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Multimodal Machine Learning-based Knee Osteoarthritis Progression Prediction from Plain Radiographs and Clinical DataApr 12 2019Knee osteoarthritis (OA) is the most common musculoskeletal disease without a cure, and current treatment options are limited to symptomatic relief. Prediction of OA progression is a very challenging and timely issue, and it could, if resolved, accelerate ... More

Multimodal Machine Learning-based Knee Osteoarthritis Progression Prediction from Plain Radiographs and Clinical DataApr 12 2019May 06 2019Knee osteoarthritis (OA) is the most common musculoskeletal disease without a cure, and current treatment options are limited to symptomatic relief. Prediction of OA progression is a very challenging and timely issue, and it could, if resolved, accelerate ... More

On the Angular Width of Diffractive Beam in Anisotropic MediaDec 15 20112-D diffraction patterns arising in the far-field region were investigated theoretically for the case, when the plane wave with non collinear group and phase velocities is incident on the wide slit in opaque screen with arbitrary orientation. This investigation ... More

Least energy radial sign-changing solution for the Schröinger-Poisson system in r3 under an asymptotically cubic nonlinearityMay 01 2018In this paper we consider the following Schr\"odinger-Poisson system in the whole $\mathbb R^{3}$, \begin{equation*} \left\{ \begin{array}{ll} -\Delta u+u+ \lambda \phi u=f(u) &\text{ in } \mathbb R^3, -\Delta \phi= u^2 &\text{ in } \mathbb R^3, \end{array} ... More

Positive semiclassical states for a fractional Schrödinger-Poisson systemJan 04 2016We consider a fractional Schr\"odinger-Poisson system in the whole space $\mathbb R^{N}$ in presence of a positive potential and depending on a small positive parameter $\varepsilon.$ We show that, for suitably small $\varepsilon$ (i.e. in the "semiclassical ... More

An odd characterization of the generalized odd graphsFeb 10 2012We show that any connected regular graph with $d+1$ distinct eigenvalues and odd-girth $2d+1$ is distance-regular, and in particular that it is a generalized odd graph.

Regular graphs with maximal energy per vertexOct 31 2012Jun 12 2014We study the energy per vertex in regular graphs. For every k, we give an upper bound for the energy per vertex of a k-regular graph, and show that a graph attains the upper bound if and only if it is the disjoint union of incidence graphs of projective ... More

Monitoring the photometric behavior of OmegaCAM with Astro-WISEDec 26 2012The OmegaCAM wide-field optical imager is the sole instrument on the VLT Survey Telescope at ESO's Paranal Observatory. The instrument, as well as the telescope, have been designed for surveys with very good, natural seeing-limited image quality over ... More

Magnetic impurities in spin-split superconductorsNov 25 2016Feb 15 2017Hybrid semiconductor-superconductor quantum dot devices are tunable physical realizations of quantum impurity models for a magnetic impurity in a superconducting host. The binding energy of the localized sub-gap Shiba states is set by the gate voltages ... More

On Form Factors in nested Bethe Ansatz systemsApr 18 2012Sep 24 2012We investigate form factors of local operators in the multi-component Quantum Non-linear Schr\"odinger model, a prototype theory solvable by the so-called nested Bethe Ansatz. We determine the analytic properties of the infinite volume form factors using ... More

Magnetic impurities in spin-split superconductorsNov 25 2016Hybrid semiconductor-superconductor quantum dot devices are tunable physical realizations of quantum impurity models for a magnetic impurity in a superconducting host. The binding energy of the localized sub-gap Shiba states is set by the gate voltages ... More

Determining the Lensing Fraction of SDSS Quasars: Methods and Results from the EDRJan 23 2003We present an algorithm for selecting gravitational lens candidates from amongst Sloan Digital Sky Survey (SDSS) quasars. In median Early Data Release (EDR) conditions, the algorithm allows for the recovery of pairs of equal flux point sources down to ... More

