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The Impact of a Percolating IGM on Redshifted 21 cm Observations of Quasar HII RegionsAug 28 2007Mar 04 2008We assess the impact of inhomogeneous reionization on detection of HII regions surrounding luminous high redshift quasars using planned low frequency radio telescopes. Our approach is to implement a semi-numerical scheme to calculate the 3-dimensional ... More

Modification of the 21-cm power spectrum by X-rays during the epoch of reionisationSep 11 2008Apr 07 2009We incorporate a contribution to reionization from X-rays within analytic and semi-numerical simulations of the 21-cm signal arising from neutral hydrogen during the epoch of reionization. We explore the impact that X-ray ionizations have on the power ... More

Modification of the 21-cm power spectrum by quasars during the epoch of reionisationApr 21 2009We assess the effect of a population of high-redshift quasars on the 21-cm power spectrum during the epoch of reionisation. Our approach is to implement a semi-numerical scheme to calculate the three-dimensional structure of ionised regions surrounding ... More

Imaging HII Regions from Galaxies and Quasars During Reionisation with SKAJan 17 2015The ionisation structure of the Intergalactic Medium (IGM) during reionisation is sensitive to the unknown galaxy formation physics that prevailed at that time. This structure introduces non-Gaussian statistics into the redshifted 21 cm fluctuation amplitudes ... More

Polarised foreground removal at low radio frequencies using rotation measure synthesis: uncovering the signature of hydrogen reionisationNov 10 2010Jul 27 2011Measurement of redshifted 21-cm emission from neutral hydrogen promises to be the most effective method for studying the reionisation history of hydrogen and, indirectly, the first galaxies. These studies will be limited not by raw sensitivity to the ... More

The Impact of HI in Galaxies on 21-cm Intensity Fluctuations During the Reionisation EpochSep 08 2008We investigate the impact of neutral hydrogen (HI) in galaxies on the statistics of 21-cm fluctuations using analytic and semi-numerical modelling. Following the reionisation of hydrogen the HI content of the Universe is dominated by damped absorption ... More

The effect of Galactic foreground subtraction on redshifted 21-cm observations of quasar HII regionsMay 01 2008We assess the impact of Galactic synchrotron foreground removal on the observation of high-redshift quasar HII regions in redshifted 21-cm emission. We consider the case where a quasar is observed in an intergalactic medium (IGM) whose ionisation structure ... More

Measurement of the baryonic acoustic oscillation scale in 21 cm intensity fluctuations during the reionisation eraMar 19 2008Jan 13 2009It has recently been suggested that the power spectrum of redshifted 21cm fluctuations could be used to measure the scale of baryonic acoustic oscillations (BAOs) during the reionisation era. The resulting measurements are potentially as precise as those ... More

Baryonic Acoustic Oscillations in 21cm Emission: A Probe of Dark Energy out to High RedshiftsSep 19 2007Low-frequency observatories are currently being constructed with the goal of detecting redshifted 21cm emission from the epoch of reionization. These observatories will also be able to detect intensity fluctuations in the cumulative 21cm emission after ... More

Dark-ages Reionization and Galaxy Formation Simulation - XIV. Gas accretion, cooling and star formation in dwarf galaxies at high redshiftFeb 12 2018Aug 06 2018We study dwarf galaxy formation at high redshift ($z\ge5$) using a suite of high- resolution, cosmological hydrodynamic simulations and a semi-analytic model (SAM). We focus on gas accretion, cooling and star formation in this work by isolating the relevant ... More

Dark-ages Reionization and Galaxy Formation Simulation - XIV. Gas accretion, cooling and star formation in dwarf galaxies at high redshiftFeb 12 2018We study dwarf galaxy formation at high redshift ($z\ge5$) using a suite of high-resolution, cosmological hydrodynamic simulations and a semi-analytic model (SAM). We focus on gas accretion, cooling and star formation in this work by isolating the relevant ... More

Dark ages reionization & galaxy formation simulation XII: Bubbles at dawnApr 18 2017Jul 21 2017Direct detection of regions of ionized hydrogen (HII) has been suggested as a promising probe of cosmic reionization. Observing the redshifted 21-cm signal of hydrogen from the epoch of reionization (EoR) is a key scientific driver behind new-generation, ... More

