The geometry of quantum learning

Concept learning provides a natural framework in which to place the problems solved by the quantum algorithms of Bernstein-Vazirani and Grover. By combining the tools used in these algorithms--quantum fast transforms and amplitude amplification--with a novel (in this context) tool--a solution method for geometrical optimization problems--we derive a general technique for quantum concept learning. We name this technique "Amplified Impatient Learning" and apply it to construct quantum algorithms solving two new problems: BATTLESHIP and MAJORITY, more efficiently than is possible classically.Comment: 20 pages, plain TeX with amssym.tex, related work at http://www.math.uga.edu/~hunziker/ and http://math.ucsd.edu/~dmeyer

Spontaneous Decisions and Free Will: Empirical Results and Philosophical Considerations

Spontaneous actions are preceded by brain signals that may sometimes be detected hundreds of milliseconds in advance of a subject's conscious intention to act. These signals have been claimed to reflect prior unconscious decisions, raising doubts about the causal role of conscious will. Murakami et al. (2014. Nat Neurosci 17: 1574–1582) have recently argued for a different interpretation. During a task in which rats spontaneously decided when to abort waiting, the authors recorded neurons in the secondary motor cortex. The neural activity and relationship to action timing was parsimoniously explained using an integration-to-bound model, similar to those widely used to account for evidence-based decisions. In this model, the brain accumulates spontaneously occurring inputs voting for or against an action, but only commits to act once a certain threshold is crossed. The model explains how spontaneous decisions can be forecast (partially predicted) by neurons that reflect either the input or output of the integrator. It therefore presents an explicit hypothesis capable of rejecting the claim that such predictive signals imply unconscious decisions. We suggest that these results can inform the current debate on free will but must be considered with caution

A Note on the Unitarity Property of the Gassner Invariant

We give a 3-page description of the Gassner invariant / representation of braids / pure braids, along with a description and a proof of its unitarity property.Comment: Mistake fixed in the accompanying Mathematica notebook (not the paper itself

Growth, Environment and Uncertain Future Preferences

The attitude of future generations towards environmental assets may well be different from ours, and it is necessary to take into account this possibility explicitly in the current debate about environmental policy. The question we are addressing here is: should uncertainty about future preferences lead to a more conservative attitude towards environment? Previous literature shows that it is the case when society expects that on average future preferences will be more in favor of environment than ours, but this result relies heavily on the assumption of a separability between consumption and environmental quality in the utility function. We show that things are less simple when preferences are non-separable: the attitude of the society now depends not only on the expectation of the change in preferences but also on the characteristics of the economy (impatience, intertemporal flexibility, natural capacities of regeneration of the environment, relative preference for the environment), on its history (initial level of the environmental quality) and on the date at which preferences are expected to change (near or far future).Growth ; Environment ; Preferences ; Uncertainty c ° 2002 Kluwer Academic Publishers. Printed in the Netherlands.

Energy dissipation of moved magnetic vortices

A two-dimensional easy-plane ferromagnetic substrate, interacting with a dipolar tip which is magnetised perpendicular with respect to the easy plane is studied numerically by solving the Landau-Lifshitz Gilbert equation. The dipolar tip stabilises a vortex structure which is dragged through the system and dissipates energy. An analytical expression for the friction force in the v$\rightarrow$0-limit based on the Thiele equation is presented. The limitations of this result which predicts a diverging friction force in the thermodynamic limit, are demonstrated by a study of the size dependence of the friction force. While for small system sizes the dissipation depends logarithmically on the system size, it saturates at a specific velocity dependent value. This size can be regarded as an effective vortex size and it is shown how this effective vortex size agrees with the infinite extension of a vortex in the thermodynamic limit. A magnetic friction number is defined which represents a general criterion for the validity of the Thiele equation and quantifies the degree of nonlinearity in the response of a driven spin configuration.Comment: 6 pages, 6 figure

Bargaining over Public Goods

In a simple public good economy, we propose a natural bar- gaining procedure, the equilibria of which converge to Lin- dahl allocations as the cost of bargaining vanishes. The pro- cedure splits the decision over the allocation in a decision about personalized prices and a decision about output levels for the public good. Since this procedure does not assume price-taking behavior, it provides a strategic foundation for the personalized taxes inherent in the Lindahl solution to the public goods problem.public goods; alternating offers bargaining