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A note on symplectic and Poisson linearization of semisimple Lie algebra actionsMar 12 2015In this note we prove that an analytic symplectic action of a semisimple Lie algebra can be locally linearized in Darboux coordinates. This result yields simultaneous analytic linearization for Hamiltonian vector fields in a neighbourhood of a common ... More

On a Poincare lemma for foliationsJan 24 2013Apr 16 2013In this paper we revisit a Poincare lemma for foliated forms, with respect to a regular foliation, and compute the foliated cohomology for local models of integrable systems with singularities of nondegenerate type. A key point in this computation is ... More

The geometry of E-manifoldsFeb 08 2018Motivated by the study of symplectic Lie algebroids, we study a describe a type of algebroid (called an $E$-tangent bundle) which is particularly well-suited to study of singular differential forms and their cohomology. This setting generalizes the study ... More

Non-commutative integrable systems on $b$-symplectic manifoldsJun 08 2016In this paper we study non-commutative integrable systems on $b$-Poisson manifolds. One important source of examples (and motivation) of such systems comes from considering non-commutative systems on manifolds with boundary having the right asymptotics ... More

Cotangent models for integrable systemsJan 19 2016May 23 2016We associate cotangent models to a neighbourhood of a Liouville torus in symplectic and Poisson manifolds focusing on a special class called $b$-Poisson/$b$-symplectic manifolds. The semilocal equivalence with such models uses the corresponding action-angle ... More

Equivariant normal form for nondegenerate singular orbits of integrable Hamiltonian systemsFeb 24 2003Jul 30 2004We consider an integrable Hamiltonian system with n-degrees of freedom whose first integrals are invariant under the symplectic action of a compact Lie group G. We prove that the singular Lagrangian foliation associated to this Hamiltonian system is symplectically ... More

Codimension one symplectic foliations and regular Poisson structuresSep 06 2010Jun 21 2011In this short note we give a complete characterization of a certain class of compact corank one Poisson manifolds, those equipped with a closed one-form defining the symplectic foliation and a closed two-form extending the symplectic form on each leaf. ... More

Symplectic and Poisson geometry on b-manifoldsJun 10 2012Feb 06 2014Let $M^{2n}$ be a Poisson manifold with Poisson bivector field $\Pi$. We say that $M$ is b-Poisson if the map $\Pi^n:M\to\Lambda^{2n}(TM)$ intersects the zero section transversally on a codimension one submanifold $Z\subset M$. This paper will be a systematic ... More

Convexity for Hamiltonian torus actions on $b$-symplectic manifoldsDec 08 2014May 11 2016In [GMPS] we proved that the moment map image of a $b$-symplectic toric manifold is a convex $b$-polytope. In this paper we obtain convexity results for the more general case of non-toric hamiltonian torus actions on $b$-symplectic manifolds. The modular ... More

Equivariant classification of $b^m$-symplectic surfaces and Nambu structuresJul 06 2016In this paper we extend the classification scheme in [S] for $b^m$-symplectic surfaces, and more generally, $b^m$-Nambu structures to the equivariant setting. When the compact group is the group of deck-transformations of an orientable covering, this ... More

Rigidity of infinitesimal momentum mapsOct 20 2014Sep 11 2015In this paper we prove rigidity theorems for Poisson Lie group actions on Poisson manifolds. In particular, we prove that close infinitesimal momentum maps associated to Poisson Lie group actions are equivalent using a normal form theorem for SCI spaces. ... More

Geometric Quantization of real polarizations via sheavesJan 11 2013Aug 06 2013In this article we develop tools to compute the Geometric Quantization of a symplectic manifold with respect to a regular Lagrangian foliation via sheaf cohomology and obtain important new applications in the case of real polarizations. The starting point ... More

A Poincare lemma in Geometric QuantisationJul 11 2013Jan 07 2014This article presents a Poincare lemma for the Kostant complex, used to compute geometric quantisation, when the polarisation is given by a Lagrangian foliation defined by an integrable system with nondegenerate singularities.