Dark-ages Reionization and Galaxy Formation Simulation - XIII. AGN quenching of high-redshift star formation in ZF-COSMOS-20115Apr 11 2017Aug 25 2017Massive quiescent galaxies (MQGs) are thought to have formed stars rapidly at early times followed by a long period of quiescence. The recent discovery of a MQG, ZF-COSMOS-20115 at $z\sim4$, only 1.5 Gyr after the big bang, places new constraints on galaxy ... More

Dark-ages Reionization & Galaxy Formation Simulation VIII. Suppressed growth of dark matter halos during the Epoch of ReionizationJan 13 2017Feb 21 2017We investigate how the hydrostatic suppression of baryonic accretion affects the growth rate of dark matter halos during the Epoch of Reionization. By comparing halo properties in a simplistic hydrodynamic simulation in which gas only cools adiabatically, ... More

Dark-ages Reionization & Galaxy Formation Simulation II: Spin and concentration parameters for dark matter haloes during the Epoch of ReionizationDec 02 2015We use high resolution N-Body simulations to study the concentration and spin parameters of dark matter haloes in the mass range $10^8\, {\rm M}_{\odot}\, h^{-1} < {\rm M} < 10^{11}\, {\rm M}_{\odot}\, h^{-1}$ and redshifts $5{<}z{<}10$, corresponding ... More

Dark-ages reionization and galaxy formation simulation--VII. The sizes of high-redshift galaxiesAug 02 2016Nov 08 2016We investigate high-redshift galaxy sizes using a semi-analytic model constructed for the Dark-ages Reionization And Galaxy-formation Observables from Numerical Simulation project. Our fiducial model, including strong feedback from supernovae and photoionization ... More

Dark-ages Reionization and Galaxy Formation Simulation - X. The small contribution of quasars to reionizationMar 15 2017Sep 26 2017Motivated by recent measurements of the number density of faint AGN at high redshift, we investigate the contribution of quasars to reionization by tracking the growth of central supermassive black holes in an update of the Meraxes semi-analytic model. ... More

Dark-ages reionization & galaxy formation simulation V: morphology and statistical signatures of reionizationDec 02 2015Aug 15 2016We use the Dark-ages, Reionization And Galaxy-formation Observables from Numerical Simulations (DRAGONS) framework to investigate the effect of galaxy-formation physics on the morphology and statistics of ionized hydrogen (HII) regions during the Epoch ... More

Dark-ages reionization and galaxy formation simulation - III. Modelling galaxy formation and the epoch of reionizationDec 02 2015Aug 18 2016We introduce Meraxes, a new, purpose-built semi-analytic galaxy formation model designed for studying galaxy growth during reionization. Meraxes is the first model of its type to include a temporally and spatially coupled treatment of reionization and ... More

Dark-ages Reionization & Galaxy Formation Simulation I: The dynamical lives of high redshift galaxiesDec 02 2015Mar 21 2016We present the Dark-ages Reionization and Galaxy-formation Observables from Numerical Simulations (DRAGONS) program and Tiamat, the collisionless N-body simulation program upon which DRAGONS is built. The primary trait distinguishing Tiamat from other ... More

Dark-ages reionization and galaxy formation simulation XI: Clustering and halo masses of high redshift galaxiesMar 15 2017Sep 15 2017We investigate the clustering properties of Lyman-break galaxies (LBGs) at $z\sim6$ - $8$. Using the semi-analytical model {\scshape Meraxes} constructed as part of the Dark-ages Reionization And Galaxy-formation Observables from Numerical Simulation ... More

Dark-ages reionization and galaxy-formation simulation - VI. The origins and fate of the highest known redshift galaxyMay 25 2016Jan 09 2017Using Hubble data, including new grism spectra, Oesch et al. recently identified GN-z11, an $M_\textrm{UV}$=-21.1 galaxy at $z$=11.1 (just 400Myr after the big bang). With an estimated stellar mass of $\sim$10$^9$M$_{\odot}$, this galaxy is surprisingly ... More

