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

Stepwise effective molarities in porphyrin oligomer complexes: preorganization results in exceptionally strong chelate cooperativity.

Complexes of zinc porphyrin oligomers with multivalent ligands can be denatured by adding a large excess of a monodentate ligand, such as quinuclidine. We have used denaturation titrations to determine the stabilities of the complexes of a cyclic zinc-porphyrin hexamer with multidentate ligands with two to six pyridyl coordination sites. The corresponding complexes of linear porphyrin oligomers were also investigated. The results reveal that the stepwise effective molarities (EMs) for the third through sixth intramolecular coordination events with the cyclic hexamer are extremely high (EM = 10(2)-10(3) M), whereas the values for the linear porphyrin oligomers are modest (EM ≈ 0.05 M). The speciation profiles for the denaturation reactions demonstrate that intermediate species are not significantly populated and that these equilibria are well described by a highly cooperative two-state model

Possible involvement of superoxide and dioxygen with cryptochrome in avian magnetoreception: Origin of Zeeman resonances observed by in vivo EPR spectroscopy

The radical pair model of the avian magnetic compass centres around magnetically sensitive chemical reactions in the retina. Recent studies of migratory birds subjected to oscillating magnetic fields found remarkably sensitive disorientation responses when the frequency of the applied field (∼1.3 MHz) matched the EPR condition of a radical with g ≈ 2 in the Earth's magnetic field (∼47 μT). The occurrence of such 'Zeeman resonances' can be understood if one of the radical pair partners is devoid of hyperfine interactions. Here we examine the possibility that this radical is either superoxide or dioxygen and conclude that neither offers a very credible explanation for these in vivo EPR 'signals'. © 2009 Elsevier B.V. All rights reserved

Alternative radical pairs for cryptochrome-based magnetoreception.

There is growing evidence that the remarkable ability of animals, in particular birds, to sense the direction of the Earth's magnetic field relies on magnetically sensitive photochemical reactions of the protein cryptochrome. It is generally assumed that the magnetic field acts on the radical pair [FAD•- TrpH•+] formed by the transfer of an electron from a group of three tryptophan residues to the photo-excited flavin adenine dinucleotide cofactor within the protein. Here, we examine the suitability of an [FAD•- Z•] radical pair as a compass magnetoreceptor, where Z• is a radical in which the electron spin has no hyperfine interactions with magnetic nuclei, such as hydrogen and nitrogen. Quantum spin dynamics simulations of the reactivity of [FAD•- Z•] show that it is two orders of magnitude more sensitive to the direction of the geomagnetic field than is [FAD•- TrpH•+] under the same conditions (50 µT magnetic field, 1 µs radical lifetime). The favourable magnetic properties of [FAD•- Z•] arise from the asymmetric distribution of hyperfine interactions among the two radicals and the near-optimal magnetic properties of the flavin radical. We close by discussing the identity of Z• and possible routes for its formation as part of a spin-correlated radical pair with an FAD radical in cryptochrome

Magnetically sensitive light-induced reactions in cryptochrome are consistent with its proposed role as a magnetoreceptor.

Among the biological phenomena that fall within the emerging field of "quantum biology" is the suggestion that magnetically sensitive chemical reactions are responsible for the magnetic compass of migratory birds. It has been proposed that transient radical pairs are formed by photo-induced electron transfer reactions in cryptochrome proteins and that their coherent spin dynamics are influenced by the geomagnetic field leading to changes in the quantum yield of the signaling state of the protein. Despite a variety of supporting evidence, it is still not clear whether cryptochromes have the properties required to respond to magnetic interactions orders of magnitude weaker than the thermal energy, k(B)T. Here we demonstrate that the kinetics and quantum yields of photo-induced flavin-tryptophan radical pairs in cryptochrome are indeed magnetically sensitive. The mechanistic origin of the magnetic field effect is clarified, its dependence on the strength of the magnetic field measured, and the rates of relevant spin-dependent, spin-independent, and spin-decoherence processes determined. We argue that cryptochrome is fit for purpose as a chemical magnetoreceptor

Current practices of partner notification among MSM with HIV, gonorrhoea and syphilis in the Netherlands: an urgent need for improvement

<p>Abstract</p> <p>Background</p> <p>Partner notification (PN) among individuals newly diagnosed with HIV/STI is seen as a vital tool to identify others at risk of infection. However, hardly any data are available on the effectiveness of PN on HIV/STI transmission in the Netherlands. This study aims to fill this gap by assessing current PN practices, case-finding effectiveness, and determinants of being notified among men having sex with men (MSM) in the Netherlands.</p> <p>Methods</p> <p>Nurses from five STI centers participated in a prospective pilot study on PN outcomes (partners being: at risk, notifiable, notified, and tested) for HIV/STI, by completing a newly developed PN registration form (PN database). PN outcomes including case-finding effectiveness (number of newly diagnosed cases in partners/number of partners being tested) for HIV, syphilis, and gonorrhoea were studied among MSM. Furthermore, the national STI database was analyzed to identify determinants of being notified. The number of infections that remained undetected was estimated based on these two databases.</p> <p>Results</p> <p>In total 105 MSM, newly diagnosed with HIV/STI, reported 612 sexual partners at risk of whom 41% were notifiable and 31% were notified. Patient referral was the predominant PN method (90%). The overall case-finding percentage was 36% (HIV: 15-33%, gonorrhoea: 17-50% and syphilis: 4-11%). Case-finding percentages were lower in the national STI database: 21% (5%, 28%, 12%). Persons with one or more sexual partners, known HIV positives, and IDU were more likely to be notified to the STI clinic. Notified clients were more likely to have HIV/STI than unnotified clients (OR 1.7-2.5). Based on these two databases, an estimated 75 to 133 infections remained undetected (HIV: 12–90; gonorrhoea: 28–97; syphilis: 5–12 infections).</p> <p>Conclusions</p> <p>Partner notification among MSM in the Netherlands is suboptimal; an extensive number of STI/HIV infections remained undetected mainly due to unnotifiable partners. To enhance PN practices, combined and innovative PN interventions such as Internet-based PN will be implemented for hard-to-reach MSM and other risk groups.</p