Strong Structural Controllability and Zero Forcing

In this chapter, we study controllability and output controllability of systems defined over graphs. Specifically, we consider a family of state-space systems, where the state matrix of each system has a zero/non-zero structure that is determined by a given directed graph. Within this setup, we investigate under which conditions all systems in this family are controllable, a property referred to as strong structural controllability. Moreover, we are interested in conditions for strong structural output controllability. We will show that the graph-theoretic concept of zero forcing is instrumental in these problems. In particular, as our first contribution, we prove necessary and sufficient conditions for strong structural controllability in terms of so-called zero forcing sets. Second, we show that zero forcing sets can also be used to state both a necessary and a sufficient condition for strong structural output controllability. In addition to these main results, we include interesting results on the controllability of subfamilies of systems and on the problem of leader selection.</p

The creatine kinase system and pleiotropic effects of creatine

The pleiotropic effects of creatine (Cr) are based mostly on the functions of the enzyme creatine kinase (CK) and its high-energy product phosphocreatine (PCr). Multidisciplinary studies have established molecular, cellular, organ and somatic functions of the CK/PCr system, in particular for cells and tissues with high and intermittent energy fluctuations. These studies include tissue-specific expression and subcellular localization of CK isoforms, high-resolution molecular structures and structure–function relationships, transgenic CK abrogation and reverse genetic approaches. Three energy-related physiological principles emerge, namely that the CK/PCr systems functions as (a) an immediately available temporal energy buffer, (b) a spatial energy buffer or intracellular energy transport system (the CK/PCr energy shuttle or circuit) and (c) a metabolic regulator. The CK/PCr energy shuttle connects sites of ATP production (glycolysis and mitochondrial oxidative phosphorylation) with subcellular sites of ATP utilization (ATPases). Thus, diffusion limitations of ADP and ATP are overcome by PCr/Cr shuttling, as most clearly seen in polar cells such as spermatozoa, retina photoreceptor cells and sensory hair bundles of the inner ear. The CK/PCr system relies on the close exchange of substrates and products between CK isoforms and ATP-generating or -consuming processes. Mitochondrial CK in the mitochondrial outer compartment, for example, is tightly coupled to ATP export via adenine nucleotide transporter or carrier (ANT) and thus ATP-synthesis and respiratory chain activity, releasing PCr into the cytosol. This coupling also reduces formation of reactive oxygen species (ROS) and inhibits mitochondrial permeability transition, an early event in apoptosis. Cr itself may also act as a direct and/or indirect anti-oxidant, while PCr can interact with and protect cellular membranes. Collectively, these factors may well explain the beneficial effects of Cr supplementation. The stimulating effects of Cr for muscle and bone growth and maintenance, and especially in neuroprotection, are now recognized and the first clinical studies are underway. Novel socio-economically relevant applications of Cr supplementation are emerging, e.g. for senior people, intensive care units and dialysis patients, who are notoriously Cr-depleted. Also, Cr will likely be beneficial for the healthy development of premature infants, who after separation from the placenta depend on external Cr. Cr supplementation of pregnant and lactating women, as well as of babies and infants are likely to be of benefit for child development. Last but not least, Cr harbours a global ecological potential as an additive for animal feed, replacing meat- and fish meal for animal (poultry and swine) and fish aqua farming. This may help to alleviate human starvation and at the same time prevent over-fishing of oceans

Postprandial chylomicron clearance rate in late teenagers with diabetes mellitus type 1

A delayed chylomicron (CM) clearance rate, a known risk factor for atherosclerosis, has been described in adults with diabetes type I (DMI). We determined the CM clearance rate in late teenagers with DM1, and the relationship between CM clearance rate and elevated plasma lipid concentrations in DMI teenagers in poor metabolic control (as characterized by HbA(1c) percentage). Plasma lipids and CM clearance were determined in nine patients with DMI (mean age +/- SD: 17.5 +/- 0.6 y) and four healthy controls (mean age +/- SD: 20.1 +/- 0.8 y), by measuring breath (CO2)-C-13, plasma triglyceride, retinyl palmitate, and C-13-labeled oleic acid concentrations, after oral administration of a fat-rich meal together with vitamin A and C-13-oleic acid. In patients with DMI, fasting triglyceride and cholesterol concentrations were positively correlated with HbA(1c) percentage (p <0.05). Neither in DM1 patients, nor in controls, was an elevated triglyceride concentration (above 1.7 mmol/L) found. Yet, in 22% of DMI patients, cholesterol concentration was above 5.2 mmol/L, but not in any of the controls. CM clearance rate in DMI patients was similar to that in controls and did not significantly correlate with HbA(1c) percentage. Fasting lipid concentrations in DMI patients were not significantly correlated with CM clearance rate. Present data indicate that elevated lipid concentrations in late teenagers with DMI are not attributable to a delay in CM clearance rate. A delayed CM clearance rate at late teenager age is not a risk factor contributing to the increased risk for atherosclerosis in DM1