Dark-ages reionization & galaxy formation simulation VI: The origins and fate of the highest known redshift galaxyMay 25 2016Using Hubble data, including new grism spectra, Oesch et al. (2016) recently identified GN-z11, a $M_\textrm{UV}$=-21.1 galaxy at $z$=11.1 (just 400 Myr after the Big Bang). With an estimated stellar mass of $\sim$10$^9$M$_\odot$, this galaxy is surprisingly ... More

Dark-ages reionization and galaxy formation simulation - IX. Economics of reionizing galaxiesMay 20 2017Jun 19 2017Using a series of high-resolution hydrodynamical simulations we show that during the rapid growth of high-redshift (z > 5) galaxies, reserves of molecular gas are consumed over a time-scale of 300Myr, almost independent of feedback scheme. We find that ... More

Dark-ages reionization & galaxy formation simulation IV: UV luminosity functions of high-redshift galaxiesDec 02 2015Apr 27 2016In this paper we present calculations of the UV luminosity function from the Dark-ages Reionization And Galaxy-formation Observables from Numerical Simulations (DRAGONS) project, which combines N-body, semi-analytic and semi-numerical modelling designed ... More

Dark-ages reionization and galaxy formation simulation--VII. The sizes of high-redshift galaxiesAug 02 2016We investigate high-redshift galaxy sizes using a semi-analytic model constructed for the Dark-ages Reionization And Galaxy-formation Observables from Numerical Simulation project. Our fiducial model, including strong feedback from supernovae and photoionization ... More

Roots and coefficients of multivariate polynomials over finite fieldOct 03 2014Kopparty and Wang studied in [3] the relation between the roots of a univariate polhynomial over GF(q) and the zero-nonzero pattern of its coefficients. We generalize their results to polynomials in more variables.

List decoding of a class of affine variety codesJan 26 2011Consider a polynomial $F$ in $m$ variables and a finite point ensemble $S=S_1 \times ... \times S_m$. When given the leading monomial of $F$ with respect to a lexicographic ordering we derive improved information on the possible number of zeros of $F$ ... More

Weighted Reed-Muller codes revisitedAug 31 2011We consider weighted Reed-Muller codes over point ensemble $S_1 \times...\times S_m$ where $S_i$ needs not be of the same size as $S_j$. For $m = 2$ we determine optimal weights and analyze in detail what is the impact of the ratio $|S_1|/|S_2|$ on the ... More

More results on the number of zeros of multiplicity at least rOct 26 2014Dec 22 2015We consider multivariate polynomials and investigate how many zeros of multiplicity at least $r$ they can have over a Cartesian product of finite subsets of a field. Here r is any prescribed positive integer and the definition of multiplicity that we ... More

Bounding the number of rational places using Weierstrass semigroupsOct 25 2007Let Lambda be a numerical semigroup. Assume there exists an algebraic function field over GF(q) in one variable which possesses a rational place that has Lambda as its Weierstrass semigroup. We ask the question as to how many rational places such a function ... More

Relative generalized Hamming weights of q-ary Reed-Muller codesJul 23 2014Nov 03 2015Coset constructions of $q$-ary Reed-Muller codes can be used to store secrets on a distributed storage system in such a way that only parties with access to a large part of the system can obtain information while still allowing for local error-correction. ... More

On affine variety codes from the Klein quarticJun 18 2017We study a family of primary affine variety codes defined from the Klein quartic. The duals of these codes have previously been treated in [12, Ex. 3.2]. Among the codes that we construct almost all have parameters as good as the best known codes according ... More

Further improvements on the Feng-Rao bound for dual codesMay 06 2013Salazar, Dunn and Graham in [Salazar et. al., 2006] presented an improved Feng-Rao bound for the minimum distance of dual codes. In this work we take the improvement a step further. Both the original bound by Salazar et. al., as well as our improvement ... More

On the number of zeros of multiplicity rDec 08 2009Dec 21 2009Let S be a finite subset of a field. For multivariate polynomials the generalized Schwartz-Zippel bound [2], [4] estimates the number of zeros over Sx...xS counted with multiplicity. It does this in terms of the total degree, the number of variables and ... More

