Results for "B. M. Hare"

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Adaptive Interpolation Strategies in Derivative-Free Optimization: a case studyNov 09 2015Derivative-Free optimization (DFO) focuses on designing methods to solve optimization problems without the analytical knowledge of gradients of the objective function. There are two main families of DFO methods: model-based methods and direct search methods. ... More
The Assouad spectrum and the quasi-Assouad dimension: a tale of two spectraApr 25 2018We consider the Assouad spectrum, introduced by Fraser and Yu, along with a natural variant that we call the `upper Assouad spectrum'. These spectra are designed to interpolate between the upper box-counting and Assouad dimensions. It is known that the ... More
The Entropy of Cantor--like measuresSep 29 2018By a Cantor-like measure we mean the unique self-similar probability measure $\mu $ satisfying $\mu =\sum_{i=0}^{m-1}p_{i}\mu \circ S_{i}^{-1}$ where $% S_{i}(x)=\frac{x}{d}+\frac{i}{d}\cdot \frac{d-1}{m-1}$ for integers $2\leq d<m\le 2d-1$ and probabilities ... More
MMTF: The Maryland-Magellan Tunable FilterAug 12 2009Nov 08 2009This paper describes the Maryland-Magellan Tunable Filter (MMTF) on the Magellan-Baade 6.5-meter telescope. MMTF is based on a 150-mm clear aperture Fabry-Perot (FP) etalon that operates in low orders and provides transmission bandpass and central wavelength ... More
Axion astronomy with microwave cavity experimentsJan 11 2017Mar 28 2017Terrestrial searches for the conversion of dark matter axions or axion-like particles into photons inside magnetic fields are sensitive to the phase space structure of the local Milky Way halo. We simulate signals in a hypothetical future experiment based ... More
On the range of the Douglas-Rachford operatorMay 15 2014Jul 31 2014The problem of finding a minimizer of the sum of two convex functions - or, more generally, that of finding a zero of the sum of two maximally monotone operators - is of central importance in variational analysis. Perhaps the most popular method of solving ... More
Directional detection of dark matter streamsOct 10 2014Nov 11 2014Directional detection of WIMPs, in which the energies and directions of the recoiling nuclei are measured, currently presents the only prospect for probing the local velocity distribution of Galactic dark matter. We investigate the extent to which future ... More
Interoperability in Planetary Research for Geospatial Data AnalysisJun 08 2017For more than a decade there has been a push in the planetary science community to support interoperable methods for accessing and working with geospatial data. Common geospatial data products for planetary research include image mosaics, digital elevation ... More
Classifying Cantor Sets by their Fractal DimensionsMay 12 2009Apr 10 2010In this article we study Cantor sets defined by monotone sequences, in the sense of Besicovitch and Taylor. We classify these Cantor sets in terms of their h-Hausdorff and h-Packing measures, for the family of dimension functions h, and characterize this ... More
Generalized Continued Logarithms and Related Continued FractionsJun 22 2016We study continued logarithms as introduced by Bill Gosper and studied by J. Borwein et. al.. After providing an overview of the type I and type II generalizations of binary continued logarithms introduced by Borwein et. al., we focus on a new generalization ... More
A Derivative-Free CoMirror AlgorithmOct 23 2012We consider $\min\{f(x):g(x) \le 0, ~x\in X\},$ where $X$ is a compact convex subset of $\RR^m$, and $f$ and $g$ are continuous convex functions defined on an open neighbourhood of $X$. We work in the setting of derivative-free optimization, assuming ... More
Generalized solutions for the sum of two maximally monotone operatorsJun 07 2013A common theme in mathematics is to define generalized solutions to deal with problems that potentially do not have solutions. A classical example is the introduction of least squares solutions via the normal equations associated with a possibly infeasible ... More
