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Identifying mediating variables with graphical models: an application to the study of causal pathways in people living with HIVJul 10 2019We empirically demonstrate that graphical models can be a valuable tool in the identification of mediating variables in causal pathways. We make use of graphical models to elucidate the causal pathway through which the treatment influences the levels ... More

The Dark Side of the UniverseAug 11 2005I will begin by reviewing the evidence for Dark Matter in the Universe, as well as the candidates for dark matter. At most 20% of the dark matter in galaxies can be in the form of MACHOs (Massive Compact Halo Objects); the remainder appears to be some ... More

Matter and Gravity in Warped Extradimensional Models: Reinterpreting Randall-SundrumOct 16 2005Warped extra dimension claims remarkable success: solving the hierarchy problem; explaining hierarchies in particle phenomenology; yielding standard cosmology, plus interesting nonstandard scenarios. Yet it has marked shortcomings: we over-rely on a single ... More

Equivalence for Rank-metric and Matrix Codes and Automorphism Groups of Gabidulin CodesApr 01 2013For a growing number of applications such as cellular, peer-to-peer, and sensor networks, efficient error-free transmission of data through a network is essential. Toward this end, K\"{o}tter and Kschischang propose the use of subspace codes to provide ... More

Cardassian Expansion: Dark Energy Density from Modified Friedmann EquationsJan 31 2005The Cardassian universe is a proposed modification to the Friedmann equation in which the universe is flat, matter dominated, and accelerating. In the ordinary Friedmann equation, the right hand side is a linear function of the energy density, $H^2 \sim ... More

Generalized Cardassian Expansion: Models in Which the Universe is Flat, Matter Dominated, and AcceleratingAug 29 2002Jul 30 2003The Cardassian universe is a proposed modification to the Friedmann Robertson Walker (FRW) equation in which the universe is flat, matter dominated, and accelerating. Here we generalize the original Cardassian proposal to include additional variants on ... More

Natural InflationOct 06 1993A pseudo-Nambu-Goldstone boson, with a potential of the form $ V(\phi) = \Lambda^4 [1 + \cos(\phi/f)]$, can naturally give rise to an epoch of inflation in the early universe (Freese, Frieman, and Olinto 1990). The potential is naturally flat (as required ... More

On Hierarchy, Charge Universality, and 4D Effective Theory in Randall-Sundrum ModelsJul 30 2004We present a variant formulation of the Randall-Sundrum model which solves both the hierarchy and charge universality problems. We first critique the rationale for hierarchy solution and 4D effective interactions in the Randall-Sundrum model. We note ... More

$τ$-invariants for knots in rational homology spheresNov 28 2016Ozsv\'ath and Szab\'o used the knot filtration on $\hat{CF}(S^3)$ to define the $\tau$-invariant for knots in $S^3$. In this article we generalize their construction and define a collection of invariants $\{\tau_\mathfrak{s}(Y,K)\}_{\mathfrak{s}\in\S(Y)}$ ... More

Higher Order Stability in the Coefficients of the Colored Jones PolynomialMar 22 2016We discuss the higher order stabilization of the coefficients of the colored Jones polynomial. In particular, we find an expression for the second stable sequence of the colored Jones polynomial of a certain class of knots. We also determine which knots ... More

The Sum of Four Squares Over Real Quadratic Number FieldsOct 21 2016May 23 2018Well-known results of Lagrange and Jacobi prove that the every $m \in \mathbb N$ can be expressed as a sum of four integer squares, and the number $r(m)$ of such representations can be given by an explicit formula in $m$. In this paper, we prove that ... More

Review of Observational Evidence for Dark Matter in the Universe and in upcoming searches for Dark StarsDec 20 2008Over the past decade, a consensus picture has emerged in which roughly a quarter of the universe consists of dark matter. The observational evidence for the existence of dark matter is reviewed: rotation curves of galaxies, weak lensing measurements, ... More

