Arcs on Determinantal Varieties

We study arc spaces and jet schemes of generic determinantal varieties. Using the natural group action, we decompose the arc spaces into orbits, and analyze their structure. This allows us to compute the number of irreducible components of jet schemes, log canonical thresholds, and topological zeta functions.Comment: 27 pages. This is part of the author's PhD thesis at the University of Illinois at Chicago. v2: Minor changes. To appear in Transactions of the American Mathematical Societ

Epistemic modality, particles and the potential optative in Classical Greek

This paper challenges the commonly held view that the Classical Greek potential optative has a subjective epistemic semantics, the result of a conceptual confusion of subjectivity and epistemic modality inherited from our standard grammars. I propose that this view becomes less convincing when the optative’s unique interaction with the subjective particles ἦ and ἄρα is incorporated into the analysis. Rather, the potential optative has a non-subjective epistemic semantics presenting an epistemic judgment as interpersonally accessible to the conversational participants. Frequencies of combination with ἦ and ἄρα, linguistic tests for subjectivity on the potential optative, and contrastive contextual analyses corroborate this view

STRATEGIC AND SOCIAL PREPLAY COMMUNICATION IN THE ULTIMATUM GAME

Pre-play face-to-face communication is known to facilitate cooperation. Various explanations exist for this effect, varying in their dependence on the strategic content of the communication. Previous studies have found similar communication effects regardless of whether strategic communication is available. These results were so far taken to support a social-preferences based explanation of the communication effects. The current experiment provides a replication and extension of previous results to show that different processes come into play, depending on the communication protocol. Specically, pre-play communication in an ultimatum game was either restricted to nongame- related content or unrestricted. The results show that strategic, but not social, communication affects responders' strategies. Thus, the existing results are cast in a new light. I conclude that pre-play communication effects may be mediated by qualitatively dierent processes, depending on the social context.

Uniform Chernoff and Dvoretzky-Kiefer-Wolfowitz-type inequalities for Markov chains and related processes

We observe that the technique of Markov contraction can be used to establish measure concentration for a broad class of non-contracting chains. In particular, geometric ergodicity provides a simple and versatile framework. This leads to a short, elementary proof of a general concentration inequality for Markov and hidden Markov chains (HMM), which supercedes some of the known results and easily extends to other processes such as Markov trees. As applications, we give a Dvoretzky-Kiefer-Wolfowitz-type inequality and a uniform Chernoff bound. All of our bounds are dimension-free and hold for countably infinite state spaces