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On Handlebody Structures of Rational BallsJun 06 2014It is known that for coprime integers $p>q\geq 1$, the lens space $L(p^2,pq-1)$ bounds a rational ball, $B_{p,q}$, arising as the 2-fold branched cover of a (smooth) slice disk in $B^4$ bounding the associated 2-bridge knot. Lekilli and Maydanskiy give ... More

Constraining primordial non-Gaussianity using two galaxy surveys and CMB lensingJun 11 2019Next-generation galaxy surveys will be able to measure perturbations on scales beyond the equality scale. On these ultra-large scales, primordial non-Gaussianity leaves signatures that can shed light on the mechanism by which perturbations in the early ... More

Learning with Analytical ModelsOct 28 2018Feb 26 2019To understand and predict the performance of scientific applications, several analytical and machine learning approaches have been proposed, each having its advantages and disadvantages. In this paper, we propose and validate a hybrid approach for performance ... More

Electromagnetic Transients Powered by Nuclear Decay in the Tidal Tails of Coalescing Compact BinariesApr 28 2011The possibility that long tidal tails formed during compact object mergers may power optical transients through the decay of freshly synthesized r-process material is investigated. Precise modeling of the merger dynamics allows for a realistic determination ... More

Considerations on the magnitude distributions of the Kuiper belt and of the Jupiter TrojansMar 05 2009By examining the absolute magnitude (H) distributions (hereafter HD) of the cold and hot populations in the Kuiper belt and of the Trojans of Jupiter, we find evidence that the Trojans have been captured from the outer part of the primordial trans-Neptunian ... More

Inelastic x-ray scattering measurements on URu2Si2Dec 29 2015We report high-resolution inelastic x ray scattering measurements of the acoustic phonons of URu2Si2. We observe minimal change in the phonon structure upon entering the Hidden Order phase. At all temperatures, the longitudinal acoustic phonons are anomalously ... More

The Absence of Superconductivity in Single Phase CaFe2As2 under Hydrostatic PressureNov 16 2008Jan 14 2009Recent high-pressure studies found that superconductivity can be achieved under very low pressure in the parent iron arsenide compound CaFe2As2, although details of the sharpness and temperature of transitions vary between liquid medium and gas medium ... More

Hyperdeterminants of PolynomialsJul 23 2011May 06 2012The hyperdeterminant of a polynomial (interpreted as a symmetric tensor) factors into several irreducible factors with multiplicities. Using geometric techniques these factors are identified along with their degrees and their multiplicities. The analogous ... More

3 List Coloring Graphs of Girth at least Five on SurfacesOct 18 2017Grotzsch proved that every triangle-free planar graph is 3-colorable. Thomassen proved that every planar graph of girth at least five is 3-choosable. As for other surfaces, Thomassen proved that there are only finitely many 4-critical graphs of girth ... More

Arbitrary Orientations Of Hamilton Cycles In Oriented GraphsJul 20 2009Aug 06 2009We use a randomised embedding method to prove that for all \alpha>0 any sufficiently large oriented graph G with minimum in-degree and out-degree \delta^+(G),\delta^-(G)\geq (3/8+\alpha)|G| contains every possible orientation of a Hamilton cycle. This ... More

Border Ranks of MonomialsAug 08 2016Jan 25 2019Young flattenings, introduced by Landsberg and Ottaviani, give determinantal equations for secant varieties and their non-vanishing provides lower bounds for border ranks of tensors and in particular polynomials. We study monomial-optimal shapes for Young ... More

Set-theoretic defining equations of the tangential variety of the Segre varietyNov 27 2009We prove a set-theoretic version of the Landsberg--Weyman Conjecture on the defining equations of the tangential variety of a Segre product of projective spaces. We introduce and study the concept of exclusive rank. For the proof of this conjecture we ... More

Are all Secant Varieties of Segre Products Arithmetically Cohen-Macaulay?Mar 29 2016Apr 06 2016When present, the Cohen-Macaulay property can be useful for finding the minimal defining equations of an algebraic variety. It is conjectured that all secant varieties of Segre products of projective spaces are arithmetically Cohen-Macaulay. A summary ... More

