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Text-based LSTM networks for Automatic Music CompositionApr 18 2016In this paper, we introduce new methods and discuss results of text-based LSTM (Long Short-Term Memory) networks for automatic music composition. The proposed network is designed to learn relationships within text documents that represent chord progressions ... More

Similarity measures for vocal-based drum sample retrieval using deep convolutional auto-encodersFeb 14 2018The expressive nature of the voice provides a powerful medium for communicating sonic ideas, motivating recent research on methods for query by vocalisation. Meanwhile, deep learning methods have demonstrated state-of-the-art results for matching vocal ... More

Convolutional Recurrent Neural Networks for Music ClassificationSep 14 2016We introduce a convolutional recurrent neural network (CRNN) for music tagging. CRNNs take advantage of convolutional neural networks (CNNs) for local feature extraction and recurrent neural networks for temporal summarisation of the extracted features. ... More

Inverting face embeddings with convolutional neural networksJun 14 2016Jul 07 2016Deep neural networks have dramatically advanced the state of the art for many areas of machine learning. Recently they have been shown to have a remarkable ability to generate highly complex visual artifacts such as images and text rather than simply ... More

Piano Transcription in the Studio Using an Extensible Alternating Directions FrameworkJun 02 2016Jul 27 2016Given a musical audio recording, the goal of automatic music transcription is to determine a score-like representation of the piece underlying the recording. Despite significant interest within the research community, several studies have reported on ... More

Telling Two Distributions Apart: a Tight CharacterizationOct 14 2011We consider the problem of distinguishing between two arbitrary black-box distributions defined over the domain [n], given access to $s$ samples from both. It is known that in the worst case O(n^{2/3}) samples is both necessary and sufficient, provided ... More

Structured Dropout for Weak Label and Multi-Instance Learning and Its Application to Score-Informed Source SeparationSep 15 2016Many success stories involving deep neural networks are instances of supervised learning, where available labels power gradient-based learning methods. Creating such labels, however, can be expensive and thus there is increasing interest in weak labels ... More

Designing Patient-Specific Optimal Neurostimulation Patterns for Seizure SuppressionJan 16 2018Neurostimulation is a promising therapy for abating epileptic seizures. However, it is extremely difficult to identify optimal stimulation patterns experimentally. In this study human recordings are used to develop a functional 24 neuron network statistical ... More

Rash spin-orbit interaction in graphene and graphene zigzag nano-ribbonsJan 01 2009May 08 2009We investigate the effects of Rashba spin-orbit interactions on the electronic band-structure and corresponding wave-functions of graphene. By exactly solving a tight-binding model Hamiltonian we obtain the expected splitting of the bands -due to the ... More

Graphene zigzag ribbons, square lattice models and quantum spin chainsOct 11 2009We present an extended study of finite-width zigzag graphene ribbons (ZGRs) based on a tight-binding model with hard-wall boundary conditions. We provide an exact analytic solution that clarifies the origin of the predicted width dependence on the conductance ... More

Towards Music Captioning: Generating Music Playlist DescriptionsAug 17 2016Descriptions are often provided along with recommendations to help users' discovery. Recommending automatically generated music playlists (e.g. personalised playlists) introduces the problem of generating descriptions. In this paper, we propose a method ... More

Explaining Deep Convolutional Neural Networks on Music ClassificationJul 08 2016Deep convolutional neural networks (CNNs) have been actively adopted in the field of music information retrieval, e.g. genre classification, mood detection, and chord recognition. However, the process of learning and prediction is little understood, particularly ... More

Towards Playlist Generation Algorithms Using RNNs Trained on Within-Track TransitionsJun 07 2016We introduce a novel playlist generation algorithm that focuses on the quality of transitions using a recurrent neural network (RNN). The proposed model assumes that optimal transitions between tracks can be modelled and predicted by internal transitions ... More

Automatic tagging using deep convolutional neural networksJun 01 2016We present a content-based automatic music tagging algorithm using fully convolutional neural networks (FCNs). We evaluate different architectures consisting of 2D convolutional layers and subsampling layers only. In the experiments, we measure the AUC-ROC ... More

Frugal Streaming for Estimating Quantiles:One (or two) memory sufficesJul 04 2014Modern applications require processing streams of data for estimating statistical quantities such as quantiles with small amount of memory. In many such applications, in fact, one needs to compute such statistical quantities for each of a large number ... More

