Geometric analysis of noisy perturbations to nonholonomic constraints

We propose two types of stochastic extensions of nonholonomic constraints for mechanical systems. Our approach relies on a stochastic extension of the Lagrange-d'Alembert framework. We consider in details the case of invariant nonholonomic systems on the group of rotations and on the special Euclidean group. Based on this, we then develop two types of stochastic deformations of the Suslov problem and study the possibility of extending to the stochastic case the preservation of some of its integrals of motion such as the Kharlamova or Clebsch-Tisserand integrals

Mechanical Systems with Symmetry, Variational Principles, and Integration Algorithms

This paper studies variational principles for mechanical systems with symmetry and their applications to integration algorithms. We recall some general features of how to reduce variational principles in the presence of a symmetry group along with general features of integration algorithms for mechanical systems. Then we describe some integration algorithms based directly on variational principles using a discretization technique of Veselov. The general idea for these variational integrators is to directly discretize Hamilton’s principle rather than the equations of motion in a way that preserves the original systems invariants, notably the symplectic form and, via a discrete version of Noether’s theorem, the momentum map. The resulting mechanical integrators are second-order accurate, implicit, symplectic-momentum algorithms. We apply these integrators to the rigid body and the double spherical pendulum to show that the techniques are competitive with existing integrators

The Social and Political Dimensions of the Ebola Response: Global Inequality, Climate Change, and Infectious Disease

The 2014 Ebola crisis has highlighted public-health vulnerabilities in Liberia, Sierra Leone, and Guinea – countries ravaged by extreme poverty, deforestation and mining-related disruption of livelihoods and ecosystems, and bloody civil wars in the cases of Liberia and Sierra Leone. Ebola’s emergence and impact are grounded in the legacy of colonialism and its creation of enduring inequalities within African nations and globally, via neoliberalism and the Washington Consensus. Recent experiences with new and emerging diseases such as SARS and various strains of HN influenzas have demonstrated the effectiveness of a coordinated local and global public health and education-oriented response to contain epidemics. To what extent is international assistance to fight Ebola strengthening local public health and medical capacity in a sustainable way, so that other emerging disease threats, which are accelerating with climate change, may be met successfully? This chapter considers the wide-ranging socio-political, medical, legal and environmental factors that have contributed to the rapid spread of Ebola, with particular emphasis on the politics of the global and public health response and the role of gender, social inequality, colonialism and racism as they relate to the mobilization and establishment of the public health infrastructure required to combat Ebola and other emerging diseases in times of climate change

Exponential Random Graph Modeling for Complex Brain Networks

Exponential random graph models (ERGMs), also known as p* models, have been utilized extensively in the social science literature to study complex networks and how their global structure depends on underlying structural components. However, the literature on their use in biological networks (especially brain networks) has remained sparse. Descriptive models based on a specific feature of the graph (clustering coefficient, degree distribution, etc.) have dominated connectivity research in neuroscience. Corresponding generative models have been developed to reproduce one of these features. However, the complexity inherent in whole-brain network data necessitates the development and use of tools that allow the systematic exploration of several features simultaneously and how they interact to form the global network architecture. ERGMs provide a statistically principled approach to the assessment of how a set of interacting local brain network features gives rise to the global structure. We illustrate the utility of ERGMs for modeling, analyzing, and simulating complex whole-brain networks with network data from normal subjects. We also provide a foundation for the selection of important local features through the implementation and assessment of three selection approaches: a traditional p-value based backward selection approach, an information criterion approach (AIC), and a graphical goodness of fit (GOF) approach. The graphical GOF approach serves as the best method given the scientific interest in being able to capture and reproduce the structure of fitted brain networks

The rolling problem: overview and challenges

In the present paper we give a historical account -ranging from classical to modern results- of the problem of rolling two Riemannian manifolds one on the other, with the restrictions that they cannot instantaneously slip or spin one with respect to the other. On the way we show how this problem has profited from the development of intrinsic Riemannian geometry, from geometric control theory and sub-Riemannian geometry. We also mention how other areas -such as robotics and interpolation theory- have employed the rolling model.Comment: 20 page