On the Minimum Number of Edges in Triangle-Free 5-Critical GraphsFeb 09 2016Aug 07 2017Kostochka and Yancey proved that every 5-critical graph G satisfies: |E(G)|>= (9/4)|V(G)| - 5/4. A construction of Ore gives an infinite family of graphs meeting this bound. We prove that there exists e,d > 0 such that if G is a 5-critical graph, then ... More

Polytope Bounds on Multivariate Value SetsOct 10 2013Feb 18 2014We improve upon the upper bounds for the cardinality of the value set of a multivariable polynomial map over a finite field using the polytope of the polynomial. This generalizes earlier bounds only dependent on the degree of a polynomial.

Linear-Time and Efficient Distributed Algorithms for List Coloring Graphs on SurfacesApr 07 2019In 1994, Thomassen proved that every planar graph is 5-list-colorable. In 1995, Thomassen proved that every planar graph of girth at least five is 3-list-colorable. His proofs naturally lead to quadratic-time algorithms to find such colorings. Here, we ... More

Obstructing Sliceness in a Family of Montesinos KnotsSep 07 2008Using Gauge theoretical techniques employed by Lisca for 2-bridge knots and by Greene-Jabuka for 3-stranded pretzel knots, we show that no member of the family of Montesinos knots M(0;[m_1+1,n_1+2],[m_2+1,n_2+2],q), with certain restrictions on m_i, n_i, ... More

The Mid-Infrared Evolution of the FU Orionis DiskSep 06 2016We present new SOFIA-FORCAST observations obtained in Feburary 2016 of the archetypal outbursting low mass young stellar object FU Orionis, and compare the continuum, solid state, and gas properties with mid-IR data obtained at the same wavelengths in ... More

Water wave transmission by an array of floating disksMar 15 2014An experimental validation of theoretical models of transmission of regular water waves by large arrays of floating disks is presented. The experiments are conducted in a wave basin. The models are based on combined potential-flow and thin-plate theories, ... More

Parabolic Regularity and Dirichlet boundary value problemsJul 03 2017We study the relationship between the Regularity and Dirichlet boundary value problems for parabolic equations of the form $Lu=\text{div}(A \nabla u)-u_t=0$ in Lip$(1,1/2)$ time-varying cylinders, where the coefficient matrix $A = \left[ a_{ij}(X,t)\right] ... More

On the Minimal Edge Density of $K_4$-free 6-critical GraphsNov 07 2018Kostochka and Yancey resolved a famous conjecture of Ore on the asymptotic density of $k$-critical graphs by proving that every $k$-critical graph $G$ satisfies $|E(G)| \geq (\frac{k}{2} - \frac{1}{k-1})|V(G)| - \frac{k(k-3)}{2(k-1)}$. The class of graphs ... More

Finite domination and Novikov homology over strongly Z-graded ringsFeb 08 2016Apr 14 2016Let L be a strongly Z-graded ring, and let C be a bounded chain complex of finitely generated L-modules. We give a homological characterisation of when C is homotopy equivalent, over L_0, to a bounded complex of finitely generated projective L_0-modules, ... More

Correspondence coloring and its application to list-coloring planar graphs without cycles of lengths 4 to 8Aug 14 2015Oct 08 2016We introduce a new variant of graph coloring called correspondence coloring which generalizes list coloring and allows for reductions previously only possible for ordinary coloring. Using this tool, we prove that excluding cycles of lengths 4 to 8 is ... More

A New Code for Proto-Neutron Star EvolutionMay 15 2012Jul 13 2012A new code for following the evolution and emissions of proto-neutron stars during the first minute of their lives is developed and tested. The code is one dimensional, fully implicit, and general relativistic. Multi-group, multi-flavor neutrino transport ... More

The Laplacian on $p$-forms on the Heisenberg groupJul 27 1998The Novikov-Shubin invariants for a non-compact Riemannian manifold M can be defined in terms of the large time decay of the heat operator of the Laplacian on square integrable p-forms on M. For the (2n+1)-dimensional Heisenberg group H, the Laplacian ... More

