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Parameterized Differential Equations over k((t))(x)Oct 30 2013In this article, we consider the inverse Galois problem for parameterized differential equations over k((t))(x) with k any field of characteristic zero and use the method of patching over fields due to Harbater and Hartmann. As an application, we prove ... More

Construction of breather solutions for nonlinear Klein-Gordon equations on periodic metric graphsDec 05 2018The purpose of this paper is to construct small-amplitude breather solutions for a nonlinear Klein-Gordon equation posed on a periodic metric graph via spatial dynamics and center manifold reduction. The major difficulty occurs from the irregularity of ... More

Designing a Disaster-resilient Network with Software Defined NetworkingFeb 22 2016Feb 23 2016With the wide deployment of network facilities and the increasing requirement of network reliability, the disruptive event like natural disaster, power outage or malicious attack has become a non-negligible threat to the current communication network. ... More

AWG-based Nonblocking Shuffle-Exchange NetworksJul 10 2019Optical shuffle-exchange networks (SENs) have wide application in different kinds of interconnection networks. This paper proposes an approach to construct modular optical SENs, using a set of arrayed waveguide gratings (AWGs) and tunable wavelength converters ... More

Neutrino Mixing: Theoretical OverviewApr 18 2013We present a concise review of the recent important experimental developments on neutrino mixing (hints for sterile neutrinos, large $\theta_{13}$, possible non maximal $\theta_{23}$, approaching sensitivity on $\delta_{CP}$) and their implications on ... More

Collider Physics within the Standard Model: a PrimerMar 12 2013Nov 04 2013The first LHC results at 7-8 TeV, with the discovery of a candidate Higgs boson and the non observation of new particles or exotic phenomena, have made a big step towards completing the experimental confirmation of the Standard Model (SM) of fundamental ... More

Particle Physics at the LHC StartOct 27 2010I present a concise review of the major issues and challenges in particle physics at the start of the LHC era. After a brief overview of the Standard Model and of QCD, I will focus on the electroweak symmetry breaking problem which plays a central role ... More

Lectures on Models of Neutrino Masses and MixingsNov 01 2007We present a concise review of models for neutrino masses and mixings with particular emphasis on recent developments and current problems. We discuss in detail attempts at reproducing approximate tri-bimaximal mixing starting from discrete symmetry groups, ... More

An Update on Models of Neutrino Masses and MixingsOct 13 2006Nov 06 2006At the School I gave three lectures on neutrino masses and mixings. Much of the material covered in my first two lectures is written down in a review on the subject that I published not long ago with F. Feruglio \cite{rev}. Here, I make a relatively short ... More

Status of the Standard Model and BeyondJun 06 2003We present a concise review of the status of the Standard Model and of the search for new physics.

Rejoinder of "Instrumental Variables: An Econometrician's Perspective"Oct 02 2014Rejoinder of "Instrumental Variables: An Econometrician's Perspective" by Guido W. Imbens [arXiv:1410.0163].

Estimation of microscopic averages from metadynamicsNov 19 2007With the help of metadynamics it is possible to calculate efficiently the free energy of systems displaying high energy barriers as a function of few selected "collective variables". In doing this, the contribution of all the other degrees of freedom ... More

Invariant curves for exact symplectic twist maps of the cylinder with Bryuno rotation numbersOct 25 2013Apr 29 2014Since Moser's seminal work it is well known that the invariant curves of smooth nearly integrable twist maps of the cylinder with Diophantine rotation number are preserved under perturbation. In this paper we show that, in the analytic class, the result ... More

The Electroweak Interactions in the Standard Model and BeyondJun 24 2004We present a concise review of the status of the Standard Model and of the models of new physics.

Neutrino 2004: Concluding TalkOct 07 2004We review the highlights of Neutrino 2004 and recall the main lessons from neutrinos in recent years that had a great impact on particle physics and cosmology.

