1,721,024 research outputs found
Characterizing Fractal Genetic Variation in the Human Genome from the Hapmap Project
Full text linkOver the last decades, the exuberant development of next-generation sequencing has revolutionized gene discovery. These technologies have boosted the mapping of single nucleotide polymorphisms (SNPs) across the human genome, providing a complex universe of heterogeneity characterizing individuals worldwide. Fractal dimension (FD) measures the degree of geometric irregularity, quantifying how "complex" a self-similar natural phenomenon is. We compared two FD algorithms, box-counting dimension (BCD) and Higuchi's fractal dimension (HFD), to characterize genome-wide patterns of SNPs extracted from the HapMap data set, which includes data from 1184 healthy subjects of eleven populations. In addition, we have used cluster and classification analysis to relate the genetic distances within chromosomes based on FD similarities to the geographical distances among the 11 global populations. We found that HFD outperformed BCD at both grand average clusterization analysis by the cophenetic correlation coefficient, in which the closest value to 1 represents the most accurate clustering solution (0.981 for the HFD and 0.956 for the BCD) and classification (79.0% accuracy, 61.7% sensitivity, and 96.4% specificity for the HFD with respect to 69.1% accuracy, 43.2% sensitivity, and 94.9% specificity for the BCD) of the 11 populations present in the HapMap data set. These results support the evidence that HFD is a reliable measure helpful in representing individual variations within all chromosomes and categorizing individuals and global populations
On robustification of digital event-based controllers for control-affine nonlinear systems
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Theoretical foundations of the total quasi-steady state approximation in enzyme kinetics.
No full textDigital output feedback event-based stabilization of nonlinear systems with state delays
Full text linkIn this paper, the stabilization problem of nonlinear time-delay systems by means of digital dynamic output feedback event-triggered controllers is addressed. In particular, for the class of control-affine nonlinear systems with state delays, a methodology for the design of quantized sampled-data observer-based event-triggered (QSOE) stabilizers is provided. As a first step, the notion of Dynamic Output Steepest Descent Feedback (DOSDF), induced by a class of Lyapunov–Krasovskii functionals, is suitably revised in order to cope with the design of QSOE stabilizers. Then, the stabilization in the sample-and-hold sense theory is used as a tool to prove the existence of a suitably fast sampling and of an accurate quantization of the input/output channels such that: the digital implementation of DOSDFs, updated through a proposed event-based mechanism, ensures the semi-global practical stability property of the related closed-loop system with arbitrarily small final target ball of the origin. In the theory here developed, aperiodic sampling and the non-uniform quantization of the input/output channels are taken into account. Possible discontinuities in the functions describing the DOSDF at hand are also managed enlarging the possibilities to successfully designing QSOE stabilizers. Moreover, the proposed QSOE stabilizer is described by easily implementable difference equations avoiding the necessity to solve differential equations for the correct application of the controller at hand. Nonlinear delay-free systems are addressed as a special case. The proposed results are validated through practical examples concerning a Glucose-Insulin system and a Continuous Stirred Tank Reactor system
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