Local Linear Convergence of Approximate Projections onto Regularized SetsAug 10 2011Sep 14 2011The numerical properties of algorithms for finding the intersection of sets depend to some extent on the regularity of the sets, but even more importantly on the regularity of the intersection. The alternating projection algorithm of von Neumann has been ... More

Symmetrization of Principal Minors and Cycle-SumsOct 08 2015Sep 15 2016We solve the Symmetrized Principal Minor Assignment Problem, that is we show how to determine if for a given vector $v\in \mathbb{C}^{n}$ there is an $n\times n$ matrix that has all $i\times i$ principal minors equal to $v_{i}$. We use a special isomorphism ... More

Bousfield lattices of non-Noetherian rings: some quotients and productsJan 18 2013Jul 14 2014In the context of a well generated tensor triangulated category, Section 3 investigates the relationship between the Bousfield lattice of a quotient and quotients of the Bousfield lattice. In Section 4 we develop a general framework to study the Bousfield ... More

Magnetic fields on resistance spacesJan 06 2015Aug 31 2016On a metric measure space $X$ that supports a regular, strongly local resistance form we consider a magnetic energy form that corresponds to the magnetic Laplacian for a particle confined to $X$. We provide sufficient conditions for closability and self-adjointness ... More

Density of 5/2-critical graphsNov 24 2014A graph G is 5/2-critical if G has no circular 5/2-coloring (or equivalently, homomorphism to C_5), but every proper subgraph of G has one. We prove that every 5/2-critical graph on n>=4 vertices has at least (5n-2)/4 edges, and list all 5/2-critical ... More

On the Walks and Bipartite Double Coverings of Graphs with the same Main EigenspaceJun 13 2019The main eigenvalues of a graph $G$ are those eigenvalues of the $(0,1)$-adjacency matrix $\mathbf A$ having a corresponding eigenvector not orthogonal to $\mathbf j = (1,\dots,1)$. The CDC of a graph $G$ is the direct product $G\times K_2$. The main ... More

A class of semiprimitive groups that are graph-restrictiveJan 14 2014We prove that an infinite family of semiprimitive groups are graph-restrictive. This adds to the evidence for the validity of the PSV Conjecture and increases the minimal imprimitive degree for which this conjecture is open to 12. Our result can be seen ... More

A note on sensitivity of principal component subspaces and the efficient detection of influential observations in high dimensionsMar 04 2008Jun 26 2008In this paper we introduce an influence measure based on second order expansion of the RV and GCD measures for the comparison between unperturbed and perturbed eigenvectors of a symmetric matrix estimator. Example estimators are considered to highlight ... More

Hyperbolic families and coloring graphs on surfacesSep 21 2016May 06 2018Let $G$ be a graph embedded in a fixed surface $\Sigma$ of genus $g$ and let $L=(L(v):v\in V(G))$ be a collection of lists such that either each list has size at least five, or each list has size at least four and $G$ is triangle-free, or each list has ... More

Five-list-coloring graphs on surfaces III. One list of size one and one list of size twoAug 19 2016Let $G$ be a plane graph with outer cycle $C$ and let $(L(v):v\in V(G))$ be a family of non-empty sets. By an $L$-coloring of $G$ we mean a (proper) coloring $\phi$ of $G$ such that $\phi(v)\in L(v)$ for every vertex $v$ of $G$. Thomassen proved that ... More

Five-list-coloring graphs on surfaces II. A linear bound for critical graphs in a diskMay 22 2015Let $G$ be a plane graph with outer cycle $C$ and let $(L(v):v\in V(G))$ be a family of sets such that $|L(v)|\ge 5$ for every $v\in V(G)$. By an $L$-coloring of a subgraph $J$ of $G$ we mean a (proper) coloring $\phi$ of $J$ such that $\phi(v)\in L(v)$ ... More

Thermal Conductance Across Harmonic-matched Epitaxial Al-sapphire Heterointerfaces: A Benchmark for Metal-nonmetal InterfacesJun 13 2019A unified understanding of interfacial thermal transport is missing due to the complicated nature of interfaces which involves complex factors such as interfacial bonding, interfacial mixing, surface chemistry, crystal orientation, roughness, contamination, ... More

