Results for "Ole Martin Brokstad"
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50 Years of Bailey's lemmaOct 12 2009Oct 14 2009This is a paper published in 2001 based on a talk given in 1999 celebrating the 50th anniversary of W. N. Bailey's influential q-series paper "Identities of the Rogers-Ramanujan type". In no more than 13 pages I give a brief but reasonably complete overview ... More The generalized Borwein conjecture. I. The Burge transformNov 27 2000Given an arbitrary ordered pair of coprime integers (a,b) we obtain a pair of identities of the Rogers--Ramanujan type. These identities have the same product side as the (first) Andrews--Gordon identity for modulus 2ab\pm 1, but an altogether different ... More Refined q-trinomial coefficients and character identitiesMay 12 2000A refinement of the q-trinomial coefficients is introduced, which has a very powerful iterative property. This ``T-invariance'' is applied to derive new Virasoro character identities related to the exceptional simply-laced Lie algebras E_6,E_7 and E_8. ... More Partial-sum analogues of the Rogers-Ramanujan identitiesAug 28 2001Aug 26 2002A new type of polynomial analogue of the Rogers-Ramanujan identities is proven. Here the product-side of the Rogers-Ramanujan identities is replaced by a partial theta sum and the sum-side by a weighted sum over Schur polynomials. Stochastic Market EfficiencyJan 24 2011It is argued that the simple trading strategy of leveraging or deleveraging an investment in the market portfolio cannot outperform the market. Such stochastic market efficiency places strong constraints on the possible stochastic properties of the market. ... More The Bailey lemma and Kostka polynomialsJul 03 2002Using the theory of Kostka polynomials, we prove an A_{n-1} version of Bailey's lemma at integral level. Exploiting a new, conjectural expansion for Kostka numbers, this is then generalized to fractional levels, leading to a new expression for admissible ... More Composition Operators on Bohr-Bergman Spaces of Dirichlet SeriesSep 10 2014Jun 15 2015For $\alpha \in \mathbb{R}$, let $\mathscr{D}_\alpha$ denote the scale of Hilbert spaces consisting of Dirichlet series $f(s) = \sum_{n=1}^\infty a_n n^{-s}$ that satisfy $\sum_{n=1}^\infty |a_n|^2/[d(n)]^\alpha < \infty$. The Gordon--Hedenmalm Theorem ... More Modular Nekrasov-Okounkov formulasFeb 09 2019Using Littlewood's map, which decomposes a partition into its $r$-core and $r$-quotient, Han and Ji have shown that many well-known hook-length formulas admit modular analogues. In this paper we present a variant of the Han-Ji `multiplication theorem' ... More A q-rious positivityMar 09 2010The $q$-binomial coefficients $\qbinom{n}{m}=\prod_{i=1}^m(1-q^{n-m+i})/(1-q^i)$, for integers $0\le m\le n$, are known to be polynomials with non-negative integer coefficients. This readily follows from the $q$-binomial theorem, or the many combinatorial ... More Laws of large numbers for Hayashi-Yoshida-type functionalsMar 15 2018In high-frequency statistics and econometrics sums of functionals of increments of stochastic processes are commonly used and statistical inference is based on the asymptotic behaviour of these sums as the mesh of the observation times tends to zero. ... More Dedekind's eta-function and Rogers-Ramanujan identitiesJan 11 2010Jan 22 2010We prove a q-series identity that generalises Macdonald's A_{2n}^{(2)} eta-function identity and the Rogers-Ramanujan identities. We conjecture our result to generalise even further to also include the Andrews-Gordon identities. On Ladder Logic Bombs in Industrial Control SystemsFeb 17 2017In industrial control systems, devices such as Programmable Logic Controllers (PLCs) are commonly used to directly interact with sensors and actuators, and perform local automatic control. PLCs run software on two different layers: a) firmware (i.e. the ... More Constant term identities and Poincare polynomialsSep 05 2012Apr 05 2013In 1982 Macdonald published his now famous constant term conjectures for classical root systems. This paper begins with the almost trivial observation that Macdonald's constant term identities admit an extra set of free parameters, thereby linking them ... More Preheating in an Asymptotically Safe Quantum Field TheoryMar 08 2016We consider reheating in a class of asymptotically safe quantum field theories recently studied in \cite{Litim:2014uca, Litim:2015iea}. These theories allow for an inflationary phase in the very early universe. Inflation ends with a period of reheating. ... More A Nekrasov-Okounkov formula for Macdonald polynomialsJun 15 2016Feb 19 2018We prove a Macdonald polynomial analogue of the celebrated Nekrasov-Okounkov hook-length formula from the theory of random partitions. As an application we obtain a proof of one of the main conjectures of Hausel and Rodriguez-Villegas from their work ... More Direct subsurface absorption of hydrogen on Pd(111)Dec 13 1995We summarize and discuss