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Element Abundances and Source Plasma Temperatures of Solar Energetic ParticlesNov 30 2016Dec 05 2016Thirty years ago Breneman and Stone observed that the enhancement or suppression of element abundances in large solar energetic-particle (SEP) events varies as a power of the mass-to-charge ratio, A/Q, of the elements. Since Q during acceleration or transport ... More

Hydrogen and the Abundances of Elements in Gradual Solar Energetic-Particle EventsFeb 08 2019Despite its dominance, hydrogen has been largely ignored in studies of the abundance patterns of the chemical elements in gradual solar energetic-particle (SEP) events; those neglected abundances show a surprising new pattern of behavior. Abundance enhancements ... More

Element Abundances and Source Plasma Temperatures of Solar Energetic ParticlesNov 30 2016Thirty years ago Breneman and Stone observed that the enhancement or suppression of element abundances in large solar energetic-particle (SEP) events varies as a power of the mass-to-charge ratio, A/Q, of the elements. Since Q during acceleration or transport ... More

Element Abundances in Solar Energetic Particles and the Solar CoronaJun 10 2013This is a study of abundances of the elements He, C, N, O, Ne, Mg, Si, S, Ar, Ca, and Fe in solar energetic particles (SEPs) in the 2 - 15 MeV amu-1 region measured on the Wind spacecraft during 54 large SEP events occurring between November 1994 and ... More

The "FIP Effect" and the Origins of Solar Energetic Particles and of the Solar WindJan 17 2018We find that the element abundances in solar energetic particles (SEPs) and in the slow solar wind (SSW), relative to those in the photosphere, show different patterns as a function of the first ionization potential (FIP) of the elements. Generally, the ... More

Hydrogen and the Abundances of Elements in Impulsive Solar Energetic-Particle EventsJan 14 2019Mar 07 2019Hydrogen has been almost completely ignored in studies of the abundance patterns of the chemical elements in solar energetic particles (SEPs). We seek to find impulsive events where H fits these abundance patterns and document the events that do not, ... More

The Origin of Element Abundance Variations in Solar Energetic ParticlesMar 20 2016Jul 21 2016Abundance enhancements, during acceleration and transport in both gradual and impulsive solar energetic particle (SEP) events, vary approximately as power laws in the mass-to-charge ratio [A/Q] of the ions. Since the Q-values depend upon the electron ... More

Hydrogen and the Abundances of Elements in Impulsive Solar Energetic-Particle EventsJan 14 2019Hydrogen has been almost completely ignored in studies of the abundance patterns of the chemical elements in solar energetic particles (SEPs). We seek to find impulsive events where H fits these abundance patterns and document the events that do not, ... More

The Abundance of Helium in the Source Plasma of Solar Energetic ParticlesAug 16 2017Studies of patterns of abundance enhancements of elements, relative to solar-coronal abundances, in large solar energetic-particle (SEP) events, and of their power-law dependence on the mass-to-charge ratio A/Q of the ions, have been used to determine ... More

Helium Suppression in Impulsive Solar Energetic-Particle EventsDec 04 2018Feb 20 2019We have studied the element abundances and energy spectra of the small "He-poor" impulsive solar energetic-particle (SEP) events, comparing them with other impulsive SEP events with more-normal abundances of He. He-poor events can have abundances as low ... More

Element abundances in solar energetic particles: two physical processes, two abundance patternsJan 03 2015Abundances of elements comprising solar energetic particles (SEPs) come with two very different patterns. Historically called "impulsive" and "gradual" events, they have been studied for 40 years, 20 years by the Wind spacecraft. Gradual SEP events measure ... More

Excess H, Suppressed He, and the Abundances of Elements in Solar Energetic ParticlesAug 06 2019Recent studies of the abundances of H and He relative to those of heavier ions in solar energetic particle (SEP) events suggest new features in the underlying physics. Impulsive SEP events, defined by uniquely large enhancements of Fe/O, emerge from magnetic ... More

The Streaming Limit of Solar Energetic-Particle IntensitiesDec 06 2014As solar energetic particles (SEPs) stream outward along the interplanetary magnetic field after acceleration by shock waves near the Sun, their intensities are limited by scattering against self-generated Alfv\'en waves, trapping the particles near their ... More