Cosmic Ray Physics with the LOFAR Radio TelescopeMar 20 2019The LOFAR radio telescope is able to measure the radio emission from cosmic ray induced air showers with hundreds of individual antennas. This allows for precision testing of the emission mechanisms for the radio signal as well as determination of the ... More
Status of the Lunar Detection Mode for Cosmic Particles of LOFARMar 20 2019Cosmic particles hitting Earth's moon produce radio emission via the Askaryan effect. If the resulting radio ns-pulse can be detected by radio telescopes, this technique potentially increases the available collective area for ZeV scale particles by several ... More
X-ray Sources in the Dwarf Spheroidal Galaxy DracoMay 01 2015Feb 21 2016We present the spectral analysis of an 87~ks \emph{XMM-Newton} observation of Draco, a nearby dwarf spheroidal galaxy. Of the approximately 35 robust X-ray source detections, we focus our attention on the brightest of these sources, for which we report ... More
Readout strategies for directional dark matter detection beyond the neutrino backgroundMay 29 2015Sep 18 2015The search for weakly interacting massive particles (WIMPs) by direct detection faces an encroaching background due to coherent neutrino-nucleus scattering. As the sensitivity of these experiments improves, the question of how to best distinguish a dark ... More
Two-dimensional Ising model with competing interactions and its application to clusters and arrays of $π$-rings and adiabatic quantum computingMay 11 2007We study planar clusters consisting of loops including a Josephson $\pi$-junction ($\pi$-rings). Each $\pi$-ring carries a persistent current and behaves as a classical orbital moment. The type of particular state associated with the orientation of orbital ... More
An Agent-Based Approach to Component ManagementOct 01 2014This paper details the implementation of a software framework that aids the development of distributed and self-configurable software systems. This framework is an instance of a novel integration strategy called SoSAA (SOcially Situated Agent Architecture), ... More
Time-integrated directional detection of dark matterAug 09 2017Oct 17 2017The analysis of signals in directional dark matter (DM) detectors typically assumes that the directions of nuclear recoils can be measured in the Galactic rest frame. However, this is not possible with all directional detection technologies. In nuclear ... More
Analytic calculation of radio emission from parameterized extensive air showers, a tool to extract shower parametersNov 28 2017The radio intensity and polarization footprint of a cosmic-ray induced extensive air shower is determined by the time-dependent structure of the current distribution residing in the plasma cloud at the shower front. In turn, the time dependence of the ... More
Attouch-Théra duality revisited: paramonotonicity and operator splittingOct 21 2011The problem of finding the zeros of the sum of two maximally monotone operators is of fundamental importance in optimization and variational analysis. In this paper, we systematically study Attouch-Th\'era duality for this problem. We provide new results ... More
A review of the discovery reach of directional Dark Matter detectionFeb 11 2016Mar 17 2016Cosmological observations indicate that most of the matter in the Universe is Dark Matter. Dark Matter in the form of Weakly Interacting Massive Particles (WIMPs) can be detected directly, via its elastic scattering off target nuclei. Most current direct ... More
Local dimensions of overlapping self-similar measuresJul 23 2018We show that any equicontractive, self-similar measure arising from the IFS of contractions $(S_{j})$, with self-similar set $[0,1]$, admits an isolated point in its set of local dimensions provided the images of $S_{j}(0,1)$ (suitably) overlap and the ... More
Quasi-doubling of self-similar measures with overlapsJul 24 2018Nov 14 2018The Assouad and quasi-Assouad dimensions of a metric space provide information about the extreme local geometric nature of the set. The Assouad dimension of a set has a measure theoretic analogue, which is also known as the upper regularity dimension. ... More
Thresholds of Prox-Boundedness of PLQ functionsNov 02 2016Introduced in the 1960s, the Moreau envelope has grown to become a key tool in non\-smooth analysis and optimization. Essentially an infimal convolution with a parametrized norm squared, the Moreau envelope is used in many applications and optimization ... More
