing experiments aim at detecting WIMP dark matter particles from the galactic halo directly through WIMP-nucleon interactions. Once such a detection is established a confirmation of the galactic origin of the signal is needed. This requires ... More

A universal density slope - velocity anisotropy relation for relaxed structuresNov 16 2004Sep 27 2005We identify a universal relation between the radial density slope \alpha (r) and the velocity anisotropy \beta (r) for equilibrated structures. This relation holds for a variety of systems, including disk galaxy mergers, spherical collapses, cold dark ... More

The origin of cores and density profiles of gaseous baryonic structuresMar 18 2003Sep 01 2003We study the origin of cores and density profiles of gaseous baryonic structures in cosmology. By treating the baryons as a viscous gas, we find that both spheres and disks are possible solutions. We find analytically that the density profiles have inner ... More

Measuring the dark matter velocity anisotropy in galaxy clustersMay 31 2007Nov 08 2007The Universe contains approximately 6 times more dark matter than normal baryonic matter, and a directly observed fundamental difference between dark matter and baryons would both be significant for our understanding of dark matter structures and provide ... More

Apparent faster than light propagation from light sterile neutrinosSep 28 2011Recent data from the OPERA experiment seem to point to neutrinos propagating faster than light. One possible physics explanation for such a result is the existence of light sterile neutrinos which can propagate in a higher dimensional bulk and achieve ... More

Neutrino masses and cosmic radiation density: Combined analysisJul 06 2006We determine the range of neutrino masses and cosmic radiation content allowed by the most recent CMB and large-scale structure data. In contrast to other recent works, we vary these parameters simultaneously and provide likelihood contours in the two-dimensional ... More

Chaotic flavor evolution in an interacting neutrino gasApr 15 2014Neutrino-neutrino refraction can lead to non-periodic flavor oscillations in dense neutrino gases, and it has been hypothesized that some solutions are chaotic in nature. This is of particular interest in the case of neutrino emission from core-collapse ... More

Graded cellular basis and Jucys-Murphy elements for generalized blob algebrasDec 28 2018Jan 18 2019We give a concrete construction of a graded cellular basis for the generalized blob algebra B_n introduced by Martin and Woodcock. The construction uses the isomorphism between KLR-algebras and cyclotomic Hecke algebras, proved by Brundan-Kleshchev and ... More

The behaviour of shape and velocity anisotropy in dark matter haloesOct 08 2012Dark matter haloes from cosmological N-body simulations typically have triaxial shapes and anisotropic velocity distributions. Recently it has been shown that the velocity anisotropy, beta, of cosmological haloes and major merger remnants depends on direction ... More

Do We Need Stars to Reionize the Universe at High Redshifts? Early Reionization by Decaying Heavy Sterile NeutrinosMay 08 2003Sep 09 2003A remarkable result of the Wilkinson Microwave Anisotropy Probe (WMAP) observations is that the universe was significantly reionized at large redshifts. The standard explanation is that massive stars formed early and reionized the universe around redshift ... More

Stringent neutron-star limits on large extra dimensionsOct 04 2001Jan 17 2002Supernovae (SNe) are copious sources for Kaluza-Klein gravitons which are generic for theories with large extra dimensions. These massive particles are produced with average velocities ~0.5 c so that many of them are gravitationally retained by the SN ... More

Detecting sterile neutrinos with KATRIN like experimentsAug 09 2010Feb 08 2011A sterile neutrino with mass in the eV range, mixing with the electron antineutrino, is allowed and possibly even preferred by cosmology and oscillation experiments. If such eV-mass neutrinos exist they provide a much better target for direct detection ... More

Neutrino Dark Energy With More Than One Neutrino SpeciesJun 12 2008May 14 2010The mass varying neutrino scenario is a model that successfully explains the origin of dark energy while at the same time solves the coincidence problem. The model is, however, heavily constrained by its stability towards the formation of neutrino bound ... More

Exact Hausdorff Measure of Certain Non-Self-Similar Cantor SetsDec 05 2013We establish a formula yielding the Hausdorff measure for a class of non-self-similar Cantor sets in terms of the canonical covers of the Cantor set.