Variations in Abundance Enhancements in Impulsive Solar Energetic-Particle Events and Related CMEs and FlaresJul 29 2014We study event-to-event variations in the abundance enhancements of the elements He through Pb for Fe-rich impulsive solar energetic-particle (SEP) events, and their relationship with properties of associated coronal mass ejections (CMEs) and solar flares. ... More

Temperature of the Source Plasma for Impulsive Solar Energetic ParticlesMay 11 2015The steep power-law dependence of element abundance enhancements on the mass-to-charge ratios [A/Q] of the ions in impulsive solar energetic-particle (SEP) events causes these enhancements to reflect the temperature-dependent pattern of Q of the ions ... More

Abundance Enhancements in Impulsive Solar Energetic-Particle Events with Associated Coronal Mass EjectionsApr 12 2014We study the abundances of the elements He through Pb in Fe-rich impulsive solar energetic-particle (SEP) events with measurable abundances of ions with atomic number Z>2 observed on the Wind spacecraft, and their relationship with coronal mass ejections ... More

Coronal Sources of Impulsive Fe-Rich Solar Energetic Particle EventsSep 30 2015We review recent work on 111 Fe-rich impulsive solar energetic ($\sim$ 3 MeV/nuc) particle (SEP) events observed from 1994 to 2013. Strong elemental abundance enhancements scale with A/Q, the ion mass-to-charge ratio, as (A/Q)$^{\alpha}$, where 2 $< \alpha ... More

The Design Of Fiber Optic Sensors For Measuring Hydrodynamic ParametersMar 31 2002We present an approximate analytic model that has been developed for examining hydrodynamic flow near the surface of a fiber optic sensor. An analysis of the conservation of momentum, the continuity equation and the Navier-Stokes equation for compressible ... More

Rapid Rotation in the Kepler Field: Not a Single Star PhenomenonSep 06 2018Feb 05 2019Tens of thousands of rotation periods have been measured in the Kepler fields, including a substantial fraction of rapid rotators. We use Gaia parallaxes to distinguish photometric binaries (PBs) from single stars on the unevolved lower main sequence, ... More

Cohomology of truncated polynomial lambda-ringsJan 28 2005The lambda-ring cohomology in dimensions 0 and 1 of certain truncated polynomial filtered lambda-rings are computed. The dimension 1 case is related to deformations of lambda-rings.

Brace operations and Deligne's Conjecture for module-algebrasJul 25 2006It is observed that Kaygun's Hopf-Hochschild cochain complex for a module-algebra is a brace algebra with multiplication. As a result, (i) an analogue of Deligne's Conjecture holds for module-algebras, and (ii) the Hopf-Hochschild cohomology of a module-algebra ... More

The Redshift of a Lensing Galaxy in PMN J0134-0931Jul 15 2002The Sloan Digital Sky Survey (SDSS) automatically targeted as a quasar candidate the recently discovered, gravitationally lensed, extremely reddened z=2.2 quasar PMN J0134-0931. The SDSS spectrum exhibits Ca II absorption at z=0.76451, which we identify ... More

The Mikheev identity in right Hom-alternative algebrasMay 01 2012It is shown that in every multiplicative right Hom-alternative algebra, a Hom-type generalization of the Mikheev identity holds. It is then inferred that a multiplicative right Hom-alternative algebra with an injective twisting map and without Hom-nilpotent ... More

Mild mixing of certain interval exchange transformationsSep 20 2016We prove that irreducible, linearly recurrent, type W interval exchange transformations are always mild mixing. For every irreducible permutation the set of linearly recurrent interval exchange transformations has full Hausdorff dimension.

Loop structures on the homotopy type of S^3 revisitedJan 28 2005We observe that the Rector invariants classifying the genus of BS^3 show up in (orthogonal and unitary) K-theory. We then use this knowledge to show purely algebraically how the K-theory of the spaces in the genus of BS^3 differ. This provides new insights ... More

Module Hom-algebrasDec 26 2008We study a twisted version of module algebras called module Hom-algebras. It is shown that module algebras deform into module Hom-algebras via endomorphisms. As an example, we construct certain q-deformations of the usual sl(2)-action on the affine plane. ... More

Hom-Novikov algebrasSep 03 2009Jan 12 2011We study a twisted generalization of Novikov algebras, called Hom-Novikov algebras, in which the two defining identities are twisted by a linear map. It is shown that Hom-Novikov algebras can be obtained from Novikov algebras by twisting along any algebra ... More

Hom-algebras and homologyDec 20 2007Aug 06 2009Classes of $G$-Hom-associative algebras are constructed as deformations of $G$-associative algebras along algebra endomorphisms. As special cases, we obtain Hom-associative and Hom-Lie algebras as deformations of associative and Lie algebras, respectively, ... More

Enveloping algebras of Hom-Lie algebrasSep 06 2007Enveloping algebras of Hom-Lie and Hom-Leibniz algebras are constructed.