New techniques for bounds on the total number of Prime Factors of an Odd Perfect NumberJan 05 2005Apr 12 2006Let $\sigma(n)$ denote the sum of the positive divisors of $n$. We say that $n$ is perfect if $\sigma(n) = 2 n$. Currently there are no known odd perfect numbers. It is known that if an odd perfect number exists, then it must be of the form $N = p^\alpha ... More
Designing Modular Software: A Case Study in Introductory StatisticsAug 08 2016Oct 20 2016Modular programming is a development paradigm that emphasizes self-contained, flexible, and independent pieces of functionality. This practice allows new features to be seamlessly added when desired, and unwanted features to be removed, thus simplifying ... More
Putting Down Roots: A Graphical Exploration of Community AttachmentAug 17 2016In this paper, we explore the relationships that individuals have with their communities. This work was prepared as part of the ASA Data Expo '13 sponsored by the Graphics Section and the Computing Section, using data provided by the Knight Foundation ... More
The absolute continuity of convolution products of orbital measures in exceptional symmetric spacesNov 18 2015Let $G$ be a non-compact group, $K$ the compact subgroup fixed by a Cartan involution and assume $G/K$ is an exceptional, symmetric space, one of Cartan type $E,F $ or $G$. We find the minimal integer, $L(G),$ such that any convolution product of $L(G)$ ... More
Introductory statistics with intRoAug 08 2016intRo is a web-based application for performing basic data analysis and statistical routines. Leveraging the power of R and Shiny, intRo implements common statistical functions in an extensible modular structure, while including a point-and-click interface ... More
MagAO: Status and on-sky performance of the Magellan adaptive optics systemJul 18 2014MagAO is the new adaptive optics system with visible-light and infrared science cameras, located on the 6.5-m Magellan "Clay" telescope at Las Campanas Observatory, Chile. The instrument locks on natural guide stars (NGS) from 0$^\mathrm{th}$ to 16$^\mathrm{th}$ ... More
A generalization of a theorem of Erdős-Rényi to $m$-fold sums and differencesApr 09 2014Sep 04 2015Let $m\geq 2$ be a positive integer. Given a set $E(\omega )\subseteq \mathbb{N}$ we define $r_{N}^{(m)}(\omega )$ to be the number of ways to represent $N\in \mathbb{Z}$ as any combination of sums $\textit{ and }$ differences of $m$ distinct elements ... More
Computing proximal points of convex functions with inexact subgradientsNov 02 2016Locating proximal points is a component of numerous minimization algorithms. This work focuses on developing a method to find the proximal point of a convex function at a point, given an inexact oracle. Our method assumes that exact function values are ... More
Light-Cone Reduction vs. TsT transformations : A Fluid Dynamics PerspectiveMar 11 2018We compute constitutive relations for a charged $(2+1)$ dimensional Schr\"odinger fluid up to first order in derivative expansion, using holographic techniques. Starting with a locally boosted, asymptotically $AdS$, $4+1$ dimensional charged black brane ... More
Smoothness of convolution products of orbital measures on rank one compact symmetric spacesOct 21 2015We prove that all convolution products of pairs of continuous orbital measures in rank one, compact symmetric spaces are absolutely continuous and determine which convolution products are in $L^{2}$ (meaning, their density function is in $L^{2})$. Characterizations ... More
Properties of Quasi-Assouad dimensionMar 07 2017May 11 2017It is shown that for controlled Moran constructions in $\mathbb{R}$, including the (sub) self-similar and more generally, (sub) self-conformal sets, the quasi-Assouad dimension coincides with the upper box dimension. This can be extended to some special ... More
Big Pharma, little science? A bibliometric perspective on big pharma's R&D declineJun 05 2013There is a widespread perception that pharmaceutical R&D is facing a productivity crisis characterised by stagnation in the numbers of new drug approvals in the face of increasing R&D costs. This study explores pharmaceutical R&D dynamics by examining ... More