Progress on Models of Neutrino Masses and MixingsMay 19 2004We review some recent results obtained by our group on models of neutrino masses and mixings in the general context of SUSY GUT's with an associated flavour symmetry.

Kaon Physics from Lattice QCDOct 01 2001The latest lattice results on kaon decays and mixing are reviewed. The discussion is focused on recent theoretical progress and new numerical calculations which appeared after Kaon 1999.

Optimal design and quantum limit for second harmonic generation in semiconductor heterostructuresNov 23 2000The optimal design for infrared second harmonic generation (SHG) is determined for a GaAs-based quantum device using a recently developed genetic approach. Both compositional parameters and electric field are simultaneously optimized, and the quantum ... More

The Extended Bigraded Toda hierarchyApr 11 2006Nov 04 2008We generalize the Toda lattice hierarchy by considering N+M dependent variables. We construct roots and logarithms of the Lax operator which are uniquely defined operators with coefficients that are $\epsilon$-series of differential polynomials in the ... More

Hadronic Weak Interactions of Light QuarksOct 05 1998In this review, three subjects are discussed: a phenomenological application of lattice predictions to $K^0$--$\bar K^0$ mixing in Super Symmetry; a discussion of the non-perturbative renormalization methods for four-fermion operators and a new approach ... More

The Electroweak Symmetry Breaking RiddleMar 16 2010Apr 28 2010I present a concise review of the Higgs problem which plays a central role in particle physics today. The Higgs of the minimal Standard Model is so far just a conjecture that needs to be verified or discarded at the LHC. Probably the reality is more complicated. ... More

DIS 2009 Concluding Talk: Outlook and PerspectiveJul 10 2009I will present here my perception on the status of Deep Inelastic Scattering physics, as I have further developed it during this Workshop, together with a number of comments on the results that have impressed me most during this week. I will emphasize ... More

A QCD PrimerApr 16 20021. Introduction 2. Massless QCD and Scale Invariance 3. The Renormalisation Group and Asymptotic Freedom 4. More on the Running Coupling 5. Application to Hard Processes 5.1 $R_{e^+e^-}$ and Related Processes 5.2 The Final State in $e^+e^-$ Annihilation ... More

Status of Neutrino Mass and MixingApr 15 2014In the last two decades experiments have established the existence of neutrino oscillations and most of the related parameters have by now been measured with reasonable accuracy. These results have accomplished a major progress for particle physics and ... More

A note on polylogarithms on curves and abelian schemesNov 15 2007In this note we investigate the connection between polylogarithms on curves and abelian schemes. The main result shows that the polylogarithm on the abelian scheme can be obtained as the push-forward of the polylogarithm on a suitable sub-curve. If the ... More

Circuit theory for decoherence in superconducting charge qubitsAug 26 2004Apr 28 2005Based on a network graph analysis of the underlying circuit, a quantum theory of arbitrary superconducting charge qubits is derived. Describing the dissipative elements of the circuit with a Caldeira-Leggett model, we calculate the decoherence and leakage ... More

ElectroWeak precision data: the minimal set of parametersMay 24 2006We show how precision electroweak data, assuming CP conservation and flavor universality, despite being sensitive to 20 dimension 6 operators, constrain severely only 9 combinations of them. We define a set of 7 oblique parameters $\hat S, \hat T, \hat ... More

Spherical subgroups of Kac-Moody groups and transitive actions on spherical varietiesAug 14 2014Mar 28 2017We define and study a class of spherical subgroups of a Kac-Moody group. In analogy with the standard theory of spherical varieties, we introduce a combinatorial object associated with such a subgroup, its homogeneous spherical datum, and we prove that ... More

Discrete surfaces of constant mean curvature via dressingNov 21 1997We translate a classification scheme for periodic CMC surfaces developed by J. Dorfmeister and the author to discrete CMC surfaces in the sense of A. Bobenko and U. Pinkall. The scheme uses the dressing action on discrete CMC surfaces to arrive at a classification ... More

Degeneration of polylogarithms and special values of L-functions for totally real fieldsOct 07 2005Dec 09 2005Replaced by revised version.

