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Topographic Constraints on the Origin of the Equatorial Ridge on IapetusApr 09 2014Saturn's moon Iapetus has an equatorial ridge system, which may be as high as 20 km, that may have formed by endogenic forces, such as tectonic and convective forces, or exogenic processes such as debris infall. We use high-resolution topographic data ... More

Rings beyond the giant planetsDec 10 2016Apr 11 2017Until 2013, only the giant planets were known to host ring systems. In June 2013, a stellar occulation revealed the presence of narrow and dense rings around Chariklo, a small Centaur object that orbits between Saturn and Uranus. Meanwhile, the Cassini ... More

Constraints on planetesimal disk mass from the cratering record and equatorial ridge on IapetusJun 26 2014Iapetus, the outermost regular satellite of Saturn, has a drastic albedo dichotomy and an equatorial circumferential ridge that reaches heights of 20 km and widths of 70 km. This moon is thought to have formed concurrently with Saturn, and so would have ... More

Constraining the Cratering Chronology of VestaJul 11 2014Vesta has a complex cratering history, with ancient terrains as well as recent large impacts that have led to regional resurfacing. Crater counts can help constrain the relative ages of different units on Vesta's surface, but converting those crater counts ... More

Density functional theory for a model quantum dot: Beyond the local-density approximationSep 17 2010We study both static and transport properties of model quantum dots, employing density functional theory as well as (numerically) exact methods. For the lattice model under consideration the accuracy of the local-density approximation generally is poor. ... More

A Manifestly Gauge-Invariant Approach to Charged ParticlesOct 07 1996In this article we provide a manifestly gauge-invariant approach to charged particles. It involves (1) Green functions of gauge-invariant operators and (2) Feynman rules which do not depend on any kind of gauge-fixing condition. First, we provide a thorough ... More

Internal-state thermometry by depletion spectroscopy in a cold guided beam of formaldehydeOct 17 2007We present measurements of the internal state distribution of electrostatically guided formaldehyde. Upon excitation with continuous tunable ultraviolet laser light the molecules dissociate, leading to a decrease in the molecular flux. The population ... More

Quantitative analyses of empirical fitness landscapesFeb 20 2012Oct 17 2012The concept of a fitness landscape is a powerful metaphor that offers insight into various aspects of evolutionary processes and guidance for the study of evolution. Until recently, empirical evidence on the ruggedness of these landscapes was lacking, ... More

Virtual Testing of Experimental ContinuationJul 05 2018We present a critical advance in experimental testing of nonlinear structures. Traditional quasi-static experimental methods control the displacement or force at one or more load-introduction points on a structure. This approach is unable to traverse ... More

Atomic Structure of Domain and Interphase Boundaries in Ferroelectric HfO$_2$Sep 23 2017Though the electrical responses of the various polymorphs found in ferroelectric polycrystalline thin film HfO$_2$ are now well characterized, little is currently understood of this novel material's grain sub-structure. In particular, the formation of ... More

Saturation of the R-mode InstabilityFeb 19 2002Feb 11 2003Rossby waves (r-modes) in rapidly rotating neutron stars are unstable because of the emission of gravitational radiation. We study saturation of this instability by nonlinear transfer of energy to stellar "inertial" oscillation modes. We present detailed ... More

A steerable UV laser system for the calibration of liquid argon time projection chambersJun 24 2014Oct 04 2014A number of liquid argon time projection chambers (LAr TPC's) are being build or are proposed for neutrino experiments on long- and short baseline beams. For these detectors a distortion in the drift field due to geometrical or physics reasons can affect ... More

Gauge-invariant Green's functions for the bosonic sector of the standard modelDec 18 1998Jun 21 2000There are many applications in gauge theories where the usually employed framework involving gauge-dependent Green's functions leads to considerable problems. In order to overcome the difficulties invariably tied to gauge dependence, we present a manifestly ... More

Adaptive estimation of linear functionals in functional linear modelsDec 13 2011We consider the estimation of the value of a linear functional of the slope parameter in functional linear regression, where scalar responses are modeled in dependence of random functions. In Johannes and Schenk [2010] it has been shown that a plug-in ... More

