We call (T (t))t≥0 an abstract delay semigroup. This notion is introduced in more detail in Section 2. The semigroup thus obtained is rarely a contraction semigroup. In this paper we will show that under very mild conditions, we may change the inner product on E into an equivalent inner product, such that the delay semigroup becomes a (generalized) contraction semigroup. A contraction semigroup...

In the recent preprint [1] S. Parrott proves the equality between the Arveson's curvature and the Fredholm index of a " pure " contraction with finite defect numbers. In the present note one derives a similar formula in the " non-pure " case. The notions of d-contraction T = (T 1 , T 2 ,. .. , T d) and its curvature was introduced by W. Arveson in a series of papers (see [2], [3], and [4]). In ...

T cells rapidly undergo contraction upon viral clearance, but how T cell function and fate are determined during this phase is unclear. During the contraction phase of an acute infection with lymphocytic choriomeningitis virus, we found that virus-specific CD8+ T cells within the splenic red pulp (RP) had higher two-dimensional (2D) effective affinity than those within the white pulp (WP). This...

Several lines of evidence from different model systems suggest that gamma interferon (IFN-gamma) is an important regulator of T-cell contraction after antigen (Ag)-driven expansion. To specifically investigate the role of IFN-gamma in regulating the contraction of Ag-specific CD4 T cells, we infected IFN-gamma-/- and IFN-gammaR1-/- mice with attenuated Listeria monocytogenes and monitored the n...

A classical result of Sz.-Nagy asserts that a Hilbert space contraction operator T can be dilated to unitary $${{\mathcal {U}}}$$ , i.e., $$T^n = P_{{\mathcal {H}}}{{\mathcal {U}}}^n|{{\mathcal {H}}}$$ for all $$n =0,1,2,\ldots $$ . more general multivariable setting these ideas is the setup where (i) unit disk replaced by domain $$\Omega contained in $${{\mathbb {C}}}^d$$ (ii) an -contraction,...

Ag-specific CD8(+) T cell contraction (contraction), which occurs after the resolution of infection, is critical for homeostasis of the immune system. Although complement components regulate the primary CD8(+) T cell response, there is insufficient evidence supporting their role in regulating contraction and memory. In this study, we show that C3-deficient (C3(-/-)) mice exhibited significantly...

It is known that muscle temperature (T(m)) increases with exercise. The purpose of this study was to examine if contraction-induced increase in T(m) was altered in rats with heart failure (HF) induced by chronic myocardial infraction (MI) as compared with healthy control animals. A temperature probe was inserted in the triceps surae muscle to continuously measure T(m) throughout experiments. St...

For a family of graphs F , the F-Contraction problem takes as an input a graph G and an integer k, and the goal is to decide if there exists S ⊆ E(G) of size at most k such that G/S belongs to F . Here, G/S is the graph obtained from G by contracting all the edges in S. Heggernes et al. [Algorithmica (2014)] were the first to study edge contraction problems in the realm of Parameterized Complex...