An improvement of the Feng-Rao bound for primary codesJul 11 2013Jul 24 2013We present a new bound for the minimum distance of a general primary linear code. For affine variety codes defined from generalised C_{ab} curves the new bound often improves dramatically on the Feng-Rao bound for primary codes. The method does not only ... More

Bounding the number of common zeros of multivariate polynomials and their consecutive derivativesJul 05 2017We upper bound the number of common zeros over a finite grid of multivariate polynomials and an arbitrary finite collection of their consecutive Hasse derivatives (in a coordinate-wise sense). To that end, we make use of the tool from Gr\"obner basis ... More

On nested code pairs from the Hermitian curveJul 11 2018Jul 18 2018Nested code pairs play a crucial role in the construction of ramp secret sharing schemes [16] and in the CSS construction of quantum codes [15]. The important parameters are (1) the codimension, (2) the relative minimum distance of the codes, and (3) ... More

Steane-Enlargement of Quantum Codes from the Hermitian CurveApr 22 2019In this paper, we study the construction of quantum codes by applying Steane-enlargement to codes from the Hermitian curve. We cover Steane-enlargement of both usual one-point Hermitian codes and of order bound improved Hermitian codes. In particular, ... More

A Note on the Injection DistanceDec 09 2009Koetter and Kschischang showed in [R. Koetter and F.R. Kschischang, "Coding for Errors and Erasures in Random Network Coding," IEEE Trans. Inform. Theory, {54(8), 2008] that the network coding counterpart of Gabidulin codes performs asymptotically optimal ... More

Generalization of the Lee-O'Sullivan List Decoding for One-Point AG CodesMar 28 2012Mar 08 2013We generalize the list decoding algorithm for Hermitian codes proposed by Lee and O'Sullivan based on Gr\"obner bases to general one-point AG codes, under an assumption weaker than one used by Beelen and Brander. Our generalization enables us to apply ... More

2H-NMR studies of supercooled and glassy aspirinJan 10 2007Acetyl salicylic acid, deuterated at the methyl group, was investigated using 2H-NMR in its supercooled and glassy states. Just above the glass transition temperature the molecular reorientations were studied using stimulated-echo spectroscopy and demonstrated ... More

Combining subspace codes with classical linear error-correcting codesJul 24 2014Jul 29 2014We discuss how subspace codes can be used to simultaneously correct errors and erasures when the network performs random linear network coding and the edges are noisy channels. This is done by combining the subspace code with a classical linear error-correcting ... More

List Decoding Algorithm based on Voting in Groebner Bases for General One-Point AG CodesMar 28 2012Feb 18 2016We generalize the unique decoding algorithm for one-point AG codes over the Miura-Kamiya Cab curves proposed by Lee, Bras-Amor\'os and O'Sullivan (2012) to general one-point AG codes, without any assumption. We also extend their unique decoding algorithm ... More

Feng-Rao decoding of primary codesOct 25 2012Oct 31 2012We show that the Feng-Rao bound for dual codes and a similar bound by Andersen and Geil [H.E. Andersen and O. Geil, Evaluation codes from order domain theory, Finite Fields Appl., 14 (2008), pp. 92-123] for primary codes are consequences of each other. ... More

On Field Size and Success Probability in Network CodingJun 27 2008Using tools from algebraic geometry and Groebner basis theory we solve two problems in network coding. First we present a method to determine the smallest field size for which linear network coding is feasible. Second we derive improved estimates on the ... More

A new method for constructing small-bias spaces from Hermitian codesMar 02 2012We propose a new method for constructing small-bias spaces through a combination of Hermitian codes. For a class of parameters our multisets are much faster to construct than what can be achieved by use of the traditional algebraic geometric code construction. ... More

List Decoding Algorithms based on Groebner Bases for General One-Point AG CodesJan 30 2012Apr 23 2012We generalize the list decoding algorithm for Hermitian codes proposed by Lee and O'Sullivan based on Gr\"obner bases to general one-point AG codes, under an assumption weaker than one used by Beelen and Brander. By using the same principle, we also generalize ... More

Energy gap for Yang-Mills connections, I: Four-dimensional closed Riemannian manifoldsDec 12 2014Apr 06 2016We extend an $L^2$ energy gap result due independently to Min-Oo and Parker (1982) for Yang-Mills connections on principal $G$-bundles, $P$, over closed, connected, four-dimensional, oriented, smooth manifolds, $X$, from the case of positive Riemannian ... More