Voltage Uncertainties in the Presence of Photovoltaic SystemsDec 05 2016With the rising demand for solar energy installation, there is a pressing need for utilities to regulate the voltages at the distribution level. In grids with high penetration of photovoltaic (PV) systems, voltage fluctuations can occur at the distribution ... More

The under-explored radio-loudness of quasars and the possibility of radio-source--environment interactionsJun 05 2003I demonstrate that radio observations in the literature to date of optically-selected quasars are largely inadequate to reveal the full extent of their jet-activity. I discuss a recent example of an optically-powerful quasar, which is radio-quiet according ... More

Extinction debt repayment via timely habitat restorationMar 25 2018Habitat destruction threatens the viability of many populations, but its full consequences can take considerable time to unfold. Much of the discourse surrounding extinction debts--the number of species that persist transiently following habitat loss, ... More

Escape, Accretion or Star Formation? The Competing Depleters of Gas in the Quasar Markarian 231Feb 02 2015Feb 16 2015We report on high resolution CO(1-0), CS(2-1) and 3mm continuum Combined Array for Research in Millimeter Astronomy (CARMA) observations of the molecular outflow host and nearest quasar Markarian 231. We use the CS(2-1) measurements to derive a dense ... More

An Enumeration of the Equivalence Classes of Self-Dual Matrix CodesMay 27 2015Jul 20 2015As a result of their applications in network coding, space-time coding, and coding for criss-cross errors, matrix codes have garnered significant attention; in various contexts, these codes have also been termed rank-metric codes, space-time codes over ... More

Radio-loud and radio-quiet quasars: one population, different epochs of observationMar 05 2008I bring together evidence for the rapidity with which quasars' radio synchrotron lobe emission fades and for the intermittency with which jet plasma is ejected from individual quasars and radio galaxies and affirm the picture presented by Nipoti et al ... More

Studying Neutral Current Elastic Scattering and the Strange Axial Form Factor in MicroBooNEJan 13 2019One of the least constrained contributions to the neutral current (NC) elastic neutrino-proton cross section is the strange axial form factor, which represents the strange quark spin contribution to the spin structure of the proton. This becomes the net ... More

A Dynamical Systems Framework for Resilience in EcologySep 28 2015Rising interest in the resilience of ecological systems has spawned diverse interpretations of the term's precise meaning. This paper classifies and explores definitions of resilience from the ecological literature using a dynamical systems framework. ... More

Higher Order Stability in the Coefficients of the Colored Jones PolynomialMar 22 2016Jun 22 2017We discuss the higher order stabilization of the coefficients of the colored Jones polynomial. In particular, we find an expression for the second stable sequence of the colored Jones polynomial of a certain class of knots. We also determine which knots ... More

A Coupling of Pseudo Nambu Goldstone Bosons to Other Scalars and Role in Double Field InflationMay 19 1994We find a coupling of Pseudo Nambu Goldstone bosons (PNGBs) to other (ordinary) scalars, and consider its importance in various contexts. Our original motivation was the model of Double Field inflation [1]. We also briefly consider the role of this coupling ... More

The Sum of Four Squares Over Real Quadratic Number FieldsOct 21 2016Well-known results of Lagrange and Jacobi prove that the every $m \in \mathbb N$ can be expressed as a sum of four integer squares, and the number $r(m)$ of such representations can be given by an explicit formula in $m$. In this paper, we prove that ... More

Active matter clusters at interfacesApr 04 2016Collective and directed motility or swarming is an emergent phenomenon displayed by many self-organized assemblies of active biological matter such as clusters of embryonic cells during tissue development, cancerous cells during tumor formation and metastasis, ... More

Probing Dark Energy Using Its Density Instead of Its Equation of StateFeb 09 2004The variation of dark energy density with redshift, $\rho_X(z)$, provides a critical clue to the nature of dark energy. Since $\rho_X(z)$ depends on the dark energy equation of state $w_X(z)$ through an integral, $\rho_X(z)$ can be constrained more tightly ... More