A note on equivariant normal forms of Poisson structuresOct 25 2005Mar 17 2006We prove an equivariant version of the local splitting theorem for tame Poisson structures and Poisson actions of compact Lie groups. As a consequence, we obtain an equivariant linearization result for Poisson structures whose transverse structure has ... More

Coupling symmetries with Poisson structuresJan 07 2013We study local normal forms for completely integrable systems on Poisson manifolds in the presence of additional symmetries. The symmetries that we consider are encoded in actions of compact Lie groups. The existence of Weinstein's splitting theorem for ... More

Geometric quantization of integrable systems with hyperbolic singularitiesAug 03 2008Feb 04 2009We construct the geometric quantization of a compact surface using a singular real polarization coming from an integrable system. Such a polarization always has singularities, which we assume to be of nondegenerate type. In particular, we compute the ... More

Weakly Hamiltonian actionsFeb 10 2016May 03 2016In this paper we generalize constructions of non-commutative integrable systems to the context of weakly Hamiltonian actions on Poisson manifolds. In particular we prove that abelian weakly Hamiltonian actions on symplectic manifolds split into Hamiltonian ... More

A singular Poincare lemmaMay 23 2004We prove a Poincare lemma for a set of r smooth functions on a 2n-dimensional smooth manifold satisfying a commutation relation determined by r singular vector fields associated to a Cartan subalgebra of $\frak{sp}(2r,\mathbb R)$. This result has a natural ... More

Desingularizing $b^m$-symplectic structuresDec 16 2015A Poisson manifold $(M^{2n} ,\Pi)$ is said to be $b^m$-symplectic if it is symplectic on the complement of a hypersurface $Z$ and has a simple Darboux canonical form at points of $Z$ (which we will describe below). In this paper we will discuss a desingularization ... More

Examples of integrable and non-integrable systems on singular symplectic manifoldsDec 28 2015We present a collection of examples borrowed from celestial mechanics and projective dynamics. In these examples symplectic structures with singularities arise naturally from regularization transformations, Appell's transformation or classical changes ... More

A note on symplectic topology of $b$-manifoldsDec 27 2013Nov 11 2015A Poisson manifold $(M^{2n},\p)$ is $b$-symplectic if $\bigwedge^n\p$ is transverse to the zero section. In this paper we apply techniques native to Symplectic Topology to address questions pertaining to $b$-symplectic manifolds. We provide constructions ... More

Rigidity of Hamiltonian actions on Poisson manifoldsFeb 01 2011Oct 16 2011This paper is about the rigidity of compact group actions in the Poisson context. The main resut is that Hamiltonian actions of compact semisimple type are rigid. We prove it via a Nash-Moser normal form theorem for closed subgroups of SCI-type. This ... More

On geometric quantization of $b$-symplectic manifoldsAug 30 2016We study a notion of pre-quantization for $b$-symplectic manifolds. We use it to construct a formal geometric quantization of $b$-symplectic manifolds equipped with Hamiltonian torus actions with nonzero modular weight. We show that these quantizations ... More

Action-angle coordinates for integrable systems on Poisson manifoldsMay 12 2008Jun 14 2008We prove the action-angle theorem in the general, and most natural, context of integrable systems on Poisson manifolds, thereby generalizing the classical proof, which is given in the context of symplectic manifolds. The topological part of the proof ... More

Action-angle variables and a KAM theorem for b-Poisson manifoldsFeb 11 2015Mar 02 2015In this article we prove an action-angle theorem for b-integrable systems on b-Poisson manifolds improving the action-angle theorem contained in [LMV11] for general Poisson manifolds in this setting. As an application, we prove a KAM-type theorem for ... More

The Fate of PlanetsJan 10 2011As a star evolves off the Main Sequence, it endures major structural changes that are capable of determining the fate of the planets orbiting it. Throughout its evolution along the Red Giant Branch, the star increases its radius by two orders of magnitude. ... More

Analysis of two- and three-dimensional fractional-order Hindmarsh-Rose type neuronal modelsMar 15 2016A theoretical analysis of two- and three-dimensional fractional-order Hindmarsh-Rose neuronal models is presented, focusing on stability properties and occurrence of Hopf bifurcations, with respect to the fractional order of the system chosen as bifurcation ... More

(A)dS Backgrounds from Asymmetric OrientifoldsJun 22 2001I present asymmetric orientifold models which, with the addition of RR fluxes, fix all the NS NS moduli including the dilaton. In critical string theory, this gives new AdS backgrounds with (discretely tunably) weak string coupling. Extrapolating to super-critical ... More