RegistersDec 05 2006Entry in: Encyclopedia of Algorithms, Ming-Yang Kao, Ed., Springer, To appear. Synonyms: Wait-free registers, wait-free shared variables, asynchronous communication hardware. Problem Definition: Consider a system of asynchronous processes that communicate ... More

Two linear transformations each tri-diagonal with respect to an eigenbasis of the other; the TD-D canonical form and the LB-UB canonical formApr 06 2003Let $\K$ denote a field and let $V$ denote a vector space over $\K$ with finite positive dimension. We consider an ordered pair of linear transformations $A:V\to V$ and $B:V\to V$ which satisfy both (i), (ii) below. (i) There exists a basis for $V$ with ... More

Relative energy gap for harmonic maps of Riemann surfaces into real analytic Riemannian manifoldsSep 15 2016Oct 12 2016We extend the well-known Sacks-Uhlenbeck energy gap result (1981) for harmonic maps from closed Riemann surfaces into closed Riemannian manifolds from the case of maps with small energy (thus near a constant map), to the case of harmonic maps with high ... More

RandomnessOct 08 2001Oct 10 2001Here we present in a single essay a combination and completion of the several aspects of the problem of randomness of individual objects which of necessity occur scattered in our texbook "An Introduction to Kolmogorov Complexity and Its Applications" ... More

Conditional Kolmogorov Complexity and Universal ProbabilityJun 05 2012Jan 22 2013The Coding Theorem of L.A. Levin connects unconditional prefix Kolmogorov complexity with the discrete universal distribution. There are conditional versions referred to in several publications but as yet there exist no written proofs in English. Here ... More

Relative energy gap for harmonic maps of Riemann surfaces into real analytic Riemannian manifoldsSep 15 2016Feb 01 2018We extend the well-known Sacks-Uhlenbeck energy gap result (1981) for harmonic maps from closed Riemann surfaces into closed Riemannian manifolds from the case of maps with small energy (thus near a constant map), to the case of harmonic maps with high ... More

Singularities in rotating black holes coupled to a massless scalar fieldMay 12 2019We employ a late-time expansion to study the interior of rotating black holes coupled to a massless scalar field in asymptotically flat spacetime. We find that decaying fluxes of scalar radiation into the black hole necessitate the existence of a null ... More

Global existence and convergence of solutions to gradient systems and applications to Yang-Mills gradient flowSep 04 2014Oct 13 2016In this monograph, we develop results on global existence and convergence of solutions to abstract gradient flows on Banach spaces for a potential function that obeys the Lojasiewicz-Simon gradient inequality. We prove a Lojasiewicz-Simon gradient inequality ... More

Analysis of Sorting Algorithms by Kolmogorov Complexity (A Survey)May 27 2009Recently, many results on the computational complexity of sorting algorithms were obtained using Kolmogorov complexity (the incompressibility method). Especially, the usually hard average-case analysis is ammenable to this method. Here we survey such ... More

Information Distance in MultiplesMay 20 2009Information distance is a parameter-free similarity measure based on compression, used in pattern recognition, data mining, phylogeny, clustering, and classification. The notion of information distance is extended from pairs to multiples (finite lists). ... More

On Empirical EntropyMar 30 2011We propose a compression-based version of the empirical entropy of a finite string over a finite alphabet. Whereas previously one considers the naked entropy of (possibly higher order) Markov processes, we consider the sum of the description of the random ... More

Critical-exponent Sobolev norms and the slice theorem for the quotient space of connectionsNov 09 1997Feb 03 1999The use of certain critical-exponent Sobolev norms is an important feature of methods employed by Taubes to solve the anti-self-dual and similar non-linear elliptic partial differential equations. Indeed, the estimates one can obtain using these critical-exponent ... More

How big are the smallest drops of quark-gluon plasma?Jan 07 2016Feb 22 2016Using holographic duality, we present results for both head-on and off-center collisions of Gaussian shock waves in strongly coupled $\mathcal N = 4$ supersymmetric Yang-Mills theory. The shock waves superficially resemble Lorentz contracted colliding ... More

A microscopic, mechanical derivation for the adiabatic gas relationOct 02 2003It is shown that the ideal gas adiabatic relation, P*V^gamma=constant, can be derived by considering the motion of a particle bouncing elastically between a stationary wall and a moving wall.

