Observations on the flight paths of the day-flying moth Virbia lamae during periods of mate location: do males have a strategy for contacting the pheromone plume?

1. To maximize the probability of rapid contact with a female’s pheromone plume, the trajectories of male foraging flights might be expected to be directed with respect to wind flow and also to be energetically efficient. 2. Flights directed either upwind, downwind, or crosswind have been proposed as optimal strategies for rapid and/or energetically efficient plume contact. Other possible strategies are random and Lévy walks, which have trajectories and turn frequencies that are not dictated by the direction of wind flow. 3. The planar flight paths of males of the day-active moth Virbia lamae were recorded during the customary time of its sexual activity. 4. We found no directional preference in these foraging flights with respect to the direction of contemporaneous wind flow, but, because crosswind encompasses twice the possible orientations of either upwind or downwind, a random orientation is in effect a de facto crosswind strategy. 5. A crosswind preference should be favoured when the plume extends farther downwind than crosswind, and this strategy is realized by V. lamae males by a random orientation of their trajectories with respect to current wind direction

Quasi-sure existence of Gaussian rough paths and large deviation principles for capacities

We construct a quasi-sure version (in the sense of Malliavin) of geometric rough paths associated with a Gaussian process with long-time memory. As an application we establish a large deviation principle (LDP) for capacities for such Gaussian rough paths. Together with Lyons' universal limit theorem, our results yield immediately the corresponding results for pathwise solutions to stochastic differential equations driven by such Gaussian process in the sense of rough paths. Moreover, our LDP result implies the result of Yoshida on the LDP for capacities over the abstract Wiener space associated with such Gaussian process.

A structure-dynamic approach to cortical organization: Number of paths and accessibility

A structure-dynamic approach to cortical systems is reported which is based on the number of paths and the accessibility of each node. The latter measurement is obtained by performing self-avoiding random walks in the respective networks, so as to simulate dynamics, and then calculating the entropies of the transition probabilities for walks starting from each node. Cortical networks of three species, namely cat, macaque and humans, are studied considering structural and dynamical aspects. It is verified that the human cortical network presents the highest accessibility and number of paths (in terms of z-scores). The correlation between the number of paths and accessibility is also investigated as a mean to quantify the level of independence between paths connecting pairs of nodes in cortical networks. By comparing the cortical networks of cat, macaque and humans, it is verified that the human cortical network tends to present the largest number of independent paths of length larger than four. These results suggest that the human cortical network is potentially the most resilient to brain injures. (C) 2009 Elsevier B.V. All rights reserved.

The number of open paths in an oriented rho-percolation model

We study the asymptotic properties of the number of open paths of length n in an oriented rho-percolation model. We show that this number is e(n alpha(rho)(1+o(1))) as n ->infinity. The exponent alpha is deterministic, it can be expressed in terms of the free energy of a polymer model, and it can be explicitly computed in some range of the parameters. Moreover, in a restricted range of the parameters, we even show that the number of such paths is n(-1/2)We (n alpha(rho))(1+o(1)) for some nondegenerate random variable W. We build on connections with the model of directed polymers in random environment, and we use techniques and results developed in this context.

On a product formula for the Conley-Zelmder index of symplectic paths and its applications

Using invariance by fixed-endpoints homotopies and a generalized notion of symplectic Cayley transform, we prove a product formula for the Conley-Zehnder index of continuous paths with arbitrary endpoints in the symplectic group. We discuss two applications of the formula, to the metaplectic group and to periodic solutions of Hamiltonian systems.

On the composite of irreducible morphisms in almost sectional paths

We study here when the composite of it irreducible morphisms in almost sectional paths is non-zero and lies in Rn+1 (C) 2007 Elsevier B.V. All rights reserved.

The benefits and pitfalls of participating in a corporate inversion: a case study of two companies on two different paths

Even though the term corporate inversion has been heard globally for decades, it has only become more prevalent in the United States during the past two years. This case study examines two United States companies that recently had very high profile and public corporate inversion experiences. Complicated tax laws and high tax rales have long eroded the ability of United States companies to remain competitive on a global scale. During the past two years, tax reform has been elevated to the Presidential and Congressional levei. Because these reform efforts have stalled, however, and in the constant search for ways to become more competitive and profitable, United States dorniciled companies have begun to more aggressively explore corporate inversion. This case study of Walgreens Alliance Boots and Mylan N.V., is undertaken because while the reasons to pursue a corporate inversion for both companies were very similar and done during the same time period, the internai process and final outcome were dramatically different. The other dynamic studied is the role both internai and externai politics had on these two cornpanies and how they influenced the decisions made by the executives. Lastly, the Obama Administration continues to threaten so called "corporate America" to remain in the country through regulatory pressure, but this has not stopped companies frorn pursing corporate inversions. Legislatively, attempts at corporate tax reform, another way to encourage Untied States companies to remain, have also failed. I will not try to determine i f a corporate inversion is the right path for a company to take. I am examining how the rise o f the practice o f corporate inversions has been elevated in boardroorns, on Wall Street, in Congress and at the White House during the past two years.

Alternative paths for insertion of probes into high inclination lunar orbits

The dynamics of the restricted three-body Earth-Moon-particle problem predicts the existence of direct periodic orbits around the Lagrangian equilibrium point L1. From these orbits, we derive a set of trajectories that form links between the Earth and the Moon and are capable of performing transfers between terrestrial and lunar orbits, in addition to defining an escape route from the Earth-Moon system. When we consider a more complex and realistic dynamical system - the four-body Sun-Earth-Moon-particle (probe) problem - the trajectories have an expressive gain of inclination when they penetrate in the lunar influence sphere, thus allowing the insertion of probes into low-altitude lunar orbits with high inclinations, including polar orbits. In this study, we present these links and investigate some possibilities for performing an Earth-Moon transfer based on these trajectories. (C) 2007 COSPAR. Published by Elsevier Ltd. All rights reserved.