Cell Decomposition for semibounded p-adic setsMay 18 2012We study a reduct L\ast of the ring language where multiplication is restricted to a neighbourhood of zero. The language is chosen such that for p-adically closed fields K, the L\ast-definable subsets of K coincide with the semi-algebraic subsets of K. ... More

Characterization of arbitrage-free marketsMar 23 2005The present paper deals with the characterization of no-arbitrage properties of a continuous semimartingale. The first main result, Theorem \refMainTheoremCharNA, extends the no-arbitrage criterion by Levental and Skorohod [Ann. Appl. Probab. 5 (1995) ... More

The global structure of moduli spaces of polarized p-divisible groupsMar 28 2007We study the global structure of moduli spaces of quasi-isogenies of polarized p-divisible groups introduced by Rapoport and Zink. Using the corresponding results for non-polarized p-divisible groups from a previous paper, we determine their dimensions ... More

On a property of Fermi curves of 2-dimensional periodic Schrödinger operatorsJun 09 2016Jun 23 2016We consider a compact Riemann surface with a holomorphic involution, two marked fixed points of the involution and a divisor obeying an equation up to linear equivalence of divisors involving all this data. Examples of such data are Fermi curves of 2-dimensional ... More

Miracle at the Gepner PointMar 23 1995Mar 26 1995A four-point function of $E_6$ singlets, of interest in elucidating the moduli space of (0,2) deformations of the quintic string vacuum, is computed using analytic and numerical methods. The conformal field theory amplitude satisfies the requisite selection ... More

Preferred frame parameters in the tensor-vector-scalar theory of gravity and its generalizationMay 25 2009Jul 01 2009The Tensor-Vector-Scalar theory of gravity, which was designed as a relativistic implementation to the modified dynamics paradigm, has fared quite well as an alternative to dark matter, on both galactic and cosmological scales. However, its performance ... More

Simple de Sitter SolutionsDec 07 2007Mar 18 2008We present a framework for de Sitter model building in type IIA string theory, illustrated with specific examples. We find metastable dS minima of the potential for moduli obtained from a compactification on a product of two Nil three-manifolds (which ... More

E-accessible Astronomy ResourcesJun 09 2010Making online resources more accessible to physically challenged library users is a topic deserving informed attention from astronomy librarians. Recommendations like WCAG 2.0 standards and section 508, in the United States, have proven valuable, and ... More

On the geometry of the Newton stratificationNov 10 2015We give an expository overview over recent results on the global structure and geometry of the Newton stratification of the reduction modulo p of Shimura varieties of Hodge type with hyperspecial level structure. More precisely, we discuss non-emptiness, ... More

Geodesic equations and algebro-geometric methodsJun 02 2015For an investigation of the physical properties of gravitational fields the observation of massive test particles and light is very useful. The characteristic features of a given space-time may be decoded by studying the complete set of all possible geodesic ... More

Stability for the determination of unknown boundary and impedance with a Robin boundary conditionApr 13 2010We consider an inverse problem arising in corrosion detection. We prove a stability result of logarithmic type for the determination of the corroded portion of the boundary and impedance by two measurements on the accessible portion of the boundary.

Toric actions on b-symplectic manifoldsSep 07 2013Mar 05 2014We study Hamiltonian actions on $b$-symplectic manifolds with a focus on the effective case of half the dimension of the manifold. In particular, we prove a Delzant-type theorem that classifies these manifolds using polytopes that reside in a certain ... More

Large-Small Equivalence in String TheoryJan 08 1992The simplest toroidally compactified string theories exhibit a duality between large and small radii: compactification on a circle, for example, is invariant under R goes to 1/R. Compactification on more general Lorentzian lattices (i.e. toroidal compactification ... More

Constructive decomposition of a function of two variables as a sum of functions of one variableAug 30 2007Given a compact set $K$ in the plane, which does not contain any triple of points forming a vertical and a horizontal segment, and a map $f\in C(K)$, we give a construction of functions $g,h\in C(\mathbb R)$ such that $f(x,y)=g(x)+h(y)$ for all $(x,y)\in ... More