Distance-regular graphsOct 23 2014Apr 15 2016This is a survey of distance-regular graphs. We present an introduction to distance-regular graphs for the reader who is unfamiliar with the subject, and then give an overview of some developments in the area of distance-regular graphs since the monograph ... More

A survival model for course-course interactions in a Massive Open Online Course platformMay 10 2019Massive Open Online Course (MOOC) platforms incorporate large course catalogs from which individual students may register multiple courses. We performed a network-based analysis of student achievement, considering how course-course interactions may positively ... More

Partially metric association schemes with a multiplicity threeJan 12 2017An association scheme is called partially metric if it has a connected relation whose distance-two relation is also a relation of the scheme. In this paper we determine the symmetric partially metric association schemes with a multiplicity three. Besides ... More

Shaped Gaussian Dictionaries for Quantized Networked Control Systems with Correlated DropoutsJun 24 2015This paper studies fixed rate vector quantisation for noisy networked control systems (NCSs) with correlated packet dropouts. In particular, a discrete-time linear time invariant system is to be controlled over an error-prone digital channel. The controller ... More

Ehrhart clutters: Regularity and Max-Flow Min-CutFeb 09 2009Apr 04 2010If C is a clutter with n vertices and q edges whose clutter matrix has column vectors V={v1,...,vq}, we call C an Ehrhart clutter if {(v1,1),...,(vq,1)} is a Hilbert basis. Letting A(P) be the Ehrhart ring of P=conv(V), we are able to show that if A is ... More

Superdirected Beam of the Surface Spin WaveNov 29 2016Visualized diffraction patterns of the surface spin wave excited by arbitrarily oriented linear transducer in tangentially magnetized ferrite film are investigated experimentally in the plane of ferrite film for the case where the transducer length D ... More

Ultra-fast treatment plan optimization for volumetric modulated arc therapy (VMAT)May 24 2010Purpose: To develop a novel aperture-based algorithm for volumetric modulated arc therapy (VMAT) treatment plan optimization with high quality and high efficiency. Methods: The VMAT optimization problem is formulated as a large-scale convex programming ... More

Graphs with many valencies and few eigenvaluesMay 14 2014May 07 2015Dom de Caen posed the question whether connected graphs with three distinct eigenvalues have at most three distinct valencies. We do not answer this question, but instead construct connected graphs with four and five distinct eigenvalues and arbitrarily ... More

Geometric formalism for constructing arbitrary single-qubit dynamically corrected gatesNov 12 2018Implementing high-fidelity quantum control and reducing the effect of the coupling between a quantum system and its environment is a major challenge in developing quantum information technologies. Here, we show that there exists a geometrical structure ... More

Embroidered Antenna Characterization for Passive UHF RFID TagsOct 05 2017For smart clothing integration with the wireless system based on radio frequency (RF) backscattering, we demonstrate an ultra-high frequency (UHF) antenna constructed from embroidered conductive threads. Sewn into a fabric backing, the T-match antenna ... More

On the Capacity of the Heat Channel, Waterfilling in the Time-Frequency Plane, and a C-NODE RelationshipDec 31 2010Jan 27 2014The heat channel is defined by a linear time-varying (LTV) filter with additive white Gaussian noise (AWGN) at the filter output. The continuous-time LTV filter is related to the heat kernel of the quantum mechanical harmonic oscillator, so the name of ... More

Design of Pulse Shapes and Digital Filters Based on Gaussian FunctionsJul 14 2009Two new pulse shapes for communications are presented. The first pulse shape is ISI-free and identical with the interpolating function (or ISI-free kernel) of a reconstruction formula in shift-invariant spaces with Gaussian generator. Several closed form ... More

Singular Eigenfunctions of Calogero-Sutherland Type Systems and How to Transform Them into Regular OnesFeb 26 2007There exists a large class of quantum many-body systems of Calogero-Sutherland type where all particles can have different masses and coupling constants and which nevertheless are such that one can construct a complete (in a certain sense) set of exact ... More

