We describe quantum-octave package of functions useful for simulations of quantum algorithms and protocols. Presented package allows to perform simulations with mixed states. We present numerical implementation of important quantum mechanical operations – partial trace and partial transpose. Those operations are used as building blocks of algorithms for analysis of entanglement and quantum erro...

Gaussian affinities are commonly used in graph-based methods such as spectral clustering or nonlinear embedding. Hinton and Roweis (2003) introduced a way to set the scale individually for each point so that it has a distribution over neighbors with a desired perplexity, or effective number of neighbors. This gives very good affinities that adapt locally to the data but are harder to compute. W...

Prompt detection and diagnosis of process malfunctions are strategically important due to economic and environmental demands required for industries to remain competitive in world markets. In this paper a new formulation of the computation of the disturbance and fault distribution matrices is suggested for Neuro-Fuzzy and De-coupling Fault Diagnosis Scheme (NFDFDS). NFDFDS is a multiple-model f...

Fixed-point conversion requires fast analytical methods to evaluate the accuracy degradation due to quantization noises. Usually, analytical methods do not consider the correlation between quantization noises. Correlation between quantization noises occurs when a data is quantized several times. This report explained, through an example, the methodology used in the ID.Fix tool to support correl...

In this paper, we study the inverse first-crossing problem. This problem originates from the Merton’s structural model [7] for credit risk management, derived as follows. Consider a company whose asset value and debt at time t ≥ 0 are denoted by A(t) and D(t) respectively. Assume the following: (1) D(0) ≤ A(0) and the company is in default at a time t > 0 if A(t) < D(t). (2) {A(t)} is a log-nor...

We present a numerical method for computing diffusive transport on a surface derived from image data. Our underlying discretization method uses a Cartesian grid embedded boundary method for computing the volume transport in a region consisting of all points a small distance from the surface. We obtain a representation of this region from image data by using a front propagation computation based...

where a, b, c, d are multi-digit integers. Since the product of two n-digit integers becomes 2n-digit, every multiplication operation doubles number of digits of the numerator and the denominator. Rational number computation divides them by their GCD to get irreducible form after every operation. We develop a computing environment in which multi-digit integer such as a, b, c, d in above express...

We establish a set-oriented algorithm for the numerical approximation of the rotation set of homeomorphisms of the two-torus homotopic to the identity. A theoretical background is given by the concept of ε-rotation sets. These are obtained by replacing orbits with ε-pseudo-orbits in the definition of the Misiurewicz-Ziemian rotation set and are shown to converge to the latter as ε decreases to ...

A numerical elimination method is presented in this paper for floating-point computation in polynomial algebra. The method is designed to calculate one or more polynomials in an elimination ideal by a sequence of matrix rank/kernel computation. The method is reliable in numerical computation with verifiable stability and a sensitivity measurement. Computational experiment shows that the method ...

In this paper, we analyse mathematical properties of spatial optical-flow computation algorithm. First by numerical analysis, we derive the convergence property on variational optical-flow computation method used for cardiac motion detection. From the convergence property of the algorithm, we clarify the condition for the scheduling of the regularisation parameters. This condition shows that fo...