Rough Set-Based Information Dilution by Non-deterministic Information

We have investigated rough set-based concepts for a given Non-deterministic Information System (NIS). In this paper, we consider generating a NIS from a Deterministic Information System (DIS) intentionally. A NIS Φ is seen as a diluted DIS ϕ, and we can hide the actual values in ϕ by using Φ. We name this way of hiding Information Dilution by non-deterministic information. This paper considers information dilution and its application to hiding the actual values in a table.14th International Workshop on Rough Sets, Fuzzy Sets, Data Mining, and Granular-Soft Computing, RSFDGrC 2013, October 11-14, 2013, Halifax, NS, Canad

Rigidity percolation on aperiodic lattices

We studied the rigidity percolation (RP) model for aperiodic (quasi-crystal) lattices. The RP thresholds (for bond dilution) were obtained for several aperiodic lattices via computer simulation using the "pebble game" algorithm. It was found that the (two rhombi) Penrose lattice is always floppy in view of the RP model. The same was found for the Ammann's octagonal tiling and the Socolar's dodecagonal tiling. In order to impose the percolation transition we used so c. "ferro" modification of these aperiodic tilings. We studied as well the "pinwheel" tiling which has "infinitely-fold" orientational symmetry. The obtained estimates for the modified Penrose, Ammann and Socolar lattices are respectively: $p_{cP} =0.836\pm 0.002$, $p_{cA} = 0.769\pm0.002$, $p_{cS} = 0.938\pm0.001$. The bond RP threshold of the pinwheel tiling was estimated to $p_c = 0.69\pm0.01$. It was found that these results are very close to the Maxwell (the mean-field like) approximation for them.Comment: 9 LaTeX pages, 3 PostScript figures included via epsf.st

Dynamics of curved interfaces

Stochastic growth phenomena on curved interfaces are studied by means of stochastic partial differential equations. These are derived as counterparts of linear planar equations on a curved geometry after a reparametrization invariance principle has been applied. We examine differences and similarities with the classical planar equations. Some characteristic features are the loss of correlation through time and a particular behaviour of the average fluctuations. Dependence on the metric is also explored. The diffusive model that propagates correlations ballistically in the planar situation is particularly interesting, as this propagation becomes nonuniversal in the new regime.Comment: Published versio

Mathematical Models for Estimating the Risk of vCJD Transmission

We present two different simple models for vCJD transmission by blood transfusion. Both models indicate that transfusions alone are unlikely to cause more than a few infections, unless the number of primary cases increases. To improve our models, future work should pursue data collection, empirical estimation of the model parameters, and examination of the underlying assumptions of our frameworks. Further improvements could also include examining susceptibility to vCJD infection by age group and iatrogenic infections introduced through surgical instruments. Regarding the latter, it may be worthwhile to conduct experiments to quantify the transmission of prions from an infected surgical instrument after repeated sterilization procedures

Size effects in statistical fracture

We review statistical theories and numerical methods employed to consider the sample size dependence of the failure strength distribution of disordered materials. We first overview the analytical predictions of extreme value statistics and fiber bundle models and discuss their limitations. Next, we review energetic and geometric approaches to fracture size effects for specimens with a flaw. Finally, we overview the numerical simulations of lattice models and compare with theoretical models.Comment: review article 19 pages, 5 figure

Asymptotics of Fingerprinting and Group Testing: Capacity-Achieving Log-Likelihood Decoders

We study the large-coalition asymptotics of fingerprinting and group testing, and derive explicit decoders that provably achieve capacity for many of the considered models. We do this both for simple decoders (fast but suboptimal) and for joint decoders (slow but optimal), and both for informed and uninformed settings. For fingerprinting, we show that if the pirate strategy is known, the Neyman-Pearson-based log-likelihood decoders provably achieve capacity, regardless of the strategy. The decoder built against the interleaving attack is further shown to be a universal decoder, able to deal with arbitrary attacks and achieving the uninformed capacity. This universal decoder is shown to be closely related to the Lagrange-optimized decoder of Oosterwijk et al. and the empirical mutual information decoder of Moulin. Joint decoders are also proposed, and we conjecture that these also achieve the corresponding joint capacities. For group testing, the simple decoder for the classical model is shown to be more efficient than the one of Chan et al. and it provably achieves the simple group testing capacity. For generalizations of this model such as noisy group testing, the resulting simple decoders also achieve the corresponding simple capacities.Comment: 14 pages, 2 figure

Quick and energy-efficient Bayesian computing of binocular disparity using stochastic digital signals

Reconstruction of the tridimensional geometry of a visual scene using the binocular disparity information is an important issue in computer vision and mobile robotics, which can be formulated as a Bayesian inference problem. However, computation of the full disparity distribution with an advanced Bayesian model is usually an intractable problem, and proves computationally challenging even with a simple model. In this paper, we show how probabilistic hardware using distributed memory and alternate representation of data as stochastic bitstreams can solve that problem with high performance and energy efficiency. We put forward a way to express discrete probability distributions using stochastic data representations and perform Bayesian fusion using those representations, and show how that approach can be applied to diparity computation. We evaluate the system using a simulated stochastic implementation and discuss possible hardware implementations of such architectures and their potential for sensorimotor processing and robotics.Comment: Preprint of article submitted for publication in International Journal of Approximate Reasoning and accepted pending minor revision