Particle Physics in the LHC Era and beyondFeb 26 2010I present a concise review of where we stand in particle physics today. First, I will discuss QCD, then the electroweak sector and finally the motivations and the avenues for new physics beyond the Standard Model.

New Physics and the LHCMay 14 2008In these lectures I start by briefly reviewing the status of the electroweak theory, in the Standard Model and beyond. I then discuss the motivation and the possible avenues for new physics, on the brink of the LHC start.

The Standard Electroweak Theory and BeyondNov 24 1998This set of lectures provides an elementary introduction to the standard electroweak theory, followed by a detailed discussion of its experimental tests. We then consider the conceptual limitations of the Standard Model and briefly review the existing ... More

The Higgs and the Excessive Success of the Standard ModelJul 08 2014Jul 17 2014The LHC runs at 7 and 8 TeV have led to the discovery of the Higgs boson at 125 GeV which will remain as one of the major physics discoveries of our time. Another very important result was the surprising absence of any signals of new physics that, if ... More

The SM and SUSY after the 2011 LHC resultsJun 07 2012We present a short review of the LHC results at 7 TeV and their implications on the Standard Model (SM) and on its Supersymmetric (SUSY) extension. In particular we discuss the exclusion range for the SM Higgs mass, the tantalizing hint of an excess at ... More

Introduction to the TerascaleNov 02 2006We briefly review the status of the electroweak theory, in the Standard Model and beyond, on the brink of the LHC start.

Eisenstein classes, elliptic Soulé elements and the $\ell$-adic elliptic polylogarithmApr 26 2013Oct 21 2013This is a completely rewritten version of the paper formerly entitled "Sheaves of Iwasawa modules, moment maps and the $\ell$-adic elliptic polylogarithm". The proof of the main result is also simplified. In the paper we study systematically the $\ell$-adic ... More

Large deviation rule for Anosov flowsMar 18 1996The volume contraction in dissipative reversible transitive Anosov flows obeys a large deviation rule (fluctuation theorem).

Renormalization of the meson-baryon SU(3) Lagrangian in chiral perturbation theory to order q^3Oct 28 1996We perform the complete regularization of all Green functions with a single incoming and outgoing baryon to order q^3 in the low energy expansion for the SU(3) meson-baryon system in chiral perturbation theory. The divergences can be extracted in a chiral ... More

Are there metric theories of gravity other than General Relativity?Nov 08 1995Nov 09 1995Current generalizations of the classical Einstein-Hilbert Lagrangian formulation of General Relativity are reviewed. Some alternative variational principles are known to reproduce Einstein's gravitational equations, and should therefore be regarded as ... More

Selective Magic HPSG ParsingJul 08 1999We propose a parser for constraint-logic grammars implementing HPSG that combines the advantages of dynamic bottom-up and advanced top-down control. The parser allows the user to apply magic compilation to specific constraints in a grammar which as a ... More

Automorphisms of wonderful varietiesFeb 29 2008Jul 31 2008Let G be a complex semisimple linear algebraic group, and X a wonderful G-variety. We determine the connected automorphism group of X and we calculate Luna's invariants of X under its action.

The Mystery of Neutrino MixingsNov 28 2011In the last years we have learnt a lot about neutrino masses and mixings. Neutrinos are not all massless but their masses are very small. Probably masses are small because neutrinos are Majorana particles with masses inversely proportional to the large ... More

Perspectives in Neutrino PhysicsJul 11 2011This is a Concluding Talk, not a Summary of the Conference. I will discuss some of the highlights that particularly impressed me (a subjective choice) and make some comments on the status and the prospects of neutrino mass and mixing.