Understanding Music PlaylistsNov 22 2015As music streaming services dominate the music industry, the playlist is becoming an increasingly crucial element of music consumption. Con- sequently, the music recommendation problem is often casted as a playlist generation prob- lem. Better understanding ... More

Interference Reduction in Music Recordings Combining Kernel Additive Modelling and Non-Negative Matrix FactorizationSep 20 2016When recording music in a live or studio scenario, unexpected sound events often lead to interferences in the signal. For non-stationary interferences, sound source separation techniques can be used to reduce the interference level in the recording. In ... More

Convolutional Recurrent Neural Networks for Music ClassificationSep 14 2016Nov 03 2016We introduce a convolutional recurrent neural network (CRNN) for music tagging. CRNNs take advantage of convolutional neural networks (CNNs) for local feature extraction and recurrent neural networks for temporal summarisation of the extracted features. ... More

Quantum and classical localization in the lowest Landau levelApr 28 2003Spatial correlations of occupation probabilities, if their decay is not too fast, can change the critical exponents for classical percolation. From numerical studies of electron dynamics in the lowest Landau level (LLL) we demonstrate the quantum analog ... More

Influence of Rashba spin-orbit coupling on the Kondo effectSep 28 2015Feb 01 2016An Anderson model for a magnetic impurity in a two-dimensional electron gas with bulk Rashba spin-orbit interaction is solved using the numerical renormalization group under two different experimental scenarios. For a fixed Fermi energy, the Kondo temperature ... More

Electron-electron and spin-orbit interactions in armchair graphene ribbonsOct 29 2007The effects of intrinsic spin-orbit and Coulomb interactions on low-energy properties of finite width graphene armchair ribbons are studied by means of a Dirac Hamiltonian. It is shown that metallic states subsist in the presence of intrinsic spin-orbit ... More

Single parameter scaling of one-dimensional systems with real-space long-range correlated disorderJun 15 2012Sep 26 2012Advances in material growth methods have renewed the interest in localization of one-dimensional systems in the presence of scale-free long-range correlated disorder potentials. We analyze the validity of single parameter scaling for the \beta-function ... More

ad-Nilpotent positively-graded Borel module subalgebrasSep 18 2012Sep 20 2012In this paper, we study certain ad-nilpotent subalgebras contained in the non-zero graded portion of a simple Z_n-graded Lie algebra. These subalgebras respect the grading on the Lie algebra and are modules for a Borel subalgebra for the grade-zero Lie ... More

Fractional quantum Hall junctions and two-channel Kondo modelsSep 19 2000A mapping between fractional quantum Hall (FQH) junctions and the two-channel Kondo model is presented. We discuss in detail this relation for the particular case of a junction of a FQH state at $\nu = 1/3$ and a normal metal. We show that in the strong ... More

Quantum spin Hall phase in neutral zigzag graphene ribbonsOct 11 2009We present a detailed description of the nature of the wavefunction and spin distribution of the zero energy modes of zigzag graphene ribbons (ZGRs) in the presence of the intrinsic spin_orbit (I-SO) interaction. These states characterize the quantum ... More

Enhanced Local Moment Formation in a Chiral Luttinger LiquidJul 11 1996We derive here a stability condition for a local moment in the presence of an interacting sea of conduction electrons. The conduction electrons are modeled as a Luttinger liquid in which chirality and spin are coupled. We show that an Anderson-U defect ... More

Anticorrelations from power-law spectral disorder and conditions for an Anderson transitionFeb 21 2013We resolve an apparent contradiction between numeric and analytic results for one-dimensional disordered systems with power-law spectral correlations. The conflict arises when considering rigorous results that constrain the set of correlation functions ... More

Interactions and Disorder in Multi-Channel Quantum WiresJan 22 1997Recent experiments have revealed that the temperature dependence of the conductance of quasi-ballistic quantum wires bears clear features of the Luttinger-liquid state. In this paper, the conductance of an N-channel quantum wire is calculated within the ... More

Correlated quantum percolation in the lowest Landau levelNov 20 2003Our understanding of localization in the integer quantum Hall effect is informed by a combination of semi-classical models and percolation theory. Motivated by the effect of correlations on classical percolation we study numerically electron localization ... More

