Random walks in directed modular networks

Because diffusion typically involves symmetric interactions, scant attention has been focused on studying asymmetric cases. However, important networked systems underlain by diffusion (e.g. cortical networks and WWW) are inherently directed. In the case of undirected diffusion, it can be shown that the steady-state probability of the random walk dynamics is fully correlated with the degree, which no longer holds for directed networks. We investigate the relationship between such probability and the inward node degree, which we call efficiency, in modular networks. Our findings show that the efficiency of a given community depends mostly on the balance between its ingoing and outgoing connections. In addition, we derive analytical expressions to show that the internal degree of the nodes do not play a crucial role in their efficiency, when considering the Erd\H{o}s-R\'enyi and Barab\'asi-Albert models. The results are illustrated with respect to the macaque cortical network, providing subsidies for improving transportation and communication systems

Quantum Lie systems and integrability conditions

The theory of Lie systems has recently been applied to Quantum Mechanics and additionally some integrability conditions for Lie systems of differential equations have also recently been analysed from a geometric perspective. In this paper we use both developments to obtain a geometric theory of integrability in Quantum Mechanics and we use it to provide a series of non-trivial integrable quantum mechanical models and to recover some known results from our unifying point of view

Study of an automatic trajectory following control system

It is shown that the estimator part of the Modified Partitioned Adaptive Controller, (MPAC) developed for nonlinear aircraft dynamics of a small jet transport can adapt to sensor failures. In addition, an investigation is made into the potential usefulness of the configuration detection technique used in the MPAC and the failure detection filter is developed that determines how a noise plant output is associated with a line or plane characteristic of a failure. It is shown by computer simulation that the estimator part and the configuration detection part of the MPAC can readily adapt to actuator and sensor failures and that the failure detection filter technique cannot detect actuator or sensor failures accurately for this type of system because of the plant modeling errors. In addition, it is shown that the decision technique, developed for the failure detection filter, can accurately determine that the plant output is related to the characteristic line or plane in the presence of sensor noise

Quantum memories based on engineered dissipation

Storing quantum information for long times without disruptions is a major requirement for most quantum information technologies. A very appealing approach is to use self-correcting Hamiltonians, i.e. tailoring local interactions among the qubits such that when the system is weakly coupled to a cold bath the thermalization process takes a long time. Here we propose an alternative but more powerful approach in which the coupling to a bath is engineered, so that dissipation protects the encoded qubit against more general kinds of errors. We show that the method can be implemented locally in four dimensional lattice geometries by means of a toric code, and propose a simple 2D set-up for proof of principle experiments.Comment: 6 +8 pages, 4 figures, Includes minor corrections updated references and aknowledgement

Jacobi multipliers, non-local symmetries and nonlinear oscillators

Constants of motion, Lagrangians and Hamiltonians admitted by a family of relevant nonlinear oscillators are derived using a geometric formalism. The theory of the Jacobi last multiplier allows us to find Lagrangian descriptions and constants of the motion. An application of the jet bundle formulation of symmetries of differential equations is presented in the second part of the paper. After a short review of the general formalism, the particular case of non-local symmetries is studied in detail by making use of an extended formalism. The theory is related to some results previously obtained by Krasil'shchi, Vinogradov and coworkers. Finally the existence of non-local symmetries for such two nonlinear oscillators is proved.Comment: 20 page

Report of the Committee on Immigration and Nationality Law of the Association of the Bar of the City of New York: An Analysis of Discrimination Resulting from Employer Sanctions and a Call for Repeal

In this Article, Ms. Davis and Messrs. Guttentag and Wernick analysis the legislative history of the Immigration Reform and Control Act (IRCA) signed into law on November 6, 1998. Their analysis indicates that in preparing the Act, the Government Accounting Officer (GAO) adopted an unduly stringent standard, limiting the types of employment discrimination relevant to its inquiry, understating the level of discrimination reflected in the data and requiring quantification of the victims of any discrimination and evidence of a wide geographic or cross-industry spread of discrimination. After setting forth its analysis, the Committee on Immigration and Nationality Law of the Association of the Bar of the City of New York highlight eight recommendations. In conclusion, the legislative history and statutory analysis indicate that the phrase widespread pattern of discrimination in the Act was not intended to be a stringent or technical test, but rather one that would alert Congress to any new or increased discrimination resulting from sanctions

Drying and cracking mechanisms in a starch slurry

Starch-water slurries are commonly used to study fracture dynamics. Drying starch-cakes benefit from being simple, economical, and reproducible systems, and have been used to model desiccation fracture in soils, thin film fracture in paint, and columnar joints in lava. In this paper, the physical properties of starch-water mixtures are studied, and used to interpret and develop a multiphase transport model of drying. Starch-cakes are observed to have a nonlinear elastic modulus, and a desiccation strain that is comparable to that generated by their maximum achievable capillary pressure. It is shown that a large material porosity is divided between pore spaces between starch grains, and pores within starch grains. This division of pore space leads to two distinct drying regimes, controlled by liquid and vapor transport of water, respectively. The relatively unique ability for drying starch to generate columnar fracture patterns is shown to be linked to the unusually strong separation of these two transport mechanisms.Comment: 9 pages, 8 figures [revised in response to reviewer comments