A  tuberculosis (TB) model with  lost sight  and multiple latent classes  is considered and studied. We derive the basic reproduction ratio $mathcal R_0$. There is always a globally asymptotically stable equilibrium state. Depending on the value of   $mathcal{R}_0$, this state can be either endemic ($mathcal{R}_0> 1$), or infection-free ($mathcal{R}_0leq 1$). The global asymptotic stability of ...

This paper first describes an algorithm that finds the approximate finite impulse response (FIR) inverse of an FIR filter by minimizing the inversion (or reconstruction) error constrained to zero-bias. The generalization of the inverse filtering problem in the two channel case is the design of perfect reconstruction filter banks that use critical sampling. These considerations lead to the deriv...

We use bivariate C 1 cubic splines to deal with convexity preserving scattered data interpolation problem. Using a necessary and suucient condition on Bernstein-B ezier polynomials, we set the convexity preserving interpolation problem into a quadratically constraint quadratic programming problem. We show the existence of convexity preserving interpolatory surfaces under certain conditions on t...

Nowadays, options are common financial derivatives. For this reason, by increase of applications for these financial derivatives, the problem of options pricing is one of the most important economic issues. With the development of stochastic models, the need for randomly computational methods caused the generation of a new field called financial engineering. In the financial engineering the pre...

7 1 Mathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade, Serbia 8 2 Department of Telecommunications, Faculty of Electronic Engineering, 9 University of Niš, Serbia 10 3 Mathematical Department, Faculty of Occupational Safety, University of Niš, Serbia 11 12 13 14 . 15 ABSTRACT 16 17 In this paper, an approximation of the optimal compressor function using the quadratic ...

1. Unconstrained finite horizon linear quadratic problem 2 1.1. Critical points of quadratic functionals 2 1.2. Shooting function and Hamiltonian flow 6 1.3. Riccati equation 8 1.4. Expression of the critical value 9 1.5. Legendre forms and minima of quadratic functions 9 1.6. Spectral analysis 12 2. Infinite horizon problems 13 2.1. Setting 13 2.2. Kalman state space theory 13 2.3. The algebra...

We study spline fitting with a roughness penalty that adapts to spatial heterogeneity in the regression function. Our estimates are pth degree piecewise polynomials with p− 1 continuous derivatives. A large and fixed number of knots is used and smoothing is achieved by putting a quadratic penalty on the jumps of the pth derivative at the knots. To be spatially adaptive, the logarithm of the pen...

Neural networks require a careful design in order to perform properly on a given task. In particular, selecting a good activation function (possibly in a data-dependent fashion) is a crucial step, which remains an open problem in the research community. Despite a large amount of investigations, most current implementations simply select one fixed function from a small set of candidates, which i...

In this paper, a new methodology is developed for knots placement for cubic spline approximation, using Simulated Annealing. It is not necessary to convert the problem into a discrete combinatorial optimization problem, as presented in other paradigms inspired in genetic algorithm or artificial immune systems, and therefore, removing the constrain of combinatorial optimization problem in the pr...

This paper presents a method for lossy compression of digital video data by parametric line and Natural cubic spline approximation. The method estimates the variation of pixel values in the temporal dimension by taking group of pixels together as keyblocks and interpolating them in Euclidean space. Break and fit criterion is used to minimize the number of keyblocks required for encoding and dec...