Deformation of dual Leibniz algebra morphismsFeb 02 2006An algebraic deformation theory of morphisms of dual Leibniz algebras is obtained.

Hom-Yang-Baxter equation, Hom-Lie algebras, and quasi-triangular bialgebrasMar 03 2009We study a twisted version of the Yang-Baxter Equation, called the Hom-Yang-Baxter Equation (HYBE), which is motivated by Hom-Lie algebras. Three classes of solutions of the HYBE are constructed, one from Hom-Lie algebras and the others from Drinfeld's ... More

Infinity Operads and Monoidal Categories with Group EquivarianceMar 09 2019This monograph provides a coherent development of operads, infinity operads, and monoidal categories, equipped with equivariant structures encoded by an action operad. A group operad is a planar operad with an action operad equivariant structure. In the ... More

Hom-quantum groups III: Representations and module Hom-algebrasNov 28 2009We study Hom-quantum groups, their representations, and module Hom-algebras. Two Twisting Principles for Hom-type algebras are formulated, and construction results are proved following these Twisting Principles. Examples include Hom-quantum n-spaces, ... More

Cohomology and deformation of module-algebrasJul 12 2006An algebraic deformation theory of module-algebras over a bialgebra is constructed. The cases of module-coalgebras, comodule-algebras, and comodule-coalgebras are also considered.

Moduli space of filtered lambda-ring structures over a filtered ringSep 04 2002Motivated by recent works on the genus of classifying spaces of compact Lie groups, here we study the set of filtered $\lambda$-ring structures over a filtered ring from a purely algebraic point of view. From a global perspective, we first show that this ... More

On adic genus, Postnikov conjugates, and lambda-ringsMay 24 2001Sufficient conditions on a space are given which guarantee that the $K$-theory ring and the ordinary cohomology ring with coefficients over a principal ideal domain are invariants of, respectively, the adic genus and the SNT set. An independent proof ... More

The Hom-Yang-Baxter equation and Hom-Lie algebrasMay 12 2009Feb 17 2011Motivated by recent work on Hom-Lie algebras, a twisted version of the Yang-Baxter equation, called the Hom-Yang-Baxter equation (HYBE), was introduced by the author in an earlier paper. In this paper, several more classes of solutions of the HYBE are ... More

Clapp-Puppe Type Lusternik-Schnirelmann (Co)category in a Model CategoryApr 27 2001We introduce Clapp-Puppe type generalized Lusternik-Schnirelmann (co)category in a Quillen model category. We establish some of their basic properties and give various characterizations of them. As the first application of these characterizations, we ... More

Deformation bicomplex of module-algebrasJul 24 2007The deformation bicomplex of a module-algebra over a bialgebra is constructed. It is then applied to study algebraic deformations in which both the module structure and the algebra structure are deformed. The cases of module-coalgebras, comodule-(co)algebras, ... More

The Role of Radioactivities in AstrophysicsSep 08 2010I present both a history of radioactivity in astrophysics and an introduction to the major applications of radioactive abundances to astronomy.

Higher dimensional algebras via colored PROPsSep 12 2008Starting from any unital colored PROP $P$, we define a category $P(P)$ of shapes called $P$-propertopes. Presheaves on $P(P)$ are called $P$-propertopic sets. For $0 \leq n \leq \infty$ we define and study $n$-time categorified $P$-algebras as $P$-propertopic ... More

The classical Hom-Yang-Baxter equation and Hom-Lie bialgebrasMay 12 2009Motivated by recent work on Hom-Lie algebras and the Hom-Yang-Baxter equation, we introduce a twisted generalization of the classical Yang-Baxter equation (CYBE), called the classical Hom-Yang-Baxter equation (CHYBE). We show how an arbitrary solution ... More

