Symbolic Dynamics for a Piecewise-Affine System with Hysteresis

In this paper we present the computation of symbolic dynamics of a one dimensional return map of a piecewise-affine hybrid system. The system arises as a simple electrical circuit with hysteresis switching, and exhibits chaotic dynamics. Our method allows us to rigorously obtain a qualitative description of the discrete behaviour of the system. We show how the discrete dynamics changes as a parameter is varied, and we compute bounds for the topological entropy to provide a measure of the complexity of the system

Discrete Dynamics of Two-Dimensional Nonlinear Hybrid Automata

In this paper, we develop an algorithm to compute under- and over-approximations to the discrete dynamics of a hybrid automaton. We represent the approximations to the dynamics as \emph{sofic shifts}, which can be generated by a discrete automaton. We restrict to two-dimensional systems, since these give rise to one-dimensional return maps, which are significantly easier to study. Given generic non-degeneracy conditions, the under- and over-approximations computed by our algorithm converge to the discrete dynamics of the hybrid automaton. We apply the algorithms to two simple nonlinear hybrid systems, an affine switching system with hysteresis, and the singularly forced van der Pol oscillator

Stability Analysis of Switched-Linear Hybrid Systems

In this paper we develop general techniques to study stability of hybrid systems with linear continuous dynamics. These techniques are based on matrix analysis and study of differentiable manifolds. These techniques operate on the space of switching times of the hybrid systems. Some special techniques for hybrid systems with three dimensional state space are also developed

The pgip family in soybean and three other legume species: evidence for a birth-and-death model of evolution

Polygalacturonase-inhibiting proteins (PGIPs) are leucine-rich repeat (LRR) plant cell wall glycoproteins involved in plant immunity. They are typically encoded by gene families with a small number of gene copies whose evolutionary origin has been poorly investigated. Here we report the complete characterization of the full complement of the pgip family in soybean (Glycine max [L.] Merr.) and the characterization of the genomic region surrounding the pgip family in four legume species. Results: BAC clone and genome sequence analyses showed that the soybean genome contains two pgip loci. Each locus is composed of three clustered genes that are induced following infection with the fungal pathogen Sclerotinia sclerotiorum (Lib.) de Bary, and remnant sequences of pgip genes. The analyzed homeologous soybean genomic regions (about 126 Kb) that include the pgip loci are strongly conserved and this conservation extends also to the genomes of the legume species Phaseolus vulgaris L., Medicago truncatula Gaertn. and Cicer arietinum L., each containing a single pgip locus. Maximum likelihood-based gene trees suggest that the genes within the pgip clusters have independently undergone tandem duplication in each species. Conclusions: The paleopolyploid soybean genome contains two pgip loci comprised in large and highly conserved duplicated regions, which are also conserved in bean, M. truncatula and C. arietinum. The genomic features of these legume pgip families suggest that the forces driving the evolution of pgip genes follow the birth-and-death model, similar to that proposed for the evolution of resistance (R) genes of NBS-LRR-type

Computation of symbolic dynamics for one-dimensional maps

AbstractIn this paper we design and implement rigorous algorithms for computing symbolic dynamics for piecewise-monotone-continuous maps of the interval. The algorithms are based on computing forwards and backwards approximations of the boundary, discontinuity and critical points. We explain how to handle the discontinuities in the symbolic dynamics which occur when the computed partition element boundaries are not disjoint. The method is applied to compute the symbolic dynamics and entropy bounds for the return map of the singular limit of a switching system with hysteresis and the forced Van der Pol equation

Role of Polygalacturonase-Inhibiting Proteins in the Arabidopsis thaliana-Fusarium graminearum interaction.