Bosons and fermions in external fieldsJul 12 2005Contribution to the Encyclopedia of Mathematical Physics (Elsevier, 2006): a brief and (hopefully) pedagogical introduction to quantum field theory models describing particles in external fields is presented. Following the instructions, the only references ... More

Interacting fermions on noncommutative spaces: Exactly solvable quantum field theories in 2n+1 dimensionsMay 28 2002I present a novel class of exactly solvable quantum field theories. They describe non-relativistic fermions on even dimensional flat space, coupled to a constant external magnetic field and a four point interaction defined with the Groenewold-Moyal star ... More

Chainable subcontinuaApr 10 2002This paper is concerned with conditions under which a metric continuum (a compact connected metric space) contains a non-degenerate chainable continuum.

Second quantization of the elliptic Calogero-Sutherland modelFeb 07 2001We use loop group techniques to construct a quantum field theory model of anyons on a circle and at finite temperature. We find an anyon Hamiltonian providing a second quantization of the elliptic Calogero-Sutherland model. This allows us to prove a remarkable ... More

Generalized Yang-Mills actions from Dirac operator determinantsApr 08 2001We consider the quantum effective action of Dirac fermions on four dimensional flat Euclidean space coupled to external vector- and axial Yang-Mills fields, i.e., the logarithm of the (regularized) determinant of a Dirac operator on flat R^4 twisted by ... More

Source identity and kernel functions for elliptic Calogero-Sutherland type systemsMar 03 2010Jul 16 2010Kernel functions related to quantum many-body systems of Calogero-Sutherland type are discussed, in particular for the elliptic case. The main result is an elliptic generalization of an identity due to Sen that is a source for many such kernel functions. ... More

An explicit solution of the (quantum) elliptic Calogero-Sutherland modelJul 21 2004Sep 06 2004We present explicit formulas for the eigenvalues and eigenfunctions of the elliptic Calogero-Sutherland (eCS) model as formal power series to all orders in the nome of the elliptic functions, for arbitrary values of the (positive) coupling constant and ... More

Correction to "A Note on Gallager's Capacity Theorem for Waveform Channels"Jul 19 2012Nov 04 2013We correct an alleged contradiction to Gallager's capacity theorem for waveform channels as presented in a poster at the 2012 IEEE International Symposium on Information Theory.

Quantum Gauge Theories and Noncommutative GeometryAug 01 1996I review results from recent investigations of anomalies in fermion--Yang Mills systems in which basic notions from noncommutative geometry (NCG) where found to naturally appear. The general theme is that derivations of anomalies from quantum field theory ... More

Cocycles for Boson and Fermion Bogoliubov TransformationsMay 05 1993Unitarily implementable Bogoliubov transformations for charged, relativistic bos\-ons and fermions are discussed, and explicit formulas for the 2-cocycles appearing in the group product of their implementers are derived. In the fermion case this provides ... More

MicroRNA Systems BiologyDec 20 2007Recently, microRNAs (miRNAs) have emerged as central posttranscriptional regulators of gene expression. miRNAs regulate many key biological processes, including cell growth, death, development and differentiation. This discovery is challenging the central ... More

Conformal field theory and the solution of the (quantum) elliptic Calogero-Sutherland systemNov 28 2004Aug 08 2005We review the construction of a conformal field theory model which describes anyons on a circle and at finite temperature, including previously unpublished results. This anyon model is closely related to the quantum elliptic Calogero-Sutherland (eCS) ... More

Explicit solution of the (quantum) elliptic Calogero-Sutherland modelJan 14 2004Dec 09 2008We derive explicit formulas for the eigenfunctions and eigenvalues of the elliptic Calogero-Sutherland model as infinite series, to all orders and for arbitrary particle numbers and coupling parameters. The eigenfunctions obtained provide an elliptic ... More