The role of brand loyalty and social media in e-commerce interfaces: survey results and implications for user interfaces

This paper explores the role of brand loyalty and social media in e-commerce interfaces. A survey consisting of 118 respondents was contacted to address the questions relating to online shopping and brand loyalty. Link between the frequency of access and time spent on an e-commerce user interface, and brand loyalty, gender and age profile differences, and the role of social media to branding and on-line shopping was analyzed. It was found that online loyalty differs from offline loyalty and loyalty also differed across genders, showing men were more loyal than women when shopping online. Information shared about products on social media by friends and family played an important role in purchase decision making. Website interface and ease of navigation were also key aspects for online shopping. The research concluded with recommendations to create multimodal websites which are more interactive and targeted so customer experience is enhanced and loyalty is achieved through the use of interactivity and social media

Singular values of the Dirac operator in dense QCD-like theories

We study the singular values of the Dirac operator in dense QCD-like theories at zero temperature. The Dirac singular values are real and nonnegative at any nonzero quark density. The scale of their spectrum is set by the diquark condensate, in contrast to the complex Dirac eigenvalues whose scale is set by the chiral condensate at low density and by the BCS gap at high density. We identify three different low-energy effective theories with diquark sources applicable at low, intermediate, and high density, together with their overlapping domains of validity. We derive a number of exact formulas for the Dirac singular values, including Banks-Casher-type relations for the diquark condensate, Smilga-Stern-type relations for the slope of the singular value density, and Leutwyler-Smilga-type sum rules for the inverse singular values. We construct random matrix theories and determine the form of the microscopic spectral correlation functions of the singular values for all nonzero quark densities. We also derive a rigorous index theorem for non-Hermitian Dirac operators. Our results can in principle be tested in lattice simulations.Comment: 3 references added, version published in JHE

Quantum magnetism and criticality

Magnetic insulators have proved to be fertile ground for studying new types of quantum many body states, and I survey recent experimental and theoretical examples. The insights and methods transfer also to novel superconducting and metallic states. Of particular interest are critical quantum states, sometimes found at quantum phase transitions, which have gapless excitations with no particle- or wave-like interpretation, and control a significant portion of the finite temperature phase diagram. Remarkably, their theory is connected to holographic descriptions of Hawking radiation from black holes.Comment: 39 pages, 10 figures, review article for non-specialists; (v2) added clarifications and references; (v3) minor corrections; (v4) added footnote on hydrodynamic long-time tail

Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms

An open quantum system, whose time evolution is governed by a master equation, can be driven into a given pure quantum state by an appropriate design of the system-reservoir coupling. This points out a route towards preparing many body states and non-equilibrium quantum phases by quantum reservoir engineering. Here we discuss in detail the example of a \emph{driven dissipative Bose Einstein Condensate} of bosons and of paired fermions, where atoms in an optical lattice are coupled to a bath of Bogoliubov excitations via the atomic current representing \emph{local dissipation}. In the absence of interactions the lattice gas is driven into a pure state with long range order. Weak interactions lead to a weakly mixed state, which in 3D can be understood as a depletion of the condensate, and in 1D and 2D exhibits properties reminiscent of a Luttinger liquid or a Kosterlitz-Thouless critical phase at finite temperature, with the role of the ``finite temperature'' played by the interactions.Comment: 9 pages, 2 figure

Multijet production in neutral current deep inelastic scattering at HERA and determination of α_{s}

Multijet production rates in neutral current deep inelastic scattering have been measured in the range of exchanged boson virtualities 10 5 GeV and –1 < η_{LAB}^{jet} < 2.5. Next-to-leading-order QCD calculations describe the data well. The value of the strong coupling constant α_{s} (M_{z}), determined from the ratio of the trijet to dijet cross sections, is α_{s} (M_{z}) = 0.1179 ± 0.0013 (stat.)_{-0.0046}^{+0.0028}(exp.)_{-0.0046}^{+0.0028}(th.)