Exponential Decay for Damped Klein-Gordon Equations on Asymptotically Cylindrical and Conic Manifolds

We study the decay of the global energy for the damped Klein-Gordon equation on non-compact manifolds with finitely many cylindrical and subconic ends up to bounded perturbation. We prove that under the Geometric Control Condition, the decay is exponential, and that under the weaker Network Control Condition, the decay is logarithmic, by developing the global Carleman estimate with multiple weights

Optimal backward uniqueness and polynomial stability of second order equations with unbounded damping

For general second order evolution equations, we prove an optimal condition on the degree of unboundedness of the damping, that rules out finite-time extinction. We show that control estimates give energy decay rates that explicitly depend on the degree of unboundedness, and establish a dilation method to turn existing control estimates for one propagator into those for another in the functional calculus. As corollaries, we prove Schr\"odinger observability gives decay for unbounded damping, weak monotonicity in damping, and quantitative unique continuation and optimal propagation for fractional Laplacians. As applications, we establish a variety of novel and explicit energy decay results to systems with unbounded damping, including singular damping, linearised gravity water waves and Euler--Bernoulli plates.Comment: 50 pages, 2 figure

Independent impacts of aging on mitochondrial DNA quantity and quality in humans

Background The accumulation of mitochondrial DNA (mtDNA) mutations, and the reduction of mtDNA copy number, both disrupt mitochondrial energetics, and may contribute to aging and age-associated phenotypes. However, there are few genetic and epidemiological studies on the spectra of blood mtDNA heteroplasmies, and the distribution of mtDNA copy numbers in different age groups and their impact on age-related phenotypes. In this work, we used whole-genome sequencing data of isolated peripheral blood mononuclear cells (PBMCs) from the UK10K project to investigate in parallel mtDNA heteroplasmy and copy number in 1511 women, between 17 and 85 years old, recruited in the TwinsUK cohorts. Results We report a high prevalence of pathogenic mtDNA heteroplasmies in this population. We also find an increase in mtDNA heteroplasmies with age (β = 0.011, P = 5.77e-6), and showed that, on average, individuals aged 70-years or older had 58.5% more mtDNA heteroplasmies than those under 40-years old. Conversely, mtDNA copy number decreased by an average of 0.4 copies per year (β = −0.395, P = 0.0097). Multiple regression analyses also showed that age had independent effects on mtDNA copy number decrease and heteroplasmy accumulation. Finally, mtDNA copy number was positively associated with serum bicarbonate level (P = 4.46e-5), and inversely correlated with white blood cell count (P = 0.0006). Moreover, the aggregated heteroplasmy load was associated with blood apolipoprotein B level (P = 1.33e-5), linking the accumulation of mtDNA mutations to age-related physiological markers. Conclusions Our population-based study indicates that both mtDNA quality and quantity are influenced by age. An open question for the future is whether interventions that would contribute to maintain optimal mtDNA copy number and prevent the expansion of heteroplasmy could promote healthy aging

mda-7/IL-24, novel anticancer cytokine: Focus on bystander antitumor, radiosensitization and antiangiogenic properties and overview of the phase I clinical experience (Review)

Subtraction hybridization applied to a ‘differentiation therapy’ model of cancer employing human melanoma cells resulted in the cloning of melanoma differentiation associated gene-7/interleukin-24 (mda-7/IL-24). Initial studies confirm an inverse correlation between mda-7 expression and melanoma development and progression. Forced expression of mda-7 by means of a plasmid or via a replication incompetent adenovirus (Ad.mda-7) promotes growth suppression and induces apoptosis in a broad array of human cancers. In contrast, mda-7 does not induce growth suppressive or toxic effects in normal cells. Based on structure (containing an IL-10 signature motif), secretion by cells (including subsets of T-cells) and location on chromosome 1q (in an area containing IL-10- family genes), mda-7 has now been renamed mda-7/IL-24. Studies by several laboratories have uncovered many of mda-7/ IL-24\u27s unique properties, including cancer-specific apoptosisinduction, cell cycle regulation, an ability to inhibit angiogenesis, potent ‘bystander antitumor activity’ and a capacity to enhance the sensitivity of tumor cells to radiation, chemo- therapy and monoclonal antibody therapy. Moreover, based on its profound cancer tropism, substantiated by in vivo human xenograft studies in nude mice, mda-7/IL-24 (administered as Ad.mda-7) was evaluated in a phase I clinical trial in patients with melanomas and solid cancers. These studies document that mda-7/IL-24 is well tolerated and demonstrates evidence of significant clinical activity. In these contexts, mda-7/IL-24 represents a unique cytokine gene with potential for therapy of human cancers. The present review focuses on three unique properties of mda-7/IL-24, namely its potent ‘bystander antitumor activity’, ability to sensitize tumor cells to radiation, and its antiangiogenesis properties. Additionally, an overview of the phase I clinical trial is provided. These studies affirm that mda-7/IL-24 has promise for the management of diverse cancers