Geometric aspects of 2-walk-regular graphsApr 10 2013Sep 15 2013A $t$-walk-regular graph is a graph for which the number of walks of given length between two vertices depends only on the distance between these two vertices, as long as this distance is at most $t$. Such graphs generalize distance-regular graphs and ... More

SDSS J115517.35+634622.0: A Newly Discovered Gravitationally Lensed QuasarDec 05 2003We report the discovery of SDSSJ115517.35+634622.0, a previously unknown gravitationally lensed quasar. The lens system exhibits two images of a $z = 2.89$ quasar, with an image separation of $1{\farcs}832 \pm 0.007$ . Near-IR imaging of the system reveals ... More

A Generalized Sampling Theorem for Frequency Localized SignalsJul 02 2007Apr 15 2009A generalized sampling theorem for frequency localized signals is presented. The generalization in the proposed model of sampling is twofold: (1) It applies to various prefilters effecting a "soft" bandlimitation, (2) an approximate reconstruction from ... More

Supersymmetric and non-supersymmetric Seiberg-like dualities for gauged Wess-Zumino-Witten theories, realised on branesJun 24 2015Oct 13 2015In this work we extend the results of previous derivations of Seiberg-like dualities (level-rank duality) between gauged Wess-Zumino-Witten theories. The arguments in use to identify a potential dual for the supersymmetric WZW theory based on the coset ... More

Descent equations of Yang--Mills anomalies in noncommutative geometryAug 02 1995Aug 01 1996Consistent Yang--Mills anomalies $\int\om_{2n-k}^{k-1}$ ($n\in\N$, $ k=1,2, \ldots ,2n$) as described collectively by Zumino's descent equations $\delta\om_{2n-k}^{k-1}+\dd\om_{2n-k-1}^{k}=0$ starting with the Chern character $Ch_{2n}=\dd\om_{2n-1}^{0}$ ... More

Exactly solvable two-level quantum systems and Landau-Zener interferometryDec 13 2012Jul 15 2013I present a simple algorithm based on a type of partial reverse-engineering that generates an unlimited number of exact analytical solutions to the Schrodinger equation for a general time-dependent two-level Hamiltonian. I demonstrate this method by deriving ... More

A 2D Luttinger modelFeb 28 2009Apr 14 2010A detailed derivation of a two dimensional (2D) low energy effective model for spinless fermions on a square lattice with local interactions is given. This derivation utilizes a particular continuum limit that is justified by physical arguments. It is ... More

Non-commutative geometry and exactly solvable systemsOct 31 2007I present the exact energy eigenstates and eigenvalues of a quantum many-body system of bosons on non-commutative space and in a harmonic oszillator confining potential at the selfdual point. I also argue that this exactly solvable system is a prototype ... More

Remarkable identities related to the (quantum) elliptic Calogero-Sutherland modelJun 24 2004Nov 04 2005We present further remarkable functional identities related to the elliptic Calogero-Sutherland (eCS) system. We derive them from a second quantization of the eCS model within a quantum field theory model of anyons on a circle and at finite temperature. ... More

A method to derive explicit formulas for an elliptic generalization of the Jack polynomialsNov 04 2005We review a method providing explicit formulas for the Jack polynomials. Our method is based on the relation of the Jack polynomials to the eigenfunctions of a well-known exactly solvable quantum many-body system of Calogero-Sutherland type. We also sketch ... More

Algorithms to solve the Sutherland modelApr 27 2001We give a self-contained presentation and comparison of two different algorithms to explicitly solve quantum many body models of indistinguishable particles moving on a circle and interacting with two-body potentials of $1/\sin^2$-type. The first algorithm ... More

Exactly solvable models for 2D correlated fermionsJun 04 2002Jun 06 2003I discuss many-body models for interacting fermions in two space dimensions which can be solved exactly using group theory. The simplest example is a model of a quantum Hall system: 2D fermions in a constant magnetic field and a particular non-local 4-point ... More