Indirect Detection of a Light Higgsino Motivated by Collider DataSep 16 1996Kane and Wells recently argued that collider data point to a Higgsino-like lightest supersymmetric partner which would explain the dark matter in our Galactic halo. They discuss direct detection of such dark-matter particles in laboratory detectors. Here, ... More

Fluid Interpretation of Cardassian ExpansionSep 26 2002Oct 13 2003A fluid interpretation of Cardassian expansion is developed. Here, the Friedmann equation takes the form $H^2 = g(\rho_M)$ where $\rho_M$ contains only matter and radiation (no vacuum). The function $g(\rhom)$ returns to the usual $8\pi\rhom/(3 m_{pl}^2)$ ... More

On degree sequences forcing the square of a Hamilton cycleDec 10 2014Jul 30 2015A famous conjecture of P\'osa from 1962 asserts that every graph on $n$ vertices and with minimum degree at least $2n/3$ contains the square of a Hamilton cycle. The conjecture was proven for large graphs in 1996 by Koml\'os, S\'ark\"ozy and Szemer\'edi. ... More

Known Unknowns of Dark Matter Annihilation over Cosmic TimeSep 30 2013Jan 21 2014Dark matter self-annihilation holds promise as one of the most robust mechanisms for the identification of the particle responsible for the Universe's missing mass. In this work, I examine the evolution of the dark matter annihilation power produced by ... More

Pattern completion in symmetric threshold-linear networksDec 02 2015May 07 2016Threshold-linear networks are a common class of firing rate models that describe recurrent interactions among neurons. Unlike their linear counterparts, these networks generically possess multiple stable fixed points (steady states), making them viable ... More

Systematic motions in the Galactic plane found in the Hipparcos Catalogue using Herschel's MethodOct 16 2005Two motions in the galactic plane have been detected and characterized, based on the determination of a common systematic component in Hipparcos catalogue proper motions. The procedure is based only on positions, proper motions and parallaxes, plus a ... More

High-z radio galaxies and the `Youth-Redshift Degeneracy'Oct 08 1999We discuss a unifying explanation for many `trends with redshift' of radio galaxies which includes the relevance of their ages (time since their jet triggering event), and the marked dependence of their ages on redshift due to the selection effect of ... More

The optically-powerful quasar E1821+643 is associated with a 300-kpc scale FRI radio structureOct 06 2001We present a deep image of the optically-powerful quasar E1821+643 at 18cm made with the Very Large Array (VLA). This image reveals radio emission, over 280 kpc in extent, elongated way beyond the quasar's host galaxy. Its radio structure has decreasing ... More

A synthetic autonomous rotary nanomotor made from and fuelled by DNAMay 30 2015DNA nanostructures are made using synthetic DNA strands, the sequences of which are designed such that they will self-assemble into the desired form by hybridization of complementary domains. Various structures and devices have been presented, including ... More

The embedding structure for linearly ordered topological spacesFeb 10 2011In this paper, the class of all linearly ordered topological spaces (LOTS) quasi-ordered by the embeddability relation is investigated. In ZFC it is proved that for countable LOTS this quasi-order has both a maximal (universal) element and a finite basis. ... More

CP Violation measurements in B to charm decays at BaBarOct 05 2006This article summarises measurements of time-dependent CP asymmetries in decays of neutral B mesons to charm final states using data collected by the BaBar detector at the PEP-II asymmetric-energy B-factory. All results are preliminary unless otherwise ... More

A universe in a global monopoleApr 06 2001We investigate brane physics in a universe with an extra dimensional global monopole and negative bulk cosmological constant. The graviton zero mode is naturally divergent; we thus invoke a physical cut-off to induce four dimensional gravity on a brane ... More

The effects of cyclical simulation on the axon hillock diameter of murine intracortical neuronsMar 22 2018Changes to the axon hillock in frequently firing neurons are known to be important predictors of early disease states. Studying this phenomenon is critical to understanding the first insult implicated in multiple neuro-degenerative disorders. To study ... More

A formula for the Dubrovnik polynomial of rational knotsMar 31 2015We provide a formula for the Dubrovnik polynomial of a rational knot in terms of the entries of the tuple associated with a braid-form diagram of the knot. Our calculations can be easily carried out using a computer algebra system.

