Distributed Formal Concept Analysis Algorithms Based on an Iterative MapReduce Framework

While many existing formal concept analysis algorithms are efficient, they are typically unsuitable for distributed implementation. Taking the MapReduce (MR) framework as our inspiration we introduce a distributed approach for performing formal concept mining. Our method has its novelty in that we use a light-weight MapReduce runtime called Twister which is better suited to iterative algorithms than recent distributed approaches. First, we describe the theoretical foundations underpinning our distributed formal concept analysis approach. Second, we provide a representative exemplar of how a classic centralized algorithm can be implemented in a distributed fashion using our methodology: we modify Ganter's classic algorithm by introducing a family of MR* algorithms, namely MRGanter and MRGanter+ where the prefix denotes the algorithm's lineage. To evaluate the factors that impact distributed algorithm performance, we compare our MR* algorithms with the state-of-the-art. Experiments conducted on real datasets demonstrate that MRGanter+ is efficient, scalable and an appealing algorithm for distributed problems.Comment: 17 pages, ICFCA 201, Formal Concept Analysis 201

On Fields with Finite Information Density

The existence of a natural ultraviolet cutoff at the Planck scale is widely expected. In a previous Letter, it has been proposed to model this cutoff as an information density bound by utilizing suitably generalized methods from the mathematical theory of communication. Here, we prove the mathematical conjectures that were made in this Letter.Comment: 31 pages, to appear in Phys.Rev.

Adiabatic following criterion, estimation of the nonadiabatic excitation fraction and quantum jumps

An accurate theory describing adiabatic following of the dark, nonabsorbing state in the three-level system is developed. An analytical solution for the wave function of the particle experiencing Raman excitation is found as an expansion in terms of the time varying nonadiabatic perturbation parameter. The solution can be presented as a sum of adiabatic and nonadiabatic parts. Both are estimated quantitatively. It is shown that the limiting value to which the amplitude of the nonadiabatic part tends is equal to the Fourier component of the nonadiabatic perturbation parameter taken at the Rabi frequency of the Raman excitation. The time scale of the variation of both parts is found. While the adiabatic part of the solution varies slowly and follows the change of the nonadiabatic perturbation parameter, the nonadiabatic part appears almost instantly, revealing a jumpwise transition between the dark and bright states. This jump happens when the nonadiabatic perturbation parameter takes its maximum value.Comment: 33 pages, 8 figures, submitted to PRA on 28 Oct. 200

Level Spacing Distribution of Critical Random Matrix Ensembles

We consider unitary invariant random matrix ensembles which obey spectral statistics different from the Wigner-Dyson, including unitary ensembles with slowly (~(log x)^2) growing potentials and the finite-temperature fermi gas model. If the deformation parameters in these matrix ensembles are small, the asymptotically translational-invariant region in the spectral bulk is universally governed by a one-parameter generalization of the sine kernel. We provide an analytic expression for the distribution of the eigenvalue spacings of this universal asymptotic kernel, which is a hybrid of the Wigner-Dyson and the Poisson distributions, by determining the Fredholm determinant of the universal kernel in terms of a Painleve VI transcendental function.Comment: 5 pages, 1 figure, REVTeX; restriction on the parameter stressed, figure replaced, refs added (v2); typos (factors of pi) in (35), (36) corrected (v3); minor changes incl. title, version to appear in Phys.Rev.E (v4

Semiclassical Theory of Coulomb Blockade Peak Heights in Chaotic Quantum Dots

We develop a semiclassical theory of Coulomb blockade peak heights in chaotic quantum dots. Using Berry's conjecture, we calculate the peak height distributions and the correlation functions. We demonstrate that the corrections to the corresponding results of the standard statistical theory are non-universal and can be expressed in terms of the classical periodic orbits of the dot that are well coupled to the leads. The main effect is an oscillatory dependence of the peak heights on any parameter which is varied; it is substantial for both symmetric and asymmetric lead placement. Surprisingly, these dynamical effects do not influence the full distribution of peak heights, but are clearly seen in the correlation function or power spectrum. For non-zero temperature, the correlation function obtained theoretically is in good agreement with that measured experimentally.Comment: 5 color eps figure

Chaos Driven Decay of Nuclear Giant Resonances: Route to Quantum Self-Organization

The influence of background states with increasing level of complexity on the strength distribution of the isoscalar and isovector giant quadrupole resonance in $^{40}$Ca is studied. It is found that the background characteristics, typical for chaotic systems, strongly affects the fluctuation properties of the strength distribution. In particular, the small components of the wave function obey a scaling law analogous to self-organized systems at the critical state. This appears to be consistent with the Porter-Thomas distribution of the transition strength.Comment: 14 pages, 4 Figures, Illinois preprint P-93-12-106, Figures available from the author

Coherently Scattering Atoms from an Excited Bose-Einstein Condensate

We consider scattering atoms from a fully Bose-Einstein condensed gas. If we take these atoms to be identical to those in the Bose-Einstein condensate, this scattering process is to a large extent analogous to Andreev reflection from the interface between a superconducting and a normal metal. We determine the scattering wave function both in the absence and the presence of a vortex. Our results show a qualitative difference between these two cases that can be understood as due to an Aharonov-Bohm effect. It leads to the possibility to experimentally detect and study vortices in this way.Comment: 5 pages of ReVTeX and 2 postscript figure

In search of green political economy: steering markets, innovation and the case of the zero carbon homes agenda in England

Advocates of a democratic ‘Green state’ challenge Hayekian free-market environmentalist proposals for a minimal state and the emphasis of ecological modernisation discourses on technological innovation as the primary route towards ecological sustainability. However, these more strongly pro-market traditions raise important questions and provide useful insights concerning the challenges of translating the political ideology of ‘ecologism’ into practical proposals for democratic governance. Hayekian thought raises vital questions concerning the capacity of political processes to address complex challenges of coordinating the formulation and delivery of the sustainability objectives of ecologism. Scholarship on ecological modernisation and the ‘new regulation’ offer important insights into how shifting interrelationships between the state and private sector in the policy process might enable this challenge to be more effectively addressed. These areas for further developing proposals for a Green state are illustrated here through a case study of the zero carbon homes policy agenda in England

Testing spatial noncommutativiy via the Aharonov-Bohm effect

The possibility of detecting noncommutative space relics is analyzed using the Aharonov-Bohm effect. We show that, if space is noncommutative, the holonomy receives non-trivial kinematical corrections that will produce a diffraction pattern even when the magnetic flux is quantized. The scattering problem is also formulated, and the differential cross section is calculated. Our results can be extrapolated to high energy physics and the bound $\theta \sim [ 10 {TeV}]^{-2}$ is found. If this bound holds, then noncommutative effects could be explored in scattering experiments measuring differential cross sections for small angles. The bound state Aharonov- Bohm effect is also discussed.Comment: 16 pp, Revtex 4, 2 fig, new references added. To appear in PR