On the Wiener disorder problem

In the Wiener disorder problem, the drift of a Wiener process changes suddenly at some unknown and unobservable disorder time. The objective is to detect this change as quickly as possible after it happens. Earlier work on the Bayesian formulation of this problem brings optimal (or asymptotically optimal) detection rules assuming that the prior distribution of the change time is given at time zero, and additional information is received by observing the Wiener process only. Here, we consider a different information structure where possible causes of this disorder are observed. More precisely, we assume that we also observe an arrival/counting process representing external shocks. The disorder happens because of these shocks, and the change time coincides with one of the arrival times. Such a formulation arises, for example, from detecting a change in financial data caused by major financial events, or detecting damages in structures caused by earthquakes. In this paper, we formulate the problem in a Bayesian framework assuming that those observable shocks form a Poisson process. We present an optimal detection rule that minimizes a linear Bayes risk, which includes the expected detection delay and the probability of early false alarms. We also give the solution of the ``variational formulation'' where the objective is to minimize the detection delay over all stopping rules for which the false alarm probability does not exceed a given constant.Comment: Published in at http://dx.doi.org/10.1214/09-AAP655 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Bridges in social capital: A review of the definitions and the social capital of social capital researchers

There has been a recent surge of interest in social economics and social capital. Articles on social capital that are published in the last five years constitute more than 60 percent of all articles on social capital. Research on social capital is now massive and spans sociology, economics, management, political science and health sciences. Despite this interest there is still not a consensus on the definition and the measurement of social capital. This paper argues that this is due to lack of interaction between disciplines. The social capital of social capital researchers is low between disciplines. Different from other theories of capital, social capital theory has concurrently been developed by various disciplines and as such, advancements in social capital research could only be achieved by conducting cross-disciplinary research.Capital, social capital, co-authorship network, network analysis, diffusion processes

Quantum Jump from Singularity to Outside of Black Hole

Considering the role of black hole singularity in quantum evolution, a resolution to the firewall paradox is presented. It is emphasized that if an observer has the singularity as a part of his spacetime, then the semi-classical evolution would be non-unitary as viewed by him. Specifically, a free-falling observer inside the black hole would have a Hilbert space with non-unitary evolution; a quantum jump for particles encountering the singularity to outside of the horizon as late Hawking radiations. The non-unitariness in the jump resembles the one in collapse of wave function, but preserves entanglements. Accordingly, we elaborate the first postulate of black hole complementarity: freely falling observers who pass through the event horizon would have non-unitary evolution, while it does not have physically measurable effects for them. Besides, no information would be lost in the singularity. Taking the modified picture into account, the firewall paradox can be resolved, respecting No Drama. A by-product of our modification is that roughly half of the entropy of the black hole is released close to the end of evaporation in the shape of very hot Hawking radiation.Comment: 7 figures, v2 more comprehensive, v3 matches the published versio