Neutrino Signatures From Young Neutron StarsDec 12 2016After a successful core collapse supernova (CCSN) explosion, a hot dense proto-neutron star (PNS) is left as a remnant. Over a time of twenty or so seconds, this PNS emits the majority of the neutrinos that come from the CCSN, contracts, and loses most ... More

r-Process Lanthanide Production and Heating Rates in KilonovaeAug 13 2015Nov 02 2015r-Process nucleosynthesis in material ejected during neutron star mergers may lead to radioactively powered transients called kilonovae. The timescale and peak luminosity of these transients depend on the composition of the ejecta, which determines the ... More

Splitting criteria for vector bundles on the symplectic isotropic GrassmannianMar 15 2010We extend a theorem of Ottaviani on cohomological splitting criterion for vector bundles over the Grassmannian to the case of the symplectic isotropic Grassmanian. We find necessary and sufficient conditions for the case of the Grassmanian of symplectic ... More

Equations for the fifth secant variety of Segre products of projective spacesFeb 01 2015Apr 01 2015We describe a computational proof that the fifth secant variety of the Segre product of five copies of the projective line is a codimension 2 complete intersection of equations of degree 6 and 16. Our computations rely on pseudo-randomness, and numerical ... More

Wide-band Rotation Measure SynthesisJun 03 2019Rotation measure synthesis allows the estimation of Faraday dispersion via a Fourier transform and is the primary tool to probe cosmic magnetic fields. We show this can be considered mathematically equivalent to the one dimensional interferometric intensity ... More

Toward a salmon conjectureSep 30 2010Feb 02 2011By using a result from the numerical algebraic geometry package Bertini we show that (up to high numerical accuracy) a specific set of degree 6 and degree 9 polynomials cut out the secant variety $\sigma_{4}(\mathbb{P}^{2}\times \mathbb{P} ^{2} \times ... More

Charged current neutrino interactions in hot and dense matterDec 08 2016Apr 06 2017We derive the charged current absorption rate of electron and anti-electron neutrinos in dense matter using a fully relativistic approach valid at arbitrary matter degeneracy. We include mean field energy shifts due to nuclear interactions and the corrections ... More

Using In-Game Shot Trajectories to Better Understand Defensive Impact in the NBAMay 02 2019As 3-point shooting in the NBA continues to increase, the importance of perimeter defense has never been greater. Perimeter defenders are often evaluated by their ability to tightly contest shots, but how exactly does contesting a jump shot cause a decrease ... More

Laplacians on the basilica Julia setFeb 22 2008Oct 13 2008We consider the basilica Julia set of the polynomial $P(z)=z^{2}-1$ and construct all possible resistance (Dirichlet) forms, and the corresponding Laplacians, for which the topology in the effective resistance metric coincides with the usual topology. ... More

Magnetic arms generated by multiple interfering galactic spiral patternsAug 02 2013Oct 28 2013Interfering two- and three-arm spiral patterns have previously been inferred to exist in many galaxies and also in numerical simulations, and invoked to explain important dynamical properties, such as lack of symmetry, kinks in spiral arms, and star formation ... More

Efficient signal processing for time-resolved fluorescence detection of nitrogen-vacancy spins in diamondNov 13 2015Room-temperature fluorescence detection of the nitrogen-vacancy center electronic spin typically has low signal to noise, requiring long experiments to reveal an averaged signal. Here, we present a simple approach to analysis of time-resolved fluorescence ... More

Sensitivity of principal Hessian direction analysisJun 11 2007We provide sensitivity comparisons for two competing versions of the dimension reduction method principal Hessian directions (pHd). These comparisons consider the effects of small perturbations on the estimation of the dimension reduction subspace via ... More

Derivations and Dirichlet forms on fractalsJun 07 2011Jul 16 2012We study derivations and Fredholm modules on metric spaces with a local regular conservative Dirichlet form. In particular, on finitely ramified fractals, we show that there is a non-trivial Fredholm module if and only if the fractal is not a tree (i.e. ... More