Algorithmic construction of the subdifferential from directional derivativesSep 09 2016The subdifferential of a function is a generalization for nonsmooth functions of the concept of gradient. It is frequently used in variational analysis, particularly in the context of nonsmooth optimization. The present work proposes algorithms to reconstruct ... More
On the Cardinality of Positively Linearly Independent SetsSep 24 2015Positive bases, which play a key role in understanding derivative free optimization methods that use a direct search framework, are positive spanning sets that are positively linearly independent. The cardinality of a positive basis in $\R^n$ has been ... More
An abstract proof of the L2-singular dichotomy for orbital measures on Lie algebras and groupsNov 28 2016Let $G$ be a compact, connected simple Lie group and $\mathfrak{g}$ its Lie algebra. It is known that if $\mu $ is any $G$-invariant measure supported on an adjoint orbit in $\mathfrak{g}$, then for each integer $k$, the $k$% -fold convolution product ... More
Calibration of the LOFAR low-band antennas using the Galaxy and a model of the signal chainMar 14 2019The LOw-Frequency ARray (LOFAR) is used to make precise measurements of radio emission from extensive air showers, yielding information about the primary cosmic ray. Interpreting the measured data requires an absolute and frequency-dependent calibration ... More
Thunderstorm electric fields probed by extensive air showers through their polarized radio emissionMar 14 2017Mar 20 2017We observe a large fraction of circular polarization in radio emission from extensive air showers recorded during thunderstorms, much higher than in the emission from air showers measured during fair-weather circumstances. We show that the circular polarization ... More
Improved Measurement of the Positive Muon Lifetime and Determination of the Fermi ConstantApr 16 2007Feb 08 2008The mean life of the positive muon has been measured to a precision of 11 ppm using a low-energy, pulsed muon beam stopped in a ferromagnetic target, which was surrounded by a scintillator detector array. The result, tau_mu = 2.197013(24) us, is in excellent ... More
Local dimensions of measures of finite type on the torusJul 12 2016The structure of the set of local dimensions of a self-similar measure has been studied by numerous mathematicians, initially for measures that satisfy the open set condition and, more recently, for measures on $\mathbb{R}$ that are of finite type. In ... More
On cycles for the doubling map which are disjoint from an intervalAug 13 2013May 14 2014Let $T:[0,1]\to[0,1]$ be the doubling map and let $0<a<b<1$. We say that an integer $n\ge3$ is bad for $(a,b)$ if all $n$-cycles for $T$ intersect $(a,b)$. Let $B(a,b)$ denote the set of all $n$ which are bad for $(a,b)$. In this paper we completely describe ... More
A new lower bound for Garsia's entropy of Bernoulli convolutionsSep 07 2016Let $\beta\in(1,2)$ and let $H_\beta$ denote Garsia's entropy for the Bernoulli convolution $\mu_\beta$ associated with $\beta$. In the present paper we show that $H_\beta>0.82$ for all $\beta \in (1, 2)$ and improve this bound for certain ranges. Combined ... More
The Relationship between $ε$-Kronecker and Sidon SetsJun 04 2015A subset $E$ of a discrete abelian group is called $\epsilon $-Kronecker if all $E$-functions of modulus one can be approximated to within $\epsilon$ by characters. $E$ is called a Sidon set if all bounded $E$-functions can be interpolated by the Fourier ... More
A lower bound for the dimension of Bernoulli convolutionsSep 07 2016Mar 01 2017Let $\beta\in(1,2)$ and let $H_\beta$ denote Garsia's entropy for the Bernoulli convolution $\mu_\beta$ associated with $\beta$. In the present paper we show that $H_\beta>0.82$ for all $\beta \in (1, 2)$ and improve this bound for certain ranges. Combined ... More
Some properties of even moments of uniform random walksJun 03 2015Jun 04 2015We build upon previous work on the densities of uniform random walks in higher dimensions, exploring some properties of the even moments of these densities and extending a result about their modularity.