Effective Field Theory of the Linear $O(N)$ Sigma ModelSep 29 1994The low energy structure of a theory containing light and heavy particle species which are separated by a mass gap can adequately be described by an effective theory which contains only the light particles. In this work we present a thorough analysis ... More

Exploring High Multiplicity Amplitudes: The QM Analogue of the Spontaneously Broken CaseNov 29 2018Calculations of high multiplicity Higgs amplitudes exhibit a rapid growth that may signal an end of perturbative behavior or even the need for new physics phenomena. As a step towards this problem we consider the quantum mechanical equivalent of $1 \to ... More

The electroweak chiral Lagrangian reanalyzedJul 09 1999Oct 26 2000In this paper we reanalyze the electroweak chiral Lagrangian with particular focus on two issues related to gauge invariance. Our analysis is based on a manifestly gauge-invariant approach that we introduced recently. It deals with gauge-invariant Green's ... More

Effective Field Theory for a Heavy Higgs: a Manifestly Gauge Invariant ApproachJul 11 1995For large values of the Higgs boson mass the low energy structure of the gauged linear sigma model in the spontaneously broken phase can adequately be described by an effective field theory. In this work we present a manifestly gauge invariant technique ... More

Selected inversion as key to a stable Langevin evolution across the QCD phase boundaryJul 27 2017We present new results of full QCD at nonzero chemical potential. In PRD 92, 094516 (2015) the complex Langevin method was shown to break down when the inverse coupling decreases and enters the transition region from the deconfined to the confined phase. ... More

Exploring High Multiplicity Amplitudes: The QM Analogue of the Spontaneously Broken CaseNov 29 2018Mar 25 2019Calculations of high multiplicity Higgs amplitudes exhibit a rapid growth that may signal an end of perturbative behavior or even the need for new physics phenomena. As a step towards this problem we consider the quantum mechanical equivalent of $1 \to ... More

Effective Field Theory for a Heavy Higgs Boson: Matching and Gauge InvarianceSep 17 1996For large values of the Higgs mass the low energy structure of the gauged linear sigma model in the spontaneously broken phase can adequately be described by an effective field theory. We present a manifestly gauge-invariant functional technique to explicitly ... More

Exploring High Multiplicity Amplitudes in Quantum MechanicsJun 05 2018Jul 19 2018Calculations of $1\to N$ amplitudes in scalar field theories at very high multiplicities exhibit an extremely rapid growth with the number $N$ of final state particles. This either indicates an end of perturbative behaviour, or possibly even a breakdown ... More

On rate optimal local estimation in functional linear modelFeb 03 2009Dec 16 2011We consider the estimation of the value of a linear functional of the slope parameter in functional linear regression, where scalar responses are modeled in dependence of random functions. The theory in this paper covers in particular point-wise estimation ... More

Synthesis of Homogeneous Manganese-Doped Titanium Oxide Nanotubes from Titanate PrecursorsNov 14 2012May 21 2013We report a novel synthesis route of homogeneously manganese-doped titanium dioxide nanotubes in a broad concentration range. The scroll-type trititanate (H(2)Ti(3)O(7)) nanotubes prepared by hydrothermal synthesis were used as precursors. Mn2+ ions were ... More

Electrostatic extraction of cold molecules from a cryogenic reservoirJun 16 2008Jan 23 2009We present a method which delivers a continuous, high-density beam of slow and internally cold polar molecules. In our source, warm molecules are first cooled by collisions with a cryogenic helium buffer gas. Cold molecules are then extracted by means ... More

Development of a camera casing suited for cryogenic and vacuum applicationsOct 24 2013We report on the design, construction, and operation of a PID temperature controlled and vacuum tight camera casing. The camera casing contains a commercial digital camera and a lighting system. The design of the camera casing and its components are discussed ... More

Extremely high negative electron affinity of diamond via magnesium adsorptionMay 24 2015Jun 20 2015We report large negative electron affinity (NEA) on diamond (100) using magnesium adsorption on a previously oxygen-terminated surface. The measured NEA is up to $(-2.01\pm0.05)$ eV, the largest reported negative electron affinity to date. Despite the ... More

