Complete solution of a constrained tropical optimization problem with application to location analysis

We present a multidimensional optimization problem that is formulated and solved in the tropical mathematics setting. The problem consists of minimizing a nonlinear objective function defined on vectors over an idempotent semifield by means of a conjugate transposition operator, subject to constraints in the form of linear vector inequalities. A complete direct solution to the problem under fairly general assumptions is given in a compact vector form suitable for both further analysis and practical implementation. We apply the result to solve a multidimensional minimax single facility location problem with Chebyshev distance and with inequality constraints imposed on the feasible location area.Comment: 20 pages, 3 figure

Dynamic analysis of repetitive decision-free discreteevent processes: The algebra of timed marked graphs and algorithmic issues

A model to analyze certain classes of discrete event dynamic systems is presented. Previous research on timed marked graphs is reviewed and extended. This model is useful to analyze asynchronous and repetitive production processes. In particular, applications to certain classes of flexible manufacturing systems are provided in a companion paper. Here, an algebraic representation of timed marked graphs in terms of reccurrence equations is provided. These equations are linear in a nonconventional algebra, that is described. Also, an algorithm to properly characterize the periodic behavior of repetitive production processes is descrbed. This model extends the concepts from PERT/CPM analysis to repetitive production processes.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44155/1/10479_2005_Article_BF02248590.pd

The ribose methylation enzyme FTSJ1 has a conserved role in neuron morphology and learning performance.

FTSJ1 is a conserved human 2'-O-methyltransferase (Nm-MTase) that modifies several tRNAs at position 32 and the wobble position 34 in the anticodon loop. Its loss of function has been linked to X-linked intellectual disability (XLID), and more recently to cancers. However, the molecular mechanisms underlying these pathologies are currently unclear. Here, we report a novel FTSJ1 pathogenic variant from an X-linked intellectual disability patient. Using blood cells derived from this patient and other affected individuals carrying FTSJ1 mutations, we performed an unbiased and comprehensive RiboMethSeq analysis to map the ribose methylation on all human tRNAs and identify novel targets. In addition, we performed a transcriptome analysis in these cells and found that several genes previously associated with intellectual disability and cancers were deregulated. We also found changes in the miRNA population that suggest potential cross-regulation of some miRNAs with these key mRNA targets. Finally, we show that differentiation of FTSJ1-depleted human neural progenitor cells into neurons displays long and thin spine neurites compared with control cells. These defects are also observed in Drosophila and are associated with long-term memory deficits. Altogether, our study adds insight into FTSJ1 pathologies in humans and flies by the identification of novel FTSJ1 targets and the defect in neuron morphology