Hom-quantum groups II: cobraided Hom-bialgebras and Hom-quantum geometryJul 10 2009A class of non-associative and non-coassociative generalizations of cobraided bialgebras, called cobraided Hom-bialgebras, is introduced. The non-(co)associativity in a cobraided Hom-bialgebra is controlled by a twisting map. Several methods for constructing ... More

Gerstenhaber structure and Deligne's conjecture for Loday algebrasJun 08 2006A method for establishing a Gerstenhaber algebra structure on the cohomology of Loday-type algebras is presented. This method is then applied to dendriform dialgebras and three types of trialgebras introduced by Loday and Ronco. Along the way, our results ... More

A lower bound for higher topological complexity of real projective spaceSep 13 2017Sep 19 2017We obtain an explicit formula for the best lower bound for the higher topological complexity, TC_k(P^n), of real projective space implied by mod 2 cohomology.

Coefficients in powers of the log seriesJan 18 2010We determine the p-exponent in many of the coefficients in the power series (log(1+x)/x)^t, where t is any integer. In our proof, we introduce a variant of multinomial coefficients. We also characterize the power series x/log(1+x) by certain zero coefficients ... More

K-theory and immersions of spatial polygon spacesJan 13 2019For ell a generic n-tuple of positive numbers, N(ell) denotes the space of isometry classes of oriented n-gons in R^3 with side lengths specified by ell. We determine the algebra K(N(ell)) and use this to obtain nonimmersions of the 2(n-3)-manifold N(ell) ... More

Topological complexity of planar polygon spaces with small genetic codeSep 25 2015Jan 20 2016We determine lower bounds for the topological complexity of many planar polygon spaces mod isometry. With very few exceptions, the upper and lower bounds given by dimension and cohomology considerations differ by 1. This is true for 130 of the 134 generic ... More

Topological complexity of spatial polygon spacesJul 06 2015Using known results about their integral cohomology ring, we prove that the topological complexity of the space of n-gons in R^3 with prescribed side lengths equals 2n-5, assuming that the space is nonempty and does not contain any straight-line polygons. ... More

Upscaled Lattice Boltzmann Method for Simulations of Flows in Heterogeneous Porous MediaDec 01 2013A upscaled lattice Boltzmann method (LBM) for flow simulations in heterogeneous porous media, at both pore and Darcy scales, is proposed in this paper. In the micro-scale simulations, we model flows using LBM with the modified Guo et al. algorithm where ... More

On reconciling quantum mechanics and local realismSep 04 2013A necessary and natural change in our application of quantum mechanics to separated systems is shown to reconcile quantum mechanics and local realism. An analysis of separation and localization justifies the proposed change in application of quantum mechanics. ... More

Comonadic Coalgebras and Bousfield LocalizationMay 29 2018For a model category, we prove that taking the category of coalgebras over a comonad commutes with left Bousfield localization in a suitable sense. Then we prove a general existence result for left-induced model structure on the category of coalgebras ... More

For objective causal inference, design trumps analysisNov 11 2008For obtaining causal inferences that are objective, and therefore have the best chance of revealing scientific truths, carefully designed and executed randomized experiments are generally considered to be the gold standard. Observational studies, in contrast, ... More

Flying in Two DimensionsOct 16 2011Diversity and specialization of behavior in insects is unmatched. Insects hop, walk, run, jump, row, swim, glide and fly to propel themselves in a variety of environments. We have uncovered an unusual mode of propulsion of aerodynamic flight in two dimensions ... More

Woofer-tweeter deformable mirror control for closed-loop adaptive optics: theory and practiceJul 30 2014Deformable mirrors with very high order correction generally have smaller dynamic range of motion than what is required to correct seeing over large aperture telescopes. As a result, systems will need to have an architecture that employs two deformable ... More

Structured Sparsity via Alternating Direction MethodsMay 04 2011Dec 15 2011We consider a class of sparse learning problems in high dimensional feature space regularized by a structured sparsity-inducing norm which incorporates prior knowledge of the group structure of the features. Such problems often pose a considerable challenge ... More

Bare Quantum Null Energy ConditionNov 07 2017Feb 13 2018The quantum null energy condition (QNEC) is a conjectured relation between a null version of quantum field theory energy and derivatives of quantum field theory von Neumann entropy. In some cases, divergences cancel between these two terms and the QNEC ... More