Algebraic aspects of solving Ring-LWE, including ring-based improvements in the Blum-Kalai-Wasserman algorithmFeb 19 2019May 13 2019We provide a reduction of the Ring-LWE problem to Ring-LWE problems in subrings, in the presence of samples of a restricted form (i.e. $(a,b)$ such that $a$ is restricted to a multiplicative coset of the subring). To create and exploit such restricted ... More

Cardassian Expansion: a Model in which the Universe is Flat, Matter Dominated, and AcceleratingJan 15 2002Jun 18 2002A modification to the Friedmann Robertson Walker equation is proposed in which the universe is flat, matter dominated, and accelerating. An additional term, which contains only matter or radiation (no vacuum contribution), becomes the dominant driver ... More

The Apollonian structure of Bianchi groupsMay 12 2015Oct 08 2015We study the orbit of $\widehat{\mathbb{R}}$ under the M\"obius action of the Bianchi group $\operatorname{PSL}_2(\mathcal{O}_K)$ on $\widehat{\mathbb{C}}$, where $\mathcal{O}_K$ is the ring of integers of an imaginary quadratic field $K$. The orbit $\mathcal{S}_K$, ... More

Exploring the Correlations between Globular Cluster Populations and Supermassive Black Holes in Giant GalaxiesOct 16 2012This paper presents an analysis of the correlation between the number of globular clusters (N_GC) in giant galaxies and the mass of the galaxies' central supermassive black hole (M_SMBH). I construct a sample of 20 elliptical, spiral, and S0 galaxies ... More

Dark Matter collisions with the Human BodyApr 05 2012Apr 11 2012We investigate the interactions of Weakly Interacting Massive Particles (WIMPs) with nuclei in the human body. We are motivated by the fact that WIMPs are excellent candidates for the dark matter in the Universe. Our estimates use a 70 kg human and a ... More

Bell Inequalities with Communication AssistanceMay 13 2014In this paper we consider the possible correlations between two parties using local machines and shared randomness with an additional amount of classical communication. This is a continuation of the work initiated by Bacon and Toner in Ref. [\textit{Phys. ... More

Reply to "A note on the innocuous implications of a minimum length in quantum gravity" by P.H. FramptonFeb 16 2009We reply to the comment "A note on the innocuous implications of a minimum length in quantum gravity" by P.H. Frampton [Class. Quantum Grav. 26 (2009) 018001, arXiv:arXiv:0808.0283] on our paper "Dangerous implications of a minimum length in quantum gravity" ... More

Dangerous implications of a minimum length in quantum gravityMar 05 2008Jul 17 2008The existence of a minimum length and a generalization of the Heisenberg uncertainty principle seem to be two fundamental ingredients required in any consistent theory of quantum gravity. In this letter we show that they would predict dangerous processes ... More

Chain Inflation in the Landscape: "Bubble Bubble Toil and Trouble"Dec 13 2004Jul 01 2005In the model of Chain Inflation, a sequential chain of coupled scalar fields drives inflation. We consider a multidimensional potential with a large number of bowls, or local minima, separated by energy barriers: inflation takes place as the system tunnels ... More

Curvature and Flatness in a Brans-Dicke UniverseDec 15 1993The evolution of a universe with Brans-Dicke gravity and nonzero curvature is investigated here. We present the equations of motion and their solutions during the radiation dominated era. In a Friedman-Robertson-Walker cosmology we show explicitly that ... More

CP-Violating Effects in Neutralino Scattering and AnnihilationAug 17 1999We show that in some regions of supersymmetric parameter space, CP violating effects that mix the CP-even and CP-odd Higgs bosons can enhance the neutralino annihilation rate, and hence the indirect detection rate of neutralino dark matter, by factors ... More