Measurement of the drift field in the ARGONTUBE LAr TPC with 266~nm pulsed laser beamsAug 28 2014Oct 30 2014ARGONTUBE is a liquid argon time projection chamber (LAr TPC) with a drift field generated in-situ by a Greinacher voltage multiplier circuit. We present results on the measurement of the drift-field distribution inside ARGONTUBE using straight ionization ... More

Surface Albedo and Spectral Variability of CeresJan 14 2016Previous observations suggested that Ceres has active but possibly sporadic water outgassing, and possibly varying spectral characteristics in a time scale of months. We used all available data of Ceres collected in the past three decades from the ground ... More

Relation between phase space coverage and entanglement for spin-1/2 systemsNov 27 2006For systems of two and three spins 1/2 it is known that the second moment of the Husimi function can be related to entanglement properties of the corresponding states. Here, we generalize this relation to an arbitrary number of spins in a pure state. ... More

Performance of cryogenic charge readout electronics with the ARGONTUBE LAr TPCAug 29 2014Oct 30 2014ARGONTUBE is a liquid argon time projection chamber (TPC) with an electron drift length of up to 5 m equipped with cryogenic charge-sensitive preamplifiers. In this work, we present results on its performance including a comparison of the new cryogenic ... More

Experimental study of electric breakdowns in liquid argon at centimeter scaleJan 26 2014Feb 11 2014In this paper we present results on measurements of the dielectric strength of liquid argon near its boiling point and cathode-anode distances in the range of 0.1 mm to 40 mm with spherical cathode and plane anode. We show that at such distances the applied ... More

Great Expectations: Plans and Predictions for New Horizons Encounter with Kuiper Belt Object 2014 MU69 ('Ultima Thule')Aug 06 2018The New Horizons encounter with the cold classical Kuiper Belt object (KBO) 2014 MU69 (informally named 'Ultima Thule,' hereafter Ultima) on 1 January 2019 will be the first time a spacecraft has ever closely observed one of the free-orbiting small denizens ... More

Three-dimensional imaging of dislocation propagation during crystal growth and dissolutionJan 13 2015Atomic level defects such as dislocations play key roles in determining the macroscopic properties of crystalline materials. Their effects are important and wide-reaching, and range from increased chemical reactivity to enhanced mechanical properties ... 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

A Recurrent Neural Model with Attention for the Recognition of Chinese Implicit Discourse RelationsApr 26 2017We introduce an attention-based Bi-LSTM for Chinese implicit discourse relations and demonstrate that modeling argument pairs as a joint sequence can outperform word order-agnostic approaches. Our model benefits from a partial sampling scheme and is conceptually ... More

Punctured Trellis-Coded ModulationJan 17 2013In classic trellis-coded modulation (TCM) signal constellations of twice the cardinality are applied when compared to an uncoded transmission enabling transmission of one bit of redundancy per PAM-symbol, i.e., rates of $\frac{K}{K+1}$ when $2^{K+1}$ ... More

Capacity of BICM Using (Bi-)Orthogonal Signal Constellations in Impulse-Radio Ultra-Wideband SystemsFeb 14 2011Apr 27 2011Bit-interleaved coded modulation (BICM) using (bi-)orthogonal signals is especially well suited for the application in impulse-radio ultra-wideband transmission systems, which typically operate in the power-limited regime and require a very low-complexity ... More

Decision-Feedback Differential Detection in Impulse-Radio Ultra-Wideband SystemsJan 17 2011In this paper we present decision-feedback differential detection (DF-DD) schemes for autocorrelation-based detection in impulse-radio ultra-wideband (IR-UWB) systems, a signaling scheme regarded as a promising candidate in particular for low-complexity ... More

Soft-Output Sphere Decoder for Multiple-Symbol Differential Detection of Impulse-Radio Ultra-WidebandJun 02 2010Power efficiency of noncoherent receivers for impulse-radio ultra-wideband (IR-UWB) transmission systems can significantly be improved, on the one hand, by employing multiple-symbol differential detection (MSDD), and, on the other hand, by providing reliability ... More