some of the available experimental and theoretical data important for understanding the role played by subsurface sites in dissociative chemisorption calculations for the H$_2$/Pd(111) system. Then we use a semi-empirical potential ... More Volterra operators on Hardy spaces of Dirichlet seriesFeb 15 2016Nov 08 2016For a Dirichlet series symbol $g(s) = \sum_{n \geq 1} b_n n^{-s}$, the associated Volterra operator $\mathbf{T}_g$ acting on a Dirichlet series $f(s)=\sum_{n\ge 1} a_n n^{-s}$ is defined by the integral $f\mapsto -\int_{s}^{+\infty} f(w)g'(w)\,dw$. We ... More Logarithmic and complex constant term identitiesDec 14 2011Mar 04 2012In recent work on the representation theory of vertex algebras related to the Virasoro minimal models M(2,p), Adamovic and Milas discovered logarithmic analogues of (special cases of) the famous Dyson and Morris constant term identities. In this paper ... More Discrete analogues of Macdonald-Mehta integralsJan 25 2016We consider discretisations of the Macdonald--Mehta integrals from the theory of finite reflection groups. For the classical groups, $\mathrm{A}_{r-1}$, $\mathrm{B}_r$ and $\mathrm{D}_r$, we provide closed-form evaluations in those cases for which the ... More Spectral WallsMar 28 2019During defect-antidefect scattering, bound modes frequently disappear into the continuous spectrum before the defects themselves collide. This leads to a structural, nonperturbative change in the spectrum of small excitations. Sometimes the effect can ... More Understanding adsorption of hydrogen atoms on grapheneAug 08 2008Adsorption of hydrogen atoms on a single graphite sheet (graphene) has been investigated by first-principles electronic structure means, employing plane-wave based, periodic density functional theory. A reasonably large 5x5 surface unit cell has been ... More I^K-convergenceSep 13 2011In this paper we introduce I^K-convergence which is a common generalization of the I^K-convergence of sequences, double sequences and nets. We show that many results that were shown before for these special cases are true for the I^K-convergence, too On the representation of polyhedra by polynomial inequalitiesMar 26 2002Oct 24 2002A beautiful result of Br\"ocker and Scheiderer on the stability index of basic closed semi-algebraic sets implies, as a very special case, that every $d$-dimensional polyhedron admits a representation as the set of solutions of at most $d(d+1)/2$ polynomial ... More Algorithmic Optimisations for Iterative Deconvolution MethodsApr 26 2013We investigate possibilities to speed up iterative algorithms for non-blind image deconvolution. We focus on algorithms in which convolution with the point-spread function to be deconvolved is used in each iteration, and aim at accelerating these convolution ... More Neutralino Dark Matter and the CurvatonNov 30 2006Mar 09 2007We build a realistic model of curvaton cosmology, in which the energy content is described by radiation, WIMP dark matter and a curvaton component. We calculate the curvature and isocurvature perturbations, allowing for arbitrary initial density perturbations ... More Automatic Generation of Security Argument GraphsMay 29 2014Graph-based assessment formalisms have proven to be useful in the safety, dependability, and security communities to help stakeholders manage risk and maintain appropriate documentation throughout the system lifecycle. In this paper, we propose a set ... More Solving systems of linear equations on a quantum computerFeb 05 2013Systems of linear equations are used to model a wide array of problems in all fields of science and engineering. Recently, it has been shown that quantum computers could solve linear systems exponentially faster than classical computers, making for one ... More Probability as a physical motiveFeb 15 2007Apr 01 2007Recent theoretical progress in nonequilibrium thermodynamics, linking the physical principle of Maximum Entropy Production ("MEP") to the information-theoretical "MaxEnt" principle of scientific inference, together with conjectures from theoretical physics ... More Greiter replies to Demler, Zhang, Meixner, and HankeMay 28 1997May 28 1997In a comment on my recent manuscript on the pi-particle [cond-mat/9705049], Demler et al. [cond-mat/9705191] argued that there is a correction to the chemical potential which enters the expression for the energy of the pi-particle given in [Demler and ... More S=1 Spin Liquids: Broken Discrete Symmetries RestoredMar 13 2002We introduce a novel kind of spin liquid, the spin 1 chirality liquid, which provides a generic paradigm for a disordered spin 1 antiferromagnet in two dimensions. It supports spinon and holon excitations, which carry a chirality quantum number. These ... More A Targeted Survey for HI Clouds in Galaxy GroupsMar 20 2001Five galaxy groups with properties similar to those of the Local Group have been surveyed for HI clouds with the Arecibo Telescope. In total 300 pointings have