On a family of self-affine sets: topology, uniqueness, simultaneous expansionsOct 15 2014May 11 2015Let $\beta_1,\beta_2>1$ and $T_i(x,y) = \bigl(\frac{x+i}{\beta_1}, \frac{y+i}{\beta_2}\bigr),\ i\in\{\pm1\}$. Let $A := A_{\beta_1, \beta_2}$ be the unique compact set satisfying $A = T_{1}(A) \cup T_{-1}(A)$. In this paper we give a detailed analysis ... More
Bulk Viscous cosmological models in Lyra geometryJul 09 2003We have investigated an LRS Bianchi Type I models with bulk viscosity in the cosmological theory based on Lyra's geometry. A new class of exact solutions have been obtained by considering a time-dependent displacement field for a constant value of the ... More
A lower bound for Garsia's entropy for certain Bernoulli convolutionsNov 18 2008Nov 13 2009Let $\beta\in(1,2)$ be a Pisot number and let $H_\beta$ denote Garsia's entropy for the Bernoulli convolution associated with $\beta$. Garsia, in 1963 showed that $H_\beta<1$ for any Pisot $\beta$. For the Pisot numbers which satisfy $x^m=x^{m-1}+x^{m-2}+...+x+1$ ... More
Plane-Symmetric Inhomogeneous Bulk Viscous Cosmological Models with Variable $Λ$Nov 01 2002A plane-symmetric non-static cosmological model representing a bulk viscous fluid distribution has been obtained which is inhomogeneous and anisotropic and a particular case of which is gravitationally radiative. Without assuming any {\it adhoc} law, ... More
Local dimensions of random homogeneous self-similar measures: strong separation and finite typeNov 27 2017We study the multifractal analysis of self-similar measures arising from random homogeneous iterated function systems. Under the assumption of the uniform strong separation condition, we see that this analysis parallels that of the deterministic case. ... More
Local dimensions of measures of finite typeApr 02 2015We study the multifractal analysis of a class of equicontractive, self-similar measures of finite type, whose support is an interval. Finite type is a property weaker than the open set condition, but stronger than the weak open set condition. Examples ... More
Local dimensions of measures of finite type II - Measures without full support and with non-regular probabilitiesMar 07 2016Consider a sequence of linear contractions $S_{j}(x)=\varrho x+d_{j}$ and probabilities $p_{j}>0$ with $\sum p_{j}=1$. We are interested in the self-similar measure $\mu =\sum p_{j}\mu \circ S_{j}^{-1}$, of finite type. In this paper we study the multi-fractal ... More
Lower Assouad Dimension of Measures and RegularityDec 13 2018Dec 20 2018In analogy with the lower Assouad dimensions of a set, we study the lower Assouad dimensions of a measure. As with the upper Assouad dimensions, the lower Assouad dimensions of a measure provide information about the extreme local behaviour of the measure. ... More
Sidon sets are proportionally Sidon with small Sidon constantsAug 09 2018In his seminal work on Sidon sets, Pisier found an important characterization of Sidonicity: A set is Sidon if and only if it is proportionally quasi-independent. Later, it was shown that Sidon sets were proportionally `special' Sidon in several other ... More
Open maps: small and large holes with unusual propertiesOct 17 2017Jun 21 2018Let $X$ be a two-sided subshift on a finite alphabet endowed with a mixing probability measure which is positive on all cylinders in $X$. We show that there exist arbitrarily small finite overlapping union of shifted cylinders which intersect every orbit ... More
Multidimensional self-affine sets: non-empty interior and the set of uniquenessJun 29 2015Jan 11 2016Let $M$ be a $d\times d$ contracting matrix. In this paper we consider the self-affine iterated function system $\{Mv-u, Mv+u\}$, where $u$ is a cyclic vector. Our main result is as follows: if $|\det M|\ge 2^{-1/d}$, then the attractor $A_M$ has non-empty ... More
Two-dimensional self-affine sets with interior points, and the set of uniquenessFeb 25 2015Sep 08 2015Let $M$ be a $2\times2$ real matrix with both eigenvalues less than~1 in modulus. Consider two self-affine contraction maps from $\mathbb R^2 \to \mathbb R^2$, \begin{equation*} T_m(v) = M v - u \ \ \mathrm{and}\ \ T_p(v) = M v + u, \end{equation*} where ... More
