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The paper considers the problem of building genetic networks from time series of gene expression data. The class of models of interest is that of systems of differential equations specifying gene-gene interactions and the goal is to infer the network structure from experimental gene expression data. As a mean to regularize the inverse problem, we assume the biologically plausible constraint which imposes limits on the number of genes interacting with any given gene. The existing algorithms for inferring gene network structure heavily rely on the transformation of the system of differential equations into an approximative discretized system. In contrast, our proposed algorithms infer the structure of the gene networks by operating with the exact solutions of the differential equations. For the case of time series of non-uniformly sampled gene expressions, we first fit an optimal sum of exponentials model to each gene, where the best fit is defined by the minimum description length (MDL) principle, the optimal model being subsequently used for interpolating the data at a finer and equidistant grid in time. As a simulating environment we take simple genetic networks, assumed to be the ground truth, where the dynamical interactions between genes are postulated to be linear differential equations. We show that we can recover the sparse structure of the original model using the data generated by the system for a wide range of model parameters (i.e. strengths of the gene-gene interactions).