Tools in the orbit space approach to the study of invariant functions: rational parametrization of strata

Functions which are equivariant or invariant under the transformations of a compact linear group $G$ acting in an euclidean space $\real^n$, can profitably be studied as functions defined in the orbit space of the group. The orbit space is the union of a finite set of strata, which are semialgebraic manifolds formed by the $G$-orbits with the same orbit-type. In this paper we provide a simple recipe to obtain rational parametrizations of the strata. Our results can be easily exploited, in many physical contexts where the study of equivariant or invariant functions is important, for instance in the determination of patterns of spontaneous symmetry breaking, in the analysis of phase spaces and structural phase transitions (Landau theory), in equivariant bifurcation theory, in crystal field theory and in most areas where use is made of symmetry adapted functions. A physically significant example of utilization of the recipe is given, related to spontaneous polarization in chiral biaxial liquid crystals, where the advantages with respect to previous heuristic approaches are shown.Comment: Figures generated through texdraw package; revised version appearing in J. Phys. A: Math. Ge

Competition and Selection Among Conventions

In many domains, a latent competition among different conventions determines which one will come to dominate. One sees such effects in the success of community jargon, of competing frames in political rhetoric, or of terminology in technical contexts. These effects have become widespread in the online domain, where the data offers the potential to study competition among conventions at a fine-grained level. In analyzing the dynamics of conventions over time, however, even with detailed on-line data, one encounters two significant challenges. First, as conventions evolve, the underlying substance of their meaning tends to change as well; and such substantive changes confound investigations of social effects. Second, the selection of a convention takes place through the complex interactions of individuals within a community, and contention between the users of competing conventions plays a key role in the convention's evolution. Any analysis must take place in the presence of these two issues. In this work we study a setting in which we can cleanly track the competition among conventions. Our analysis is based on the spread of low-level authoring conventions in the eprint arXiv over 24 years: by tracking the spread of macros and other author-defined conventions, we are able to study conventions that vary even as the underlying meaning remains constant. We find that the interaction among co-authors over time plays a crucial role in the selection of them; the distinction between more and less experienced members of the community, and the distinction between conventions with visible versus invisible effects, are both central to the underlying processes. Through our analysis we make predictions at the population level about the ultimate success of different synonymous conventions over time--and at the individual level about the outcome of "fights" between people over convention choices.Comment: To appear in Proceedings of WWW 2017, data at https://github.com/CornellNLP/Macro

Nonlinear magneto-optical rotation of frequency-modulated light resonant with a low-J transition

A low-light-power theory of nonlinear magneto-optical rotation of frequency-modulated light resonant with a J=1->J'=0 transition is presented. The theory is developed for a Doppler-free transition, and then modified to account for Doppler broadening and velocity mixing due to collisions. The results of the theory are shown to be in qualitative agreement with experimental data obtained for the rubidium D1 line.Comment: 11 pages, 5 figures, v.2 edited for clarit

Collective Decision Dynamics in the Presence of External Drivers

We develop a sequence of models describing information transmission and decision dynamics for a network of individual agents subject to multiple sources of influence. Our general framework is set in the context of an impending natural disaster, where individuals, represented by nodes on the network, must decide whether or not to evacuate. Sources of influence include a one-to-many externally driven global broadcast as well as pairwise interactions, across links in the network, in which agents transmit either continuous opinions or binary actions. We consider both uniform and variable threshold rules on the individual opinion as baseline models for decision-making. Our results indicate that 1) social networks lead to clustering and cohesive action among individuals, 2) binary information introduces high temporal variability and stagnation, and 3) information transmission over the network can either facilitate or hinder action adoption, depending on the influence of the global broadcast relative to the social network. Our framework highlights the essential role of local interactions between agents in predicting collective behavior of the population as a whole.Comment: 14 pages, 7 figure

Genome-Scale Multilocus Microsatellite Typing of Trypanosoma cruzi Discrete Typing Unit I Reveals Phylogeographic Structure and Specific Genotypes Linked to Human Infection