The 3 x 3 x 3 hyperdeterminant as a polynomial in the fundamental invariants for SL(3,C) x SL(3,C) x SL(3,C)Oct 11 2013Feb 17 2014We briefly review previous work on the invariant theory of 3 x 3 x 3 arrays. We then recall how to generate arrays of arbitrary size m_1 x ... x m_k with hyperdeterminant 0. Our main result is an explicit formula for the 3 x 3 x 3 hyperdeterminant as ... More

The Discrete Unbounded Coagulation-Fragmentation Equation with Growth, Decay and SedimentationAug 31 2018In this paper we study the discrete coagulation--fragmentation models with growth, decay and sedimentation. We demonstrate the existence and uniqueness of classical global solutions provided the linear processes are sufficiently strong. This paper extends ... More

Discussion of "Riemann manifold Langevin and Hamiltonian Monte Carlo methods'' by M. Girolami and B. CalderheadOct 30 2010This technical report is the union of two contributions to the discussion of the Read Paper "Riemann manifold Langevin and Hamiltonian Monte Carlo methods" by B. Calderhead and M. Girolami, presented in front of the Royal Statistical Society on October ... More

Using Quantum Mechanics to Cluster Time SeriesMay 04 2018In this article we present a method by which we can reduce a time series into a single point in $\mathbb{R}^{13}$. We have chosen 13 dimensions so as to prevent too many points from being labeled as "noise." When using a Euclidean (or Mahalanobis) metric, ... More

A Dirac type result on Hamilton cycles in oriented graphsSep 07 2007Jun 04 2008We show that for each \alpha>0 every sufficiently large oriented graph G with \delta^+(G),\delta^-(G)\ge 3|G|/8+ \alpha |G| contains a Hamilton cycle. This gives an approximate solution to a problem of Thomassen. In fact, we prove the stronger result ... More

Optimization on Spheres: Models and Proximal Algorithms with Computational Performance ComparisonsOct 05 2018We present a unified treatment of the abstract problem of finding the best approximation between a cone and spheres in the image of affine transformations. Prominent instances of this problem are phase retrieval and source localization. The common geometry ... More

Secant varieties of P^2 x P^n embedded by O(1,2)Sep 07 2010We describe the defining ideal of the rth secant variety of P^2 x P^n embedded by O(1,2), for arbitrary n and r at most 5. We also present the Schur module decomposition of the space of generators of each such ideal. Our main results are based on a more ... More

On the Feasibility of Maintenance Algorithms in Dynamic GraphsJul 14 2011Feb 17 2012Near ubiquitous mobile computing has led to intense interest in dynamic graph theory. This provides a new and challenging setting for algorithmics and complexity theory. For any graph-based problem, the rapid evolution of a (possibly disconnected) graph ... More

Hamiltonians and canonical coordinates for spinning particles in curved space-timeAug 20 2018Jan 19 2019The spin-curvature coupling as captured by the so-called Mathisson-Papapetrou-Dixon (MPD) equations is the leading order effect of the finite size of a rapidly rotating compact astrophysical object moving in a curved background. It is also a next-to-leading ... More

Origin and evolution of long-period cometsApr 01 2019We develop an evolutionary model of the long-period comet (LPC) population, starting from their birthplace in a massive trans-Neptunian disk that was dispersed by migrating giant planets. Most comets that remain bound to the Solar system are stored in ... More

Nonparametric hierarchical Bayesian quantilesMay 11 2016Here we develop a method for performing nonparametric Bayesian inference on quantiles. Relying on geometric measure theory and employing a Hausdorff base measure, we are able to specify meaningful priors for the quantile while treating the distribution ... More

Cycles Of Given Length In Oriented GraphsJun 05 2008Aug 13 2009We show that for each \ell\geq 4 every sufficiently large oriented graph G with \delta^+(G), \delta^-(G) \geq \lfloor |G|/3 \rfloor +1 contains an \ell-cycle. This is best possible for all those \ell\geq 4 which are not divisible by 3. Surprisingly, for ... More