An Accelerating Universe from Dark Matter Interactions with Negative PressureNov 26 2002As an explanation for the acceleration of the universe, we propose dark matter with self-interactions characterized by a negative pressure; there is no vacuum energy whatsoever in this Cardassian model. These self-interactions may arise due to a long-range ... More

Patterns of Negative Shifts and Beta-ShiftsDec 14 2015Jan 29 2016The $\beta$-shift is the transformation from the unit interval to itself that maps $x$ to the fractional part of $\beta x$. Permutations realized by the relative order of the elements in the orbits of these maps have been studied for positive integer ... More

Symplectic embeddings of four-dimensional polydisks into ballsOct 03 2016In this paper we obtain new obstructions to symplectic embeddings of the four-dimensional polydisk $P(a,1)$ into the ball $B(c)$ for $2\leq a<\frac{\sqrt{7}-1} {\sqrt{7}-2} \approx 2.549$, extending work done by Hind-Lisi and Hutchings. Schlenk's folding ... More

Blogging in the physics classroom: A research-based approach to shaping students' attitudes towards physicsAug 13 2007Jun 25 2008Even though there has been a tremendous amount of research done in how to help students learn physics, students are still coming away missing a crucial piece of the puzzle: why bother with physics? Students learn fundamental laws and how to calculate, ... More

Calculation of Particle Production by Nambu Goldstone Bosons with Application to Inflation Reheating and BaryogenesisOct 22 1994A semiclassical calculation of particle production by a scalar field in a potential is performed. We focus on the particular case of production of fermions by a Nambu-Goldstone boson $\theta$. We have derived a (non)local equation of motion for the $\theta$-field ... More

X-ray emission around the z=4.1 radio galaxy TNJ1338-1942 and the potential role of far-infrared photons in AGN FeedbackJul 05 2013We report the discovery in an 80-ks observation of spatially-extended X-ray emission around the high-redshift radio galaxy TNJ1388-1942 (z=4.11) with the Chandra X-ray Observatory. The X-ray emission extends over a ~30-kpc diameter region and although ... More

Distinguishing among dark matter annihilation channels with neutrino telescopesJan 31 2012Jul 05 2012We investigate the prospects for distinguishing dark matter annihilation channels using the neutrino flux from gravitationally captured dark matter particles annihilating inside the sun. We show that, even with experimental error in energy reconstruction ... More

Science with an ngVLA: Accreting Supermassive Black Holes in Nearby Low-mass GalaxiesOct 15 2018The ngVLA will facilitate deep surveys capable of detecting the faint and compact signatures of accreting supermassive black holes (SMBHs) with masses below one million solar-masses hosted by low-mass ($< 10^9$ solar-masses) galaxies. This will provide ... More

Jet velocity in SS433: its anti-correlation with precession-cone angle and dependence on orbital phaseOct 19 2004Feb 15 2005We present a re-analysis of the optical spectroscopic data on SS433 from the last quarter-century and demonstrate that these data alone contain systematic and identifiable deviations from the traditional kinematic model for the jets: variations in speed, ... More

The sensual Apollonian circle packingAug 23 2012Mar 12 2014The curvatures of the circles in integral Apollonian circle packings, named for Apollonius of Perga (262-190 BC), form an infinite collection of integers whose Diophantine properties have recently seen a surge in interest. Here, we give a new description ... More

Towards Physical Hybrid SystemsMay 23 2019Some hybrid systems models are unsafe for mathematically correct but physically unrealistic reasons. For example, mathematical models can classify a system as being unsafe on a set that is too small to have physical importance. In particular, differences ... More

Patterns of Negative Shifts and Beta-ShiftsDec 14 2015Nov 16 2016The $\beta$-shift is the transformation from the unit interval to itself that maps $x$ to the fractional part of $\beta x$. Permutations realized by the relative order of the elements in the orbits of these maps have been studied for positive integer ... More