Unscreened Coulomb interactions and quantum spin Hall phase in neutral zigzag graphene ribbonsJun 26 2008Feb 17 2009A study of the effect of unscreened Coulomb interactions on the quantum spin Hall (QSH) phase of finite-width neutral zigzag graphene ribbons is presented. By solving a tight-binding Hamiltonian that includes the intrinsic spin-orbit interaction (I-SO), ... More

The Cloudy UniverseJul 20 1999Modelling of Extreme Scattering Events suggests that the Galaxy's dark matter is an undetected population of cold, AU-sized, planetary-mass gas clouds. None of the direct observational constraints on this picture -- thermal/non-thermal emission, extinction ... More

A Probabilistic Model of Compound NounsSep 06 1994Compound nouns such as example noun compound are becoming more common in natural language and pose a number of difficult problems for NLP systems, notably increasing the complexity of parsing. In this paper we develop a probabilistic model for syntactically ... More

High velocity gas from the Galactic dark haloNov 13 1998We present the germ of a new model for High Velocity Clouds, derived from the idea that the dark matter halo of our Galaxy is in the form of cold, planetary-mass gas clouds. In this picture HVCs arise as a result of disruptive collisions between dark ... More

Order-Revealing Encryption and the Hardness of Private LearningMay 03 2015An order-revealing encryption scheme gives a public procedure by which two ciphertexts can be compared to reveal the ordering of their underlying plaintexts. We show how to use order-revealing encryption to separate computationally efficient PAC learning ... More

Thermal stability of cold clouds in galaxy halosJul 02 1999Oct 14 1999We consider the thermal properties of cold, dense clouds of molecular hydrogen and atomic helium. For cloud masses below 10^-1.7 Msun, the internal pressure is sufficient to permit the existence of particles of solid or liquid hydrogen at temperatures ... More

From adiabatic to non-adiabatic pumping in graphene nanoribbonsMar 18 2012Non-equilibrium two-parameter pumping transport through graphene ribbons, attached to reservoirs is described. A tight-binding model is solved using Keldysh formalism, and the crossover between adiabatic and non-adiabatic regimes is studied. Pumped dc ... More

Extreme scattering events and Galactic dark matterFeb 10 1998Mar 20 1998Extreme Scattering Events (ESEs) are attributed to radio-wave refraction by a cloud of free-electrons crossing the line-of-sight. We present a new model in which these electrons form the photo-ionized 'skin' of an underlying cool, self-gravitating cloud ... More

Interchain conductivity of coupled Luttinger liquids and organic conductorsJan 06 2000We reconsider the theory of dc and ac interchain conductivity in quasi-one dimensional systems. Our results are in good agreement with the measured c-axis optical conductivity of (TMTSF)_2{ClO}_4 and suggest that the c-axis dc-conductivity of (TMTSF)_2{PF}_6 ... More

Hybridization and anisotropy in the exchange interaction in 3D Dirac semimetalsNov 21 2015We study the Ruderman-Kittel-Kasuya-Yosida interaction in 3D Dirac semimetals. Using retarded Green's functions in real space, we obtain and analyze asymptotic expressions for the interaction, with magnetic impurities at different distances and relative ... More

Enhancement of the Kondo effect through Rashba spin-orbit interactionsMay 18 2011Jan 31 2012We analyze the physics of a one-orbital Anderson impurity model in a two-dimensional electron gas in the presence of Rashba spin-orbit (RSO) interactions in the Kondo regime. The spin SU(2) symmetry breaking results in an effective two-band electron gas ... More

Kondo screening suppression by spin-orbit interaction in quantum dotsFeb 19 2009We study the transport properties of a quantum dot embedded in an Aharonov-Bohm ring in the presence of spin-orbit interactions. Using a numerical renormalization group analysis of the system in the Kondo regime, we find that the competition of Aharonov-Bohm ... More

RKKY interaction and intervalley processes in p-doped transition metal dichalcogenidesSep 26 2014We study the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in p-doped transition metal dichalcogenides such as MoS$_2$ and WS$_2$. We consider magnetic impurities hybridized to the Mo d-orbitals characteristic of the valence bands. Using the Matsubara ... More

The mass and radius evolution of globular clusters in tidal fieldsJan 23 2013We present a simple theory for the evolution of initially compact clusters in a tidal field. The fundamental ingredient of the model is that a cluster conducts a constant fraction of its own energy through the half-mass radius by two-body interactions ... More

Electroweak Measurements from Hadron MachinesDec 14 1999A review of recent electroweak results from hadron machines including the measurements of the top quark and W boson mass.