Understanding genomic alterations in cancer genomes using an integrative network approachSep 10 2014In recent years, cancer genome sequencing and other high-throughput studies of cancer genomes have generated many notable discoveries. In this review, Novel genomic alteration mechanisms, such as chromothripsis (chromosomal crisis) and kataegis (mutation ... More

A model-independent technique to determine one-dimensional radio source structure from interplanetary scintillation (IPS) observationsFeb 24 2009Mar 05 2009We outline a method of deriving one-dimensional phaseless visibility along solar wind direction from interplanetary scintillation power spectrum, together with the known visibility of a calibration source. The method is illustrated briefly. Details may ... More

Accuracy vs. Efficiency: Achieving Both through FPGA-Implementation Aware Neural Architecture SearchJan 31 2019A fundamental question lies in almost every application of deep neural networks: what is the optimal neural architecture given a specific dataset? Recently, several Neural Architecture Search (NAS) frameworks have been developed that use reinforcement ... More

Blue horizontal branch stars in the Sloan Digital Sky Survey: I. Sample selection and structure in the Galactic haloNov 13 2003We isolate samples of 733 bright (g < 18) and 437 faint (g > 18) high-Galactic latitude blue horizontal branch stars with photometry and spectroscopy in the Sloan Digital Sky Survey (SDSS). Comparison of independent photometric and spectroscopic selection ... More

Broadband analysis techniques for Herschel/HIFI spectral surveys of chemically rich star-forming regionsAug 07 2012The Heterodyne Instrument for the Far Infrared (HIFI) aboard the Herschel Space Observatory has acquired high-resolution broadband molecular spectra of star-forming regions in a wavelength range that is mostly inaccessible from ground-based astronomical ... More

Effective field theory, three-loop perturbative expansion, and their experimental implications in graphene many-body effectsJan 27 2014Jun 30 2014Many-body electron-electron interaction effects are theoretically considered in monolayer graphene from a continuum effective field-theoretic perspective by going beyond the standard leading-order perturbative renormalization group (RG) analysis. Given ... More

Waterfilling Theorems in the Time-Frequency Plane for the Heat Channel and a Related SourceApr 02 2014Apr 28 2014The capacity of the heat channel, a linear time-varying (LTV) filter with additive white Gaussian noise (AWGN), is characterized by waterfilling in the time-frequency plane. Similarly, the rate distortion function for a related nonstationary source is ... More

Astrometric asteroid masses: a simultaneous determinationFeb 18 2014Using over 89 million astrometric observations of 349,737 numbered minor planets, an attempt was made to determine the masses of 230 of them by simultaneously solving for corrections to all orbital elements and the masses. For 132 minor planets an acceptable ... More

Coulomb and spin-orbit interaction matrix elements in d^2d' configurationSep 10 1998Oct 10 1998The $d^2d'$ configuration is analysed in group-theoretical terms. Starting from the table given by Condon and Odabasi (1980) for the configuration $d^2d'$, we determine a set of convenient group-theoretical basis states, and rewrite the Coulomb matrix ... More

Waterfilling Theorems for Linear Time-Varying Channels and Related Nonstationary SourcesSep 18 2015Sep 30 2016The capacity of the linear time-varying (LTV) channel, a continuous-time LTV filter with additive white Gaussian noise, is characterized by waterfilling in the time-frequency plane. Similarly, the rate distortion function for a related nonstationary source ... More

On anomalies and noncommutative geometryJul 17 1995I discuss examples where basic structures from Connes' noncommutative geometry naturally arise in quantum field theory. The discussion is based on recent work, partly collaboration with J. Mickelsson.