Particle Physics at the LHC StartFeb 16 2009I present a concise review of where we stand in particle physics today. First, I will discuss the status of the Standard Model, its open problems and the expected answers from the LHC. Then I will briefly review the avenues for New Physics that can be ... More

Models of Neutrino Masses and MixingsNov 09 2006We present a concise review of model building for neutrino masses and mixings, with special emphasis on recent developments.

Particle Physics: a Progress ReportSep 11 2006We present a concise review of where we stand in particle physics today. First we discuss QCD, then the electroweak sector and finally the motivations and the avenues for new physics beyond the Standard Model.

Deep Narrow Boltzmann Machines are Universal ApproximatorsNov 14 2014Apr 10 2015We show that deep narrow Boltzmann machines are universal approximators of probability distributions on the activities of their visible units, provided they have sufficiently many hidden layers, each containing the same number of units as the visible ... More

The Space Missions WAXS/WFXT and SWIFT: New Targets for the VLTMay 04 1999At OAB we were, during the year 1998, deeply involved in planning two important space missions for which very large ground based telescopes, VLT in particular, would play a very large and important role in the optical followup. The study of the first ... More

The structure of AGNs from X-ray absorption variabilityDec 10 2009We present new evidence of X-ray absorption variability on time scales from a few hours to a few days for several nearby bright AGNs. The observed N_H variations imply that the X-ray absorber is made of clouds eclipsing the X-ray source with velocities ... More

Non-Markovian qubit dynamics in the presence of 1/f noiseMar 05 2008Mar 24 2009Within the lowest-order Born approximation, we calculate the exact dynamics of a single qubit in the presence of 1/f noise, without making any Markov approximation. We show that the non-Markovian qubit time-evolution exhibits asymmetries and beatings ... More

Theory of solid state quantum information processingSep 23 2004Nov 12 2004Recent theoretical work on solid-state proposals for the implementation of quantum computation and quantum information processing is reviewed. The differences and similarities between microscopic and macroscopic qubits are highlighted and exemplified ... More

The Standard Model of Particle PhysicsOct 21 2005A concise introduction to the Standard Model of fundamental particle interactions is presented.

Sterile neutrinos: from cosmology to experimentsMay 11 2004We analyze the oscillation signals generated by one extra sterile neutrino. We fully take into account the effects of the established oscillations among active neutrinos. We analyze the effects in solar, atmospheric, reactor and beam experiments, cosmology ... More

Magic for Filter Optimization in Dynamic Bottom-up ProcessingApr 29 1996Off-line compilation of logic grammars using Magic allows an incorporation of filtering into the logic underlying the grammar. The explicit definite clause characterization of filtering resulting from Magic compilation allows processor independent and ... More

Leggett-Garg Inequalities, Pilot Waves and ContextualitySep 14 2014Dec 01 2014In this paper we first analyse Leggett and Garg's argument to the effect that macroscopic realism contradicts quantum mechanics. After making explicit all the assumptions in Leggett and Garg's reasoning, we argue against the plausibility of their auxiliary ... More

A numerical analysis of Quicksort: How many cases are bad cases?Jul 15 2015We present numerical results for the probability of bad cases for Quicksort, i.e. cases of input data for which the sorting cost considerably exceeds that of the average. Dynamic programming was used to compute solutions of the recurrence for the frequency ... More

On reductive automorphism groups of regular embeddingsJun 05 2012Jan 19 2015Let G be a connected reductive complex algebraic group acting on a smooth complete complex algebraic variety X. We assume that X under the action of G is a regular embedding, a condition satisfied in particular by smooth toric varieties and flag varieties. ... More

Simple Immersions of Wonderful VarietiesJun 29 2005Jun 23 2006Let G be a semisimple connected linear algebraic group over C, and X a wonderful G-variety. We study the possibility of realizing X as a closed subvariety of the projective space of a simple G-module. We describe the wonderful varieties having this property ... More

