Quantum gambling using mesoscopic ring qubits

Quantum Game Theory provides us with new tools for practising games and some other risk related enterprices like, for example, gambling. The two party gambling protocol presented by Goldenberg {\it et al} is one of the simplest yet still hard to implement applications of Quantum Game Theory. We propose potential physical realisation of the quantum gambling protocol with use of three mesoscopic ring qubits. We point out problems in implementation of such game.Comment: 4 pages, 1 figure, poster during XXX Intern. Conf. of Theoretical Physics, Electron correlations in nano- and microsystems, Ustron 9-14 September 2006. Minor corrections, references added; to appear in physica status solidi

Giffen paradoxes in quantum market games

Recent development in quantum computation and quantum information theory allows to extend the scope of game theory for the quantum world. The paper presents the history and basic ideas of quantum game theory. Description of Giffen paradoxes in this new formalism is discussed.Comment: 12 pages (2 figs), LaTe

Quantum extension of European option pricing based on the Ornstein-Uhlenbeck process

In this work we propose a option pricing model based on the Ornstein-Uhlenbeck process. It is a new look at the Black-Scholes formula which is based on the quantum game theory. We show the differences between a classical look which is price changing by a Wiener process and the pricing is supported by a quantum model

Constraints on the optical precursor to the naked-eye burst GRB080319B from Pi of the Sky observations

I present the results of the search for an optical precursor to the naked-eye burst - GRB080319B, which reached 5.87m optical peak luminosity in the "Pi of the Sky" data. A burst of such a high brightness could have been preceded by an optical precursor luminous enough to be in detection range of our experiment. The "Pi of the Sky" cameras observed the coordinates of the GRB for about 20 minutes prior to the explosion, thus provided crucial data for the precursor search. No signal within 3 sigma limit was found. A limit of 12m (V-band equivalent) was set based on the data combined from two cameras, the most robust limit to my knowledge for this precursor.Comment: Accepted for publication in Astronomy and Astrophysics on 07 February 201

Geometry of Financial Markets -- Towards Information Theory Model of Markets

Most of parameters used to describe states and dynamics of financial market depend on proportions of the appropriate variables rather than on their actual values. Therefore, projective geometry seems to be the correct language to describe the theater of financial activities. We suppose that the object of interest of agents, called here baskets, form a vector space over the reals. A portfolio is defined as an equivalence class of baskets containing assets in the same proportions. Therefore portfolios form a projective space. Cross ratios, being invariants of projective maps, form key structures in the proposed model. Quotation with respect to an asset X (i.e. in units of X) are given by linear maps. Among various types of metrics that have financial interpretation, the min-max metrics on the space of quotations can be introduced. This metrics has an interesting interpretation in terms of rates of return. It can be generalized so that to incorporate a new numerical parameter (called temperature) that describes agent's lack of knowledge about the state of the market. In a dual way, a metrics on the space of market quotation is defined. In addition, one can define an interesting metric structure on the space of portfolios/quotation that is invariant with respect to hyperbolic (Lorentz) symmetries of the space of portfolios. The introduced formalism opens new interesting and possibly fruitful fields of research.Comment: Talk given at the APFA5 Conference, Torino, 200

Localization of Brain Activity from EEG/MEG Using MV-PURE Framework

We consider the problem of localization of sources of brain electrical activity from electroencephalographic (EEG) and magnetoencephalographic (MEG) measurements using spatial filtering techniques. We propose novel reduced-rank activity indices based on the minimum-variance pseudo-unbiased reduced-rank estimation (MV-PURE) framework. The main results of this paper establish the key unbiasedness property of the proposed indices and their higher spatial resolution compared with full-rank indices in challenging task of localizing closely positioned and possibly highly correlated sources, especially in low signal-to-noise regime. A numerical example is provided to illustrate the practical applicability of the proposed activity indices. Simulations presented in this paper use open-source EEG/MEG spatial filtering framework freely available at https://github.com/IS-UMK/supFunSim.git.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl