The lattice of balanced equivalence relations of a coupled cell network

A coupled cell system is a collection of dynamical systems, or ‘cells’, that are coupled together. The associated coupled cell network is a labelled directed graph that indicates how the cells are coupled, and which cells are equivalent. Golubitsky, Stewart, Pivato and Török have presented a framework for coupled cell systems that permits a classification of robust synchrony in terms of the concept of a ‘balanced equivalence relation’, which depends solely on the network architecture. In their approach the network is assumed to be finite. We prove that the set of all balanced equivalence relations on a network forms a lattice, in the sense of a partially ordered set in which any two elements have a meet and a join. The partial order is defined by refinement. Some aspects of the theory make use of infinite networks, so we work in the category of networks of ‘finite type’, a class that includes all locally finite networks. This context requires some modifications to the standard framework. As partial compensation, the lattice of balanced equivalence relations can then be proved complete. However, the intersection of two balanced equivalence relations need not be balanced, as we show by a simple example, so this lattice is not a sublattice of the lattice of all equivalence relations with its usual operations of meet and join. We discuss the structure of this lattice and computational issues associated with it. In particular, we describe how to determine whether the lattice contains more than the equality relation. As an example, we derive the form of the lattice for a linear chain of identical cells with feedback

A contextual behavioral approach to the study of (persecutory) delusions

Throughout the past century the topic of delusions has mainly been studied by researchers operating at the mental level of analysis. According to this perspective, delusional beliefs, as well as their emergence and persistence, stem from an interplay between (dysfunctional) mental representations and processes. Our paper aims to provide a starting point for researchers and clinicians interested in examining the topic of delusions from a functional-analytic perspective. We begin with a brief review of the research literature with a particular focus on persecutory delusions. Thereafter we introduce Contextual Behavioral Science (CBS), Relational Frame Theory (RFT) and a behavioral phenomenon known as arbitrarily applicable relational responding (AARR). Drawing upon AARR, and recent empirical developments within CBS, we argue that (persecutory) delusions may be conceptualized, studied and influenced using a functional-analytic approach. We consider future directions for research in this area as well as clinical interventions aimed at influencing delusions and their expression

Making "fetch" happen: The influence of social and linguistic context on nonstandard word growth and decline

In an online community, new words come and go: today's "haha" may be replaced by tomorrow's "lol." Changes in online writing are usually studied as a social process, with innovations diffusing through a network of individuals in a speech community. But unlike other types of innovation, language change is shaped and constrained by the system in which it takes part. To investigate the links between social and structural factors in language change, we undertake a large-scale analysis of nonstandard word growth in the online community Reddit. We find that dissemination across many linguistic contexts is a sign of growth: words that appear in more linguistic contexts grow faster and survive longer. We also find that social dissemination likely plays a less important role in explaining word growth and decline than previously hypothesized

The classification of bifurcations with hidden symmetries

We set up a singularity-theoretic framework for classifying one-parameter steady-state bifurcations with hidden symmetries. This framework also permits a non-trivial linearization at the bifurcation point. Many problems can be reduced to this situation; for instance, the bifurcation of steady or periodic solutions to certain elliptic partial differential equations with Neumann or Dirichlet boundary conditions. We formulate an appropriate equivalence relation with its associated tangent spaces, so that the usual methods of singularity theory become applicable. We also present an alternative method for computing those matrix-valued germs that appear in the equivalence relations employed in the classification of equivariant bifurcation problems. This result is motivated by hidden symmetries appearing in a class of partial differential equations defined on an N-dimensional rectangle under Neumann boundary conditions

Some Reflections on the Expert Panel Report on Business Innovation in Canada

This article reviews the Council of Canadian Academies Expert Panel report on business innovation. It finds the report comprehensive in its gathering and assessment of available research, innovative, in its own right, in its analysis of innovation as an outcome of business strategy formation, and impressively well ordered and written. Both lay readers and professional students of innovation and labour productivity will find the report to be of great value.Review, innovation, productivity