Dimensional Mutation and Spacelike SingularitiesOct 05 2005Feb 27 2006I argue that string theory compactified on a Riemann surface crosses over at small volume to a higher dimensional background of supercritical string theory. Several concrete measures of the count of degrees of freedom of the theory yield the consistent ... More

Propagation of Gravitational Waves in Generalized TeVeSJan 11 2010Efforts are underway to improve the design and sensitivity of gravitational waves detectors, with the hope that the next generation of these detectors will observe a gravitational wave signal. Such a signal will not only provide information on dynamics ... More

Minimal geodesics and topological entropy on T^2Jul 04 2007Let (T^2, g) be a two-dimensional Riemannian torus. In this paper we prove that the topological entropy of the geodesic flow restricted to the set of initial conditions of minimal geodesics vanishes, independent of the choice of the Riemannian metric. ... More

AdS and dS Entropy from String JunctionsAug 26 2003Flux compactifications of string theory exhibiting the possibility of discretely tuning the cosmological constant to small values have been constructed. The highly tuned vacua in this discretuum have curvature radii which scale as large powers of the ... More

TASI/PiTP/ISS Lectures on Moduli and MicrophysicsMay 09 2004I review basic forces on moduli that lead to their stabilization, for example in the supercritical and KKLT models of de Sitter space in string theory, as well as an $AdS_4\times S^3\times S^3$ model I include which is not published elsewhere. These forces ... More

Inflation in string theory confronts data/Les modèles d'inflation en théorie des cordes face aux observationsDec 07 2015Following the 2015 Planck release, we briefly comment on the status and some ongoing opportunities in the interface between inflationary cosmology, string theory, and CMB data. The constraints in the $r$-$n_s$ plane introduce a new parameter into inflationary ... More

Electronic Structure Calculations with LDA+DMFTNov 25 2014The LDA+DMFT method is a very powerful tool for gaining insight into the physics of strongly correlated materials. It combines traditional ab-initio density-functional techniques with the dynamical mean-field theory. The core aspects of the method are ... More

Stable determination of the surface impedance of an obstacle by far field measurementsMay 13 2005We deal with the inverse scattering problem of determining the surface impedance of a partially coated obstacle. We prove a stability estimate of logarithmic type for the impedance term by the far field measurements.

Gradient flow for the Boltzmann entropy and Cheeger's energy on time-dependent metric measure spacesNov 29 2016We introduce notions of dynamic gradient flows on time-dependent metric spaces as well as on time-dependent Hilbert spaces. We prove existence of solutions for a class of time dependent energy functionals in both settings. In particular we are interested ... More

Neuroevolutionary optimizationApr 20 2010This paper presents an application of evolutionary search procedures to artificial neural networks. Here, we can distinguish among three kinds of evolution in artificial neural networks, i.e. the evolution of connection weights, of architectures, and ... More

Cell decomposition for semi-affine structures on p-adic fieldsNov 14 2011May 17 2012We use cell decomposition techniques to study additive reducts of p- adic fields. We consider a very general class of fields, including fields with infinite residue fields, which we study using a multi-sorted language. The results are used to obtain cell ... More

Bibliometric Evaluation of the Changing Finnish AstronomyJun 09 2010This is a follow-up on the bibliometric evaluation of Finnish astronomy presented by the author at the LISA V conference in 2006. The data from the previous study are revisited to determine how a wider institutional base and mergers affect comparisons ... More

Les Houches lectures on inflationary observables and string theoryNov 10 2013These lectures cover the theoretical structure and phenomenology of some basic mechanisms for inflation. A full treatment of the problem requires `ultraviolet completion' because of the sensitivity of inflation to quantum gravity effects, while the observables ... More

Towards a Paraconsistent Quantum Set TheoryNov 05 2015In this paper, we will attempt to establish a connection between quantum set theory, as developed by Ozawa, Takeuti and Titani, and topos quantum theory, as developed by Isham, Butterfield and Doring, amongst others. Towards this end, we will study algebraic ... More

Radix and Pseudodigit Representations in Z^nFeb 22 2010We define radix representations for vectors in Z^n analogously with radix representations in Z, and give a sufficient condition for a matrix A:Z^n -> Z^n to yield a radix representation with a given canonical digit set. We relate our results to a sufficient ... More