Non--commutative Integration CalculusJan 20 1995We discuss a non--commutative integration calculus arising in the mathematical description of anomalies in fermion--Yang--Mills systems. We consider the differential complex of forms $u_0\ccr{\eps}{u_1}\cdots\ccr{\eps}{u_n}$ with $\eps$ a grading operator ... More

Fermion Current Algebras and Schwinger Terms in 3+1 DimensionsApr 24 1993Apr 24 1993We discuss the restricted linear group in infinite dimensions modeled by the Schatten class of rank $2p=4$ which contains $(3+1)$-dimensional analog of the loop groups and is closely related to Yang-Mills theory with fermions in $(3+1)$-dimensions. We ... More

Initial conditions to cosmological N-body simulations, or how to run an ensemble of simulationsMar 04 2005Jun 11 2005The conventional method of generating initial conditions for cosmological N-body simulations introduces a significant error in the real-space statistical properties of the particles. More specifically, the finite box size leads to a significant underestimate ... More

A two dimensional analogue of the Luttinger modelJun 17 2006Apr 14 2010We present a fermion model that is, as we suggest, a natural 2D analogue of the Luttinger model. We derive this model as a partial continuum limit of a 2D spinless lattice fermion system with local interactions and away from half filling. In this derivation, ... More

Differential and holomorphic differential operators on noncommutative algebrasSep 18 2012This paper deals with sheaves of differential operators on noncommutative algebras. The sheaves are defined by quotienting a the tensor algebra of vector fields (suitably deformed by a covariant derivative) to ensure zero curvature. As an example we can ... More

Anyons and the elliptic Calogero-Sutherland modelJul 27 2000Feb 07 2001We obtain a second quantization of the elliptic Calogero-Sutherland (eCS) model by constructing a quantum field theory model of anyons on a circle and at a finite temperature. This yields a remarkable identity involving anyon correlation functions and ... More

Blue horizontal branch stars in the Sloan Digital Sky Survey: II. Kinematics of the Galactic haloNov 13 2003We carry out a maximum-likelihood kinematic analysis of a sample of 1170 blue horizontal branch (BHB) stars from the Sloan Digital Sky Survey presented in Sirko et al. (2003) (Paper I). Monte Carlo simulations and resampling show that the results are ... More

PAC: A Novel Self-Adaptive Neuro-Fuzzy Controller for Micro Aerial VehiclesNov 09 2018There exists an increasing demand of a flexible and computationally efficient controller for micro aerial vehicles (MAVs) due to a high degree of environmental perturbations. In this work, an evolving neuro-fuzzy controller namely Parsimonious Controller ... More

Intersection Information based on Common RandomnessOct 06 2013Jun 10 2015The introduction of the partial information decomposition generated a flurry of proposals for defining an intersection information that quantifies how much of "the same information" two or more random variables specify about a target random variable. ... More

On the Measurement of Elemental Abundance Ratios in Inner Galaxy H II RegionsApr 20 2004Although variations in elemental abundance ratios in the Milky Way Galaxy certainly exist, details remain uncertain, particularly in the inner Galaxy, where stars and H II regions in the Galactic plane are obscured optically. In this paper we revisit ... More

Propagation of short lightpulses in microring resonators: ballistic transport versus interference in the frequency domainFeb 04 2012The propagation of short lightpulses in waveguiding structures with optical feedback, in our case optical microresonators, has been studied theoretically and experimentally. It appears that, dependent on the measurement set-up, ballistic transport or ... More

Multiple Loop Self-Triggered Model Predictive Control for Network Scheduling and ControlFeb 11 2015We present an algorithm for controlling and scheduling multiple linear time-invariant processes on a shared bandwidth limited communication network using adaptive sampling intervals. The controller is centralized and computes at every sampling instant ... More

Strong Hyperfine-Induced Modulation of an Optically-Driven Hole Spin in an InAs Quantum DotJul 11 2013Sep 26 2013Compared to electrons, holes in InAs quantum dots have a significantly weaker hyperfine interaction that leads to less dephasing from nuclear spins. Thus many recent studies have suggested that nuclear spins are unimportant for hole spin dynamics compared ... More