Jet Vetoes Interfering with H->WW

Far off-shell Higgs production in $H \rightarrow WW,ZZ$, is a particularly powerful probe of Higgs properties, allowing one to disentangle Higgs width and coupling information unavailable in on-shell rate measurements. These measurements require an understanding of the cross section in the far off-shell region in the presence of realistic experimental cuts. We analytically study the effect of a $p_T$ jet veto on far off-shell cross sections, including signal-background interference, by utilizing hard functions in the soft collinear effective theory that are differential in the decay products of the $W/Z$. Summing large logarithms of $\sqrt{\hat s}/p_T^{veto}$, we find that the jet veto induces a strong dependence on the partonic centre of mass energy, $\sqrt{\hat s}$, and modifies distributions in $\sqrt{\hat s}$ or $M_T$. The example of $gg\rightarrow H \rightarrow WW$ is used to demonstrate these effects at next to leading log order. We also discuss the importance of jet vetoes and jet binning for the recent program to extract Higgs couplings and widths from far off-shell cross sections.Comment: 31 pages, 8 figures. v2: Journal Versio

Symmetry groupoids and admissible vector fields for coupled cell networks

The space of admissible vector fields, consistent with the structure of a network of coupled dynamical systems, can be specified in terms of the network's symmetry groupoid. The symmetry groupoid also determines the robust patterns of synchrony in the network – those that arise because of the network topology. In particular, synchronous cells can be identified in a canonical manner to yield a quotient network. Admissible vector fields on the original network induce admissible vector fields on the quotient, and any dynamical state of such an induced vector field can be lifted to the original network, yielding an analogous state in which certain sets of cells are synchronized. In the paper, necessary and sufficient conditions are specified for all admissible vector fields on the quotient to lift in this manner. These conditions are combinatorial in nature, and the proof uses invariant theory for the symmetric group. Also the symmetry groupoid of a quotient is related to that of the original network, and it is shown that there is a close analogy with the usual normalizer symmetry that arises in group-equivariant dynamics

The intraocular pressure response to dehydration: a pilot study

This study was designed to determine the Intraocular Pressure (IOP) response to differing levels of dehydration. Seven males participated in a 90 minute treadmill walk (5 km/h and 1 % grade) in both a cool (22 °C) and hot (43 °C) climate. At Baseline and at 30 minute intervals measurements of IOP, by tonometery, and indicators of hydration status (nude weight and plasma osmolality (Posm)) were taken. Body temperature and heart rate were also measured at these time points. Statistically significant interactions (time point (4) by trial (2)) were observed for IOP (F = 10.747, p = 0.009) and body weight loss (F = 50.083, p < 0.001) to decrease, and Posm (F = 34.867, p < 0.001) to increase, by a significantly greater amount during the hot trial compared to the cool. A univariate general linear model showed a significant relationship between IOP and body weight loss (F = 37.63, p < 0.001) and Posm (F = 38.53, p < 0.001). A significant interaction was observed for body temperature (F = 20.908, p < 0.001) and heart rate (F = 25.487, p < 0.001) between the trials and time points, but there was negligible association between these variables and IOP (Pearson correlation coefficient < ±0.5). The present study provides evidence to suggest that IOP is influenced by hydration status

Subleading Power Factorization with Radiative Functions

The study of amplitudes and cross sections in the soft and collinear limits allows for an understanding of their all orders behavior, and the identification of universal structures. At leading power soft emissions are eikonal, and described by Wilson lines. Beyond leading power the eikonal approximation breaks down, soft fermions must be added, and soft radiation resolves the nature of the energetic partons from which they were emitted. For both subleading power soft gluon and quark emissions, we use the soft collinear effective theory (SCET) to derive an all orders gauge invariant bare factorization, at both amplitude and cross section level. This yields universal multilocal matrix elements, which we refer to as radiative functions. These appear from subleading power Lagrangians inserted along the lightcone which dress the leading power Wilson lines. The use of SCET enables us to determine the complete set of radiative functions that appear to $\mathcal{O}(\lambda^2)$ in the power expansion, to all orders in $\alpha_s$. For the particular case of event shape observables in $e^+e^-\to$ dijets we derive how the radiative functions contribute to the factorized cross section to $\mathcal{O}(\lambda^2)$.Comment: 62 pages + appendices, many pretty and colorful figures. v2: journal versio