Mathematical Models in Schema TheoryDec 27 2005In this paper, a mathematical schema theory is developed. This theory has three roots: brain theory schemas, grid automata, and block-shemas. In Section 2 of this paper, elements of the theory of grid automata necessary for the mathematical schema theory ... More

The Rise and Fall of the Church-Turing ThesisJul 12 2002The essay consists of three parts. In the first part, it is explained how theory of algorithms and computations evaluates the contemporary situation with computers and global networks. In the second part, it is demonstrated what new perspectives this ... More

Affine type A crystal structure on tensor products of rectangles, Demazure characters, and nilpotent varietiesApr 07 1998Answering a question of Kuniba, Misra, Okado, Takagi, and Uchiyama, it is shown that certain Demazure characters of affine type A, coincide with the graded characters of coordinate rings of closures of conjugacy classes of nilpotent matrices. This entails ... More

Reluctant Paraphrase: Textual Restructuring under an Optimisation ModelJul 03 1997This paper develops a computational model of paraphrase under which text modification is carried out reluctantly; that is, there are external constraints, such as length or readability, on an otherwise ideal text, and modifications to the text are necessary ... More

A path property of Dyson gaps, Plancherel measures for $Sp(\infty)$, and random surface growthJun 29 2015Jul 13 2015We pursue applications for symplectic Plancherel growth based on a repulsion phenomenon arising in its diffusion limit and on intermediate representation theory underlying its correlation structure. Under diffusive scaling, the dynamics converge to interlaced ... More

Random vectors in the isotropic positionAug 19 1996Let $y$ be a random vector in \rn, satisfying $$ \Bbb E \, \tens{y} = id. $$ Let $M$ be a natural number and let $y_1 \etc y_M$ be independent copies of $y$. We prove that for some absolute constant $C$ $$ \enor{\frac{1}{M} \sum_i \tens{y_i} - id} \le ... More

On the Modulus of a Union of Nested AnnuliAug 23 2011Aug 24 2011We prove a result which gives sufficient conditions for a conformal annulus which is a countable union of nested conformal annuli to have bounded modulus. Our theorem also gives estimates for the modulus of such an annulus and is proved using an interpolation ... More

Short Separating Geodesics for Multiply Connected DomainsMar 13 2011Apr 15 2011We consider the following questions: given a hyperbolic plane domain and a separation of its complement into two disjoint closed sets each of which contains at least two points, what is the shortest closed hyperbolic geodesic which separates these sets ... More

Bollinger Bands Thirty Years LaterDec 20 2012Jan 01 2013The goal of this study is to explain and examine the statistical underpinnings of the Bollinger Band methodology. We start off by elucidating the rolling regression time series model and deriving its explicit relationship to Bollinger Bands. Next we illustrate ... More

Enstrophy and dissipation must have the same scaling exponent in the high Reynolds number limit of fluidturbulenceJun 16 1998Jan 25 1999Writing the Poisson equation for the pressure in the vorticity-strain form, we show that the pressure has a finite inertial range spectrum for high Reynolds number isotropic turbulence only if the anomalous scaling exponents $\mu$ and $\mu_{\omega}$ for ... More

A note on the definition of small overlap monoidsOct 23 2009Small overlap conditions are simple and natural combinatorial conditions on semigroup and monoid presentations, which serve to limit the complexity of derivation sequences between equivalent words in the generators. They were introduced by J.H.Remmers, ... More

On strict monotonicity of the speed for excited random walks in one dimensionFeb 24 2015We give a "direct" coupling proof of strict monotonicity of the speed for 1-dimensional multi-excited random walks with positive speed. This reproves (and extends) a recent result of Peterson without using branching processes.