Singular Riemannian Foliations: Exceptional Leaves; TautnessDec 17 2008For a singular Riemannian foliation whose leaves are properly embedded, we show in the first part of this article the existence of global tubular neighbourhoods, and we develop a global description of the foliation as stratification by types of leaves. ... More

Torsion Sections of Semistable Elliptic SurfacesAug 21 1992Let S be a torsion section of an elliptic surface with only I_n fibers. This article addresses the question: which components of singular fibers can S pass through? We give necessary criteria for the "component numbers", and show an equidistribution result ... More

Criteria for Conformal Invariance of (0,2) ModelsMar 30 1995Nov 03 1999It is argued that many linear (0,2) models flow in the infrared to conformally invariant solutions of string theory. The strategy in the argument is to show that the effective space-time superpotential must vanish because there is no place where it can ... More

Observational Comparison of Star Formation in Different Galaxy TypesSep 07 2010Galaxies cover a wide range of masses and star formation histories. In this review, I summarize some of the evolutionary key features of common galaxy types. At the high-mass end, very rapid, efficient early star formation is observed, accompanied by ... More

Dwarf Galaxies in the Local Group and in the Local VolumeJul 11 2001After summarizing the characteristics of different types of dwarf galaxies I briefly review our current state of knowledge of dwarf galaxy evolution in the Local Group, for which we now have a fairly detailed although by no means comprehensive picture. ... More

A Map of the Northern Sky: The Sloan Digital Sky Survey in Its First YearMay 09 2001The Sloan Digital Sky Survey (SDSS) is the largest and most ambitious optical CCD survey undertaken to date. It will ultimately map out one quarter of the sky with precision photometry in five bands, high-quality astrometry, and spectra of all galaxies ... More

Evolutionary Histories of Dwarf Galaxies in the Local GroupDec 24 1998The star formation histories of Local Group (LG) dwarf galaxies and more distant potential LG members are reviewed. Problems in defining the spatial extent of the LG and membership are briefly discussed. The morphological types found in the LG are presented, ... More

Complete analytic solution of the geodesic equation in Schwarzschild--(anti) de Sitter space--timesMay 29 2015The complete set of analytic solutions of the geodesic equation in a Schwarzschild--(anti) de Sitter space--time is presented. The solutions are derived from the Jacobi inversion problem restricted to the theta--divisor. In its final form the solutions ... More

Performance of the coupled cluster singles and doubles method on two-dimensional quantum dotsApr 23 2010An implementation of the coupled-cluster single- and double excitations (CCSD) method on two-dimensional quantum dots is presented. Advantages and limitations are studied through comparison with other high accuracy approaches for two to eight confined ... More

Ionization branching ratio control with a resonance attosecond clockApr 08 2010Jun 10 2010We investigate the possibility to monitor the dynamics of autoionizing states in real time and control the yields of different ionization channels in helium by simulating XUV-pump IR-probe experiments focused on the N=2 threshold. The XUV pulse creates ... More

The Tachyon at the End of the UniverseJun 16 2005Aug 03 2005We show that a tachyon condensate phase replaces the spacelike singularity in certain cosmological and black hole spacetimes in string theory. We analyze explicitly a set of examples with flat spatial slices in various dimensions which have a winding ... More

Embeddings of maximal tori in orthogonal groupsMay 15 2013We give necessary and sufficient conditions for an orthogonal group defined over a field of characteristic not 2 to contain a maximal torus of a given type.

Analytical solution methods for geodesic motionJun 02 2015The observation of the motion of particles and light near a gravitating object is until now the only way to explore and to measure the gravitational field. In the case of exact black hole solutions of the Einstein equations the gravitational field is ... More

String-theoretic breakdown of effective field theory near black hole horizonsApr 21 2015We investigate the validity of the equivalence principle near horizons in string theory, analyzing the breakdown of effective field theory caused by longitudinal string spreading effects. An experiment is set up where a detector is thrown into a black ... More

The Scaling of the No Scale Potential and de Sitter Model BuildingFeb 18 2004Oct 14 2004We propose a variant of the KKLT (A)dS flux vacuum construction which does not require an antibrane to source the volume modulus. The strategy is to find nonzero local minima of the no-scale potential in the complex structure and dilaton directions in ... More

