Hermitian Curvature and Plurisubharmonicity of Energy on Teichm\"uller Space

Let $M$ be a closed Riemann surface, $N$ a Riemannian manifold of Hermitian non-positive curvature, $f:M\to N$ a continuous map, and $E$ the function on the Teichm\"uller space of $M$ that assigns to a complex structure on $M$ the energy of the harmonic map homotopic to $f$. We show that $E$ is a plurisubharmonic function on the Teichm\"uller space of $M$. If $N$ has strictly negative Hermitian curvature, we characterize the directions in which the complex Hessian of $E$ vanishes.Comment: Revised version incorporating suggestions by the referees. To appear in GAF

Structure of radiative interferences and g=2 for vector mesons

The result by Burnett-Kroll (BK) states that for radiative decays the interference of ${\cal O}(\omega^{-1})$ in the photon energy $\omega$, vanishes after sum over polarizations of the involved particles. Using radiative decays of vector mesons we show that if the vector meson is polarized the ${\cal O}(\omega^{-1})$ terms are null only for the canonical value of the magnetic dipole moment of the vector meson, namely ${\bf g}=2$ in Bohr's magneton units. A subtle cancellation of all ${\cal O}(\omega^{-1})$ terms happens when summing over all polarizations to recover the Burnett-Kroll result. We also show the source of these terms and the corresponding cancellation for the unpolarized case and exhibit a global structure that can make them individually vanish in a particular kinematical region.Comment: 10 pages latex, 1 figure. To appear in PR

Extracting vector mesons magnetic dipole moment from radiative decays

The possibility that the magnetic dipole moment (MDM) of light charged vector mesons could be measured from radiative processes involving the production (\tau \to \rho \nu \gamma) and decay(\rho \to \pi \pi \gamma) of vector mesons is studied in a model independent way, via the soft-photon approximation. The angular and energy distribution of photons emitted at small angles respect to the final charged particle is found be sensitive to the effects of the MDM. We also show that model dependent contributions have a general structure, by gauge invariance requirements, that allows suppress them in the same kinematical region where the MDM effect is more important in the model independent approach.Comment: 3 pages,plain tex, 2 figures. To appear in the proceedings of the 5th Int.Conf. "Quark confinement and the hadron spectrum", Gargnano, Garda Lake,Italy. 10-14th September 200

Genetic algorithms for the numerical solution of variational problems without analytic trial functions

A coding of functions that allows a genetic algorithm to minimize functionals without analytic trial functions is presented and implemented for solving numerically some instances of variational problems from physics.Comment: 3 page

Effective Stiffness: Generalizing Effective Resistance Sampling to Finite Element Matrices

We define the notion of effective stiffness and show that it can used to build sparsifiers, algorithms that sparsify linear systems arising from finite-element discretizations of PDEs. In particular, we show that sampling $O(n\log n)$ elements according to probabilities derived from effective stiffnesses yields a high quality preconditioner that can be used to solve the linear system in a small number of iterations. Effective stiffness generalizes the notion of effective resistance, a key ingredient of recent progress in developing nearly linear symmetric diagonally dominant (SDD) linear solvers. Solving finite elements problems is of considerably more interest than the solution of SDD linear systems, since the finite element method is frequently used to numerically solve PDEs arising in scientific and engineering applications. Unlike SDD systems, which are relatively easy to solve, there has been limited success in designing fast solvers for finite element systems, and previous algorithms usually target discretization of limited class of PDEs like scalar elliptic or 2D trusses. Our sparsifier is general; it applies to a wide range of finite-element discretizations. A sparsifier does not constitute a complete linear solver. To construct a solver, one needs additional components (e.g., an efficient elimination or multilevel scheme for the sparsified system). Still, sparsifiers have been a critical tools in efficient SDD solvers, and we believe that our sparsifier will become a key ingredient in future fast finite-element solvers.Comment: 21 page

Classification of cubic vertex-transitive tricirculants

A finite graph is called a tricirculant if admits a cyclic group of automorphism which has precisely three orbits on the vertex-set of the graph, all of equal size. We classify all finite connected cubic vertex-transitive tricirculants. We show that except for some small exceptions of order less than 54, each of these graphs is either a prism of order 6k with k odd, a M\"obius ladder, or it falls into one of two infinite families, each family containing one graph for every order of the form 6k with k odd

How Accurate is inv(A)*b?

Several widely-used textbooks lead the reader to believe that solving a linear system of equations Ax = b by multiplying the vector b by a computed inverse inv(A) is inaccurate. Virtually all other textbooks on numerical analysis and numerical linear algebra advise against using computed inverses without stating whether this is accurate or not. In fact, under reasonable assumptions on how the inverse is computed, x = inv(A)*b is as accurate as the solution computed by the best backward-stable solvers. This fact is not new, but obviously obscure. We review the literature on the accuracy of this computation and present a self-contained numerical analysis of it

\chi-Systems for Correlation Functions

We consider the strong coupling limit of 4-point functions of heavy operators in N=4 SYM dual to strings with no spin in AdS. We restrict our discussion for operators inserted on a line. The string computation factorizes into a state-dependent sphere part and a universal AdS contribution which depends only on the dimensions of the operators and the cross ratios. We use the integrability of the AdS string equations to compute the AdS part for operators of arbitrary conformal dimensions. The solution takes the form of TBA-like integral equations with the minimal AdS string-action computed by a corresponding free-energy-like functional. These TBA-like equations stem from a peculiar system of functional equations which we call a \chi-system. In principle one could use the same method to solve for the AdS contribution in the N-point function. An interesting feature of the solution is that it encodes multiple string configurations corresponding to different classical saddle-points. The discrete data that parameterizes these solutions enters through the analog of the chemical-potentials in the TBA-like equations. Finally, for operators dual to strings spinning in the same equator in S^5 (i.e. BPS operators of the same type) the sphere part is simple to compute. In this case (which is generically neither extremal nor protected) we can construct the complete, strong-coupling 4-point function.Comment: 66 pages, 24 figures; v2: Corrections to the discussion of spikes and the constant WKB contribution. Main results are unaffecte

Bounded negativity of self-intersection numbers of Shimura curves on Shimura surfaces

Shimura curves on Shimura surfaces have been a candidate for counterexamples to the bounded negativity conjecture. We prove that they do not serve this purpose: there are only finitely many whose self-intersection number lies below a given bound. Previously, this result has been shown in [BHK+13] for compact Hilbert modular surfaces using the Bogomolov-Miyaoka-Yau inequality. Our approach uses equidistribution and works uniformly for all Shimura surfaces.Comment: 12 page

Generic Integral Manifolds for Weight Two Period Domains

We define the notion of a generic integral element for the Griffiths distribution on a weight two period domain, draw the analogy with the classical contact distribution, and then show how to explicitly construct an infinite-dimensional family of integral manifolds tangent to a given element