Signals of Inflationary Models with Cosmic StringsJun 02 2011A class of well-motivated models of inflation end by producing cosmic strings. The current status of efforts to calculate and observe the signals from such models are outlined, with a particular emphasis on cosmic strings, and on the Cosmic Microwave ... More

Quantum fields in disequilibrium: neutral scalar bosons with long-range, inhomogeneous perturbationsAug 15 1995Using Schwinger's quantum action principle, dispersion relations are obtained for neutral scalar mesons interacting with bi-local sources. These relations are used as the basis of a method for representing the effect of interactions in the Gaussian approximation ... More

Chern-Simons vortices in an open systemMay 02 1995A gauge invariant quantum field theory with a spacetime dependent Chern-Simons coefficient is studied. Using a constraint formalism together with the Schwinger action principle it is shown that non-zero gradients in the coefficient induce magnetic-moment ... More

Quasars and their host galaxiesJan 12 2006This review attempts to describe developments in the fields of quasar and quasar host galaxies in the past five. In this time period, the Sloan and 2dF quasar surveys have added several tens of thousands of quasars, with Sloan quasars being found to z>6. ... More

HST imaging of two z>4 radio galaxiesSep 09 1999We have imaged 8C 1435+635 (z=4.25; Lacy et al. 1994; Spinrad, Dey & Graham 1995) and 6C 0140+326 (z=4.41; Rawlings et al. 1996) in both continuum and Lyalpha plus continuum bands with the HST. Our images show patchy distributions of continuum and line ... More

Spectra and symmetric spectra in general model categoriesApr 09 2000Jun 09 2000(This is an updated version; following an idea of Voevodsky, we have strengthened our results so all of them apply to one form of motivic homotopy theory). We give two general constructions for the passage from unstable to stable homotopy that apply to ... More

Morita theory for Hopf algebroids and presheaves of groupoidsMay 16 2001Comodules over Hopf algebroids are of central importance in algebraic topology. It is well-known that a Hopf algebroid is the same thing as a presheaf of groupoids on Aff, the opposite category of commutative rings. We show in this paper that a comodule ... More

Properties of High Redshift Cluster EllipticalsMar 06 1997Cluster ellipticals are often thought to be among the oldest galaxies in the universe, with the bulk of their stellar mass formed at early cosmic epochs. I review recent observations of color evolution in early-type cluster galaxies at high redshift, ... More

Galaxy Evolution at 0 < z < 2 from the NICMOS HDF-NorthApr 03 2000We have carried out a deep infrared imaging survey (1.1um and 1.6um) of the Hubble Deep Field North (HDF-N) using NICMOS on board the Hubble Space Telescope. The combined WFPC2+NICMOS data set lets us study galaxy morphologies, colors and luminosities ... More

Orthogonal apartments in Hilbert GrassmanniansDec 03 2015Dec 15 2015Let $H$ be an infinite-dimensional complex Hilbert space and let ${\mathcal L}(H)$ be the logic formed by all closed subspaces of $H$. For every natural $k$ we denote by ${\mathcal G}_{k}(H)$ the Grassmannian consisting of $k$-dimensional subspaces. An ... More

Embeddings of Grassmann graphsSep 26 2011Let $V$ and $V'$ be vector spaces of dimension $n$ and $n'$, respectively. Let $k\in\{2,...,n-2\}$ and $k'\in\{2,...,n'-2\}$. We describe all isometric and $l$-rigid isometric embeddings of the Grassmann graph $\Gamma_{k}(V)$ in the Grassmann graph $\Gamma_{k'}(V')$. ... More

Isometric embeddings of Johnson graphs in Grassmann graphsMar 17 2010Sep 14 2010Let $V$ be an $n$-dimensional vector space ($4\le n <\infty$) and let ${\mathcal G}_{k}(V)$ be the Grassmannian formed by all $k$-dimensional subspaces of $V$. The corresponding Grassmann graph will be denoted by $\Gamma_{k}(V)$. We describe all isometric ... More

Explicit lower bounds on the modular degree of an elliptic curveAug 10 2004We derive an explicit zero-free region for symmetric square L-functions of elliptic curves, and use this to derive an explicit lower bound for the modular degree of rational elliptic curves. The techniques are similar to those used in the classical derivation ... More

Tautly foliated 3-manifolds with no R-covered foliationsNov 17 2000A foliation of a manifold M is called R-covered if its lift to the universal cover of M has space of leaves R. We show that there are many graph manifolds which admit taut foliations, but which do not admit any R-covered foliations. On the other hand, ... More