Mixture decompositions of exponential families using a decomposition of their sample spacesAug 01 2010Feb 25 2013We study the problem of finding the smallest $m$ such that every element of an exponential family can be written as a mixture of $m$ elements of another exponential family. We propose an approach based on coverings and packings of the face lattice of ... More

Resummation of perturbation series and reducibility for Bryuno skew-product flowsDec 01 2005We consider skew-product systems on T^d x SL(2,R) for Bryuno base flows close to constant coefficients, depending on a parameter, in any dimension d, and we prove reducibility for a large measure set of values of the parameter. The proof is based on a ... More

Thermodynamics of scalar fields in Kerr's geometryOct 28 1997Jan 22 1998The one-loop contributions to the entropy for a massive scalar field in a Kerr black hole are investigated using an approximation of the metric, which, after a conformal transformation, permits to work in a Rindler-like spacetime. Of course, as for the ... More

Concluding Talk: QCD 2005Oct 07 2005This is neither a summary talk (too much for too short a talk) nor a conclusion (a gigantic work is in progress and we are not at the end of a particular phase), rather an overview of the field as reflected at this Conference.

Normal and Special Models of Neutrino Masses and MixingsAug 04 2005One can make a distinction between "normal" and "special" models. For normal models $\theta_{23}$ is not too close to maximal and $\theta_{13}$ is not too small, typically a small power of the self-suggesting order parameter $\sqrt{r}$, with $r=\Delta ... More

Models of neutrino masses and mixingsJun 08 2001We briefly review models of neutrino masses and mixings. In view of the existing experimental ambiguities many possibilities are still open. After an overview of the main alternative options we focus on the most constrained class of models based on three ... More

The Standard Model and BeyondSep 25 1998Content 1. Why we do Believe in the Standard Model 2. Why we do not Believe in the Standard Model 2.1Conceptual Problems 2.2Hints from Experiment --2.2.1 Unification of Couplings --2.2.2 Dark Matter --2.2.3 Baryogenesis --2.2.4 Neutrino Masses --2.2.5 ... More

Status of Neutrino Masses and Mixing in 2010Nov 24 2010We present a short summary of our present knowledge and understanding of neutrino masses and mixing.

Status of Neutrino Masses and Mixing in 2009May 20 2009We present a very concise summary of the status of our knowledge and understanding of neutrino masses and mixing.

Theoretical Models of Neutrino Mixing: Recent DevelopmentsMay 14 2009The data on neutrino mixing are at present compatible with Tri-Bimaximal (TB) mixing. If one takes this indication seriously then the models that lead to TB mixing in first approximation are particularly interesting and A4 models are prominent in this ... More

Models of Neutrino Masses and Mixings: a Progress ReportMay 07 2007We present some recent developments on model building for neutrino masses and mixings. In particular, we review tri-bimaximal neutrino mixing derived from discrete groups, notably A4. We discuss the problems encountered with extending the symmetry to ... More

The Higgs: so simple yet so unnaturalAug 02 2013Dec 04 2013We present a concise outlook of particle physics after the first LHC results at 7-8 TeV. The discovery of the Higgs boson at 126 GeV will remain as one of the major physics discoveries of our time. But also the surprising absence of any signals of new ... More

The QCD Running Coupling and its MeasurementMar 25 2013In this lecture, after recalling the basic definitions and facts about the running coupling in QCD, I present a critical discussion of the methods for measuring $\alpha_s$ and select those that appear to me as the most reliably precise

Modular Covariance, PCT, Spin and StatisticsJul 05 1995The notion of modular covariance is reviewed and the reconstruction of the Poincar\'e group extended to the low-dimensional case. The relations with the PCT symmetry and the Spin and Statistics theorem are described.

Extended Toda LatticeJul 03 2003We introduce nonlocal flows that commute with those of the classical Toda hierarchy. We define a logarithm of the difference Lax operator and use it to obtain a Lax representation of the new flows.

