Complex valued Ray-Singer torsion

In the spirit of Ray and Singer we define a complex valued analytic torsion using non-selfadjoint Laplacians. We establish an anomaly formula which permits to turn this into a topological invariant. Conjecturally this analytically defined invariant computes the complex valued Reidemeister torsion, including its phase. We establish this conjecture in some non-trivial situations.Comment: Fixed two sign mistakes and added a few more details here and ther

Dilution Effects in Two-dimensional Quantum Orbital System

We study dilution effects in a Mott insulating state with quantum orbital degree of freedom, termed the two-dimensional orbital compass model. This is a quantum and two-dimensional version of the orbital model where the interactions along different bond directions cause frustration between different orbital configurations. A long-range correlation of a kind of orbital at each row or column, termed the directional order, is studied by means of the quantum Monte-Carlo method. It is shown that decrease of the ordering temperature due to dilution is much stronger than that in spin models. Quantum effect enhances the effective dimensionality in the system and makes the directional order robust against dilution. We discuss an essential mechanism of the dilute orbital systems.Comment: 5pages, 4 figure

Optimal control methods for simulating the perception of causality in young infants

There is a growing debate among developmental theorists concerning the perception of causality in young infants. Some theorists advocate a top-down view, e.g., that infants reason about causal events on the basis of intuitive physical principles. Others argue instead for a bottom-up view of infant causal knowledge, in which causal perception emerges from a simple set of associative learning rules. In order to test the limits of the bottom-up view, we propose an optimal control model (OCM) of infant causal perception. OCM is trained to find an optimal pattern of eye movements for maintaining sight of a target object. We first present a series of simulations which illustrate OCM's ability to anticipate the outcome of novel, occluded causal events, and then compare OCM's performance with that of 9-month-old infants. The impications for developmental theory and research are discusse

Divergence of opinion and risk : an empirical analysis of the Ex Ante beliefs of institutional investors

Bibliography: p. [24-25