Strong Mie scattering signatures hamper the chemical interpretation and multivariate analysis of the infrared microscopy spectra of single cells and tissues. During recent years, several numerical Mie scatter correction algorithms for the infrared spectroscopy of single cells have been published. In the paper at hand, we critically reviewed existing algorithms for the correction of Mie scattering and suggest improvements. We developed an iterative algorithm based on Extended Multiplicative Scatter Correction (EMSC), for the retrieval of pure absorbance spectra from highly distorted infrared spectra of single cells. The new algorithm uses the van de Hulst approximation formula for the extinction efficiency employing a complex refractive index. The iterative algorithm involves the establishment of an EMSC meta-model. While existing iterative algorithms for the correction of resonant Mie scattering employ three independent parameters for establishing a meta-model, we could decrease the number of parameters from three to two independent parameters, which reduced the calculation time for the Mie scattering curves for the iterative EMSC meta-model by a factor of 10. Moreover, by employing the Hilbert transform for evaluating the Kramers-Kronig relations based on a FFT algorithm in Matlab, we further improved the speed of the algorithm by a factor of 100. For testing the algorithm we simulate distorted apparent absorbance spectra by utilizing the exact theory for the scattering of infrared light at absorbing spheres, taking into account the high numerical aperture of infrared microscopes employed for the analysis of single cells and tissues. In addition, the algorithm was applied to measured absorbance spectra of single lung cancer cells.

The appearance of fringes in the infrared spectroscopy of thin films seriously hinders the interpretation of chemical bands because fringes change the relative peak heights of chemical spectral bands. Thus, for the correct interpretation of chemical absorption bands, physical properties need to be separated from chemical characteristics. In the paper at hand we revisit the theory of the scattering of infrared radiation at thin absorbing films. Although, in general, scattering and absorption are connected by a complex refractive index, we show that for the scattering of infrared radiation at thin biological films, fringes and chemical absorbance can in good approximation be treated as additive. We further introduce a model-based pre-processing technique for separating fringes from chemical absorbance by extended multiplicative signal correction (EMSC). The technique is validated by simulated and experimental FTIR spectra. It is further shown that EMSC, as opposed to other suggested filtering methods for the removal of fringes, does not remove information related to chemical absorption.

We analyze the impacts of pollution on fishery sector using a dynamical system approach. The proposed model presupposes that the economic development causes emissions that either remediate or accumulate in the oceans. The model possesses a block structure where the solutions of the rate equations for the pollutant and the economic activity act as an input for the biomass and effort equation. We also account for distributed delay effects in both the pollution level and the economic activity level in our modeling framework.The weight functions in the delay terms are expressed in terms of exponentially decaying functions, which in turn enable us to convert the modeling framework to a higher-order autonomous dynamical system by means of a linear chain trick. When both the typical delay time for the economic activity and the typical delay time for the pollution level are much smaller than the biomass time scale, the governing system is analyzed by means of the theory for singularly perturbed dynamical systems. Contrary to what is found for population dynamical systems with absolute delays, we readily find that the impact of the distributed time lags

We study piecewise synergetic systems originating from Biochemical Systems Theory. In the first part of the paper, the emphasis is put on practical calculations with such systems. We consider four examples: calculation of trajectories and steady states, solution of an optimization problem and a method of estimation of parameters (kinetic orders), all examples being biologically motivated. In the second part of the paper, we study convergence of solutions, in particularly, steady states, of a sequence of piecewise synergetic systems approximating an arbitrary compartment model. This convergence analysis is then applied to the optimization problem and the method of estimating sensitivities (kinetic orders) in a generic compartment model. In this paper we put forward arguments for the importance of the theoretical and numerical analysis of piecewise synergetic systems.