The WAXS/WFXT MissionFeb 12 1999I present the science goals and give a brief summary of the Wide Angle X-ray survey with a Wide Field X-ray Telescope (WAXS/WFXT) mission proposal (Phase A) which will be submitted to the Italian Space Agency (ASI) following the call for proposal under ... More

Large Scale Structure. The seventies & Forty years later: From Clusters to ClustersMay 13 2013Jul 11 2013I describe the beginning, ~ 1970, of the spectroscopic redshift surveys and the discovery of the superclusters filamentary structures and voids. This changed the view of the distribution of luminous light from the way we knew it at the end of the sixties, ... More

The Hamiltonian structures of the two-dimensional Toda lattice and R-matricesMar 26 2004Jan 13 2005We construct the tri-Hamiltonian structure of the two-dimensional Toda hierarchy using the R-matrix theory.

Search for Galactic dark matter substructures with Cherenkov telescopesAug 14 2015Weakly interacting massive dark matter (DM) particles are expected to self-annihilate or decay, generating high-energy photons in these processes. This establishes the possibility for indirect detection of DM by \gamma-ray telescopes. For probing the ... More

Lamé polynomials, hyperelliptic reductions and Lamé band structureSep 01 2003Jul 17 2004The band structure of the Lam\'e equation, viewed as a one-dimensional Schr\"odinger equation with a periodic potential, is studied. At integer values of the degree parameter l, the dispersion relation is reduced to the l=1 dispersion relation, and a ... More

The Integration of Three-Dimensional Lotka-Volterra SystemsNov 25 2012The general solutions of many three-dimensional Lotka-Volterra systems, previously known to be at least partially integrable, are constructed with the aid of special functions. Examples include certain ABC and May-Leonard systems. The special functions ... More

Extensions of the Classical Transformations of 3F2Aug 09 2018Jan 13 2019It is shown that the classical quadratic and cubic transformation identities satisfied by the hypergeometric function ${}_3F_2$ can be extended to include additional parameter pairs, which differ by integers. In the extended identities, which involve ... More

The Uniformization of Certain Algebraic Hypergeometric FunctionsJun 18 2009Dec 10 2013The hypergeometric functions ${}_nF_{n-1}$ are higher transcendental functions, but for certain parameter values they become algebraic, because the monodromy of the defining hypergeometric differential equation becomes finite. It is shown that many algebraic ... More

Multiwavelength observations of a TeV-Flare from W ComJul 23 2009We report results from an intensive campaign of multiwavelength observations of the intermediate-frequency-peaked BL Lacertae object W Com (z=0.102) during a strong outburst of very high energy (VHE; E > 180 GeV) gamma-ray emission in June 2008. The initial ... More

A duality-based optimization approach for model adaptivity in heterogeneous multiscale problemsNov 28 2016This paper introduces a novel framework for model adaptivity in the context of heterogeneous multiscale problems. The framework is based on the idea to interpret model adaptivity as a minimization problem of local error indicators, that are derived in ... More

A Theory of Magnetization Reversal in NanowiresJul 17 2004Magnetization reversal in a ferromagnetic nanowire which is much narrower than the exchange length is believed to be accomplished through the thermally activated growth of a spatially localized nucleus, which initially occupies a small fraction of the ... More

Algebraic Generating Functions for Gegenbauer PolynomialsJul 18 2016Sep 18 2017It is shown that several of Brafman's generating functions for the Gegenbauer polynomials are algebraic functions of their arguments, if the Gegenbauer parameter differs from an integer by one-fourth or one-sixth. Two examples are given, which come from ... More

Information Criteria for Deciding between Normal Regression ModelsMay 23 2013May 24 2013Regression models fitted to data can be assessed on their goodness of fit, though models with many parameters should be disfavored to prevent over-fitting. Statisticians' tools for this are little known to physical scientists. These include the Akaike ... More