The design, construction and performance of the MICE scintillating fibre trackersMay 19 2010Jul 11 2010Charged-particle tracking in the international Muon Ionisation Cooling Experiment (MICE) will be performed using two solenoidal spectrometers, each instrumented with a tracking detector based on 350 {\mu}m diameter scintillating fibres. The design and ... More
High-speed Ejecta from the Gamma-ray Binary PSR B1259-63/LS 2883Mar 02 2019Observing the famous high-mass, eccentric X-ray and gamma-ray binary PSR B1259-63/LS 2883 with Chandra, we detected X-ray emitting clumps moving from the binary with speeds of about 0.1 of the speed of light, possibly with acceleration. The clumps are ... More
Optimizing horizontal alignment of roads in a specified corridorJul 09 2015Finding an optimal alignment connecting two end-points in a specified corridor is a complex problem that requires solving three interrelated sub-problems, namely the horizontal alignment, vertical alignment and earthwork optimization problems. In this ... More
Assouad dimensions of complementary setsApr 05 2016Given a positive, decreasing sequence $a,$ whose sum is $L$, we consider all the closed subsets of $[0,L]$ such that the lengths of their complementary open intervals are in one to one correspondence with the sequence $a$. The aim of this note is to investigate ... More
Almost sure Assouad-like Dimensions of Complementary setsMar 19 2019Given a non-negative, decreasing sequence $a$ with sum $1$, we consider all the closed subsets of $[0,1]$ such that the lengths of their complementary open intervals are given by the terms of $a$, the so-called complementary sets. In this paper we determine ... More
Most Reinhardt polygons are sporadicMay 20 2014Oct 25 2014A \textit{Reinhardt polygon} is a convex $n$-gon that, for $n$ not a power of $2$, is optimal in three different geometric optimization problems, for example, it has maximal perimeter relative to its diameter. Some such polygons exhibit a particular periodic ... More
Transmittance and near-field characterization of sub-wavelength tapered optical fibersFeb 20 2008We have produced high transmission sub-wavelength tapered optical fibers for the purpose of whispering gallery mode coupling in fused silica microcavities at 780 nm. A detailed analysis of the fiber transmittance evolution during tapering is demonstrated ... More
Neodymium Photoluminescence in Whispering Gallery Modes of Toroidal MicrocavitiesNov 14 2008We report on light emission from high-Q neodymium-implanted silica microtoroids. Following the description of the fabrication process of microtoroids, neodymium light emission is analysed. This emission is coupled to various cavity modes. Using evanescent ... More
Three Series for the Generalized Golden MeanJan 23 2014As is well-known, the ratio of adjacent Fibonacci numbers tends to phi = (1 + sqrt(5))/2, and the ratio of adjacent Tribonacci numbers (where each term is the sum of the three preceding numbers) tends to the real root eta of X^3 - X^2 - X - 1 = 0. Letting ... More
There are no two non-real conjugates of a Pisot number with the same imaginary partOct 07 2014We show that the number $\alpha=(1+\sqrt{3+2\sqrt{5}})/2$ with minimal polynomial $x^4-2x^3+x-1$ is the only Pisot number whose four distinct conjugates $\alpha_1,\alpha_2,\alpha_3,\alpha_4$ satisfy the additive relation $\alpha_1+\alpha_2=\alpha_3+\alpha_4$. ... More
On the height of the Sylvester ResultantOct 17 2003May 13 2004Let n be a positive integer. We consider the Sylvester Resultant of f and g, where f is a generic polynomial of degree 2 or 3 and g is a generic polynomial of degree n. If f is a quadratic polynomial, we find the resultant's height. If f is a cubic polynomial, ... More
Transferring spherical multipliers on compact symmetric spacesOct 19 2017We prove a two-sided transference theorem between $L^{p}$ spherical multipliers on the compact symmetric space $U/K$ and $L^{p}$ multipliers on the vector space $i\mathfrak{p},$ where the Lie algebra of $U$ has Cartan decomposition $\mathfrak{k\oplus ... More