On the Alexander polynomial of links in lens spacesJun 10 2016Aug 22 2016We explore properties of the Alexander polynomial and twisted Alexander polynomial of links in the lens spaces. In particular, we calculate the Alexander polynomial of some families of links and show how the Alexander polynomial is connected with the ... More

Neighborhood radius estimation in Variable-neighborhood Random FieldsFeb 25 2010Feb 24 2011We consider random fields defined by finite-region conditional probabilities depending on a neighborhood of the region which changes with the boundary conditions. To predict the symbols within any finite region it is necessary to inspect a random number ... More

On Sound Compilation of RealsSep 10 2013Writing accurate numerical software is hard because of many sources of unavoidable uncertainties, including finite numerical precision of implementations. We present a programming model where the user writes a program in a real-valued implementation and ... More

Isometries of quadratic spacesMay 21 2013Sep 10 2013Let k be a field of characteristic not 2, let q be a quadratic space over k and let f be an irreducible polynomial with coefficients in k. In 1969, Milnor raised the following question : how can we decide whether q has an isometry with minimal polynomial ... More

Effects of Body Elasticity on Stability of Underwater LocomotionOct 17 2012We examine the stability of the "coast" motion of fish, that is to say, the motion of a neutrally buoyant fish at constant speed in a straight line. The forces and moments acting on the fish body are thus perfectly balanced. The fish motion is said to ... More

Affine Deligne-Lusztig varieties and the action of JJul 10 2015Sep 14 2016We propose a new stratification of the reduced subschemes of Rapoport-Zink spaces and of affine Deligne-Lusztig varieties that highlights the relation between the geometry of these spaces and the action of the associated automorphism group. We show that ... More

Effects of screened Coulomb impurities on autoionizing two-electron resonances in spherical quantum dotsMay 03 2010In a recent paper (Phys. Rev. B {\bf 78}, 075316 (2008)), Sajeev and Moiseyev demonstrated that the bound-to-resonant transitions and lifetimes of autoionizing states in spherical quantum dots can be controlled by varying the confinment strength. In the ... More

Infrared Variability from Circumbinary Disc Temperature ModulationsJul 10 2015The temperature of a circumbinary disc edge should undulate due to variations in illumination as a function of binary orbital phase. We explore circumbinary disc temperature variations as a source of broad-band infrared light curve variability. Approximating ... More

Effective rates from thermodynamically consistent coarse-graining of models for molecular motors with probe particlesJan 29 2015Many single molecule experiments for molecular motors comprise not only the motor but also large probe particles coupled to it. The theoretical analysis of these assays, however, often takes into account only the degrees of freedom representing the motor. ... More

A New Handle on de Sitter CompactificationsNov 30 2004Dec 04 2004We construct a large new class of de Sitter (and anti de Sitter) vacua of critical string theory from flux compactifications on products of Riemann surfaces. In the construction, the leading effects stabilizing the moduli are perturbative. We show that ... More

Nonlinear effects in E$\otimes(b_1+b_2)$ Jahn-Teller model: Variational approach with excited phonon states and mode correlationsFeb 26 2003Interplay of nonlinear and quantum effects in the ground state of the E$\otimes (b_1+b_2)$ Jahn-Teller model was investigated by the {\it variational approach and exact numerical simulations}. They result in the recognition of (i) importance of the admixture ... More

Stellar Populations in the Local Group of GalaxiesAug 04 2005The characteristics and properties of the stellar populations and evolutionary histories of Local Group galaxies are summarized and compared to predictions of cosmological models. No clear signature of the re-ionization epoch is observed; in particular, ... More

The Star Formation History of the Local GroupMay 14 2000The star formation histories of Local Group galaxies are summarized. The three large spirals are discussed individually, whereas the discussion of the Local Group dwarfs concentrates on differences and commonalities. While Local Group galaxies exhibit ... More

Tracing the tidal streams of the Sagittarius dSph, and halo Milky Way features, with carbon-rich long-period variablesJul 24 2015We assemble 121 spectroscopically-confirmed halo carbon stars, drawn from the literature, exhibiting measurable variability in the Catalina Surveys. We present their periods and amplitudes, which are used to estimate distances from period-luminosity relationships. ... More

Lipschitz stability for the inverse conductivity problem for a conformal class of anisotropic conductivitiesMay 02 2014We consider the stability issue of the inverse conductivity problem for a conformal class of anisotropic conductivities in terms of the local Dirichlet-to-Neumann map. We extend here the stability result obtained by Alessandrini and Vessella in Advances ... More