Enumerating lattices of subsetsNov 26 2013Dec 10 2013Given k sets such that no one is contained in another, there is an associated lattice on the power set P([k]) corresponding to inclusion relations among unions of the sets. Two lattices on P([k]) are equivalent if there is a permutation of [k] under which ... More

Efficient Subsampled Gauss-Newton and Natural Gradient Methods for Training Neural NetworksJun 05 2019We present practical Levenberg-Marquardt variants of Gauss-Newton and natural gradient methods for solving non-convex optimization problems that arise in training deep neural networks involving enormous numbers of variables and huge data sets. Our methods ... More

Clauser-Horne/Eberhard inequality violation by a local modelJul 22 2015Feb 25 2016Thanks to its immunity to the detection loophole, the Clauser-Horne/Eberhard inequality plays an important role in tests of locality and in certification of quantum information protocols based on entanglement. I describe a local model that violates the ... More

A Local Realist Account of the Weihs et al EPRB ExperimentJan 08 2013Apr 07 2013Quantum mechanics stands in conflict with local realism only in its treatment of separated systems. A modification of quantum mechanics that changes the handling of separated systems is suggested that can reconcile quantum mechanics with local realism. ... More

The Quantum Prediction for Einstein-Podolsky-Rosen (EPR) ExperimentsJul 05 2016Aug 07 2016Quantum mechanics allows for multiple predictions for the outcome of an EPR experiment. The correct calculation must be used, guided by the physical conditions of the experiment. The quantum joint prediction for EPR correlation is derived and shown to ... More

Homotopical Adjoint Lifting TheoremJun 06 2016This paper provides a homotopical version of the adjoint lifting theorem in category theory, allowing for Quillen equivalences to be lifted from monoidal model categories to categories of algebras over colored operads. The generality of our approach allows ... More

2-adic Stirling functions and their zerosFeb 03 2014Let $P_n(x)=\frac1{n!}\sum\binom n{2i+1}(2i+1)^x$. This extends to a continuous function on the 2-adic integers, the $n$th 2-adic partial Stirling function. We show that $(-1)^{n+1}P_n$ is the only 2-adically continuous approximation to $S(x,n)$, the ... More

Minimizing Squared Vertical and Squared Horizontal ErrorsDec 02 2005The slope of the best fit line from minimizing the sum of both the squared vertical errors and the squared horizontal errors is shown to be the root of a fourth degree polynomial.

Lattices of subalgebras of Leibniz algebrasFeb 27 2011I describe the lattice of subalgebras of a one-generator Leibniz algebra. Using this, I show that, apart from one special case, a lattice isomorphism between Leibniz algebras L, L' maps the Leibniz kernel of L to that of L'.

Schunck classes of soluble Leibniz algebrasJan 16 2011Jan 25 2011I set out the theory of Schunck classes and projectors for soluble Leibniz algebras, parallel to that for Lie algebras. Primitive Leibniz algebras come in pairs, one (Lie) symmetric, the other antisymmetric. A Schunck formation containing one member of ... More

An approach to the topological complexity of the Klein bottleDec 08 2016Feb 02 2017Recently, Cohen and Vandembroucq proved that the reduced topological complexity of the Klein bottle is 4. Simultaneously and independently, we announced a proof of the same result. Mistakes were found in our argument, which was quite different than theirs. ... More

Topological complexity of some planar polygon spacesApr 03 2015Jul 06 2015Using known results about their mod-2 cohomology ring, we prove that the topological complexity of the space of isometry classes of n-gons in the plane with one side of length r and all others of length 1 equals either 2n-5 or 2n-6, provided that n-r ... More

Real projective space as a space of planar polygonsJan 12 2015Jan 16 2015We prove that real projective space RP^{n-3} is homeomorphic to the space of all isometry classes of n-gons in the plane with one side of length n-2 and all other sides of length 1. This makes the topological complexity of real projective space more relevant ... More

Small spherical nilpotent orbits and K-types of Harish Chandra modulesDec 31 2006Let G be a connected linear semisimple Lie group with Lie algebra g and maximal compact subgroup K. Let K_C -> Aut(p_C) be the complexified isotropy representation at the identity coset of the corresponding symmetric space. Suppose that O is a nilpotent ... More