Free subgroups of finitely generated free profinite groupsJan 06 2015We give new and improved results on the freeness of subgroups of free profinite groups: A subgroup containing the normal closure of a finite word in the elements of a basis is free; Every infinite index subgroup of a finitely generated nonabelian free ... More

Generalised Holographic Electroweak Symmetry Breaking Models and the Possibility of Negative SApr 20 2011Jun 28 2011Within an AdS/CFT inspired model of electroweak symmetry breaking the effects of various boundary terms and modifications to the background are studied. The effect on the S precision parameter is discussed with particular attention to its sign and whether ... More

Metrics of positive scalar curvature and generalised Morse functions, part 1Nov 08 2008It is well known that isotopic metrics of positive scalar curvature are concordant. Whether or not the converse holds is an open question, at least in dimensions greater than four. We show that for a particular type of concordance, constructed using the ... More

Conceptual Association for Compound Noun AnalysisSep 06 1994Sep 11 1996This paper describes research toward the automatic interpretation of compound nouns using corpus statistics. An initial study aimed at syntactic disambiguation is presented. The approach presented bases associations upon thesaurus categories. Association ... More

Magnet stability and reproducibilityMar 08 2011Magnet stability and reproducibility have become increasingly important as greater precision and beams with smaller dimension are required for research, medical and other purpose. The observed causes of mechanical and electrical instability are introduced ... More

Dense Quark Matter in NatureDec 01 2003According to quantum chromodynamics (QCD), matter at ultra-high densities will take the form of a color-superconducting quark liquid, in which there is a condensate of Cooper pairs of quarks near the Fermi surface. I present a review of the physics of ... More

Comment on "Ambiguities in the Up-Quark Mass"Mar 04 2005Aug 18 2014Creutz [hep-ph/0312225] has argued that nonperturbative effects in QCD lead to an additive ambiguity in the up quark mass, and that "this calls into question the acceptability of attempts to solve the strong CP problem via a vanishing mass for the lightest ... More

Subjective and Objective Probabilities in Quantum MechanicsJan 03 2005Jan 14 2005We discuss how the apparently objective probabilities predicted by quantum mechanics can be treated in the framework of Bayesian probability theory, in which all probabilities are subjective. Our results are in accord with earlier work by Caves, Fuchs, ... More

Comment on "Spatial Correlation in Quantum Chaotic Systems with Time-Reversal Symmetry: Theory and Experiment" by V. N. Prigodin et al [cond-mat/9504089]Dec 14 1995We show that the results of Prigodin et al can be reproduced and simplified by making use of Berry's conjecture that the energy eigenfunctions in a quantized chaotic system are gaussian random variables.

Does Quantum Chaos Explain Quantum Statistical Mechanics?Oct 14 1994Apr 20 1995If a many-body quantum system approaches thermal equilibrium from a generic initial state, then the expectation value $\langle\psi(t)|A_i|\psi(t)\rangle$, where $|\psi(t)\rangle$ is the system's state vector and $A_i$ is an experimentally accessible observable, ... More

Chaos and Quantum ThermalizationMar 14 1994Apr 29 1994We show that a bounded, isolated quantum system of many particles in a specific initial state will approach thermal equilibrium if the energy eigenfunctions which are superposed to form that state obey {\it Berry's conjecture}. Berry's conjecture is expected ... More

Quantum Field Theory: Spin ZeroSep 02 2004This is a draft version of Part I of a three-part textbook on quantum field theory.

Relic Abundances and the Boltzmann EquationMay 17 2000Jul 10 2000I discuss the validity of the quantum Boltzmann equation for the calculation of WIMP relic densities.