Lattice points in vector-dilated polytopesApr 27 2012For $A\in\mathbb{Z}^{m\times n}$ we investigate the behaviour of the number of lattice points in $P_A(b)=\{x\in\mathbb{R}^n:Ax\leq b\}$, depending on the varying vector $b$. It is known that this number, restricted to a cone of constant combinatorial ... More

Percolation on stationary tessellations: models, mean values and second order structureDec 22 2013We consider a stationary face-to-face tessellation $X$ of $\mathbb{R}^d$ and introduce several percolation models by colouring some of the faces black in a consistent way. Our main model is cell percolation, where cells are declared black with probability ... More

Linear Systems on Edge-Weighted GraphsMay 02 2011Let R be any subring of the reals. We present a generalization of linear systems on graphs where divisors are R-valued functions on the set of vertices and graph edges are permitted to have nonegative weights in R. Using this generalization, we provide ... More

Quantum Cohomology of Rational SurfacesOct 27 1994In this article formulas for the quantum product of a rational surface are given, and used to give an algebro-geometric proof of the associativity of the quantum product for strict Del Pezzo surfaces, those for which $-K$ is very ample. An argument for ... More

Degenerations of Planar Linear SystemsFeb 21 1997Apr 03 1998Fixing $n$ general points $p_i$ in the plane, what is the dimension of the space of plane curves of degree $d$ having multiplicity $m_i$ at $p_i$ for each $i$? In this article we propose an approach to attack this problem, and demonstrate it by successfully ... More

Theory of tangential idealizers and tangentially free idealsAug 06 2009Jun 20 2017We generalize the theory of logarithmic derivations through a self-contained study of modules here dubbed tangential idealizers. We establish reflexiveness criteria for such modules, provided the ring is a factorial domain. As a main consequence, necessary ... More

Observables for bound orbital motion in axially symmetric space-timesJul 26 2011Apr 11 2012The periastron shift and the Lense-Thirring effect of bound orbital motion in a general axially symmetric space-time given by Pleba\'nski and Demia\'nski are analyzed. We also define a measure for the conicity of the orbit and give analytic expressions ... More

Non-existence of periodic solutions in fractional-order dynamical systems and a remarkable difference between integer and fractional-order derivatives of periodic functionsAug 13 2011Nov 24 2011Using the Mellin transform approach, it is shown that, in contrast with integer-order derivatives, the fractional-order derivative of a periodic function cannot be a function with the same period. The three most widely used definitions of fractional-order ... More

Monodromy in the CMB: Gravity Waves and String InflationMar 21 2008Mar 23 2008We present a simple mechanism for obtaining large-field inflation, and hence a gravitational wave signature, from string theory compactified on twisted tori. For Nil manifolds, we obtain a leading inflationary potential proportional to phi^(2/3) in terms ... More

Characterization of geodesic flows on T^2 with and without positive topological entropyJul 04 2007Jun 30 2010In the present work we consider the behavior of the geodesic flow on the unit tangent bundle of the 2-torus $T^2$ for an arbitrary Riemannian metric. A natural non-negative quantity which measures the complexity of the geodesic flow is the topological ... More

Scalar Speed Limits and Cosmology: Acceleration from D-ccelerationOct 23 2003Jul 20 2004Causality on the gravity side of the AdS/CFT correspondence restricts motion on the moduli space of the N=4 super Yang Mills theory by imposing a speed limit on how fast the scalar field may roll. This effect can be traced to higher derivative operators ... More

Stability of Underwater Periodic LocomotionApr 18 2013Jun 28 2013Most aquatic vertebrates swim by lateral flapping of their bodies and caudal fins. While much effort has been devoted to understanding the flapping kinematics and its influence on the swimming efficiency, little is known about the stability (or lack of) ... More

Superconducting High Pressure Phases Composed of Hydrogen and IodineJul 09 2015Evolutionary structure searches predict three new phases of iodine polyhydrides stable under pressure. Insulating P1-H5I, consisting of zigzag chains of HI (delta+)and H2(delta-) molecules, is stable between 30-90 GPa. Cmcm-H2I and P6/mmm-H4I are found ... More