A contour integral approach to the computation of invariant pairs

We study some aspects of the invariant pair problem for matrix polynomials, as introduced by Betcke and Kressner [3] and by Beyn and Thümmler [6]. Invariant pairs extend the notion of eigenvalue–eigenvector pairs, providing a counterpart of invariant subspaces for the nonlinear case. We compute formulations for the condition numbers and the backward error for invariant pairs and solvents. We then adapt the Sakurai–Sugiura moment method [1] to the computation of invariant pairs, including some classes of problems that have multiple eigenvalues. Numerical refinement via a variant of Newton's method is also studied. Furthermore, we investigate the relation between the matrix solvent problem and the triangularization of matrix polynomials

Rejuvenating somatotropic signaling: a therapeutical opportunity for premature aging?

We have recently reported that progeroid Zmpste24−/− mice, which exhibit multiple defects that phenocopy Hutchinson-Gilford progeria syndrome, show a profound dysregulation of somatotropic axis, mainly characterized by the occurrence of very high circulating levels of growth hormone (GH) and a drastic reduction in insulin-like growth factor-1 (IGF-1). We have also shown that restoration of the proper GH/IGF-1 balance in Zmpste24−/− mice by treatment with recombinant IGF-1 delays the onset of many progeroid features in these animals and significantly extends their lifespan. Here, we summarize these observations and discuss the importance of GH/IGF-1 balance in longevity as well as its modulation as a putative therapeutic strategy for the treatment of human progeroid syndromes

Career Development & Learning at Jesuit Colleges & Universities During the COVID-19 Pandemic & Beyond

Today’s youth are often interested in how they can work toward social justice, not just in their spare time, but also as part of their educations and careers. This includes students who are drawn to the social justice missions of Jesuit colleges and universities. In 2020, the COVID-19 public health crisis disrupted education and career plans, placing major obstacles along young adults’ pathways. Guided by the Engagement of Hope theoretical model, the current study examines student supports and how they may facilitate hope and learning. Mixed methods data were collected from five undergraduate students from a Jesuit university in a Midwestern city, using in-depth interviews and an online survey conducted in 2021. The findings reveal that students depicted their hopes for later careers, described learning numerous skills, used a wide array of college supports, and discussed the role of families in their education and career pathways. The authors reflect on adaptations made to student supports during the pandemic and on how student service programs at Jesuit institutions might continue to evolve in the post-pandemic era

Finite type approximations of Gibbs measures on sofic subshifts

Consider a H\"older continuous potential $\phi$ defined on the full shift A^\nn, where $A$ is a finite alphabet. Let X\subset A^\nn be a specified sofic subshift. It is well-known that there is a unique Gibbs measure $\mu_\phi$ on $X$ associated to $\phi$. Besides, there is a natural nested sequence of subshifts of finite type $(X_m)$ converging to the sofic subshift $X$. To this sequence we can associate a sequence of Gibbs measures $(\mu_{\phi}^m)$. In this paper, we prove that these measures weakly converge at exponential speed to $\mu_\phi$ (in the classical distance metrizing weak topology). We also establish a strong mixing property (ensuring weak Bernoullicity) of $\mu_\phi$. Finally, we prove that the measure-theoretic entropy of $\mu_\phi^m$ converges to the one of $\mu_\phi$ exponentially fast. We indicate how to extend our results to more general subshifts and potentials. We stress that we use basic algebraic tools (contractive properties of iterated matrices) and symbolic dynamics.Comment: 18 pages, no figure

Experimental evidence of a natural parity state in 26^{26}Mg and its impact to the production of neutrons for the s process

We have studied natural parity states in $^{26}$Mg via the $^{22}$Ne($^{6}$Li,d)$^{26}$Mg reaction. Our method significantly improves the energy resolution of previous experiments and, as a result, we report the observation of a natural parity state in $^{26}$Mg. Possible spin-parity assignments are suggested on the basis of published $\gamma$-ray decay experiments. The stellar rate of the $^{22}$Ne($\alpha$,$\gamma$)$^{26}$Mg reaction is reduced and may give rise to an increase in the production of s-process neutrons via the $^{22}$Ne($\alpha$,n)$^{25}$Mg reaction.Comment: Published in PR