On the wave nature of matterMay 02 2005Following the spirit of de Broglie and Einstein, we think the concepts of matter and radiation should be unified. In part 1, we examine the physical nature of matter wave. We propose that: (1) Like the photon, a particle is not a point-like object; instead, ... More

Maximizing a combinatorial expression arising from crowd estimationOct 29 2009We determine, within 1, the value of N for which sum (s1 choose i)(s2 choose N)(s1 choose N-i)(N choose i) achieves its maximum value. Here s1 and s2 are fixed integers. This problem arises in studying the most likely value for the size of the union of ... More

Faithful completely reducible representations of modular Lie algebrasMar 06 2016May 19 2016The Ado-Iwasawa Theorem asserts that a finite-dimensional Lie algebra $L$ over a field $F$ has a finite-dimensional faithful module $V$. There are several extensions asserting the existence of such a module with various additional properties. In particular, ... More

Induced modules for modular Lie algebrasDec 01 2013Sep 13 2016Let $L$ be a finite-dimensional Lie algebra over a field of non-zero characteristic and let $S$ be a subalgebra. Suppose that $X$ is a finite set of finite-dimensional $L$-modules. Let $D$ be the category of all finite-dimensional $S$-modules. Then there ... More

A Bayesian semi-parametric model for small area estimationMay 21 2008In public health management there is a need to produce subnational estimates of health outcomes. Often, however, funds are not available to collect samples large enough to produce traditional survey sample estimates for each subnational area. Although ... More

After 50+ Years in Statistics, An ExchangeJul 24 2012This is an exchange between Jerome Sacks and Donald Ylvisaker covering their career paths along with some related history and philosophy of Statistics.

Algebraic methods toward higher-order probability inequalities, IIOct 06 2004Let (L,\preccurlyeq) be a finite distributive lattice, and suppose that the functions f_1,f_2:L\to R are monotone increasing with respect to the partial order \preccurlyeq. Given \mu a probability measure on L, denote by E(f_i) the average of f_i over ... More

Manifold properties of planar polygon spacesApr 05 2018May 08 2018We prove that the tangent bundle of a generic space of planar n-gons with specified side lengths, identified under isometry, plus a trivial line bundle is isomorphic to (n-2) times a canonical line bundle. We then discuss consequences for orientability, ... More

Simple Perturbatively Traversable Wormholes from Bulk FermionsAug 12 2019A new class of traversable wormholes was recently constructed which relies only on local bulk dynamics rather than an explicit coupling between distinct boundaries. Here we begin with a four-dimensional Weyl fermion field of any mass $m$ propagating on ... More

p-adic Stirling numbers of the second kindJul 29 2013Let S(n,k) denote the Stirling numbers of the second kind. We prove that the p-adic limit of S(p^e a + c, p^e b + d) as e goes to infinity exists for all integers a, b, c, and d. We call the limiting p-adic integer S(p^\infty a + c, p^\infty b + d). When ... More

v1-Periodic 2-exponents of SU(2^e) and SU(2^e + 1)Sep 22 2011We determine precisely the largest v1-periodic homotopy groups of SU(2^e) and SU(2^e + 1). This gives new results about the largest actual homotopy groups of these spaces. Our proof relies on results about 2-divisibility of restricted sums of binomial ... More

Divisibility by 2 and 3 of certain Stirling numbersJul 16 2008The numbers e_p(k,n) defined as min(nu_p(S(k,j)j!): j >= n) appear frequently in algebraic topology. Here S(k,j) is the Stirling number of the second kind, and nu_p(-) the exponent of p. The author and Sun proved that if L is sufficiently large, then ... More

Statistical Implications of the Revenue Transfer Methodology in the Affordable Care ActMar 03 2017Jun 07 2018The Affordable Care Act (ACA) includes a permanent revenue transfer methodology which provides financial incentives to health insurance plans that have higher than average actuarial risk. In this paper, we derive some statistical implications of the revenue ... More

The symmetrized topological complexity of the circleMar 15 2017We determine the symmetrized topological complexity of the circle, using primarily just general topology.

Bounds for higher topological complexity of real projective space implied by BPJan 18 2018We use Brown-Peterson cohomology to obtain lower bounds for the higher topological complexity, TC_k(RP^n), of real projective spaces, which are often much stronger than those implied by ordinary mod-2 cohomology.