The Kilo-Degree SurveyJun 06 2012The Kilo Degree Survey (KiDS) is a 1500 square degree optical imaging survey with the recently commissioned OmegaCAM wide-field imager on the VLT Survey Telescope (VST). A suite of data products will be delivered to the European Southern Observatory (ESO) ... More

Astrobiology: An Astronomer's PerspectiveSep 18 2013In this review we explore aspects of the field of astrobiology from an astronomical viewpoint. We therefore focus on the origin of life in the context of planetary formation, with additional emphasis on tracing the most abundant volatile elements, C, ... More

The Chemistry of Dark Clouds: New Astrochemical Tools for Star Formation StudiesNov 26 2002The past decade has led to significant improvements in our understanding of the physical structure of the molecular cores of cold dark clouds. Observational efforts, in combination with improved knowledge of cloud structure, now provide clear evidence ... More

Deformed Calogero-Sutherland model and fractional Quantum Hall effectMar 19 2016Apr 29 2016The deformed Calogero-Sutherland (CS) model is a quantum integrable system with arbitrary numbers of two types of particles and reducing to the standard CS model in special cases. We show that a known collective field description of the CS model, which ... More

Explicit formulas for the eigenfunctions of the N-body Calogero modelNov 10 2005We consider the quantum Calogero model, which describes N non-distinguishable quantum particles on the real line confined by a harmonic oscillator potential and interacting via two-body interactions proportional to the inverse square of the inter-particle ... More

Series solutions of the non-stationary Heun equationSep 08 2016We consider the non-stationary Heun equation, also known as quantum Painlev\'e VI, which has appeared in different works on quantum integrable models and conformal field theory. We use a generalized kernel function identity to transform the problem to ... More

Vacuum Polarization Renormalization and the Geometric PhaseDec 17 1996As an application of the renormalization method introduced by the second author we give a causal definition of the phase of the quantum scattering matrix for fermions in external Yang-Mills potentials. The phase is defined using parallel transport along ... More

Mesoscale simulations of shockwave energy dissipation via chemical reactionsFeb 02 2015We use a particle-based mesoscale model that incorporates chemical reactions at a coarse-grained level to study the response of materials that undergo volume-reducing chemical reactions under shockwave-loading conditions. We find that such chemical reactions ... More

Invariants of complex structures on nilmanifoldsFeb 26 2013Mar 15 2013Let $(N, J)$ be a simply connected $2n$-dimensional nilpotent Lie group endowed with an invariant complex structure. We define a left invariant Riemannian metric on $N$ compatible with $J$ to be minimal, if it minimizes the norm of the invariant part ... More

Characterising and recognising game-perfect graphsOct 29 2018Consider a vertex colouring game played on a simple graph with $k$ permissible colours. Two players, a maker and a breaker, take turns to colour an uncoloured vertex such that adjacent vertices receive different colours. The game ends once the graph is ... More

Holographic Corrections to Meson Scattering AmplitudesNov 01 2016Feb 28 2017We compute meson scattering amplitudes using the holographic duality between confining gauge theories and string theory, in order to consider holographic corrections to the Veneziano amplitude and associated higher-point functions. The generic nature ... More

Holographic Corrections to the Veneziano AmplitudeJul 15 2016Jun 02 2017We propose a holographic computation of the $2\rightarrow 2$ meson scattering in a curved string background, dual to a QCD-like theory. We recover the Veneziano amplitude and compute a perturbative correction due to the background curvature. The result ... More

GeneNetMiner: accurately mining gene regulatory networks from literatureSep 06 2014GeneNetMiner is standalone software which parses the sentences of iHOP and captures regulatory relations. The regulatory relations are either gene gene regulations or gene biological processes relations. Capturing of gene biological process relations ... More