Sequential derivativesJan 12 2018Consider a real valued function defined, but not differentiable at some point. We use sequences approaching the point of interest to define and study sequential concepts of secant and cord derivatives of the function at the point of interest. If the function ... More

A detailed statistical analysis of the mass profiles of galaxy clustersJul 06 2009May 06 2011The distribution of mass in the halos of galaxies and galaxy clusters has been probed observationally, theoretically, and in numerical simulations. Yet there is still confusion about which of several suggested parameterized models is the better representation, ... More

Zeldovich pancakes at redshift zero: the equilibration state and phase space propertiesNov 24 2014One of the components of the cosmic web are sheets, which are commonly referred to as Zeldovich pancakes. These are structures which have only collapsed along one dimension, as opposed to filaments or galaxies and cluster, which have collapsed along two ... More

On Intersections of Cantor Sets: Self-SimilarityMay 11 2012Jun 28 2012Let C be a Cantor set. For a real number t let C+t be the translate of C by t, We say two real numbers s,t are equivalent if the intersection of C and C+s is a translate of the intersection of C and C+t. We consider a class of Cantor sets determined by ... More

On Intersections of Cantor Sets: Hausdorff MeasureMar 19 2012Jun 21 2012We establish formulas for bounds on the Haudorff measure of the intersection of certain Cantor sets with their translates. As a consequence we obtain a formula for the Hausdorff dimensions of these intersections.

A derivation of (half) the dark matter distribution functionJun 22 2012All dark matter structures appear to follow a set of universalities, such as phase-space density or velocity anisotropy profiles, however, the origin of these universalities remains a mystery. Any equilibrated dark matter structure can be fully described ... More

Asymmetric velocity anisotropies in remnants of collisionless mergersMay 08 2012Jun 28 2012Dark matter haloes in cosmological N-body simulations are affected by processes such as mergers, accretion and the gravitational interaction with baryonic matter. Typically the analysis of dark matter haloes is performed in spherical or elliptical bins ... More

The velocity anisotropy - density slope relationOct 21 2005One can solve the Jeans equation analytically for equilibrated dark matter structures, once given two pieces of input from numerical simulations. These inputs are 1) a connection between phase-space density and radius, and 2) a connection between velocity ... More

Constraining the helium abundance with CMBJun 27 2003Oct 13 2003We consider for the first time the ability of present-day cosmic microwave background (CMB) anisotropies data to determine the primordial helium mass fraction, Y_p. We find that CMB data alone gives the confidence interval 0.160 < Y_p < 0.501 (at 68% ... More

Observational constraints on the inflaton potential combined with flow-equations in inflaton spaceSep 26 2001Jun 28 2002Direct observations provide constraints on the first two derivatives of the inflaton potential in slow roll models. We discuss how present day observations, combined with the flow equations in slow roll parameter space, provide a non-trivial constraint ... More

Time, Space, and Energy in Reversible ComputingApr 20 2005We survey results of a quarter century of work on computation by reversible general-purpose computers (in this setting Turing machines), and general reversible simulation of irreversible computations, with respect to energy-, time- and space requirements. ... More

A result of Lemmermeyer on class numbersSep 21 2010I present Franz Lemmermeyer's proof that if p is a prime congruent to 9 mod 16 then the class number of Q(p^(1/4)) is congruent to 2 mod 4.

A Hecke algebra attached to mod 2 modular forms of level 3Aug 30 2015Oct 09 2016Let $D$ in $Z/2[[x]]$ be $\sum x^{n^{2}}$, $n>0$ and prime to $6$. Let $W$ be spanned by the $D^{k}$, $k>0$ and prime to $6$. Then the formal Hecke operators $T_{p}$, $p>3$, stabilize $W$, and it can be shown that they act locally nilpotently. We show ... More

A memo on chains and their topologiesDec 07 2013We summarize some facts on chains (totally ordered sets), from an order-theoretic and from a topological point of view. We highlight the fact that many classical theorems that are true for partially ordered sets under some completeness assumption remain ... More

Finite-dimensional irreducible $U_q(\mathfrak{sl}_2)$-modules from the equitable point of viewMar 25 2013We consider the quantum algebra $U_q(\mathfrak{sl}_2)$ with $q$ not a root of unity. We describe the finite-dimensional irreducible $U_q(\mathfrak{sl}_2)$-modules from the point of view of the equitable presentation.