A survey of Galois theory of curves in characteristic pApr 13 2010This survey is about Galois theory of curves in characteristic p, a topic which has inspired major research in algebraic geometry and number theory and which contains many open questions. We illustrate important phenomena which occur for covers of curves ... More

$k$-means: Fighting against Degeneracy in Sequential Monte Carlo with an Application to TrackingNov 13 2015For regular particle filter algorithm or Sequential Monte Carlo (SMC) methods, the initial weights are traditionally dependent on the proposed distribution, the posterior distribution at the current timestamp in the sampled sequence, and the target is ... More

Bayesian Epidemic Detection in Multiple PopulationsSep 14 2015Traditional epidemic detection algorithms make decisions using only local information. We propose a novel approach that explicitly models spatial information fusion from several metapopulations. Our method also takes into account cost-benefit considerations ... More

Axions, Inflation and the Anthropic PrincipleNov 03 2009The QCD axion is the leading solution to the strong-CP problem, a dark matter candidate, and a possible result of string theory compactifications. However, for axions produced before inflation, symmetry-breaking scales of $f_a \gtrsim 10^{12}$ GeV (which ... More

Twisted Alice Loops as MonopolesApr 17 2003Dec 05 2003Symmetry breaking can produce ``Alice'' strings, which alter scattered charges and carry monopole number and charge when twisted into loops. We apply recent topological results, fixing Alice strings' stability and prescribing their twisting into loops ... More

Constraints on Primordial Black Holes with Extended Mass FunctionsJan 25 2017Feb 22 2017Constraints on primordial black holes in the range $10^{-18} M_{\odot}$ to $10^{3} M_{\odot}$ are reevaluated for a general class of extended mass functions. Whereas previous work has assumed that PBHs are produced with one single mass, instead there ... More

Symplectic embeddings of four-dimensional polydisks into ballsOct 03 2016Nov 14 2017In this paper we obtain new obstructions to symplectic embeddings of the four-dimensional polydisk $P(a,1)$ into the ball $B(c)$ for $2\leq a<\frac{\sqrt{7}-1} {\sqrt{7}-2} \approx 2.549$, extending work done by Hind-Lisi and Hutchings. Schlenk's folding ... More

Pointless Continuous Spatial Surface ReconstructionSep 27 2017The analysis of area-level aggregated summary data is common in many disciplines including epidemiology and the social sciences. Typically, Markov random field spatial models have been employed to acknowledge spatial dependence and allow data-driven smoothing. ... More

Random Walk Null Models for Time Series DataOct 05 2017Permutation entropy has become a standard tool for time series analysis that exploits the temporal properties of these data sets. Many current applications use an approach based on Shannon entropy, which implicitly assumes an underlying uniform distribution ... More

Free Energy of Multiple Overlapping ChainsNov 16 2011How accurate is pair additivity in describing interactions between soft polymer-based nanoparticles? Using numerical simulations we compute the free energy cost required to overlap multiple chains in the same region of space, and provide a quantitative ... More

On degree sequences forcing the square of a Hamilton cycleDec 10 2014Nov 24 2016A famous conjecture of P\'osa from 1962 asserts that every graph on $n$ vertices and with minimum degree at least $2n/3$ contains the square of a Hamilton cycle. The conjecture was proven for large graphs in 1996 by Koml\'os, S\'ark\"ozy and Szemer\'edi. ... More

Integral points on elliptic curves and explicit valuations of division polynomialsAug 15 2011Dec 29 2014Assuming Lang's conjectured lower bound on the heights of non-torsion points on an elliptic curve, we show that there exists an absolute constant C such that for any elliptic curve E/Q and non-torsion point P in E(Q), there is at most one integral multiple ... More

Free boundary stable hypersurfaces in manifolds with density and rigidity resultsNov 08 2013Let $M$ be a weighted manifold with boundary $\partial M$, i.e., a Riemannian manifold where a density function is used to weight the Riemannian Hausdorff measures. In this paper we compute the first and the second variational formulas of the interior ... More

