A characterization of quadric constant mean curvature hypersurfaces of spheres

Let $\phi:M\to\mathbb{S}^{n+1}\subset\mathbb{R}^{n+2}$ be an immersion of a complete $n$-dimensional oriented manifold. For any $v\in\mathbb{R}^{n+2}$, let us denote by $\ell_v:M\to\mathbb{R}$ the function given by $\ell_v(x)=\phi(x),v$ and by $f_v:M\to\mathbb{R}$, the function given by $f_v(x)=\nu(x),v$, where $\nu:M\to\mathbb{S}^{n}$ is a Gauss map. We will prove that if $M$ has constant mean curvature, and, for some $v\ne{\bf 0}$ and some real number $\lambda$, we have that $\ell_v=\lambda f_v$, then, $\phi(M)$ is either a totally umbilical sphere or a Clifford hypersurface. As an application, we will use this result to prove that the weak stability index of any compact constant mean curvature hypersurface $M^n$ in $\mathbb{S}^{n+1}$ which is neither totally umbilical nor a Clifford hypersurface and has constant scalar curvature is greater than or equal to $2n+4$.Comment: Final version (February 2008). To appear in the Journal of Geometric Analysi

A Study of Heuristic Guesses for Adiabatic Quantum Computation

Adiabatic quantum computation (AQC) is a universal model for quantum computation which seeks to transform the initial ground state of a quantum system into a final ground state encoding the answer to a computational problem. AQC initial Hamiltonians conventionally have a uniform superposition as ground state. We diverge from this practice by introducing a simple form of heuristics: the ability to start the quantum evolution with a state which is a guess to the solution of the problem. With this goal in mind, we explain the viability of this approach and the needed modifications to the conventional AQC (CAQC) algorithm. By performing a numerical study on hard-to-satisfy 6 and 7 bit random instances of the satisfiability problem (3-SAT), we show how this heuristic approach is possible and we identify that the performance of the particular algorithm proposed is largely determined by the Hamming distance of the chosen initial guess state with respect to the solution. Besides the possibility of introducing educated guesses as initial states, the new strategy allows for the possibility of restarting a failed adiabatic process from the measured excited state as opposed to restarting from the full superposition of states as in CAQC. The outcome of the measurement can be used as a more refined guess state to restart the adiabatic evolution. This concatenated restart process is another heuristic that the CAQC strategy cannot capture.Chemistry and Chemical Biolog

Estudio comparativo de dos métodos de radiografías forzadas para detectar la insuficiencia del ligamento cruzado anterior

En 32 pacientes con rotura unilateral de ligamento cruzado anterior (LCA) comprobada mediante artroscopia se efectuó previamente una radiografía forzada de ambas rodillas para estudiar el desplazamiento anterior de la tibia. Cada paciente fue estudiado mediante dos métodos diferentes, Lachman activo radiológico (LAR) y TelosR. Se asumió el diagnóstico radiológico de inestabilidad cuando la diferencia en el desplazamiento entre la rodilla lesionada y su control fue superior a 3 mm. Los resultados demuestran que la diferencia media del desplazamiento entre la rodilla lesionada y la normal fue superior a 3 mm con ambos métodos. En el lado interno 3,7 ± 3,7 mm con el LAR y 4,8 ± 5,8 mm con el Telos (diferencias no significativas). En el lado externo esta diferencia fue de 4,3 ± 4,7 nun con el LAR y de 6,8 ± 6 mm con el Telos (p < 0,05). A pesar de estos resultados, ambos métodos mostraron una sensibilidad para la detección de la insuficiencia ligamentosa inferior al 70%, lo que cuestiona su valor para el diagnóstico de la misma.In a prospective study, 32 patients with arthroscopically proved anterior cruciate ligament rupture were previously stressradiographied on both knees through two methods: the quadriceps-contraction technique (QCT) and the TelosR device. Instability was assumed when radiological differential displacement between injured and normal knee was greated than 3 mm. Results showed that this differential displacement was greater than 3 mm with both methods: 3,7 ± 3,7 mm v.s. 4,8 ± 5,8 mm in the medial side (differences not significant) and 4,3 ± 4,7 mm v.s. 6,8 ± 6 mm (p < 0.05) for the lateral side with the QCT and TelosR respectively. In spite of these differences, both methods showed a sensitivity lower than 70%

A new combined quasigeoid model in Tierra del Fuego

This work focuses on the development of a combined quasigeoid model for Tierra del Fuego province. The Equivalent Source Technique (EST) is applied together with the remove-compute-restore technique in order to combine gravity and GPS/levelling observations and to obtain a quasigeoid model. This model features an improved accuracy in relation to previous models. A discussion about the geodetic reference system is also presented. Geodetic coordinates of all stations used were transformed to TDF08 to be in accordance with the new geodetic reference frame of Argentina. After a cross validation procedure it is determined that a 5cm (r.m.s.) quasigeoid model has been achieved for the major part of the province, fulfilling the requirements for its practical use. New Global Geopotential Models (GGM) are introduced in the discussion, particularly the EGM2008 which is used for evaluation purposes. It shows a 9cm agreement after its evaluation on the levelling lines

Water use in bean and cowpea: efficiency or effective use of water?

Water stress is one of the major abiotic stress limitations for grain legume production in smallholder agricultural systems. Phenotypic characterization of water consumption by different species of legumes and genotypes within them plays a key role in adaptation to drought. Dynamics of water use may differ depending on the origin and evolution of the species of legume and the agro-climatic conditions faced by the legumes. The supply of nitrogen from symbiotic fixation is also critical for filling seeds and is even more limiting than water in bean, but not in cowpea

Minimal cubic cones via Clifford algebras

We construct two infinite families of algebraic minimal cones in $R^{n}$. The first family consists of minimal cubics given explicitly in terms of the Clifford systems. We show that the classes of congruent minimal cubics are in one to one correspondence with those of geometrically equivalent Clifford systems. As a byproduct, we prove that for any $n\ge4$, $n\ne 16k+1$, there is at least one minimal cone in $R^{n}$ given by an irreducible homogeneous cubic polynomial. The second family consists of minimal cones in $R^{m^2}$, $m\ge2$, defined by an irreducible homogeneous polynomial of degree $m$. These examples provide particular answers to the questions on algebraic minimal cones posed by Wu-Yi Hsiang in the 1960's.Comment: Final version, corrects typos in Table

Classical Ising model test for quantum circuits

We exploit a recently constructed mapping between quantum circuits and graphs in order to prove that circuits corresponding to certain planar graphs can be efficiently simulated classically. The proof uses an expression for the Ising model partition function in terms of quadratically signed weight enumerators (QWGTs), which are polynomials that arise naturally in an expansion of quantum circuits in terms of rotations involving Pauli matrices. We combine this expression with a known efficient classical algorithm for the Ising partition function of any planar graph in the absence of an external magnetic field, and the Robertson-Seymour theorem from graph theory. We give as an example a set of quantum circuits with a small number of non-nearest neighbor gates which admit an efficient classical simulation.Comment: 17 pages, 2 figures. v2: main result strengthened by removing oracular settin