Maximum principles for boundary-degenerate second-order linear elliptic differential operatorsApr 30 2012Sep 12 2013We prove weak and strong maximum principles, including a Hopf lemma, for smooth subsolutions to equations defined by linear, second-order, partial differential operators whose principal symbols vanish along a portion of the domain boundary. The boundary ... More

Discreteness for energies of Yang-Mills connections over four-dimensional manifoldsMay 26 2015We generalize our previous results (Theorem 1 and Corollary 2 in arXiv:1412.4114) and Theorem 1 in arXiv:1502.00668) on the existence of an $L^2$-energy gap for Yang-Mills connections over closed four-dimensional manifolds and energies near the ground ... More

On the Morse-Bott property of analytic functions on Banach spaces with Lojasiewicz exponent one halfMar 30 2018Apr 04 2018It is a consequence of the Morse-Bott Lemma on Banach spaces that a smooth Morse-Bott function on an open neighborhood of a critical point in a Banach space obeys a Lojasiewicz gradient inequality with the optimal exponent one half. In this article we ... More

Perturbations of local maxima and comparison principles for boundary-degenerate linear differential equationsMay 22 2013Jun 25 2013We develop strong and weak maximum principles for boundary-degenerate elliptic and parabolic linear second-order partial differential operators, $Au := -\tr(aD^2u)-<b, Du> + cu$, with \emph{partial Dirichlet boundary conditions}. The coefficient, $a(x)$, ... More

Oscillon Lifetime in the Presence of Quantum FluctuationsJan 23 2014Jul 23 2014We consider the stability of oscillons in 2+1 space-time dimensions, in the presence of quantum fluctuations. Taking the oscillon to be the inhomogeneous mean field of a self-interacting quantum scalar field, we compare its classical evolution to the ... More

Compression-based SimilarityOct 20 2011First we consider pair-wise distances for literal objects consisting of finite binary files. These files are taken to contain all of their meaning, like genomes or books. The distances are based on compression of the objects concerned, normalized, and ... More

A Kato-Yau inequality for harmonic spinors and decay estimate for eigenspinorsMar 02 1999Aug 09 2000We show that harmonic spinors obey a strengthened version of the well-known pointwise Kato inequality for sections of a vector bundle with a connection. We then prove a decay estimate for eigenspinors using this Kato-Yau estimate and resulting differential ... More

Colliding shock waves and hydrodynamics in small systemsJun 07 2015Dec 15 2015Using numerical holography, we study the collision of a planar sheet of energy with a bounded localized distribution of energy. The collision, which mimics proton-nucleus collisions, produces a localized lump of debris with transverse size $R \sim 1/T_{\rm ... More

Gauge/gravity duality and jets in strongly coupled plasmaJul 26 2009Oct 08 2009We discuss jets in strongly coupled N = 4 supersymmetric Yang-Mills plasma and their dual gravitational description.

A New Approximation to the Normal Distribution Quantile FunctionFeb 02 2010Feb 03 2010We present a new approximation to the normal distribution quantile function. It has a similar form to the approximation of Beasley and Springer [3], providing a maximum absolute error of less than $2.5 \cdot 10^{-5}$. This is less accurate than [3], but ... More

Trading leads to scale-free self-organizationMay 29 2009Financial markets display scale-free behavior in many different aspects. The power-law behavior of part of the distribution of individual wealth has been recognized by Pareto as early as the nineteenth century. Heavy-tailed and scale-free behavior of ... More

Recrudescence of massive fermion production by oscillonsDec 06 2016In this letter we bring together the physics of preheating, following a period of inflation, and the dynamics of non-topological solitons, namely oscillons. We show that the oscillating condensate that makes up an oscillon can be an efficient engine for ... More