Instability and Subsequent Evolution of Electroweak BubblesAug 04 1992Bubbles in a first-order electroweak phase transition are nucleated with radii $R_0$ and expand with velocity $v$. If $v$ is subsonic, a bubble becomes unstable to non-spherical perturbations when its radius is roughly $10^4\, R_0$. These perturbations ... More

Effects of CP-Violation in Neutralino Scattering and AnnihilationJan 10 2000We summarize our paper hep-ph/9908390, where we find that in some regions of supersymmetric parameter space, CP violating effects that mix the CP-even and CP-odd Higgs bosons can enhance the neutralino annihilation rate by factors of 10^6, and reduce ... More

A Topological Criterion for Alice StringsApr 17 2003Dec 05 2003Symmetry breaking can produce ``Alice'' strings, which alter scattered charges and carry monopole number and charge when twisted into loops. Alice behavior arises algebraically, when a string's untraced Wilson loop obstructs unbroken symmetries -- a fragile ... More

A Wide-Field Survey of the Globular Cluster Systems of Giant GalaxiesMay 12 2006I present selected results from a wide-field CCD survey of the globular cluster systems of giant galaxies, including showing how measurements of the specific frequency of metal-poor globular clusters can constrain the redshift of their formation.

First Test of High Frequency Gravity Waves from Inflation using ADVANCED LIGOMay 24 2013Jan 11 2015Inflation models ending in a first order phase transition produce gravitational waves (GW) via bubble collisions of the true vacuum phase. We demonstrate that these bubble collisions can leave an observable signature in Advanced LIGO, an upcoming ground-based ... More

Jet propulsion of wind ejecta from a major flare in the black hole microquasar SS433Apr 14 2011We present direct evidence, from Adaptive-Optics near-infra-red imaging, of the jets in the Galactic microquasar SS433 interacting with enhanced wind-outflow off the accretion disc that surrounds the black hole in this system. Radiant quantities of gas ... More

Symmetry in the changing jets of SS433 and its true distance from usOct 19 2004We present the deepest yet radio image of the Galactic jet source, SS433, which reveals over two full precession cycles (> 2 x 163 days) of the jet axis. Systematic and identifiable deviations from the traditional kinematical model for the jets are found: ... More

Concentration of the number of solutions of random planted CSPs and Goldreich's one-way candidatesApr 30 2015This paper shows that the logarithm of the number of solutions of a random planted $k$-SAT formula concentrates around a deterministic $n$-independent threshold. Specifically, if $F^*_{k}(\alpha,n)$ is a random $k$-SAT formula on $n$ variables, with clause ... More

Inferring Information Flow in Spike-train Data Sets using a Trial-Shuffle MethodFeb 17 2018Oct 25 2018Understanding information processing in the brain requires the ability to determine the functional connectivity between the different regions of the brain. We present a method using transfer entropy to extract this flow of information between brain regions ... More

Elliptic nets and elliptic curvesOct 05 2007Sep 12 2010An elliptic divisibility sequence is an integer recurrence sequence associated to an elliptic curve over the rationals together with a rational point on that curve. In this paper we present a higher-dimensional analogue over arbitrary base fields. Suppose ... More

The space of graded traces for holomorphic VOAs of small central chargeJun 12 2006It is one of the remarkable results of vertex operator algebras (VOAs) that the graded traces (one-point correlation functions) of holomorphic VOAs are modular functions. This paper explores the question of which modular functions arise as the graded ... More

Odd behavior in the coefficients of reciprocals of binary power seriesNov 06 2014Let $\mathcal{A}$ be a finite subset of $\mathbb{N}$ including $0$ and $f_\mathcal{A}(n)$ be the number of ways to write $n=\sum_{i=0}^{\infty}\epsilon_i2^i$, where $\epsilon_i\in\mathcal{A}$. The sequence $\left(f_\mathcal{A}(n)\right) \bmod 2$ is always ... More