Comunicazione oral

Vitamin K and Osteoporosis

Vitamin K acts as a coenzyme of carboxylase, catalyzing the carboxylation of several vitamin K dependent proteins. Beyond its well-known effects on blood coagulation, it also exerts relevant effects on bone and the vascular system. In this review, we point out the relevance of an adequate vitamin K intake to obtain sufficient levels of carboxylated (active form) vitamin K dependent proteins (such as Osteocalcin and matrix Gla protein) to prevent bone health. Another bone-related action of Vitamin K is being a ligand of the nuclear steroid and xenobiotic receptor (SXR). We also discuss the recommended intake, deficiency, and assessment of vitamin K. Furthermore, we review the few available studies that have as pre-specified outcome bone fractures, indicating that we need more clinical studies to confirm that vitamin K is a potential therapeutic agent for bone fractures

Oral calcitriol use, vertebral fractures, and vitamin K in hemodialysis patients: a cross‐sectional study

Fractures and vascular calcifications (VCs) are common in patients with chronic kidney disease (CKD). They are related to abnormalities in vitamin D metabolism, calcium, phosphorus, parathyroid hormone, and fibroblast growth factor 23 (FGF23)/Klotho that occur with CKD. Impaired vitamin D metabolism and abnormal levels of calcium, phosphate, parathyroid hormone (PTH), and FGF23/Klotho drive bone and vascular changes in CKD. It is unclear if oral calcitriol safely mitigates fracture risk without increasing the burden of calcifications. Therefore, we investigated whether treatment with calcitriol affected the prevalence of fractures and VC progression in hemodialysis (HD) patients. This report is a secondary analysis of the Vitamin K Italian (VIKI) study, a cross-sectional study involving 387 HD patients. We assessed vitamin 25(OH)D, alkaline phosphatase, PTH, calcium, phosphate, osteocalcin or bone Gla protein, matrix Gla protein, and vitamin K levels. Vertebral fractures (VFs) and VCs were determined by spine radiograph. A reduction of >20% of vertebral body height was considered a VF. VCs were quantified by the length of calcific lesions along the arteries. The patients treated with oral calcitriol were 177 of 387 patients (45.7%). The prevalence of VF was lower in patients receiving oral calcitriol than in those untreated (48.6% versus 61.0%, p = 0.015), whereas the presence of aortic and iliac calcifications was similar (aortic: 81.9% versus 79.5%, respectively, p = 0.552; iliac: 52.0% and 59.5%, respectively, p = 0.167). In multivariable logistic regression analysis, oral calcitriol was associated with a 40.2% reduced odds of fracture (OR 0.598; 95% confidence interval [CI], 0.363-0.985; p = 0.043). In conclusion, we found a significant association between oral calcitriol and lower VF in HD patients without an increase in the burden of VC. Further prospective and interventional studies are needed to confirm these findings. © 2021 American Society for Bone and Mineral Research (ASBMR)

The vessels-bone axis: iliac artery calcifications, vertebral fractures and vitamin K from VIKI study

Vascular calcification and fragility fractures are associated with high morbidity and mortality, especially in end-stage renal disease. We evaluated the relationship of iliac arteries calcifications (IACs) and abdominal aortic calcifications (AACs) with the risk for vertebral fractures (VFs) in hemodialysis patients. The VIKI study was a multicenter cross-sectional study involving 387 hemodialysis patients. The biochemical data included bone health markers, such as vitamin K levels, vitamin K-dependent proteins, vitamin 25(OH)D, alkaline phosphatase, parathormone, calcium, and phosphate. VF, IACs and AACs was determined through standardized spine radiograms. VF was defined as >20% reduction of vertebral body height, and VC were quantified by measuring the length of calcium deposits along the arteries. The prevalence of IACs and AACs were 56.1% and 80.6%, respectively. After adjusting for confounding variables, the presence of IACs was associated with 73% higher odds of VF (p = 0.028), whereas we found no association (p = 0.294) for AACs. IACs were associated with VF irrespective of calcification severity. Patients with IACs had lower levels of vitamin K2 and menaquinone 7 (0.99 vs. 1.15 ng/mL; p = 0.003), and this deficiency became greater with adjustment for triglycerides (0.57 vs. 0.87 ng/mL; p < 0.001). IACs, regardless of their extent, are a clinically relevant risk factor for VFs. The association is enhanced by adjusting for vitamin K, a main player in bone and vascular health. To our knowledge these results are the first in the literature. Prospective studies are needed to confirm these findings both in chronic kidney disease and in the general population