Random solids and random solidification: What can be learned by exploring systems obeying permanent random constraints?Nov 11 1999In many interesting physical settings, such as the vulcanization of rubber, the introduction of permanent random constraints between the constituents of a homogeneous fluid can cause a phase transition to a random solid state. In this random solid state, ... More

New Rain Rate Statistics for Emerging Regions: Implications for Wireless Backhaul PlanningSep 01 2016As demand for broadband service increases in emerging regions, high-capacity wireless links can accelerate and cost-reduce the deployment of new networks (both backhaul and customer site connection). Such links are increasingly common in developed countries, ... More

Generalized Arf invariants and reduced power operations in cyclic homologyMar 24 2005In this thesis we consider two constructions generalizing the classical Arf invariant. In the first construction an $\epsilon$-symmetric quadratic form over a ring with involution $R$ is lifted to an $\epsilon(1+T)$-symmetric quadratic form over the ring ... More

Optimal Lojasiewicz-Simon inequalities and Morse-Bott Yang-Mills energy functionsJun 28 2017Jun 13 2018For any compact Lie group $G$, we prove that the Yang-Mills energy function obeys an optimal gradient inequality of {\L}ojasiewicz-Simon type (exponent $1/2$) near the critical set of flat connections on a principal $G$-bundle over a closed Riemannian ... More

Sharp bounds on the number of solutions of $X^{2}-\left( a^{2}+b^{2} \right) Y^{4}=-b^{2}$Jul 11 2018We generalise and improve a result of Stoll, Walsh and Yuan by showing that there are at most two solutions in coprime positive integers of the equation in the title when $b=p^{m}$ where $m$ is a non-negative integer, $p$ is prime, $(a,p)=1$, $a^{2}+p^{2m}$ ... More

Geometry of the ends of the moduli space of anti-self-dual connectionsApr 22 2015Let $X$ be a closed, four-dimensional, oriented, smooth manifold with a Riemannian metric, $g$, let $G$ be a compact Lie group, and $P$ be a principal $G$ bundle over $X$. D. Groisser and T. Parker (1987, 1989) and S. K. Donaldson (1990) conjectured that ... More

Restricted permutations refined by number of crossings and nestingsAug 11 2018Jan 13 2019Let $st=\{st_1,st_2,...,st_k\}$ be a set of k statistics on permutations with $k\geq 1$. We say that two given subset of permutations $T$ and $T'$ are $st$-Wilf-equivalent if the joint distributions of all statistics in st over the sets of $T$-avoiding ... More

A classical Perron method for existence of smooth solutions to boundary value and obstacle problems for degenerate-elliptic operators via holomorphic mapsFeb 07 2013Apr 18 2013We prove existence of solutions to boundary value problems and obstacle problems for degenerate-elliptic, linear, second-order partial differential operators with partial Dirichlet boundary conditions using a new version of the Perron method. The elliptic ... More

Energy gap for Yang-Mills connections, II: Arbitrary closed Riemannian manifoldsFeb 02 2015Jul 29 2016In this sequel to [arXiv:1412.4114], we prove an $L^{d/2}$ energy gap result for Yang-Mills connections on principal $G$-bundles, $P$, over arbitrary, closed, Riemannian, smooth manifolds of dimension $d\geq 2$. We apply our version of the Lojasiewicz-Simon ... More

Distributed elections in an Archimedean ring of processorsMay 27 2009Unlimited asynchronism is intolerable in real physically distributed computer systems. Such systems, synchronous or not, use clocks and timeouts. Therefore the magnitudes of elapsed absolute time in the system need to satisfy the axiom of Archimedes. ... More

Primitive divisors of Lucas and Lehmer sequencesJan 31 2012Stewart reduced the problem of determining all Lucas and Lehmer sequences whose $n$-th element does not have a primitive divisor to solving certain Thue equations. Using the method of Tzanakis and de Weger for solving Thue equations, we determine such ... More

Resolution of singularities and geometric proofs of the Lojasiewicz inequalitiesAug 31 2017Dec 20 2018The Lojasiewicz inequalities for real analytic functions on Euclidean space were first proved by Stanislaw Lojasiewicz (1965) using methods of semianalytic and subanalytic sets, arguments later simplified by Bierstone and Milman (1988). In this article, ... More

