The men who weren't even there: Legislative voting with absentees

Voting power in voting situations is measured by the probability of changing decisions by altering the cast 'yes' or 'no' votes. Recently this analysis has been extended by strategic abstention. Abstention, just as 'yes' or 'no' votes can change decisions. This theory is often applied to weighted voting situations, where voters can cast multiple votes. Measuring the power of a party in a national assembly seems to fit this model, but in fact its power comprises of votes of individual representatives each having a single vote. These representatives may vote yes or no, or may abstain, but in some cases they are not even there to vote. We look at absentees not due to a conscious decision, but due to illness, for instance. Formally voters will be absent, say, ill, with a certain probability and only present otherwise. As in general not all voters will be present, a thin majority may quickly melt away making a coalition that is winning in theory a losing one in practice. A simple model allows us to differentiate between winning and more winning and losing and less losing coalitions reected by a voting game that is not any more simple. We use data from Scotland, Hungary and a number of other countries both to illustrate the relation of theoretical and effective power and show our results working in the practice.a priori voting power; power index; being absent from voting; minority; Shapley-Shubik index; Shapley value

Wave-number dependence of the transitions between traveling and standing vortex waves and their mixed states in the Taylor-Couette system

Previous numerical investigations of the stability and bifurcation properties of different nonlinear combination structures of spiral vortices in a counterrotating Taylor-Couette system that were done for fixed axial wavelengths are supplemented by exploring the dependence of the vortex phenomena waves on their wavelength. This yields information about the experimental and numerical accessability of the various bifurcation scenarios. Also backwards bifurcating standing waves with oscillating amplitudes of the constituent traveling waves are found.Comment: 4 pages, 5 figure

Bifurcation of standing waves into a pair of oppositely traveling waves with oscillating amplitudes caused by a three-mode interaction

A novel flow state consisting of two oppositely travelling waves (TWs) with oscillating amplitudes has been found in the counterrotating Taylor-Couette system by full numerical simulations. This structure bifurcates out of axially standing waves that are nonlinear superpositions of left and right handed spiral vortex waves with equal time-independent amplitudes. Beyond a critical driving the two spiral TW modes start to oscillate in counterphase due to a Hopf bifurcation. The trigger for this bifurcation is provided by a nonlinearly excited mode of different symmetry than the spiral TWs. A three-mode coupled amplitude equation model is presented that captures this bifurcation scenario. The mode-coupling between two symmetry degenerate critical modes and a nonlinearly excited one that is contained in the model can be expected to occur in other structure forming systems as well.Comment: 4 pages, 5 figure

The use of multilayer network analysis in animal behaviour

Network analysis has driven key developments in research on animal behaviour by providing quantitative methods to study the social structures of animal groups and populations. A recent formalism, known as \emph{multilayer network analysis}, has advanced the study of multifaceted networked systems in many disciplines. It offers novel ways to study and quantify animal behaviour as connected 'layers' of interactions. In this article, we review common questions in animal behaviour that can be studied using a multilayer approach, and we link these questions to specific analyses. We outline the types of behavioural data and questions that may be suitable to study using multilayer network analysis. We detail several multilayer methods, which can provide new insights into questions about animal sociality at individual, group, population, and evolutionary levels of organisation. We give examples for how to implement multilayer methods to demonstrate how taking a multilayer approach can alter inferences about social structure and the positions of individuals within such a structure. Finally, we discuss caveats to undertaking multilayer network analysis in the study of animal social networks, and we call attention to methodological challenges for the application of these approaches. Our aim is to instigate the study of new questions about animal sociality using the new toolbox of multilayer network analysis.Comment: Thoroughly revised; title changed slightl

Competition between Traveling Fluid Waves of Left and Right Spiral Vortices and Their Different Amplitude Combinations

Stability, bifurcation properties, and the spatiotemporal behavior of different nonlinear combination structures of spiral vortices in the counter rotating Taylor-Couette system are investigated by full numerical simulations and by coupled amplitude equation approximations. Stable cross-spiral structures with continuously varying content of left and right spiral modes are found. They provide a stability transferring connection between the initially stable, axially counter propagating wave states of pure spirals and the axially standing waves of so-called ribbons that become stable slightly further away from onset of vortex flow.Comment: 4 pages, 5 figure

Controlling the stability transfer between oppositely traveling waves and standing waves by inversion-symmetry-breaking perturbations

The effect of an externally applied flow on symmetry degenerated waves propagating into opposite directions and standing waves that exchange stability with the traveling waves via mixed states is analyzed. Wave structures that consist of spiral vortices in the counter rotating Taylor-Couette system are investigated by full numerical simulations and explained quantitatively by amplitude equations containing quintic coupling terms. The latter are appropriate to describe the influence of inversion symmetry breaking perturbations on many oscillatory instabilities with O(2) symmetry.Comment: 4 pages, 4 figure

Home Values and Firm Behavior

The homes of firm owners are an important source of finance for ongoing businesses. We use UK microdata to show that a £1 increase in the value of the homes of a firm's directors increases the firm's investment by £0.03. This effect is concentrated among firms whose directors' homes are valuable relative to the firm's assets, that are financially constrained, and that have directors who are personally highly levered. An aggregation exercise shows that directors' homes are as important as corporate property for collateral driven fluctuations in aggregate investment demand