Sphericons and D-forms: a crocheted connectionMar 01 2016Jun 15 2016Sphericons and D-forms are 3D objects created and described by artists, which have separately received attention in the mathematical literature in the last 15 or so years. The attempt to classify a seamed, crocheted form geometrically led to the observation, ... More

Apparent shape of super-spinning black holesDec 07 2008Feb 03 2009We consider the possibility that astrophysical Black Holes (BHs) can violate the Kerr bound; i.e., they can have angular momentum greater than BH mass, $J > M$. We discuss implications on the BH apparent shape. Even if the bound is violated by a small ... More

A Bound on the Flux of Magnetic Monopoles from Catalysis of Nucleon Decay in White DwarfsApr 15 1998Catalysis of nucleon decay in white dwarfs is used to constrain the abundance of magnetic monopoles arising from Grand Unified Theories. Recent discoveries of the dimmest white dwarf ever observed, WD 1136-286 with $L = 10^{-4.94} L_{\odot}$, place limits ... More

Chamber Surface Roughness and Electron Cloud for the Advanced Photon Source Superconducting UndulatorJul 19 2013The electron cloud is a possible heat source in the superconducting undulator (SCU) designed for the Advanced Photon Source (APS), a 7-GeV electron synchrotron radiation source at Argonne National Laboratory. In electron cloud generation extensive research ... More

Some experiments with integral Apollonian circle packingsJan 11 2010Bounded Apollonian circle packings (ACP's) are constructed by repeatedly inscribing circles into the triangular interstices of a configuration of four mutually tangent circles, one of which is internally tangent to the other three. If the original four ... More

Gravity Waves from Chain InflationNov 14 2008Chain inflation proceeds through a series of first order phase transitions, which can release considerable gravitational waves (GW). We demonstrate that bubble collisions can leave an observable signature for future high-frequency probes of GWs, such ... More

Dark Matter: A PrimerJun 12 2010Jan 24 2011Dark matter is one of the greatest unsolved mysteries in cosmology at the present time. About 80% of the universe's gravitating matter is non-luminous, and its nature and distribution are for the most part unknown. In this paper, we will outline the history, ... More

Charge Violation and Alice Behavior in Global and Textured StringsMar 28 2001Spontaneous breaking of global symmetries can produce ``Alice'' strings: line defects which make unbroken symmetries multivalued, induce apparent charge violation via Aharonov-Bohm interactions, and form point defects when twisted into loops. We demonstrate ... More

Skyrmions and Semilocal Strings in CosmologyApr 05 1993It has been pointed out that cosmic string solutions can exist in gauge field theories with broken symmetry even when $\pi _1(G/H)$ is trivial. The stability of such semilocal defects is not guaranteed by topology and depends on dynamical considerations. ... More

Visualising the arithmetic of imaginary quadratic fieldsOct 01 2014Mar 28 2015We study the orbit of $\mathbb{R}$ under the Bianchi group $\operatorname{PSL}_2(\mathcal{O}_K)$, where $K$ is an imaginary quadratic field. The orbit, called a Schmidt arrangement $\mathcal{S}_K$, is a geometric realisation, as an intricate circle packing, ... More

Transit timing to first order in eccentricitySep 04 2015Apr 27 2016Characterization of transiting planets with transit timing variations (TTVs) requires understanding how to translate the observed TTVs into masses and orbital elements of the planets. This can be challenging in multi-planet transiting systems, but fortunately ... More

The bandwidth theorem for locally dense graphsJul 25 2018The Bandwidth theorem of B\"ottcher, Schacht and Taraz gives a condition on the minimum degree of an $n$-vertex graph $G$ that ensures $G$ contains every $r$-chromatic graph $H$ on $n$ vertices of bounded degree and of bandwidth $o(n)$, thereby proving ... More

On the origin of radio core emission in radio-quiet quasarsAug 21 2007We present a model for the radio emission from radio-quiet quasar nuclei. We show that a thermal origin for the high brightness temperature, flat spectrum point sources (known as radio ``cores'') is possible provided the emitting region is hot and optically-thin. ... More