A unified construction of generalised classical polynomials associated with operators of Calogero-Sutherland typeMar 30 2007Jul 15 2009In this paper we consider a large class of many-variable polynomials which contains generalisations of the classical Hermite, Laguerre, Jacobi and Bessel polynomials as special cases, and which occur as the polynomial part in the eigenfunctions of Calogero-Sutherland ... More

Gravity induced from quantum spacetimeMay 10 2013Oct 21 2013We show that tensoriality constraints in noncommutative Riemannian geometry in the 2-dimensional bicrossproduct model quantum spacetime algebra [x,t]=\lambda x drastically reduce the moduli of possible metrics g up to normalisation to a single real parameter ... More

M-partitions: Optimal partitions of weight for one scale panNov 14 2003An M-partition of a positive integer m is a partition with as few parts as possible such that any positive integer less than m has a partition made up of parts taken from that partition of m. This is equivalent to partitioning a weight m so as to be able ... More

Bachet's Problem: as few weights to weigh them allOct 26 2010A problem that enjoys an enduring popularity asks: "what is the least number of pound weights that can be used on a scale pan to weigh any integral number of pounds from 1 to 40 inclusive, if the weights can be placed in either of the scale pans ?" W.W. ... More

An Explicit Formula for the Local zeta Function of a Laurent PolynomialFeb 21 2014Apr 08 2016In a recent paper Z\'u\~niga-Galindo and the author begun the study of the local zeta functions for Laurent polynomials. In this work we continue this study by giving a very explicit formula for the local zeta function associated to a Laurent polynomial ... More

Classification of Minimal Polygons with Specified Singularity ContentMar 15 2017It is known that there are only finitely many mutation-equivalence classes with a given singularity content, and each of these equivalence classes contains only finitely many minimal polygons. We describe an efficient algorithm to classify these minimal ... More

Finding and solving Calogero-Moser type systems using Yang-Mills gauge theoriesSep 16 1999Sep 21 1999Yang-Mills gauge theory models on a cylinder coupled to external matter charges provide powerful means to find and solve certain non-linear integrable systems. We show that, depending on the choice of gauge group and matter charges, such a Yang-Mills ... More

The Majid-Ruegg model and the Planck scalesJun 19 2013Nov 13 2013A novel differential calculus with central inner product is introduced for kappa-Minkowski space. The `bad' behaviour of this differential calculus is discussed with reference to symplectic quantisation and A-infinity algebras. Using this calculus in ... More

Source identity and kernel functions for Inozemtsev-type systemsFeb 16 2012The Inozemtsev Hamiltonian is an elliptic generalization of the differential operator defining the BC_N trigonometric quantum Calogero-Sutherland model, and its eigenvalue equation is a natural many-variable generalization of the Heun differential equation. ... More

Series Solutions of the Non-Stationary Heun EquationSep 08 2016Feb 16 2018We consider the non-stationary Heun equation, also known as quantum Painlev\'e VI, which has appeared in different works on quantum integrable models and conformal field theory. We use a generalized kernel function identity to transform the problem to ... More

On the marginal likelihood and cross-validationMay 21 2019In Bayesian statistics, the marginal likelihood, also known as the evidence, is used to evaluate model fit as it quantifies the joint probability of the data under the prior. In contrast, non-Bayesian models are typically compared using cross-validation ... More

Noncommutative geodesics and the KSGNS constructionNov 19 2018We study parallel transport and geodesics in noncommutative geometry by means of bimodule connections and completely positive maps using the Kasparov, Stinespring, Gel'fand, Naimark & Segal (KSGNS) construction. This is motivated from classical geometry, ... More

A Leray spectral sequence for noncommutative differential fibrationsAug 25 2011This paper describes the Leray spectral sequence associated to a differential fibration. The differential fibration is described by base and total differential graded algebras. The cohomology used is noncommutative differential sheaf cohomology. For this ... More