Trypanosoma cruzi is the most important parasitic infection in Latin America and is also genetically highly diverse, with at least six discrete typing units (DTUs) reported: Tc I, IIa, IIb, IIc, IId, and IIe. However, the current six-genotype classification is likely to be a poor reflection of the total genetic diversity present in this undeniably ancient parasite. To determine whether epidemiologically important information is “hidden” at the sub-DTU level, we developed a 48-marker panel of polymorphic microsatellite loci to investigate population structure among 135 samples from across the geographic distribution of TcI. This DTU is the major cause of resurgent human disease in northern South America but also occurs in silvatic triatomine vectors and mammalian reservoir hosts throughout the continent. Based on a total dataset of 12,329 alleles, we demonstrate that silvatic TcI populations are extraordinarily genetically diverse, show spatial structuring on a continental scale, and have undergone recent biogeographic expansion into the southern United States of America. Conversely, the majority of human strains sampled are restricted to two distinct groups characterised by a considerable reduction in genetic diversity with respect to isolates from silvatic sources. In Venezuela, most human isolates showed little identity with known local silvatic strains, despite frequent invasion of the domestic setting by infected adult vectors. Multilocus linkage indices indicate predominantly clonal parasite propagation among all populations. However, excess homozygosity among silvatic strains and raised heterozygosity among domestic populations suggest that some level of genetic recombination cannot be ruled out. The epidemiological significance of these findings is discussed

Abelian symmetries in multi-Higgs-doublet models

N-Higgs doublet models (NHDM) are a popular framework to construct electroweak symmetry breaking mechanisms beyond the Standard model. Usually, one builds an NHDM scalar sector which is invariant under a certain symmetry group. Although several such groups have been used, no general analysis of symmetries possible in the NHDM scalar sector exists. Here, we make the first step towards this goal by classifying the elementary building blocks, namely the abelian symmetry groups, with a special emphasis on finite groups. We describe a strategy that identifies all abelian groups which are realizable as symmetry groups of the NHDM Higgs potential. We consider both the groups of Higgs-family transformations only and the groups which also contain generalized CP transformations. We illustrate this strategy with the examples of 3HDM and 4HDM and prove several statements for arbitrary N.Comment: 33 pages, 2 figures; v2: conjecture 3 is proved and becomes theorem 3, more explanations of the main strategy are added, matches the published versio

Social networks and implementation of evidence-based practices in public youth-serving systems: a mixed-methods study

<p>Abstract</p> <p>Background</p> <p>The present study examines the structure and operation of social networks of information and advice and their role in making decisions as to whether to adopt new evidence-based practices (EBPs) among agency directors and other program professionals in 12 California counties participating in a large randomized controlled trial.</p> <p>Methods</p> <p>Interviews were conducted with 38 directors, assistant directors, and program managers of county probation, mental health, and child welfare departments. Grounded-theory analytic methods were used to identify themes related to EBP adoption and network influences. A web-based survey collected additional quantitative information on members of information and advice networks of study participants. A mixed-methods approach to data analysis was used to create a sociometric data set (n = 176) for examination of associations between advice seeking and network structure.</p> <p>Results</p> <p>Systems leaders develop and maintain networks of information and advice based on roles, responsibility, geography, and friendship ties. Networks expose leaders to information about EBPs and opportunities to adopt EBPs; they also influence decisions to adopt EBPs. Individuals in counties at the same stage of implementation accounted for 83% of all network ties. Networks in counties that decided not to implement a specific EBP had no extra-county ties. Implementation of EBPs at the two-year follow-up was associated with the size of county, urban versus rural counties, and in-degree centrality. Collaboration was viewed as critical to implementing EBPs, especially in small, rural counties where agencies have limited resources on their own.</p> <p>Conclusions</p> <p>Successful implementation of EBPs requires consideration and utilization of existing social networks of high-status systems leaders that often cut across service organizations and their geographic jurisdictions.</p> <p>Trial Registration</p> <p><a href="http://www.clinicaltrials.gov/ct2/show/NCT00880126">NCT00880126</a></p

Interpreting syndepositional sediment remobilization and deformation beneath submarine gravity flows; a kinematic boundary layer approach

Turbidite sandstones and related deposits commonly contain deformation structures and remobilized sediment that might have resulted from post-depositional modification such as downslope creep (e.g. slumping) or density-driven loading by overlying deposits. However, we consider that deformation can occur during the passage of turbidity currents that exerted shear stress on their substrates (whether entirely pre-existing strata, sediment deposited by earlier parts of the flow itself or some combination of these). Criteria are outlined here, to avoid confusion with products of other mechanisms (e.g. slumping or later tectonics), which establish the synchronicity between the passage of overriding flows and deformation of their substrates. This underpins a new analytical framework for tracking the relationship between deformation, deposition and the transit of the causal turbidity current, through the concept of kinematic boundary layers. Case study examples are drawn from outcrop (Miocene of New Zealand, and Apennines of Italy) and subsurface examples (Britannia Sandstone, Cretaceous, UK Continental Shelf). Example structures include asymmetric flame structures, convolute lamination, some debritic units and injection complexes, together with slurry and mixed slurry facies. These structures may provide insight into the rheology and dynamics of submarine flows and their substrates, and have implications for the development of subsurface turbidite reservoirs