Spatial Correlations in Chaotic EigenfunctionsDec 09 1997At short distances, energy eigenfunctions of chaotic systems have spatial correlations that are well described by assuming a microcanonical density in phase space for the corresponding Wigner function. However, this is not correct on large scales. The ... More

Effects of Compensation, Connectivity and Tau in a Computational Model of Alzheimer's DiseaseJun 30 2011This work updates an existing, simplistic computational model of Alzheimer's Disease (AD) to investigate the behaviour of synaptic compensatory mechanisms in neural networks with small-world connectivity, and varying methods of calculating compensation. ... More

Examples of Special Lagrangian FibrationsDec 01 2000Jan 04 2001We explore a number of examples of special Lagrangian fibrations on non-compact Calabi-Yau manifolds invariant under torus actions. These include fibrations on crepant resolutions of canonical toric singularities (already found by Goldstein), proper versions ... More

Deforming Calabi-Yau ThreefoldsJun 26 1995This paper first generalises the Bogomolov-Tian-Todorov unobstructedness theorem to the case of Calabi-Yau threefolds with canonical singularities. The deformation space of such a Calabi-Yau threefold is no longer smooth, but the general principle is ... More

Special Lagrangian Fibrations I: TopologyOct 06 1997In 1996, Strominger, Yau and Zaslow made a conjecture about the geometric relationship between two mirror Calabi-Yau manifolds. Roughly put, if X and Y are a mirror pair of such manifolds, then X should possess a special Lagrangian torus fibration $f:X\to ... More

Maximum nonlocality and minimum uncertainty using magic statesJan 21 2015We prove that magic states from the Clifford hierarchy give optimal solutions for tasks involving nonlocality and entropic uncertainty with respect to Pauli measurements. For both the nonlocality and uncertainty tasks, stabilizer states are the worst ... More

Coherence as a resource in decision problems: The Deutsch-Jozsa algorithm and a variationDec 07 2015Feb 15 2016That superpositions of states can be useful for performing tasks in quantum systems has been known since the early days of quantum information, but only recently has quantitative theory of quantum coherence been proposed. Here we apply that theory to ... More

Random Surfaces and Lattice GravityOct 01 1997Oct 15 1997In this talk I review some of the recent developments in the field of random surfaces and the Dynamical Triangulation approach to simplicial quantum gravity. In two dimensions I focus on the c=1 barrier and the fractal dimension of two-dimensional quantum ... More

Universal Extra Dimensions and Charged LKPsNov 12 2003We consider the possibility of charged stable Kaluza-Klein leptons in orbifold models in which all the Standard Model fields propagate (UED models). At tree level the masses of the 1st mode states are nearly identical and kinematics can prevent the decays ... More

Complex dimensions of real manifolds, attached analytic discs and parametric argument principleApr 23 2007Sep 05 2007Let $\Omega$ be a smooth real analytic submanifold of a complex manifold $X$. We establish and study the link between the following 3 subjects: 1) topological properties of smooth families of attached analytic discs, the manifold $\Omega$ admits, 2) lower ... More

Propagation of boundary CR foliations and Morera type theorems for manifolds with attached analytic discsNov 07 2005Sep 19 2006We prove that generic homologically nontrivial $(2n-1)$-parameter family of analytic discs attached by their boundaries to a CR manifold $\Omega$ in $\mathbb C^n, n \le 2$ tests CR functions: if a smooth function on $\Omega$ extends analytically inside ... More

Mirror Symmetry and the Strominger-Yau-Zaslow conjectureDec 18 2012Sep 20 2013This survey was written for the Current Developments in Mathematics conference, 2012, and is an updating of my article "The Strominger-Yau-Zaslow conjecture: From torus fibrations to degenerations," in the Seattle 2005 proceedings. We trace progress and ... More

Extension operators via semigroupsJul 29 2010The Roper--Suffridge extension operator and its modifications are powerful tools to construct biholomorphic mappings with special geometric properties. The first purpose of this paper is to analyze common properties of different extension operators and ... More

On the Circular Orbit Approximation for Binary Compact Objects In General RelativityMay 06 2003One often-used approximation in the study of binary compact objects (i.e., black holes and neutron stars) in general relativity is the instantaneously circular orbit assumption. This approximation has been used extensively, from the calculation of innermost ... More

General Relativistic Initial Data for the Binary Black Hole / Neutron Star System in Quasicircular OrbitJun 06 2001We present an algorithm for solving the general relativistic initial value equations for a corotating polytropic star in quasicircular orbit with a nonspinning black hole. The algorithm is used to obtain initial data for cases where the black hole mass ... More

A large class of sofic monoidsJan 28 2014We prove that a monoid is sofic, in the sense recently introduced by Ceccherini-Silberstein and Coornaert, whenever the J-class of the identity is a sofic group, and the quotients of this group by orbit stabilisers in the rest of the monoid are amenable. ... More