Parabolic $L^p$ Dirichlet Boundary Value Problem and VMO-type time-varying domainsMay 18 2018We prove the solvability of the parabolic $L^p$ Dirichlet boundary value problem for $1 < p \leq \infty$ for a PDE of the form $u_t = \mbox{div} (A \nabla u) + B \cdot \nabla u$ on time-varying domains where the coefficients $A= [a_{ij}(X, t)]$ and $B=[b_i]$ ... More

Bounds for Finite Semiprimitive Permutation Groups: Order, Base Size, and Minimal DegreeJun 04 2018In this paper we study finite semiprimitive permutation groups, that is, groups in which each normal subgroup is transitive or semiregular. We give bounds on the order, base size, minimal degree, fixity, and chief length of an arbitrary finite semiprimitive ... More

Convergence Analysis of the Relaxed Douglas-Rachford AlgorithmNov 28 2018May 23 2019Motivated by nonconvex, inconsistent feasibility problems in imaging, the relaxed alternating averaged reflections algorithm, or relaxed Douglas-Rachford algorithm (DR$\lambda$), was first proposed over a decade ago. Convergence results for this algorithm ... More

Alternating Projections and Douglas-Rachford for Sparse Affine FeasibilityJul 08 2013Mar 14 2014The problem of finding a vector with the fewest nonzero elements that satisfies an underdetermined system of linear equations is an NP-complete problem that is typically solved numerically via convex heuristics or nicely-behaved nonconvex relaxations. ... More

Characterising CCA Sylow cyclic groups whose order is not divisible by fourFeb 22 2017Apr 05 2017A Cayley graph on a group $G$ has a natural edge-colouring. We say that such a graph is CCA if every automorphism of the graph that preserves this edge-colouring is an element of the normaliser of the regular representation of $G$. A group $G$ is then ... More

Reducing Communication in Algebraic Multigrid with Multi-step Node Aware CommunicationApr 11 2019Algebraic multigrid (AMG) is often viewed as a scalable $\mathcal{O}(n)$ solver for sparse linear systems. Yet, parallel AMG lacks scalability due to increasingly large costs associated with communication, both in the initial construction of a multigrid ... More

Reducing Communication in Algebraic Multigrid with Multi-step Node Aware CommunicationApr 11 2019Apr 24 2019Algebraic multigrid (AMG) is often viewed as a scalable $\mathcal{O}(n)$ solver for sparse linear systems. Yet, parallel AMG lacks scalability due to increasingly large costs associated with communication, both in the initial construction of a multigrid ... More

Muon spin relaxation studies of magnetic order and superfluid density in antiferromagnetic NdOFeAs, BaFe2As2 and superconducting (Ba,K)Fe2As2Jul 07 2008Zero-field (ZF) muon spin relaxation ($\mu$SR) measurements have revealed static commensurate magnetic order of Fe moments in NdOFeAs below $T_{N} \sim 135$ K, with the ordered moment size nearly equal to that in LaOFeAs, and confirmed similar behavior ... More

Massive Black Hole Binary Mergers in Dynamical Galactic EnvironmentsJun 06 2016Oct 05 2016Gravitational Waves (GW) have now been detected from stellar-mass black hole binaries, and the first observations of GW from Massive Black Hole (MBH) Binaries are expected within the next decade. Pulsar Timing Arrays (PTA), which can measure the years ... More

The Complexity of CampaigningJun 20 2017Jul 17 2017In "The Logic of Campaigning", Dean and Parikh consider a candidate making campaign statements to appeal to the voters. They model these statements as Boolean formulas over variables that represent stances on the issues, and study optimal candidate strategies ... More

Moment conditions and Bayesian nonparametricsJul 30 2015Jan 13 2016Models phrased though moment conditions are central to much of modern inference. Here these moment conditions are embedded within a nonparametric Bayesian setup. Handling such a model is not probabilistically straightforward as the posterior has support ... More

Distribution theory on p.c.f. fractalsMar 24 2009We construct a theory of distributions in the setting of analysis on post-critically finite self-similar fractals, and on fractafolds and products based on such fractals. The results include basic properties of test functions and distributions, a structure ... More