been observed on grids of approximately 2.5 x 1.5 Mpc centred on the groups. The 4.5 sigma ... More A short note on vector bundles on curvesSep 21 2010Beauville and Laszlo give an interpretation of the affine Grassmannian for Gl_n over a field k as a moduli space of, loosely speaking, vector bundles over a projective curve together with a trivialization over the complement of a fixed closed point. In ... More Global Fluctuations in General Beta Dyson Brownian MotionOct 25 2006We consider a system of diffusing particles on the real line in a quadratic external potential and with repulsive electrostatic interaction. The empirical measure process is known to converge weakly to a deterministic measure-valued process as the number ... More Quasi-4-Connected ComponentsFeb 14 2016We introduce a new decomposition of a graphs into quasi-4-connected components, where we call a graph quasi-4-connected if it is 3-connected and it only has separations of order 3 that remove a single vertex. Moreover, we give a cubic time algorithm computing ... More Design and Status of IceCubeMay 01 2004IceCube is a kilometer-scale high energy neutrino detector that builds on the wealth of experience accumulated with its smaller predecessor, AMANDA. An international collaboration has begun construction of key components of the IceCube detector and deployment ... More A Critique of the CAP TheoremSep 17 2015Sep 18 2015The CAP Theorem is a frequently cited impossibility result in distributed systems, especially among NoSQL distributed databases. In this paper we survey some of the confusion about the meaning of CAP, including inconsistencies and ambiguities in its definitions, ... More Search for CP Violation in the Decay Z -> b (b bar) gAug 01 1996About three million hadronic decays of the Z collected by ALEPH in the years 1991-1994 are used to search for anomalous CP violation beyond the Standard Model in the decay Z -> b \bar{b} g. The study is performed by analyzing angular correlations between ... More M-branes on U-foldsDec 27 2007We give a preliminary discussion of how the addition of extra coordinates in M-theory, which together with the original ones parametrise a U-fold, can serve as a tool for formulating brane dynamics with manifest U-duality. The redundant degrees of freedom ... More World-volume fields and background coupling of branesJun 18 1998This is the written version of an invited talk delivered at the workshop ``Quantum gravity in the Southern Cone'' held in San Carlos de Bariloche, Argentina, January 7-10, 1998. After giving a brief introduction to the concept of branes and their role ... More Aspects of D-brane actionsDec 14 1996A couple of issues concerning the effective dynamics of D-branes in string theory are discussed. Primarily, I am concerned with linearization of the actions by introduction of non-propagating fields and a full super- and kappa-symmetric description of ... More T-duality and non-geometric solutions from double geometrySep 15 2014Although the introduction of generalised and extended geometry has been motivated mainly by the appearance of dualities upon reductions on tori, it has until now been unclear how (all) the duality transformations arise from first principles in extended ... More Thoughts on Membranes, Matrices and Non-CommutativityOct 11 2004We review the passage from the supermembrane to matrix theory via a consistent truncation following a non-commutative deformation in light-cone gauge. Some indications are given that there should exist a generalisation of non-commutativity involving a ... More Confinement at Weak CouplingNov 03 2005The free energy of U(N) and SU(N) gauge theory was recently found to be of order N^0 to all orders of a perturbative expansion about a center-symmetric orbit of vanishing curvature. Here I consider extended models for which this expansion is perturbatively ... More Quantization in the Presence of Gribov AmbiguitiesOct 21 1998The non-perturbative validity of covariant BRST-quantization of gauge theories on compact Euclidean space-time manifolds is reviewed. BRST-quantization is related to the construction of a Topological Quantum Field Theory (TQFT) of Witten type on the gauge ... More Charge-Ordering Phenomena in One-Dimensional SolidsMay 13 2007As the dimensionality is reduced, the world becomes more and more interesting; novel and fascinating phenomena show up which call for understanding. Physics in one dimension is a fascinating topic for theory and experiment: for the former often a simplification, ... More NNLO contributions to epsilon_K and rare kaon decaysSep 11 2009We discuss the theory prediction of epsilon_K and the rare K -> pi nu nu-bar decays and review the structure and current status of higher-order contributions to these flavour changing processes in the standard model in some detail. This includes the next-to-next-to-leading ... More Elementary thermodynamics of trapped particlesOct 12 2002I develop simple thermodynamic