Relative energy gap for harmonic maps of Riemann surfaces into real analytic Riemannian manifoldsSep 15 2016We extend the well-known Sacks-Uhlenbeck energy gap result (1981) for harmonic maps from closed Riemann surfaces into closed Riemannian manifolds from the case of maps with small energy (thus near a constant map), to the case of harmonic maps with high ... More

On The Average-Case Complexity of ShellsortJan 26 2015Jan 27 2015We prove a lower bound expressed in the increment sequence on the average-case complexity (number of inversions which is proportional to the running time) of Shellsort. This lower bound is sharp in every case where it could be checked. We obtain new results ... More

Quantum Kolmogorov Complexity Based on Classical DescriptionsFeb 21 2001Oct 09 2001We develop a theory of the algorithmic information in bits contained in an individual pure quantum state. This extends classical Kolmogorov complexity to the quantum domain retaining classical descriptions. Quantum Kolmogorov complexity coincides with ... More

Generic metrics, irreducible rank-one PU(2) monopoles, and transversalitySep 01 1998Aug 03 2000We prove that the moduli space of solutions to the PU(2) monopole equations is a smooth manifold of the expected dimension for simple, generic parameters such as (and including) the Riemannian metric on the given four-manifold. In a previous article, ... More

Carbon isotope measurements in the Solar SystemJan 28 2009Feb 02 2010I make publicly available my literature study into carbon isotope ratios in the Solar System, which formed a part of Woods & Willacy (2009). As far as I know, I have included here all measurements of 12C/13C in Solar System objects (excluding those of ... More

Correct interpretation of trace normalized density matrices as ensemblesJun 25 1996May 03 1997A density operator, $\rho = {P}_{\alpha } |\alpha > <\alpha | + {P}_{\beta } |\beta > <\beta |$, with ${P}_{\alpha }$ and ${P}_{\beta }$ linearly independent normalized wave functions, must be traced normalized, so ${P}_{\beta } = 1 - {P}_{\alpha }$. ... More

Signature of Kondo breakdown quantum criticality in optical conductivityJul 05 2009Apr 29 2010We study the finite-frequency inter-band transition peak in the optical conductivity of a heavy fermion system close to a Kondo breakdown quantum critical point, where the lattice Kondo temperature vanishes. As the system approaches the phase transition ... More

Lattice effects on nematic quantum criticality in metalsOct 19 2016Metals near a nematic quantum critical point, where systems are poised to undergo a zero temperature continuous phase transition that breaks rotational symmetry, are of great interest for studying the iron superconductors, cuprates, ruthanates, and quantum ... More

Transforming Metastable Memories: The Nonequilibrium Thermodynamics of ComputationAug 10 2018Framing computation as the transformation of metastable memories, we explore its fundamental thermodynamic limits. The true power of information follows from a novel decomposition of nonequilibrium free energy derived here, which provides a rigorous thermodynamic ... More

Energy gap for Yang-Mills connections, II: Arbitrary closed Riemannian manifoldsFeb 02 2015Jul 10 2017In this sequel to [arXiv:1412.4114], we prove an $L^{d/2}$ energy gap result for Yang-Mills connections on principal $G$-bundles, $P$, over arbitrary, closed, Riemannian, smooth manifolds of dimension $d\geq 2$. We apply our version of the Lojasiewicz-Simon ... More

The Candy-Passing Game for c\geq3n-2Sep 13 2007Nov 25 2007We determine the behavior of Tanton's candy-passing game for all distributions of at least 3n-2 candies, where n is the number of students. Specifically, we show that the configuration of candy in such a game eventually becomes fixed.

Universal entire functions that define order isomorphisms of countable real setsJul 08 2018Dec 23 2018In 1895, Cantor showed that between every two countable dense real sets, there is an order isomorphism. In fact, there is always such an order isomorphism, which is the restriction of a universal entire function.

Resolution of singularities and geometric proofs of the Lojasiewicz inequalitiesAug 31 2017May 02 2019The Lojasiewicz inequalities for real analytic functions on Euclidean space were first proved by Stanislaw Lojasiewicz (1965) using methods of semianalytic and subanalytic sets, arguments later simplified by Bierstone and Milman (1988). In this article, ... More