Phase Transitions in a Forest-Fire ModelJan 09 1997We investigate a forest-fire model with the density of empty sites as control parameter. The model exhibits three phases, separated by one first-order phase transition and one 'mixed' phase transition which shows critical behavior on only one side and ... More

The self-organized critical forest-fire model on large scalesMay 06 2001We discuss the scaling behavior of the self-organized critical forest-fire model on large length scales. As indicated in earlier publications, the forest-fire model does not show conventional critical scaling, but has two qualitatively different types ... More

Hedging without sweat: a genetic programming approachMay 29 2013Hedging in the presence of transaction costs leads to complex optimization problems. These problems typically lack closed-form solutions, and their implementation relies on numerical methods that provide hedging strategies for specific parameter values. ... More

Adaptive Bayesian estimation in indirect Gaussian sequence space modelsFeb 01 2015In an indirect Gaussian sequence space model lower and upper bounds are derived for the concentration rate of the posterior distribution of the parameter of interest shrinking to the parameter value $\theta^\circ$ that generates the data. While this establishes ... More

Matched Decoding for Punctured Convolutional Encoded Transmission Over ISI-ChannelsAug 01 2012Matched decoding is a technique that enables the efficient maximum-likelihood sequence estimation of convolutionally encoded PAM-transmission over ISI-channels. Recently, we have shown that the super-trellis of encoder and channel can be described with ... More

Compositional bowing of band energies and their deformation potentials in strained InGaAs ternary alloys: a first-principles studyMay 21 2015Aug 25 2015Using first-principles calculations, we show that the conduction and valence band energies and their deformation potentials exhibit a non-negligible compositional bowing in strained ternary semiconductor alloys such as InGaAs. The electronic structure ... More

Exchangeable exogenous shock modelsFeb 05 2016We characterize a comprehensive family of $d$-variate exogenous shock models. Analytically, we consider a family of multivariate distribution functions that arises from ordering, idiosyncratically distorting, and finally multiplying the arguments. Necessary ... More

Chaotic provinces in the kingdom of the Red QueenJul 06 2016The interplay between parasites and their hosts is found in all kinds of species and plays an important role in understanding the principles of evolution and coevolution. Usually, the different genotypes of hosts and parasites oscillate in their abundances. ... More

Reduced Complexity Super-Trellis Decoding for Convolutionally Encoded Transmission Over ISI-ChannelsJul 19 2012Oct 04 2012In this paper we propose a matched encoding (ME) scheme for convolutionally encoded transmission over intersymbol interference (usually called ISI) channels. A novel trellis description enables to perform equalization and decoding jointly, i.e., enables ... More

Distributed-Pair Programming can work well and is not just Distributed Pair-ProgrammingNov 25 2013Background: Distributed Pair Programming can be performed via screensharing or via a distributed IDE. The latter offers the freedom of concurrent editing (which may be helpful or damaging) and has even more awareness deficits than screen sharing. Objective: ... More

On Large Scale Diagonalization Techniques for the Anderson Model of LocalizationAug 05 2005We propose efficient preconditioning algorithms for an eigenvalue problem arising in quantum physics, namely the computation of a few interior eigenvalues and their associated eigenvectors for the largest sparse real and symmetric indefinite matrices ... 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

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

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

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

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

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

Convection in a volatile nitrogen-ice-rich layer drives Pluto's geological vigorMar 13 2019The vast, deep, volatile-ice-filled basin informally named Sputnik Planum is central to Pluto's geological activity[1,2]. Composed of molecular nitrogen, methane, and carbon monoxide ices[3], but dominated by N2-ice, this ice layer is organized into cells ... 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

Maximum principles for boundary-degenerate linear parabolic differential operatorsJun 20 2013Jul 19 2013We develop weak and strong maximum principles for boundary-degenerate, linear, parabolic, second-order partial differential operators, $Lu := -u_t-\tr(aD^2u)-\langle b, Du\rangle + cu$, with \emph{partial} Dirichlet boundary conditions. The coefficient, ... 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