On the distribution of class groups of number fields

We propose a modification of the predictions of the Cohen--Lenstra heuristic for class groups of number fields in the case where roots of unity are present in the base field. As evidence for this modified formula we provide a large set of computational data which show close agreement.Comment: 14 pages. To appear in Experimental Mat

Attributions as Behavior Explanations: Toward a New Theory

Attribution theory has played a major role in social-psychological research. Unfortunately, the term attribution is ambiguous. According to one meaning, forming an attribution is making a dispositional (trait) inference from behavior; according to another meaning, forming an attribution is giving an explanation (especially of behavior). The focus of this paper is on the latter phenomenon of behavior explanations. In particular, I discuss a new theory of explanation that provides an alternative to classic attribution theory as it dominates the textbooks and handbooks—which is typically as a version of Kelley’s (1967) model of attribution as covariation detection. I begin with a brief critique of this theory and, out of this critique, develop a list of requirements that an improved theory has to meet. I then introduce the new theory, report empirical data in its support, and apply it to a number of psychological phenomena. I finally conclude with an assessment of how much progress we have made in understanding behavior explanations and what has yet to be learned

The Simple Ree groups 2F4(q2){}^2F_4(q^2) are determined by the set of their character degrees

Let $G$ be a finite group. Let ${\rm{cd}}(G)$ be the set of all complex irreducible character degrees of $G.$ In this paper, we will show that if ${\rm{cd}}(G)={\rm{cd}}(H),$ where $H$ is the simple Ree group ${}^2F_4(q^2),q^2\geq 8,$ then $G\cong H\times A,$ where $A$ is an abelian group. This verifies Huppert's Conjecture for the simple Ree groups ${}^2F_4(q^2)$ when $q^2\geq 8.$Comment: 14 pages, to appear in Journal of Algebr

Folk Theory of Mind: Conceptual Foundations of Social Cognition

The human ability to represent, conceptualize, and reason about mind and behavior is one of the greatest achievements of human evolution and is made possible by a “folk theory of mind” — a sophisticated conceptual framework that relates different mental states to each other and connects them to behavior. This chapter examines the nature and elements of this framework and its central functions for social cognition. As a conceptual framework, the folk theory of mind operates prior to any particular conscious or unconscious cognition and provides the “framing” or interpretation of that cognition. Central to this framing is the concept of intentionality, which distinguishes intentional action (caused by the agent’s intention and decision) from unintentional behavior (caused by internal or external events without the intervention of the agent’s decision). A second important distinction separates publicly observable from publicly unobservable (i.e., mental) events. Together, the two distinctions define the kinds of events in social interaction that people attend to, wonder about, and try to explain. A special focus of this chapter is the powerful tool of behavior explanation, which relies on the folk theory of mind but is also intimately tied to social demands and to the perceiver’s social goals. A full understanding of social cognition must consider the folk theory of mind as the conceptual underpinning of all (conscious and unconscious) perception and thinking about the social world

The relation between language and theory of mind in development and evolution

Considering the close relation between language and theory of mind in development and their tight connection in social behavior, it is no big leap to claim that the two capacities have been related in evolution as well. But what is the exact relation between them? This paper attempts to clear a path toward an answer. I consider several possible relations between the two faculties, bring conceptual arguments and empirical evidence to bear on them, and end up arguing for a version of co-evolution. To model this co-evolution, we must distinguish between different stages or levels of language and theory of mind, which fueled each other’s evolution in a protracted escalation process

Symmetric groups are determined by their character degrees

Let $G$ be a finite group. Let $X_1(G)$ be the first column of the ordinary character table of $G.$ In this paper, we will show that if $X_1(G)=X_1(S_n),$ then $G\cong S_n.$ As a consequence, we show that $S_n$ is uniquely determined by the structure of the complex group algebra \C S_n.Comment: 12 pages, to appear in Journal of Algebr