A discrete time relativistic Toda lattice

Four integrable symplectic maps approximating two Hamiltonian flows from the relativistic Toda hierarchy are introduced. They are demostrated to belong to the same hierarchy and to examplify the general scheme for symplectic maps on groups equiped with quadratic Poisson brackets. The initial value problem for the difference equations is solved in terms of a factorization problem in a group. Interpolating Hamiltonian flows are found for all the maps.Comment: 32 pages, LaTe

High resolution Ge/Li/ spectrometer reduces rate-dependent distortions at high counting rates

Modified spectrometer system with a low-noise preamplifier reduces rate-dependent distortions at high counting rates, 25,000 counts per second. Pole-zero cancellation minimizes pulse undershoots due to multiple time constants, baseline restoration improves resolution and prevents spectral shifts

Metamorphosis of plasma turbulence-shear flow dynamics through a transcritical bifurcation

The structural properties of an economical model for a confined plasma turbulence governor are investigated through bifurcation and stability analyses. A close relationship is demonstrated between the underlying bifurcation framework of the model and typical behavior associated with low- to high-confinement transitions such as shear flow stabilization of turbulence and oscillatory collective action. In particular, the analysis evinces two types of discontinuous transition that are qualitatively distinct. One involves classical hysteresis, governed by viscous dissipation. The other is intrinsically oscillatory and non-hysteretic, and thus provides a model for the so-called dithering transitions that are frequently observed. This metamorphosis, or transformation, of the system dynamics is an important late side-effect of symmetry-breaking, which manifests as an unusual non-symmetric transcritical bifurcation induced by a significant shear flow drive.Comment: 17 pages, revtex text, 9 figures comprised of 16 postscript files. Submitted to Phys. Rev.

Excitation Thresholds for Nonlinear Localized Modes on Lattices

Breathers are spatially localized and time periodic solutions of extended Hamiltonian dynamical systems. In this paper we study excitation thresholds for (nonlinearly dynamically stable) ground state breather or standing wave solutions for networks of coupled nonlinear oscillators and wave equations of nonlinear Schr\"odinger (NLS) type. Excitation thresholds are rigorously characterized by variational methods. The excitation threshold is related to the optimal (best) constant in a class of discr ete interpolation inequalities related to the Hamiltonian energy. We establish a precise connection among $d$, the dimensionality of the lattice, $2\sigma+1$, the degree of the nonlinearity and the existence of an excitation threshold for discrete nonlinear Schr\"odinger systems (DNLS). We prove that if $\sigma\ge 2/d$, then ground state standing waves exist if and only if the total power is larger than some strictly positive threshold, $\nu_{thresh}(\sigma, d)$. This proves a conjecture of Flach, Kaldko& MacKay in the context of DNLS. We also discuss upper and lower bounds for excitation thresholds for ground states of coupled systems of NLS equations, which arise in the modeling of pulse propagation in coupled arrays of optical fibers.Comment: To appear in Nonlinearit

The class of n-entire operators

We introduce a classification of simple, regular, closed symmetric operators with deficiency indices (1,1) according to a geometric criterion that extends the classical notions of entire operators and entire operators in the generalized sense due to M. G. Krein. We show that these classes of operators have several distinctive properties, some of them related to the spectra of their canonical selfadjoint extensions. In particular, we provide necessary and sufficient conditions on the spectra of two canonical selfadjoint extensions of an operator for it to belong to one of our classes. Our discussion is based on some recent results in the theory of de Branges spaces.Comment: 33 pages. Typos corrected. Changes in the wording of Section 2. References added. Examples added. arXiv admin note: text overlap with arXiv:1104.476

Concentration analysis and cocompactness

Loss of compactness that occurs in may significant PDE settings can be expressed in a well-structured form of profile decomposition for sequences. Profile decompositions are formulated in relation to a triplet $(X,Y,D)$, where $X$ and $Y$ are Banach spaces, $X\hookrightarrow Y$, and $D$ is, typically, a set of surjective isometries on both $X$ and $Y$. A profile decomposition is a representation of a bounded sequence in $X$ as a sum of elementary concentrations of the form $g_kw$, $g_k\in D$, $w\in X$, and a remainder that vanishes in $Y$. A necessary requirement for $Y$ is, therefore, that any sequence in $X$ that develops no $D$-concentrations has a subsequence convergent in the norm of $Y$. An imbedding $X\hookrightarrow Y$ with this property is called $D$-cocompact, a property weaker than, but related to, compactness. We survey known cocompact imbeddings and their role in profile decompositions

Participatory Militias: An Analysis of an Armed Movement's Online Audience

Armed groups of civilians known as "self-defense forces" have ousted the powerful Knights Templar drug cartel from several towns in Michoacan. This militia uprising has unfolded on social media, particularly in the "VXM" ("Valor por Michoacan," Spanish for "Courage for Michoacan") Facebook page, gathering more than 170,000 fans. Previous work on the Drug War has documented the use of social media for real-time reports of violent clashes. However, VXM goes one step further by taking on a pro-militia propagandist role, engaging in two-way communication with its audience. This paper presents a descriptive analysis of VXM and its audience. We examined nine months of posts, from VXM's inception until May 2014, totaling 6,000 posts by VXM administrators and more than 108,000 comments from its audience. We describe the main conversation themes, post frequency and relationships with offline events and public figures. We also characterize the behavior of VXM's most active audience members. Our work illustrates VXM's online mobilization strategies, and how its audience takes part in defining the narrative of this armed conflict. We conclude by discussing possible applications of our findings for the design of future communication technologies.Comment: Participatory Militias: An Analysis of an Armed Movement's Online Audience. Saiph Savage, Andres Monroy-Hernandez. CSCW: ACM Conference on Computer-Supported Cooperative Work 201

Defining appropriateness in coach-athlete sexual relationships: The voice of coaches

The sporting culture, with omnipotent coaches, fierce competition for recognition and funding, and ‘win at all cost’ ethos, creates an environment conducive to sexual exploitation of athletes. Recent increased public awareness and the development of child protection policies in sport have led to the questioning of previously accepted coach-athlete relationships. This study is an exploratory investigation into male swimming coaches’ perceptions of appropriateness of coach-athlete sexual relationships. Sexual relationships with athletes under the age of 16 were unanimously considered totally inappropriate. With regard to sexual relationships with athletes above the age of consent for heterosexual sex, opinions ranged from “totally inappropriate” to “it’s a question of civil liberties.” These results are discussed in relation to how coaches have adapted their own behaviours in the face of public scrutiny but are still reluctant to restrict the rights of their fellow coaches

Can health trainers make a difference with difficult-to-engage clients? A multisite case study

A political attempt in the United Kingdom to address health inequalities in the past decade has been the government’s initiative to employ local health trainers (HTs) or health trainer champions (HTCs) to support disadvantaged individuals with aspects of their health-related behaviors. HT/HTCs provide health-related information and support to individuals with healthy eating, physical activity, and smoking cessation. They undertake community engagement and direct individuals to relevant health services. They differ in that HTs are trained to provide health interventions to individuals or groups and to make referrals to specialist health care services when necessary. This article provides an evaluation of HT/HTCs interventions across three sites, including one prison, one probation service (three teams), and one mental health center. An evaluation framework combining process and outcome measures was employed that used mixed methods to capture data relating to the implementation of the service, including the context of the HT/HTCs interventions, the reactions of their clients, and the outcomes reported. It was found that HT/HTCs interventions were more effective in the prison and mental health center compared with the probation site largely as a result of contextual factors