Line bundles for which a projectivized jet bundle is a product

We characterize the triples (X,L,H), consisting of holomorphic line bundles L and H on a complex projective manifold X, such that for some positive integer k, the k-th holomorphic jet bundle of L, J_k(L), is isomorphic to a direct sum H+...+H. Given the geometrical constrains imposed by a projectivized line bundle being a product of the base and a projective space it is natural to expect that this would happen only under very rare circumstances. It is shown, in fact, that X is either an Abelian variety or projective space. In the former case L\cong H is any line bundle of Chern class zero. In the later case for k a positive integer, L=O_{P^n}(q) with J_k(L)=H+...+H if and only if H=O_{P^n}(q-k) and either q\ge k or q\le -1.Comment: Latex file, 5 page

A comparison of personality traits of gifted word learner and typical border collies

While personality and cognition are distinct domains, some personality traits may affect the capacity for problem-solving. It was suggested that there is a positive association between the Playfulness trait and problem-solving performance in humans. Studies on giftedness (extremely good capacity in the case of a specific skill), typically aimed to reveal the genetic, experiential, and mental origins of such extreme inter-individual variation. We exploited recent findings on giftedness in a specific cognitive skill, object label learning, in dogs to explore the potential association between this exceptional skill and personality traits. We administered the Dog Personality Questionnaire to 21 gifted dog owners and compared the personality traits of their dogs to those of matched samples of 43 Hungarian and 101 Austrian typical dogs, i.e., dogs lacking this exceptional capacity. Since most Gifted Word Learner dogs are Border collies, we restricted our analysis to dogs of this breed. We hypothesized that the Gifted Word Learner dogs may show higher levels of Playfulness. As expected, we found that the gifted Border collies were rated as more playful than both the Hungarian and Austrian typical ones. Our results suggest that an extremely high level of Playfulness is associated with giftedness in a specific cognitive trait in dogs: the capacity to learn object verbal labels, thus opening new possibilities for comparative research on the relationship between giftedness and personality

Contractility parameters of human -cardiac myosin with the hypertrophic cardiomyopathy mutation R403Q show loss of motor function

Hypertrophic cardiomyopathy (HCM) is the most frequently occurring inherited cardiovascular disease. It is caused by mutations in genes encoding the force-generating machinery of the cardiac sarcomere, including human ?-cardiac myosin. We present a detailed characterization of the most debated HCM-causing mutation in human ?-cardiac myosin, R403Q. Despite numerous studies, most performed with nonhuman or noncardiac myosin, there is no consensus about the mechanism of action of this mutation on the function of the enzyme. We use recombinant human ?-cardiac myosin and new methodologies to characterize in vitro contractility parameters of the R403Q myosin compared to wild type. We extend our studies beyond pure actin filaments to include the interaction of myosin with regulated actin filaments containing tropomyosin and troponin. We find that, with pure actin, the intrinsic force generated by R403Q is ~15% lower than that generated by wild type. The unloaded velocity is, however, ~10% higher for R403Q myosin, resulting in a load-dependent velocity curve that has the characteristics of lower contractility at higher external loads compared to wild type. With regulated actin filaments, there is no increase in the unloaded velocity and the contractility of the R403Q myosin is lower than that of wild type at all loads. Unlike that with pure actin, the actin-activated adenosine triphosphatase activity for R403Q myosin with Ca2+-regulated actin filaments is ~30% lower than that for wild type, predicting a lower unloaded duty ratio of the motor. Overall, the contractility parameters studied fit with a loss of human ?-cardiac myosin contractility as a result of the R403Q mutation

A Special Homotopy Continuation Method For A Class of Polynomial Systems

A special homotopy continuation method, as a combination of the polyhedral homotopy and the linear product homotopy, is proposed for computing all the isolated solutions to a special class of polynomial systems. The root number bound of this method is between the total degree bound and the mixed volume bound and can be easily computed. The new algorithm has been implemented as a program called LPH using C++. Our experiments show its efficiency compared to the polyhedral or other homotopies on such systems. As an application, the algorithm can be used to find witness points on each connected component of a real variety

Numerical Algebraic Geometry: A New Perspective on String and Gauge Theories

The interplay rich between algebraic geometry and string and gauge theories has recently been immensely aided by advances in computational algebra. However, these symbolic (Gr\"{o}bner) methods are severely limited by algorithmic issues such as exponential space complexity and being highly sequential. In this paper, we introduce a novel paradigm of numerical algebraic geometry which in a plethora of situations overcomes these short-comings. Its so-called 'embarrassing parallelizability' allows us to solve many problems and extract physical information which elude the symbolic methods. We describe the method and then use it to solve various problems arising from physics which could not be otherwise solved.Comment: 36 page