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A Centroid Neural Network with Weighted Features (CNN-WF) is proposed and presented in this paper. The proposed CNN-WF is based on a Centroid Neural Network (CNN), an effective clustering tool that has been successfully applied to various problems. In order to evaluate the importance of each feature in a set of data, a feature weighting concept is introduced to the Centroid Neural Network in the proposed algorithm. The weight update equations for CNN-WF are derived by applying the Lagrange multiplier procedure to the objective function constructed for CNN-WF in this paper. The use of weighted features makes it possible to assess the importance of each feature and to reject features that can be considered as noise in data. Experiments on a synthetic data set and a typical image compression problem show that the proposed CNN-WF can assess the importance of each feature and the proposed CNN-WF outperforms conventional algorithms including the Self-Organizing Map (SOM) and CNN in terms of clustering accuracy. [ABSTRACT FROM AUTHOR]

Neural network was introduced to sneak circuit analysis (SCA) in previous works. However, it may generate suspect results which were hard to explain. To overcome the shortcomings, this paper proposed a novel neural network model based on circuit architecture, named CArNN, which is used as an individual of an ensemble. In CArNN, neurons represented system components, and weights represented the joints between components. Models of neurons are sigmoid functions. Clone selection algorithm was used to train CArNNs population. The trained antibodies were used as individuals of an ensemble. The inputs of CArNN are states of switches, and the outputs are states of functional components. Ensemble predicted all possible functions of circuit. The sneak circuits can be discovered by comparing the predicted and designed functions. The results revealed that CArNNs can exactly discover sneak circuits. [ABSTRACT FROM AUTHOR]

The goal of this paper is to solve mathematical model equations on solid tumour growth and compute their parameter values by applying growth rates of prostate cancer cell lines in vivo. For these computations, we investigate previously developed C3(1)/Tag transgenic models of prostate cancer. To make the computations fast, we have constructed an algorithm, which is based on small amounts of spatial grid-points and obtained a correspondence between the in vivo growth of tumours and the solutions of the model equations. [ABSTRACT FROM AUTHOR]

In this paper, we examine the wavelet characterization of Hardy space H1, and show that the H1-norm is a good choice for modelizing the oscillating patterns. Furthermore, we give the discrete representation of H1-norm by using wavelet coefficients, and apply it to the variational image decomposition models. Finally, we give the iterative algorithm, and present various numerical results on images to demonstrate the potential of our methods. [ABSTRACT FROM AUTHOR]

A recent paper by Matuttis and Ito questions the numerical accuracy of a widely-used fermion Monte Carlo algorithm. They also claim that the increase in the d-wave pairfield susceptibility χd(T) of a doped 4×4 Hubbard model at low temperature, previously found using this algorithm, is an artifact due to numerical errors. Here, we provide tests which show that this algorithm is numerically accurate and show that the simulation of χd for a 2×2 lattice agrees with exact diagonalization results. We also provide more complete data for χd on a 4×4 lattice that is consistent with our previous results. [ABSTRACT FROM AUTHOR]

A finite word w ∈ {0, 1}* is balanced if for every equal-length factors u and v of every cyclic shift of w we have ||u|1 - |v|1| ≤ 1. This new class of finite words was defined in [O. Jenkinson and L. Q. Zamboni, Characterisations of balanced words via orderings, Theoret. Comput. Sci. 310(1-3) (2004) 247-271]. In [O. Jenkinson, Balanced words and majorization, Discrete Math. Algorithms Appl. 1(4) (2009) 463-484], there was proved several results considering finite balanced words and majorization. One of the main results was that the base-2 orbit of the balanced word is the least element in the set of orbits with respect to partial sum. It was also proved that the product of the elements in the base-2 orbit of a word is maximized precisely when the word is balanced. It turns out that the words 0q-p1p have similar extremal properties, opposite to the balanced words, which makes it meaningful to call these words the most unbalanced words. This paper contains the counterparts of the results mentioned above. We will prove that the orbit of the word u = 0q-p1p is the greatest element in the set of orbits with respect to partial sum and that it has the smallest product. We will also prove that u is the greatest element in the set of orbits with respect to partial product. [ABSTRACT FROM AUTHOR]

