Abstract: In this paper, we propose a new method to describe fractal shapes using parametric l-systems. First we introduce scaling factors in the production rules of the parametric l-systems grammars. Then we decorticate these grammars with scaling factors using turtle algebra to show the mathematical relation between l-systems and iterated function systems (IFS). We demonstrate that with specific values of the scaling factors, we find the exact relationship established by Prusinkiewicz and Hammel between l-systems and IFS.
Abstract: A mathematical model for the transmission of SARS is developed. In addition to dividing the population into susceptible (high and low risk), exposed, infected, quarantined, diagnosed and recovered classes, we have included a class called untraced. The model simulates the Gompertz curves which are the best representation of the cumulative numbers of probable SARS cases in Hong Kong and Singapore. The values of the parameters in the model which produces the best fit of the observed data for each city are obtained by using a differential evolution algorithm. It is seen that the values for the parameters needed to simulate the observed daily behaviors of the two epidemics are different.
Abstract: The effect of a time delay on the transmission on
dengue fever is studied. The time delay is due to the presence of an
incubation period for the dengue virus to develop in the mosquito
before the mosquito becomes infectious. The conditions for the
existence of a Hopf bifurcation to limit cycle behavior are
established. The conditions are different from the usual one and they
are based on whether a particular third degree polynomial has
positive real roots. A theorem for determining whether for a given
set of parameter values, a critical delay time exist is given. It is
found that for a set of realistic values of the parameters in the model,
a Hopf bifurcation can not occur. For a set of unrealistic values of
some of the parameters, it is shown that a Hopf bifurcation can occur.
Numerical solutions using this last set show the trajectory of two of
the variables making a transition from a spiraling orbit to a limit
cycle orbit.
Abstract: This work deals with aspects of support vector machine learning for large-scale data mining tasks. Based on a decomposition algorithm for support vector machine training that can be run in serial as well as shared memory parallel mode we introduce a transformation of the training data that allows for the usage of an expensive generalized kernel without additional costs. We present experiments for the Gaussian kernel, but usage of other kernel functions is possible, too. In order to further speed up the decomposition algorithm we analyze the critical problem of working set selection for large training data sets. In addition, we analyze the influence of the working set sizes onto the scalability of the parallel decomposition scheme. Our tests and conclusions led to several modifications of the algorithm and the improvement of overall support vector machine learning performance. Our method allows for using extensive parameter search methods to optimize classification accuracy.
Abstract: The incidences of dengue hemorrhagic disease (DHF)
over the long term exhibit a seasonal behavior. It has been
hypothesized that these behaviors are due to the seasonal climate
changes which in turn induce a seasonal variation in the incubation
period of the virus while it is developing the mosquito. The standard
dynamic analysis is applied for analysis the Susceptible-Exposed-
Infectious-Recovered (SEIR) model which includes an annual
variation in the length of the extrinsic incubation period (EIP). The
presence of both asymptomatic and symptomatic infections is
allowed in the present model. We found that dynamic behavior of the
endemic state changes as the influence of the seasonal variation of
the EIP becomes stronger. As the influence is further increased, the
trajectory exhibits sustained oscillations when it leaves the chaotic
region.
Abstract: Prime Factorization based on Quantum approach in
two phases has been performed. The first phase has been achieved at
Quantum computer and the second phase has been achieved at the
classic computer (Post Processing). At the second phase the goal is to
estimate the period r of equation xrN ≡ 1 and to find the prime factors
of the composite integer N in classic computer. In this paper we
present a method based on Randomized Approach for estimation the
period r with a satisfactory probability and the composite integer N
will be factorized therefore with the Randomized Approach even the
gesture of the period is not exactly the real period at least we can find
one of the prime factors of composite N. Finally we present some
important points for designing an Emulator for Quantum Computer
Simulation.
Abstract: The fuzzy set theory has been applied in many fields,
such as operations research, control theory, and management
sciences, etc. In particular, an application of this theory in decision
making problems is linear programming problems with fuzzy
numbers. In this study, we present a new method for solving fuzzy
number linear programming problems, by use of linear ranking
function. In fact, our method is similar to simplex method that was
used for solving linear programming problems in crisp environment
before.