Topological representation zeta functions of unipotent groups

Inspired by work surrounding Igusa's local zeta function, we introduce topological representation zeta functions of unipotent algebraic groups over number fields. These group-theoretic invariants capture common features of established $p$-adic representation zeta functions associated with pro-$p$ groups derived from unipotent groups. We investigate fundamental properties of the topological zeta functions considered here. We also develop a method for computing them under non-degeneracy assumptions. As an application, among other things, we obtain a complete classification of topological representation zeta functions of unipotent algebraic groups of dimension at most six.Comment: 27 page

Computing topological zeta functions of groups, algebras, and modules, II

Building on our previous work (arXiv:1405.5711), we develop the first practical algorithm for computing topological zeta functions of nilpotent groups, non-associative algebras, and modules. While we previously depended upon non-degeneracy assumptions, the theory developed here allows us to overcome these restrictions in various interesting cases.Comment: 33 pages; sequel to arXiv:1405.571

The problem of causality in cultivation research

This paper offers an up-to-date review of problems in determining causal relationships in cultivation research, and considers the research rationales of various approaches with special reference to causal interpretation. It describes in turn a number of methodologies for addressing the problem and resolving it as far as this is possible. The issue of causal inference arises not only in cultivation research, however, but is basic to all media effects theories and approaches primarily at the macro-level whose main methodology rests on correlational studies (agenda-setting, spiral of silence, knowledge gap hypothesis, etc.). We therefore first discuss problems of causal interpretation in connection with the cultivation hypothesis, and then sketch in summary how these problems arise with other media effects theories. We first set out the basic features of the cultivation approach, then consider the difficulties with correlational studies and discuss alternative research designs - designs which are not original to us, but have been adapted for cultivation research. These comprise laboratory experiments, sequential studies, social studies and time-series procedures. Finally, we argue for multiple approaches that complement one another's advantages and balance out their disadvantages