Zeros of Ramanujan polynomials

Abstract. In this paper, we investigate the properties of Ramanujan polynomials, a family of reciprocal polynomials with real coefficients originating from Ramanujan’s work. We begin by finding their number of real zeros, establishing a bound on their sizes, and determining their limiting values. Next, we prove that all nonreal zeros of Ramanujan polynomials lie on the unit circle, and are asymptotically uniformly distributed there. Finally, for each Ramunujan polynomial, we find all its zeros that are roots of unity. 1

Hierarchical Models for Relational Event Sequences

Interaction within small groups can often be represented as a sequence of events, where each event involves a sender and a recipient. Recent methods for modeling network data in continuous time model the rate at which individuals interact conditioned on the previous history of events as well as actor covariates. We present a hierarchical extension for modeling multiple such sequences, facilitating inferences about event-level dynamics and their variation across sequences. The hierarchical approach allows one to share information across sequences in a principled manner---we illustrate the efficacy of such sharing through a set of prediction experiments. After discussing methods for adequacy checking and model selection for this class of models, the method is illustrated with an analysis of high school classroom dynamics

Social investment after neoliberalism : policy paradigms and political platforms

The concept of the ‘social investment state’ refocuses attention on the productive function of social policy eclipsed for some time by the emphasis on its social protection or compensation roles. Here we distinguish between different social investment strategies, the Nordic ‘heavy’ and the Liberal ‘light’, with particular reference to the inclusive growth approach adopted in Australia. In 2007, social democrats in Australia returned to government with a clear mandate to reject the labour market deregulation and other neoliberal policies of its predecessor, and to tackle entrenched social and economic disadvantage in Australian society. For the last five years, social investment and inclusive growth has been at the centre of the Australian social policy agenda. Against this background, the article examines and critically assesses the (re)turn to ‘social investment’ thinking in Australia during Labor’s term in office (2007–13). Analysis focuses not just on what was actually achieved, but also on the constraining role of prevailing economic and political circumstances and on the processes that were used to drive social investment reform. Inmany ways, the article goes some way to exposing ongoing tensions surrounding the distinctiveness of ‘social investment’ strategies pursued by leftist parties within the (neo)liberal state