"Active-set complexity" of proximal gradient: How long does it take to find the sparsity pattern?Dec 10 2017Sep 06 2018Proximal gradient methods have been found to be highly effective for solving minimization problems with non-negative constraints or L1-regularization. Under suitable nondegeneracy conditions, it is known that these algorithms identify the optimal sparsity ... More
Learning Representations of Sets through Optimized PermutationsDec 10 2018Jan 15 2019Representations of sets are challenging to learn because operations on sets should be permutation-invariant. To this end, we propose a Permutation-Optimisation module that learns how to permute a set end-to-end. The permuted set can be further processed ... More
Best practices for comparing optimization algorithmsSep 24 2017Comparing, or benchmarking, of optimization algorithms is a complicated task that involves many subtle considerations to yield a fair and unbiased evaluation. In this paper, we systematically review the benchmarking process of optimization algorithms, ... More
The smoothness of convolutions of orbital measures on complex Grassmannian symmetric spacesMar 27 2019It is well known that if $G/K$ is any irreducible symmetric space and $\mu _{a}$ is a continuous orbital measure supported on the double coset $KaK,$ then the convolution product, $\mu _{a}^{k},$ is absolutely continuous for some suitably large $k\leq ... More
Automatic Matching of Bullet LandsJan 21 2016Oct 08 2016In 2009, the National Academy of Sciences published a report questioning the scientific validity of many forensic methods including firearm examination. Firearm examination is a forensic tool used to help the court determine whether two bullets were fired ... More
A compound figure of merit for photonic applications of metal nanocompositesSep 07 2006Selecting nanocomposites for photonic switching applications requires optimizing their thermal, nonlinear and two-photon absorption characteristics. We simplify this step by defining a compound figure of merit (FOM_{C}) for nanocomposites of noble metals ... More
Visualization of the ε-Subdifferential of Piecewise Linear-Quadratic FunctionsSep 24 2017Computing explicitly the {\epsilon}-subdifferential of a proper function amounts to computing the level set of a convex function namely the conjugate minus a linear function. The resulting theoretical algorithm is applied to the the class of (convex univariate) ... More
Characterizing the absolute continuity of the convolution of orbital measures in a classical Lie algebraOct 20 2014Let $\mathfrak{g}$ be a compact, simple Lie algebra of dimension $d$. It is a classical result that the convolution of any $d$ non-trivial, $G$ -invariant, orbital measures is absolutely continuous with respect to Lebesgue measure on $\mathfrak{g}$ and ... More
The Ubiquity of Sidon Sets That Are Not $I_0$Jan 26 2016We prove that every infinite, discrete abelian group admits a pair of $I_0$ sets whose union is not $I_0$. In particular, this implies that every such group contains a Sidon set that is not $I_{0}$.
Exact Kronecker Constants of Three Element SetsMar 26 2015For any three element set of positive integers, $\{a,b,n\}$, with $a<b<n$, $n$ sufficiently large and $\gcd(a,b)=1$, we find the least $\alpha$ such that given any real numbers $t_1$, $t_2$, $t_3$, there is a real number $x$ such that \begin{equation*} ... More
Upper and Lower Bounds for Kronecker Constants of Three-Element Sets of IntegersAug 18 2011Aug 19 2011Various upper and lower bounds are provided for the (angular) Kronecker constants of sets of integers. Some examples are provided where the bounds are attained. It is proved that 5=16 bounds the angular Kronecker constants of 3-element sets of positive ... More
Intermediate Assouad-like dimensionsMar 17 2019Mar 20 2019We introduce and study bi-Lipschitz-invariant dimensions that range between the box and Assouad dimensions. The quasi-Assouad dimensions and $\theta$-spectrum are other special examples of these intermediate dimensions. These dimensions are localized, ... More
Sporadic Reinhardt polygonsMar 19 2012Sep 27 2012Let $n$ be a positive integer, not a power of two. A \textit{Reinhardt polygon} is a convex $n$-gon that is optimal in three different geometric optimization problems: it has maximal perimeter relative to its diameter, maximal width relative to its diameter, ... More