A duality-based optimization approach for model adaptivity in heterogeneous multiscale problemsNov 28 2016Dec 01 2017This paper introduces a novel framework for model adaptivity in the context of heterogeneous multiscale problems. The framework is based on the idea to interpret model adaptivity as a minimization problem of local error indicators, that are derived in ... More

P-symbols, Heun Identities, and 3F2 IdentitiesDec 28 2007Dec 30 2007The usefulness of Riemann P-symbols in deriving identities involving the parametrized special function Hl is explored. Hl is the analytic local solution of the Heun equation, the canonical second-order differential equation on the Riemann sphere with ... More

Nonlinear Differential Equations Satisfied by Certain Classical Modular FormsJul 07 2008Jun 13 2010A unified treatment is given of low-weight modular forms on \Gamma_0(N), N=2,3,4, that have Eisenstein series representations. For each N, certain weight-1 forms are shown to satisfy a coupled system of nonlinear differential equations, which yields a ... More

The 192 Solutions of the Heun EquationAug 23 2004Mar 14 2006A machine-generated list of 192 local solutions of the Heun equation is given. They are analogous to Kummer's 24 solutions of the Gauss hypergeometric equation, since the two equations are canonical Fuchsian differential equations on the Riemann sphere ... More

Energy calibration via correlationDec 11 2015The main task of an energy calibration is to find a relation between pulse-height values and the corresponding energies. Doing this for each pulse-height channel individually requires an elaborated input spectrum with an excellent counting statistics ... More

Stability of Impurities with Coulomb Potential in Graphene with Homogeneous Magnetic FieldSep 26 2011Jun 05 2012Given a 2-dimensional no-pair Weyl operator with a point nucleus of charge Z, we show that a homogeneous magnetic field does not lower the critical charge beyond which it collapses.

Parametrized Stochastic Grammars for RNA Secondary Structure PredictionJan 24 2007We propose a two-level stochastic context-free grammar (SCFG) architecture for parametrized stochastic modeling of a family of RNA sequences, including their secondary structure. A stochastic model of this type can be used for maximum a posteriori estimation ... More

Associated Legendre Functions and Spherical Harmonics of Fractional Degree and OrderFeb 27 2017Feb 01 2018Trigonometric formulas are derived for certain families of associated Legendre functions of fractional degree and order, for use in approximation theory. These functions are algebraic, and when viewed as Gauss hypergeometric functions, belong to types ... More

Legendre Functions of Fractional Degree: Transformations and EvaluationsFeb 09 2016Associated Legendre functions of fractional degree appear in the solution of boundary value problems in wedges or in toroidal geometries, and elsewhere in applied mathematics. In the classical case when the degree is half an odd integer, they can be expressed ... More

Instrumental Variables: An Econometrician's PerspectiveOct 01 2014I review recent work in the statistics literature on instrumental variables methods from an econometrics perspective. I discuss some of the older, economic, applications including supply and demand models and relate them to the recent applications in ... More

On the partition functions of higher spin black holesOct 16 2013Oct 21 2013We reconsider black hole solutions of D = 3 higher-spin gravity in the $hs[\lambda]\oplus hs[\lambda]$ Chern-Simons formulation. A suitable generalisation of the BTZ black hole has a spin-3 chemical potential $\alpha$, and non-zero values of all the conserved ... More

The virtual scaling function of twist operators in the N=6 Chern-Simons theoryMay 07 2009May 11 2009We consider twist-L operators in the planar N=6 superconformal Chern-Simons ABJM theory. Their anomalous dimension gamma_L^{CS}(N) is a function of the twist L, the spin N, and the dressed coupling of ABJM. We show that at next-to-leading order in the ... More

Memory and Self OrganizationOct 29 1994The main result of this letter is that SOC naturally arises as a result of memory effects. We show that memory effects provide the mechanism for self organization. A general procedure to investigate this issue in models that display self organized critical ... More