Topological complexity (within 1) of the space of isometry classes of planar n-gons for sufficiently large nAug 30 2016Sep 07 2016Hausmann and Rodriguez classified spaces of isometry classes of planar n-gons according to their genetic code, which is a collection of sets (called genes) containing n. Omitting the n yields what we call gees. We prove that, for a set of gees with largest ... More

Explicit modular forms from the divided beta familyJun 21 2019We compute modular forms known to arise from the order 5 generators of the 5-local Adams-Novikov spectral sequence 2-line, generalizing and contextualizing previous computations of M. Behrens and G. Laures. We exhibit analogous computations at other primes ... More

Convergence of fixed-point continuation algorithms for matrix rank minimizationJun 18 2009Dec 29 2010The matrix rank minimization problem has applications in many fields such as system identification, optimal control, low-dimensional embedding, etc. As this problem is NP-hard in general, its convex relaxation, the nuclear norm minimization problem, is ... More

Integral Transform Methods in Goodness-of-Fit Testing, II: The Wishart DistributionsMar 06 2019We initiate the study of goodness-of-fit testing when the data consist of positive definite matrices. Motivated by the recent appearance of the cone of positive definite matrices in numerous areas of applied research, including diffusion tensor imaging, ... More

Integral Transform Methods in Goodness-of-Fit Testing, I: The Gamma DistributionsOct 16 2018We apply the method of Hankel transforms to develop goodness-of-fit tests for gamma distributions with given shape parameter and unknown rate parameter, thereby extending results of Baringhaus and Taherizadeh (2010) on the exponential distributions. We ... More

Homotopical Adjoint Lifting TheoremJun 06 2016Dec 30 2018This paper provides a homotopical version of the adjoint lifting theorem in category theory, allowing for Quillen equivalences to be lifted from monoidal model categories to categories of algebras over colored operads. The generality of our approach allows ... More

Right Bousfield Localization and Operadic AlgebrasDec 23 2015Feb 01 2018It is well known that under some general conditions right Bousfield localization exists. We provide general conditions under which right Bousfield localization yields a monoidal model category. Then we address the questions of when this monoidal model ... More

Rejoinder to Causal Inference Through Potential Outcomes and Principal Stratification: Application to Studies with "Censoring" Due to DeathDec 27 2006Rejoinder on Causal Inference Through Potential Outcomes and Principal Stratification: Application to Studies with ``Censoring'' Due to Death by D. B. Rubin [math.ST/0612783]

Intersections of conjugates of Magnus subgroups of one-relator groupsApr 08 2009Apr 21 2009In the theory of one-relator groups, Magnus subgroups, which are free subgroups obtained by omitting a generator that occurs in the given relator, play an essential structural role. In a previous article, the author proved that if two distinct Magnus ... More

Loading Monotonicity of Weighted Premiums, and Total Positivity Properties of Weight FunctionsJun 10 2018Feb 21 2019We consider the construction of insurance premiums that are monotonically increasing with respect to a loading parameter. By introducing weight functions that are totally positive of higher order, we derive higher monotonicity properties of weighted transformed ... More

On Levi's Theorem for Leibniz algebrasSep 06 2011A Lie algebra over a field of characteristic 0 splits over its soluble radical and all complements are conjugate. I show that the splitting theorem extends to Leibniz algebras but that the conjugacy theorem does not.

Introductory Lectures on Stochastic Population SystemsMay 10 2017These notes provide a review of basic stochastic population models including branching processes and models of population genetics. Measure-valued population models including superprocesses and Fleming-Viot processes are also introduced together some ... More

Divisibility by 2 of partial Stirling numbersSep 22 2011The partial Stirling numbers T_n(k) used here are defined as the sum over odd values of i of (n choose i) i^k. Their 2-exponents nu(T_n(k)) are important in algebraic topology. We provide many specific results, applying to all values of n, stating that, ... More

On the cohomology classes of planar polygon spacesApr 14 2016We obtain an explicit formula for the Poincare duality isomorphism H^{n-3}(Mbar(ell)) to Z/2 for the space of isometry classes of n-gons with specified side lengths, if ell is monogenic in the sense of Hausmann-Rodriguez. This has potential application ... More