List coloring with requestsDec 27 2016Nov 17 2018Let G be a graph with a list assignment L. Suppose a preferred color is given for some of the vertices; how many of these preferences can be respected when L-coloring G? We explore several natural questions arising in this context, and propose directions ... More

FFT, FMM, and Multigrid on the Road to Exascale: performance challenges and opportunitiesOct 28 2018FFT, FMM, and multigrid methods are widely used fast and highly scalable solvers for elliptic PDEs. However, emerging large-scale computing systems are introducing challenges in comparison to current petascale computers. Recent efforts have identified ... More

Reply to Comment on "Spin Ice: Magnetic Excitations without Monopole Signatures using Muon Spin Rotation"May 04 2012May 21 2012We respond to the comment of Bramwell et al (arXiv:1111.4168v1) to our original publication (S. R. Dunsiger et al, Phys. Rev. Lett. 107, 207207 (2011)), detailing muon spin rotation measurements of the Spin Ice compound Dy2Ti2O7.

The Safe Lambda CalculusJan 16 2009Feb 19 2009Safety is a syntactic condition of higher-order grammars that constrains occurrences of variables in the production rules according to their type-theoretic order. In this paper, we introduce the safe lambda calculus, which is obtained by transposing (and ... More

Hamiltonicity of the Cayley Digraph on the Symmetric Group Generated by σ = (1 2 ... n) and τ = (1 2)Jul 09 2013Oct 27 2013The symmetric group is generated by {\sigma} = (1 2 ... n) and {\tau} = (1 2). We answer an open problem of Nijenhuis and Wilf by constructing a Hamilton path in the directed Cayley graph for all n, and a Hamilton cycle for odd n.

The noncommutative Choquet boundaryJan 11 2007Feb 19 2007Let S be an operator system -- a self-adjoint linear subspace of a unital C*-algebra A such that contains 1 and A=C*(S) is generated by S. A boundary representation for S is an irreducible representation \pi of C*(S) on a Hilbert space with the property ... More

Hausdorff dimension of the spectrum of the square Fibonacci HamiltonianOct 12 2014Oct 22 2014Denoting the Hausdorff dimension of the Fibonacci Hamiltonian with coupling $\lambda$ by $\mathrm{HD}_\lambda$, we prove that for all but countably many $\lambda$, the Hausdorff dimension of the spectrum of the square Fibonacci Hamiltonian with coupling ... More

Exponential sum approximations and fast evaluation of fractional integralsJun 01 2016Given $\beta>0$ and $\delta>0$, the function $t^{-\beta}$ may be approximated for $t$ in the interval $[\delta,1]$ by a sum of terms of the form $we^{-at}$, with parameters $w>0$ and $a>0$. A basic approximation is obtained by applying quadratures to ... More

Finding paths of length k in O*(2^k) timeJul 18 2008Nov 09 2008We give a randomized algorithm that determines if a given graph has a simple path of length at least k in O(2^k poly(n,k)) time.

The quark-gluon vertex in Landau gauge bound-state studiesApr 09 2014Apr 21 2015We present a practical method for the solution of the quark-gluon vertex for use in Bethe--Salpeter and Dyson--Schwinger calculations. The efficient decomposition into the necessary covariants is detailed, with the numerical algorithm outlined for both ... More

Faster all-pairs shortest paths via circuit complexityDec 23 2013May 22 2014We present a new randomized method for computing the min-plus product (a.k.a., tropical product) of two $n \times n$ matrices, yielding a faster algorithm for solving the all-pairs shortest path problem (APSP) in dense $n$-node directed graphs with arbitrary ... More

Episodic mass transfer: A trigger for nova outbursts?Aug 24 2011High resolution spectra of postoutburst novae show multiple components of ejected gas that are kinematically distinct. We interpret the observations in terms of episodes of enhanced mass transfer originating from the secondary star that result in the ... More