relations for a collection of noninteracting classical particles confined in a harmonic trap. The volume of such a trap is not a good thermodynamic variable, so conventional expressions of the first law of thermodynamics ... More Performance potential for simulating spin models on GPUJan 07 2011Feb 20 2012Graphics processing units (GPUs) are recently being used to an increasing degree for general computational purposes. This development is motivated by their theoretical peak performance, which significantly exceeds that of broadly available CPUs. For practical ... More Quantum geometry and quantum dynamics at the Planck scaleOct 15 2009Canonical quantum gravity provides insights into the quantum dynamics as well as quantum geometry of space-time by its implications for constraints. Loop quantum gravity in particular requires specific corrections due to its quantization procedure, which ... More Quantum gravity, space-time structure, and cosmologyJun 12 2012A set of diverse but mutually consistent results obtained in different settings has spawned a new view of loop quantum gravity and its physical implications, based on the interplay of operator calculations and effective theory: Quantum corrections modify, ... More Comment on "Quantum bounce and cosmic recall" [arXiv:0710.4543]Nov 17 2008A recently derived inequality on volume fluctuations of a bouncing cosmology, valid for states which are semiclassical long after the bounce, does not restrict pre-bounce fluctuations sufficiently strongly to conclude that the pre-bounce state was semiclassical ... More How quantum is the big bang?May 08 2008When quantum gravity is used to discuss the big bang singularity, the most important, though rarely addressed, question is what role genuine quantum degrees of freedom play. Here, complete effective equations are derived for isotropic models with an interacting ... More Singularities and Quantum GravityFeb 27 2007Although there is general agreement that a removal of classical gravitational singularities is not only a crucial conceptual test of any approach to quantum gravity but also a prerequisite for any fundamental theory, the precise criteria for non-singular ... More Universe scenarios from loop quantum cosmologyNov 18 2005Loop quantum cosmology is an application of recent developments for a non-perturbative and background independent quantization of gravity to a cosmological setting. Characteristic properties of the quantization such as discreteness of spatial geometry ... More The Semiclassical Limit of Loop Quantum CosmologyMay 29 2001The continuum and semiclassical limits of isotropic, spatially flat loop quantum cosmology are discussed, with an emphasis on the role played by the Barbero-Immirzi parameter \gamma in controlling space-time discreteness. In this way, standard quantum ... More Renormalization group flow of reduced string actionsSep 22 2005It has been argued that certain reduced actions play a role in AdS/CFT when comparing fast moving strings to long single trace operators in gauge theories. Such actions arise in two ways: as a limit of the string action and as a description of long single ... More Spiky strings and single trace operators in gauge theoriesOct 24 2004Jun 24 2005We consider single trace operators of the form O_{m_1 ... m_n} = tr D_+^{m_1} F ... D_+^{m_n} F which are common to all gauge theories. We argue that, when all m_i are equal and large, they have a dual description as strings with cusps, or spikes, one ... More Wilson loops and anomalous dimensions in cascading theoriesOct 03 2003Nov 07 2003We use light-like Wilson loops and the AdS/CFT correspondence to compute the anomalous dimensions of twist two operators in the cascading (Klebanov-Strassler) theory. The computation amounts to find a minimal surface in the UV region of the KS background ... More The Origin of Fat TailsOct 16 2013May 16 2014We propose a random walk model of asset returns where the parameters depend on market stress. Stress is measured by, e.g., the value of an implied volatility index. We show that model parameters including standard deviations and correlations can be estimated ... More Geometrical theory of diffraction and spectral statisticsOct 06 1999We investigate the influence of diffraction on the statistics of energy levels in quantum systems with a chaotic classical limit. By applying the geometrical theory of diffraction we show that diffraction on singularities of the potential can lead to ... More Parallel Magnetic Resonance ImagingJan 25 2015Jul 17 2015The main disadvantage of Magnetic Resonance Imaging (MRI) are its long scan times and, in consequence, its sensitivity to motion. Exploiting the complementary information from multiple receive coils, parallel imaging is able to recover images from under-sampled ... More Dressing curvesAug 03 2015We present a loop group description for curves in $\mathbb{R}^3$, and apply it to classify the circletons: Circles dressed by simple factors.