This paper introduces a new disambiguation algorithm for finite automata and functional finite-state transducers. It gives a full description of this algorithm, including a detailed pseudocode and analysis, and several illustrating examples. The algorithm is often more efficient and the result dramatically smaller than the one obtained using determinization for finite automata or the construction of Schützenberger. The unambiguous automaton or transducer created by our algorithm are never larger than those generated by the construction of Schützenberger. In fact, in a variety of cases, the size of the unambiguous transducer returned by our algorithm is only linear in that of the input transducer while the transducer created by the construction of Schützenberger is exponentially larger. Our algorithm can be used effectively in many applications to make automata and transducers more efficient to use. [ABSTRACT FROM AUTHOR]

We design a novel algorithm for solving Mean-Payoff Games (MPGs). Besides solving an MPG in the usual sense, our algorithm computes more information about the game, information that is important with respect to applications. The weights of the edges of an MPG can be thought of as a gained/consumed energy - depending on the sign. For each vertex, our algorithm computes the minimum amount of initial energy that is sufficient for player Max to ensure that in a play starting from the vertex, the energy level never goes below zero. Our algorithm is not the first algorithm that computes the minimum sufficient initial energies, but according to our experimental study it is the fastest algorithm that computes them. The reason is that it utilizes the strategy improvement technique which is very efficient in practice. [ABSTRACT FROM AUTHOR]

Event-driven method (EDM) and the time-driven method (TDM) are two main branches of discrete element methods (DEM) for the simulations of granular materials. A new algorithm is introduced in this paper where different models are used for different local volume fractions. TDM time step is used for the cases with high volume fractions and EDM time step is used for the cases with low volume fractions. Whether the local volume fraction is low or high is determined by the number of neighbors in the Verlet table. While the time step updating the Verlet table is the same as the time step for those particles without neighbors in the Verlet table. [ABSTRACT FROM AUTHOR]

Let R be a non-commutative ring and let C(R) be the center of R. The non-commuting graph ΓR of R associated to R is defined as a graph with R\C(R) as the vertices and two distinct vertices x and y are joined whenever xy ≠ yx. We study various graph theoretical properties of this graph. [ABSTRACT FROM AUTHOR]

For a poset P = (X, ≤P), the strict-double-bound graph(P) is the graph on X for which vertices u and v of (P) are adjacent if and only if u ≠ v and there exist x and y in X distinct from u and v such that x ≤ P u ≤ P y and x ≤ P v ≤ P y. The strict-double-bound numberζ(G) of a graph G is defined as is a strict-double-bound graph}. We obtain that for a caterpillar n(m,m,...,m)(n ≥ 3). We also have that for [ABSTRACT FROM AUTHOR]

Based on a detailed analysis for the one-dimensional intrinsic mode function, a model of the bidimensional intrinsic mode function is found firstly. Then a new bidimensional empirical mode decomposition algorithm is developed by using the Radon transform. The existing methods have to locate the maxima and minima in a bidimensional function, and further, produce bidimensional envelopes. Those are usually hard for a real two-dimensional function. The proposed algorithm successfully avoids these difficulties. Experiments show encouraging results. [ABSTRACT FROM AUTHOR]

We show that numerical quasi-one-dimensional renormalization group allows accurate study of weakly coupled spin chains with modest computational effort. We perform a systematic comparison with exact diagonalization results in two- and three-leg spin ladders with a transverse Hamiltonian that can involve frustration. Due to the variational nature of the algorithm, the accuracy can be arbitrarily improved enlarging the basis of eigenstates in the transverse direction. We observe that the precision of the algorithm is directly correlated to the binding of the chains. We also show that the method performs especially well in magnetically frustrated systems. [ABSTRACT FROM AUTHOR]

Viability theory can be applied for determining viable capture basin for control problem in presence of uncertainty. We first recall the concepts of viability theory which allow to develop numerical methods for computing viable capture basin for control problems and guaranteed control problems. Recent developments of option pricing in the framework of dynamical games with constraints lead to the formulation of guaranteed valuation in terms of guaranteed viable-capture basin of a dynamical game. As an application we show how the viability/capturability algorithm evaluates and manages portfolios. Regarding viability/capturability issues, stochastic control is a particular use of tychastic control. We replace the standard translation of uncertainty by stochastic control problem by tychastic ones and the concept of stochastic viability by the one of guaranteed viability kernel. Considering the Cox—Rubinstein model, we extend algorithms for hedging portfolios in the presence of transaction costs and dividends using recent developments on hybrid calculus. [ABSTRACT FROM AUTHOR]