Quantum Forbidden-Interval Theorems for Stochastic Resonance

We extend the classical forbidden-interval theorems for a stochastic-resonance noise benefit in a nonlinear system to a quantum-optical communication model and a continuous-variable quantum key distribution model. Each quantum forbidden-interval theorem gives a necessary and sufficient condition that determines whether stochastic resonance occurs in quantum communication of classical messages. The quantum theorems apply to any quantum noise source that has finite variance or that comes from the family of infinite-variance alpha-stable probability densities. Simulations show the noise benefits for the basic quantum communication model and the continuous-variable quantum key distribution model.Comment: 13 pages, 2 figure

Generalized additive and fuzzy models in environmental flow assessment: A comparison employing the West Balkan trout (Salmo farioides; Karaman, 1938)

Human activities have altered flow regimes resulting in increased pressures and threats on river biota. Physical habitat simulation has been established as a standard approach among the methods for Environmental Flow Assessment (EFA). Traditionally, in EFA, univariate habitat suitability curves have been used to evaluate the habitat suitability at the microhabitat scale whereas Generalized Additive Models (GAMs) and fuzzy logic are considered the most common multivariate approaches to do so. The assessment of the habitat suitability for three size classes of the West Balkan trout (Salmo farioides; Karaman, 1938) inferred with these multivariate approaches was compared at three different levels. First the modelled patterns of habitat selection were compared by developing partial dependence plots. Then, the habitat assessment was spatially explicitly compared by calculating the fuzzy kappa statistic and finally, the habitat quantity and quality was compared broadly and at relevant flows under a hypothetical flow regulation, based on the Weighted Usable Area (WUA) vs. flow curves. The GAMs were slightly more accurate and the WUA-flow curves demonstrated that they were more optimistic in the habitat assessment with larger areas assessed with low to intermediate suitability (0.2 0.6). Nevertheless, both approaches coincided in the habitat assessment (the optimal areas were spatially coincident) and in the modelled patterns of habitat selection; large trout selected microhabitats with low flow velocity, large depth, coarse substrate and abundant cover. Medium sized trout selected microhabitats with low flow velocity, middle-to-large depth, any kind of substrate but bedrock and some elements of cover. Finally small trout selected microhabitats with low flow velocity, small depth, and light cover only avoiding bedrock substrate. Furthermore, both approaches also rendered similar WUA-flow curves and coincided in the predicted increases and decreases of the WUA under the hypothetical flow regulation. Although on an equal footing, GAMs performed slightly better, they do not automatically account for variables interactions. Conversely, fuzzy models do so and can be easily modified by experts to include new insights or to cover a wider range of environmental conditions. Therefore, as a consequence of the agreement between both approaches, we would advocate for combinations of GAMs and fuzzy models in fish-based EFA.This study was supported by the ECOFLOW project funded by the Hellenic General Secretariat of Research and Technology in the framework of the NSRF 2007-2013. We are grateful for field assistance of Dimitris Kommatas, Orfeas Triantafillou and Martin Palt and to Alcibiades N. Economou for assistance in discussions on trout biology and ecology.Muñoz Mas, R.; Papadaki, C.; Martinez-Capel, F.; Zogaris, S.; Ntoanidis, L.; Dimitriou, E. (2016). Generalized additive and fuzzy models in environmental flow assessment: A comparison employing the West Balkan trout (Salmo farioides; Karaman, 1938). Ecological Engineering. 91:365-377. doi:10.1016/j.ecoleng.2016.03.009S3653779

Noise benefits in the array of brain-computer interface classification systems

This paper shows that noise can improve the accuracy of brain-computer interface (BCI) systems. Additive Gaussian noise can benefit arrays of ensemble support vector machines (ESVMs) that classify P300 or motor imagery (MI) activities in electroencephalogram (EEG) signals. We show these noise benefits in 64-channel EEG signals from the BCI Competitions II dataset IIb and BCI Competitions III dataset II for the P300 speller paradigm and in 3-channel EEG signals from the BCI Competitions II dataset III and BCI Competitions III dataset IIIa for MI classification systems. We also show that noise can improve the accuracy of EEG classifications based on restricted channel positions in commercial recording systems, such as the 14-channel Emotiv Epoc headset. The experimental results show that noise can provide classifiers with higher accuracy and can reduce the data collection time for P300 classification. The results also show that training ESVMs with a concatenated original dataset and noise-added datasets can improve MI classification. Noise can improve the accuracy of P300 classification for both intra-subject and inter-subject classification systems for multiple users. Addition of noise can significantly affect the parameters of polynomial kernel functions and the number of support vectors of the SVM. This leads to an expansion of the margin between two parallel hyperplanes that eventually improve the classification accuracy. Particle swarm optimization (PSO) can be used to search for the optimal noise intensity. Keywords: P300, Motor imagery, Stochastic resonance, Array systems, Ensemble support vector machine, Particle swarm optimizatio

The Shape of Fuzzy Sets in Adaptive Function Approximation

The shape of if-part fuzzy sets affects how well feedforward fuzzy systems approximate continuous functions. We explore a wide range of candidate if-part sets and derive supervised learning laws that tune them. Then we test how well the resulting adaptive fuzzy systems approximate a battery of test functions. No one set shape emerges as the best shape. The sinc function often does well and has a tractable learning law. But its undulating sidelobes may have no linguistic meaning. This suggests that the engineering goal of function-approximation accuracy may sometimes have to outweigh the linguistic or philosophical interpretations of fuzzy sets that have accompanied their use in expert systems. We divide the if-part sets into two large classes. The first class consists of-dimensional joint sets that factor into scalar sets as found in almost all published fuzzy systems. These sets ignore the correlations among vector components of input vectors. Fuzzy systems that use factorable if-part sets suffer in general from exponential rule explosion in high dimensions when they blindly approximate functions without knowledge of the functions. The factorable fuzzy sets themselves also suffer from what we call the second curse of dimensionality: The fuzzy sets tend to become binary spikes in high dimension. The second class of if-part sets consists of the more general but less common-dimensional joint sets that do not factor into scalar fuzzy sets. We present a method for constructing such unfactorable joint sets from scalar distance measures. Fuzzy systems that use unfactorable if-part sets need not suffer from exponential rule explosion but their increased complexity may lead to intractable learning laws and inscrutable if-then rules. We prove that some of these unfactorable join..

What is the Best Shape for a Fuzzy Set in Function Approximation?

The choice of fuzzy set functions affects how well fuzzy systems approximate functions. The most common fuzzy sets are triangles, trapezoids, and Gaussian bell curves. We compared these sets with many others on a wide range of approximand functions in one, two, and three dimensions. Supervised learning tuned the ifpart set functions and the centroids and volumes of the then-part sets. We compared the set functions based on how closely the adaptive fuzzy system converged to the approximand. The sinc function sin(x)=x performed best or nearly best in most cases. 1 Fuzzy Sets and Function Approximation A fuzzy system F : R n ! R p stores m if-then rules and can uniformly approximate continuous and bounded measurable functions on compact domains [4]. This approximation theorem allows any choice of ifpart fuzzy sets A j ae R n . It also allows any choice of the then-part fuzzy sets B j ae R p because the system uses only the centroid c j and volume V j of B j to compute the output..