Automatic Matching of Bullet LandsJan 21 2016Aug 08 2016In 2009, the National Academy of Sciences published a report questioning the scientific validity of many forensic methods including firearm examination. Firearm examination is a forensic tool used to help the court determine whether two bullets were fired ... More
Torchbearer: A Model Fitting Library for PyTorchSep 10 2018We introduce torchbearer, a model fitting library for pytorch aimed at researchers working on deep learning or differentiable programming. The torchbearer library provides a high level metric and callback API that can be used for a wide range of applications. ... More
A derivative-free $\mathcal{VU}$-algorithm for convex finite-max problemsMar 26 2019The $\mathcal{VU}$-algorithm is a superlinearly convergent method for minimizing nonsmooth, convex functions. At each iteration, the algorithm works with a certain $\mathcal{V}$-space and its orthogonal $\U$-space, such that the nonsmoothness of the objective ... More
The absolute continuity of convolutions of orbital measures in symmetric spacesMay 05 2015We characterize the absolute continuity of convolution products of orbital measures on the classical, irreducible Riemannian symmetric spaces $G/K$ of Cartan type $III$, where $G$ is a non-compact, connected Lie group and $K$ is a compact, connected subgroup. ... More
Multiple-Path Selection for new Highway Alignments using Discrete AlgorithmsJul 30 2015This paper addresses the problem of finding multiple near-optimal, spatially-dissimilar paths that can be considered as alternatives in the decision making process, for finding optimal corridors in which to construct a new road. We further consider combinations ... More
Packing and Hausdorff measures of Cantor sets associated with seriesMar 30 2015We study a generalization of Mor\'an's sum sets, obtaining information about the $h$-Hausdorff and $h$-packing measures of these sets and certain of their subsets.
The baker's map with a convex holeMay 01 2017Jan 30 2018We consider the baker's map $B$ on the unit square $X$ and an open convex set $H\subset X$ which we regard as a hole. The survivor set $\mathcal J(H)$ is defined as the set of all points in $X$ whose $B$-trajectories are disjoint from $H$. The main purpose ... More
The monic integer transfinite diameterJul 14 2005We study the problem of finding nonconstant monic integer polynomials, normalized by their degree, with small supremum on an interval I. The monic integer transfinite diameter t_M(I) is defined as the infimum of all such supremums. We show that if I has ... More
Diffraction-limited Visible Light Images of Orion Trapezium Cluster With the Magellan Adaptive Secondary AO System (MagAO)Aug 19 2013We utilized the new high-order (250-378 mode) Magellan Adaptive Optics system (MagAO) to obtain very high spatial resolution observations in "visible light" with MagAO's VisAO CCD camera. In the good-median seeing conditions of Magellan (0.5-0.7") we ... More
The sum of digits of $n$ and $n^2$Jan 23 2010Let $s_q(n)$ denote the sum of the digits in the $q$-ary expansion of an integer $n$. In 2005, Melfi examined the structure of $n$ such that $s_2(n) = s_2(n^2)$. We extend this study to the more general case of generic $q$ and polynomials $p(n)$, and ... More
Stolarsky's conjecture and the sum of digits of polynomial valuesJan 23 2010Let $s_q(n)$ denote the sum of the digits in the $q$-ary expansion of an integer $n$. In 1978, Stolarsky showed that $$ \liminf_{n\to\infty} \frac{s_2(n^2)}{s_2(n)} = 0. $$ He conjectured that, as for $n^2$, this limit infimum should be 0 for higher powers ... More
On (a,b) Pairs in Random Fibonacci SequencesAug 11 2016We study the random Fibonacci tree, which is an infinite binary tree with non-negative numbers at each node defined as follows. The root consists of the number 1 with a single child also the number 1. Then we define the tree recursively in the following ... More
When is an automatic set an additive basis?Oct 23 2017We characterize those $k$-automatic sets $S$ of natural numbers that form an additive basis for the natural numbers, and we show that this characterization is effective. In addition, we give an algorithm to determine the smallest $j$ such that $S$ forms ... More