Geometry and General Relativity in the Groupoid Model with a Finite Structure Group

In a series of papers we proposed a model unifying general relativity and quantum mechanics. The idea was to deduce both general relativity and quantum mechanics from a noncommutative algebra ${\cal A}_{\Gamma}$ defined on a transformation groupoid $\Gamma$ determined by the action of the Lorentz group on the frame bundle $(E, \pi_M, M)$ over space-time $M$. In the present work, we construct a simplified version of the gravitational sector of this model in which the Lorentz group is replaced by a finite group $G$ and the frame bundle is trivial $E=M\times G$. The model is fully computable. We define the Einstein-Hilbert action, with the help of which we derive the generalized vacuum Einstein equations. When the equations are projected to space-time (giving the "general relativistic limit"), the extra terms that appear due to our generalization can be interpreted as "matter terms", as in Kaluza-Klein-type models. To illustrate this effect we further simplify the metric matrix to a block diagonal form, compute for it the generalized Einstein equations and find two of their "Friedmann-like" solutions for the special case when $G =\mathbb{Z}_2$. One of them gives the flat Minkowski space-time (which, however, is not static), another, a hyperbolic, linearly expanding universe.Comment: 32 page

Application of serious games to sport, health and exercise

Use of interactive entertainment has been exponentially expanded since the last decade. Throughout this 10+ year evolution there has been a concern about turning entertainment properties into serious applications, a.k.a "Serious Games". In this article we present two set of Serious Game applications, an Environment Visualising game which focuses solely on applying serious games to elite Olympic sport and another set of serious games that incorporate an in house developed proprietary input system that can detect most of the human movements which focuses on applying serious games to health and exercise

Settlement Experienced at a Recently Licensed Nuclear Station

The settlement experienced at a recently licensed nuclear station demonstrated the need for coordination among geologists, geotechnical engineers and structural engineers to ensure that essential geological knowledge and experience is applied to the design and construction of the structures. The nuclear station had been under construction for a number of years when unexpected settlements were noticed which caused significant concrete cracking of the nuclear service water intake structure. The “seismic Category I” intake structure has an internal dimension of 12 feet wide by 15 feet high, a length of 167 feet with the thickness of walls and roof varied from 2 feet 6 inches to 3 feet. This paper describes the details of the problem including the original exploration and design, the extent of investigation following the discovery of the structural cracks, the evaluation of the causes of settlement and conclusions

Relativistic J-matrix method

The relativistic version of the J-matrix method for a scattering problem on the potential vanishing faster than the Coulomb one is formulated. As in the non-relativistic case it leads to a finite algebraic eigenvalue problem. The derived expression for the tangent of phase shift is simply related to the non-relativistic case formula and gives the latter as a limit case. It is due to the fact that the used basis set satisfies the ``kinetic balance condition''.Comment: 21 pages, RevTeX, accepted for publication in Phys. Rev.

The legal framework for private sector development in a transitional economy : the case of Poland

The economies of Central and Eastern Europe are in the midst of a historic transition from central planning and state ownership to development of a market-driven private sector. This transition requires comprehensive changes in"rules of the game"- including the legal framework for economic activity. A market economy presupposes a set of property rights and a system of laws or customs that allow the exchange of those rights. The legal framework in a market economy has at least three basic functions: defining the universe of property rights; setting the rules for entry into and exit from productive activities; and setting the rules of market exchange. These legal tasks are accomplished by areas of law such as: company, foreign investment, bankruptcy, contract and competition law. Poland has a rich legal tradition dating from pre-socialist times, which was suppressed but not eliminated during its forty years of socialism. This tradition is being revised as the country moves toward a private market economy. The current legal framework in Poland closely follows other continental jurisdictions and has a clear and reasonable internal logic. Many of the laws are old, but most are flexible enough to permit a wide range of modern, market-oriented activity. Property law, however, remains a"jungle". The wide discretion and general lack of precedent create tremendous legal uncertainty that is sure to hamper private sector development.Environmental Economics&Policies,Banks&Banking Reform,Municipal Housing and Land,Legal Products,Land and Real Estate Development

Algorithm for Linear Response Functions at Finite Temperatures: Application to ESR spectrum of s=1/2 Antiferromagnet Cu benzoate

We introduce an efficient and numerically stable method for calculating linear response functions $\chi(\vec{q},\omega)$ of quantum systems at finite temperatures. The method is a combination of numerical solution of the time-dependent Schroedinger equation, random vector representation of trace, and Chebyshev polynomial expansion of Boltzmann operator. This method should be very useful for a wide range of strongly correlated quantum systems at finite temperatures. We present an application to the ESR spectrum of s=1/2 antiferromagnet Cu benzoate.Comment: 4 pages, 4 figure

Representational capacity of a set of independent neurons

The capacity with which a system of independent neuron-like units represents a given set of stimuli is studied by calculating the mutual information between the stimuli and the neural responses. Both discrete noiseless and continuous noisy neurons are analyzed. In both cases, the information grows monotonically with the number of neurons considered. Under the assumption that neurons are independent, the mutual information rises linearly from zero, and approaches exponentially its maximum value. We find the dependence of the initial slope on the number of stimuli and on the sparseness of the representation.Comment: 19 pages, 6 figures, Phys. Rev. E, vol 63, 11910 - 11924 (2000

Antiferromagnetic Order in MnO Spherical Nanoparticles

We have performed unpolarized and polarized neutron diffraction experiments on monodisperse 8 nm and 13 nm antiferromagnetic MnO nanoparticles. For the 8 nm sample, the antiferromagnetic transition temperature $T_N$ (114 K) is suppressed compared to the bulk material (119 K) while for the 13 nm sample $T_N$ (120 K) is comparable to the bulk. The neutron diffraction data of the nanoparticles is well described using the bulk MnO magnetic structure but with a substantially reduced average magnetic moment of 4.2$\pm$0.3 $\mu_B$/Mn for the 8 nm sample and 3.9$\pm$0.2 $\mu_B$/Mn for the 13 nm sample. An analysis of the polarized neutron data on both samples shows that in an individual MnO nanoparticle about 80$$ of Mn ions order. These results can be explained by a structure in which the monodisperse nanoparticles studied here have a core that behaves similar to the bulk with a surface layer which does not contribute significantly to the magnetic order.Comment: 7 pages, 5 figure