Symbolic methods to investigate Hopf bifurcation problems of vector fields arising in the context of algebraic biology have recently obtained renewed attention. However, the symbolic investigations have not been fully algorithmic but required a sequence of symbolic computations intervened with ad hoc insights and decisions made by a human. In this paper we discuss the use of algebraic and logical methods to reduce questions on the existence of Hopf bifurcations in parameterized polynomial vector fields to quantifier elimination problems over the reals combined with the use of the quantifier elimination over the reals and simplification techniques available in REDLOG. We can reconstruct most of the results given in the literature within a few seconds of computation time and extend the investigations on these systems to previously not analyzed related systems. Especially we discuss cases in which one suspects that no Hopf bifurcation fixed point exists for biologically relevant values of parameters and system variables. Here we focus on logical and algebraic techniques of finding subconditions being inconsistent with the hypothesis of the existence of Hopf bifurcation fixed points.

We investigate algorithmic methods to tackle the following problem: Given a system of parametric ordinary differential equations built by a biological model, does there exist ranges of values for the model parameters and variables which are both meaningful from a biological point of view and where oscillating trajectories, can be found? We show that in the common case of polynomial vector fields known criteria excluding the existence of non-constant limit cycles lead to quantifier elimination problems over the reals.We apply these criteria to various models that have been previously investigated in the context of algebraic biology.

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Abstract-In this paper a novel color image compression technique for efficient storage and delivery of data is proposed. The proposed compression technique started by RGB to YCbCr color transformation process. Secondly, the canny edge detection method is used to classify the blocks into the edge and non-edge blocks. Each color component Y, Cb, and Cr compressed by discrete cosine transform (DCT) process, quantizing and coding step by step using adaptive arithmetic coding. Our technique is concerned with the compression ratio, bits per pixel and peak signal to noise ratio, and produce better results than JPEG and more recent published schemes (like CBDCT-CABS and MHC). The provided experimental results illustrate the proposed technique that is efficient and feasible in terms of compression ratio, bits per pixel and peak signal to noise ratio.