Bethe-Salpeter studies of mesons beyond rainbow-ladderDec 17 2009We investigate the masses of light mesons from a coupled system of Dyson-Schwinger and Bethe-Salpeter equations. The dominant non-Abelian and sub-leading Abelian contributions to the dressed quark-gluon vertex are explicitly taken into account. We also ... More

Multi-meson States in Lattice QCDOct 07 2008In this contribution, I summarise the studies of the properties of Bose-Einstein condensed systems composed of up to twelve pions or kaons carried out by the NPLQCD collaboration. These investigations have provided precise determination the I=2 pi-pi ... More

Generators of Noncommutative DynamicsJan 15 2002For a fixed C*-algebra A, we consider all noncommutative dynamical systems that can be generated by A. More precisely, an A-dynamical system is a triple (i,B,\alpha) where $\alpha$ is a *-endomorphism of a C*-algebra B, and i: A --> B is the inclusion ... More

Interactions in noncommutative dynamicsOct 29 1999Nov 07 1999A mathematical notion of interaction is introduced for noncommutative dynamical systems, i.e., for one parameter groups of *-automorphisms of $\Cal B(H)$ endowed with a certain causal structure. With any interaction there is a well-defined "state of the ... More

The index of a quantum dynamical semigroupMay 25 1997A numerical index is introduced for semigroups of completely positive maps of $\Cal B(H)$ which generalizes the index of E_0-semigroups. It is shown that the index of a unital completely positive semigroup agrees with the index of its dilation to an E_0-semigroup, ... More

Yi's Unique Range Set Construction in the Number Field CaseMay 17 2006Feb 18 2013H. X. Yi's construction of unique range sets for entire functions is translated to the number theory setting to illustrate that his construction would work in the number theory setting if one knew a version of Schmidt's Subspace Theorem with truncated ... More

Exponential sum approximations for $t^{-β}$Jun 01 2016Oct 21 2016Given $\beta>0$ and $\delta>0$, the function $t^{-\beta}$ may be approximated for $t$ in a compact interval $[\delta,T]$ by a sum of terms of the form $we^{-at}$, with parameters $w>0$ and $a>0$. One such an approximation, studied by Beylkin and Monz\'on, ... More

The formation of stars in groupsNov 15 2001Observations of the dust and gas around embedded stellar clusters reveal some of the processes involved in their formation and evolution. Large scale mass infall with rates dM/dt=4e-4 solar masses/year is found to be disrupted on small scales by protostellar ... More

Uniformization By Classical Schottky GroupsJan 12 2006Mar 08 2006This paper has been withdrawn by the author due to an error in an inequality in the proof of Theorem 1.1.

Analysis of Rapidity Gap Cuts in Diffractive DISMay 31 1999The requirement of a large pseudo-rapidity gap to select diffractive DIS events at HERA restricts the kinematically accessible region of phase space for a significant range of $Q^2$, $\beta$ and $\xpom$. Consequences of this include a breakdown of $\xpom$-factorization ... More

Computations of the slice genus of virtual knotsJun 26 2017Aug 29 2017A virtual knot is an equivalence class of embeddings of $ S^1 $ into thickened (closed oriented) surfaces, up to self-diffeomorphism of the surface and certain handle stabilisations. The slice genus of a virtual knot is defined diagrammatically, in direct ... More

Overpartition $M2$-rank differences, class number relations, and vector-valued mock Eisenstein seriesAug 08 2017Sep 25 2018We prove that the generating function of overpartition $M2$-rank differences is, up to coefficient signs, a component of the vector-valued mock Eisenstein series attached to a certain quadratic form. We use this to compute analogs of the class number ... More

Graded rings of paramodular forms of levels $5$ and $7$Apr 23 2019We compute generators and relations for the graded rings of paramodular forms of degree two and levels 5 and 7. The generators are expressed as quotients of Gritsenko lifts and Borcherds products. The computation is made possible by a characterization ... More

Q-Systems, Factorization Dynamics, and the Twist AutomorphismOct 24 2013We provide a concrete realization of the cluster algebras associated with Q-systems as amalgamations of cluster structures on double Bruhat cells in simple algebraic groups. For nonsimply-laced groups, this provides a cluster-algebraic formulation of ... More