Action Contraction

The question we consider in this paper is: “When can a combination of fine-grain execution steps be contracted into an atomic action execution”? Our answer is basically: “When no observer can see the difference.” This is worked out in detail by defining a notion of coupled split/atomic simulation refinement between systems which differ in the atomicity of their actions, and proving that this collapses to Parrow and Sjödin’s coupled similarity when the systems are composed with an observer

筋収縮後の再酸素化実験に関する研究

博甲第38号生命システム科学博士県立広島大

Canonical decomposition of operators associated with the symmetrized polydisc

A tuple of commuting operators $(S_1,\dots,S_{n-1},P)$ for which the closed symmetrized polydisc $\Gamma_n$ is a spectral set is called a $\Gamma_n$-contraction. We show that every $\Gamma_n$-contraction admits a decomposition into a $\Gamma_n$-unitary and a completely non-unitary $\Gamma_n$-contraction. This decomposition is an analogue to the canonical decomposition of a contraction into a unitary and a completely non-unitary contraction. We also find new characterizations for the set $\Gamma_n$ and $\Gamma_n$-contractions.Comment: Complex Analysis and Operator Theory, Published online on August 28, 2017. arXiv admin note: text overlap with arXiv:1610.0093

Calcium-independent contraction in lysed cell models of teleost retinal cones: activation by unregulated myosin light chain kinase or high magnesium and loss of cAMP inhibition.

The retinal cones of teleost fish contract at dawn and elongate at dusk. We have previously reported that we can selectively induce detergent-lysed models of cones to undergo either reactivated contraction or reactivated elongation, with rates and morphology comparable to those observed in vivo. Reactivated contraction is ATP dependent, activated by Ca2+, and inhibited by cAMP. In addition, reactivated cone contraction exhibits several properties that suggest that myosin phosphorylation plays a role in mediating Ca2+-activation (Porrello, K., and B. Burnside, 1984, J. Cell Biol., 98:2230-2238). We report here that lysed cone models can be induced to contract in the absence of Ca2+ by incubation with trypsin-digested, unregulated myosin light chain kinase (MLCK) obtained from smooth muscle. This observation provides further evidence that MLCK plays a role in regulating cone contraction. We also report here that lysed cone models can be induced to contract in the absence of Ca2+ by incubation with high concentrations of MgCl2 (10-20 mM). Mg2+-induced reactivated contraction is supported by inosine triphosphate (ITP) just as well as by ATP. Because ITP will not serve as a substrate for MLCK, this finding suggests that Mg2+-activation of contraction does not require myosin phosphorylation. Although Ca2+-induced contraction is completely blocked by cAMP at concentrations less than 10 microM, cAMP has no effect on cone contraction activated by unregulated MLCK or by high Mg2+ in the absence of Ca2+. Because trypsin digestion of MLCK cleaves off not only the Ca2+/calmodulin-binding site but also the site phosphorylated by cAMP-dependent protein kinase, and because Mg2+ activation of cone contraction circumvents MLCK action altogether, both these observations would be expected if cAMP inhibits reactivated cone contraction by catalyzing the phosphorylation of MLCK and thus reducing its affinity for Ca2+, as has been described for smooth muscle. Together our results suggest that in lysed cone models, myosin phosphorylation is sufficient for activating cone contraction, even in the absence of other Ca2+-mediated events, that cAMP inhibition of contraction is mediated by cAMP-dependent phosphorylation of MLCK, and that 10-20 mM Mg2+ can activate actin-myosin interaction to produce contraction in the absence of myosin phosphorylation

Canonical decomposition of a tetrablock contraction and operator model

A triple of commuting operators for which the closed tetrablock $\overline{\mathbb E}$ is a spectral set is called a tetrablock contraction or an $\mathbb E$-contraction. The set $\mathbb E$ is defined as $$\mathbb E = \{ (x_1,x_2,x_3)\in\mathbb C^3\,:\, 1-zx_1-wx_2+zwx_3\neq 0 \textup{ whenever } |z|\leq 1, |w|\leq 1 \}.$$ We show that every $\mathbb E$-contraction can be uniquely written as a direct sum of an $\mathbb E$-unitary and a completely non-unitary $\mathbb E$-contraction. It is analogous to the canonical decomposition of a contraction operator into a unitary and a completely non-unitary contraction. We produce a concrete operator model for such a triple satisfying some conditions.Comment: To appear in Journal of Mathematical Analysis and Application

Contraction groups and scales of automorphisms of totally disconnected locally compact groups

We study contraction groups for automorphisms of totally disconnected locally compcat groups using the scale of the automorphism as a tool. The contraction group is shown to be unbounded when the inverse automorphism has non-trivial scale and this scale is shown to be the inverse value of the modular function on the closure of the contraction group at the automorphism. The closure of the contraction group is represented as acting on a homogenous tree and closed contraction groups are characterised.Comment: revised version, 29 pages, to appear in Israel Journal of Mathematics, please note that document starts on page