The motion of whips and chains

We study the motion of an inextensible string (a whip) fixed at one point in the absence of gravity, satisfying the equations $$\eta_{tt} = \partial_s(\sigma \eta_s), \qquad \sigma_{ss}-\lvert \eta_{ss}\rvert^2 = -\lvert \eta_{st}\rvert^2, \qquad \lvert \eta_s\rvert^2 \equiv 1$$ with boundary conditions $\eta(t,1)=0$ and $\sigma(t,0)=0$. We prove local existence and uniqueness in the space defined by the weighted Sobolev energy $$\sum_{\ell=0}^m \int_0^1 s^{\ell} \lvert \partial_s^{\ell}\eta_t\rvert^2 \, ds + \int_0^1 s^{\ell+1} \lvert \partial_s^{\ell+1}\eta\rvert^2 \, ds,$$ when $m\ge 3$. In addition we show persistence of smooth solutions as long as the energy for $m=3$ remains bounded. We do this via the method of lines, approximating with a discrete system of coupled pendula (a chain) for which the same estimates hold.Comment: 47 pages, 8 figure

Failure patterns in resected pancreas adenocarcinoma: lack of predicted benefit to SMAD4 expression.

OBJECTIVE: To determine whether SMAD4 expression is associated with recurrence pattern after resection for pancreatic ductal adenocarcinoma (PDA). BACKGROUND: SMAD4 expression status has been reported to be associated with patterns of failure in PDA, but studies have not examined recurrence patterns after resection. METHODS: A tissue microarray was constructed including 127 patients with resected PDA and either short-term (\u3c12 \u3emonths) or long-term (\u3e30 months) survival. SMAD4 expression was evaluated by immunohistochemistry and categorized as present or lost in tumor cells. Conventional pathologic features (lymph node metastases, positive resection margin, poor grade, and tumor size) were recorded, and disease-specific outcomes (eg, recurrence pattern and early cancer-specific mortality) were determined. RESULTS: Loss of SMAD4 expression in pancreatic adenocarcinoma was identified in 40 of 127 patients (32%). SMAD4 loss occurred in 27% of patients who experienced isolated local recurrence, 33% of patients with a distant recurrence, 33% of patients who experienced local and distant site recurrences, and 25% of patients who were without evidence of recurrence (Fisher exact, P = 0.9). In a multivariate analysis, the presence of regional lymph node metastases was the only factor associated with the development of distant metastases (odds ratio = 4.7, P = 0.02). SMAD4 was neither associated with recurrence pattern (odds ratio = 0.9, P = 0.9) nor associated with early death (odds ratio = 0.5, P = 0.15). CONCLUSIONS: Primary tumor SMAD4 expression status was not a predictor of recurrence pattern in a large cohort of patients with resected PDA

Hyperoxia impairs alveolar formation and induces senescence through decreased histone deacetylase activity and up-regulation of p21 in neonatal mouse lung

Alveolar development comprises the transition of lung architecture from saccules to gas-exchange units during late gestation and early postnatal development. Exposure to hyperoxia disrupts developmental signaling pathways and causes alveolar hypoplasia as seen in bronchopulmonary dysplasia affecting preterm human newborns. Expanding literature suggests that epigenetic changes due to environmental triggers during development may lead to genetically heritable changes in gene expression. Given recent data on altered histone deacetylase (HDAC) activity in lungs of humans and animal models with airspace enlargement/emphysema, we hypothesized that alveolar hypoplasia from hyperoxia exposure in neonatal mice is a consequence of cell cycle arrest and reduced HDAC activity and up-regulation of the cyclin-dependent kinase inhibitor, p21. We exposed newborn mice to hyperoxia and compared lung morphologic and epigenetic changes to room air controls. Further, we pretreated a subgroup of animals with the macrolide antibiotic azithromycin (AZM), known to possess anti-inflammatory properties. Our results showed that hyperoxia exposure resulted in alveolar hypoplasia and was associated with decreased HDAC1 and HDAC2 and increased p53 and p21 expression. Further, AZM did not confer protection against hyperoxia-induced alveolar changes. These findings suggest that alveolar hypoplasia due to hyperoxia is mediated by epigenetic changes affecting cell cycle regulation/senescence during lung development

A unique androgen excess signature in idiopathic intracranial hypertension is linked to cerebrospinal fluid dynamics

Idiopathic intracranial hypertension (IIH) is a condition of unknown etiology, characterized by elevated intracranial pressure frequently manifesting with chronic headaches and visual loss. Similar to polycystic ovary syndrome (PCOS), IIH predominantly affects obese women of reproductive age. In this study, we comprehensively examined the systemic and cerebrospinal fluid (CSF) androgen metabolome in women with IIH in comparison with sex-, BMI-, and age-matched control groups with either simple obesity or PCOS (i.e., obesity and androgen excess). Women with IIH showed a pattern of androgen excess distinct to that observed in PCOS and simple obesity, with increased serum testosterone and increased CSF testosterone and androstenedione. Human choroid plexus expressed the androgen receptor, alongside the androgen-activating enzyme aldoketoreductase type 1C3. We show that in a rat choroid plexus cell line, testosterone significantly enhanced the activity of Na+/K+-ATPase, a surrogate of CSF secretion. We demonstrate that IIH patients have a unique signature of androgen excess and provide evidence that androgens can modulate CSF secretion via the choroid plexus. These findings implicate androgen excess as a potential causal driver and therapeutic target in IIH

Metabolic Concepts in Idiopathic Intracranial Hypertension and Their Potential for Therapeutic Intervention.

BACKGROUND Traditional risk factors associated with idiopathic intracranial hypertension (IIH) include obesity, weight gain, and female sex. The incidence of IIH is increasing and yet the underlying trigger and the fueling pathological mechanisms are still poorly understood. EVIDENCE ACQUISITION Review of ophthalmology, neurology, general surgery, obesity, endocrinology, nutrition, and neurosurgery literature was made. RESULTS The facts that implicate sex and obesity in IIH and headache are examined. The role of fat distribution in IIH is questioned, and the concept of adipose tissue functioning as an endocrine organ driving IIH is discussed. The impact of androgen metabolism in IIH is reviewed as is the emerging role of glucagon-like-peptide-1 analogues in modulating intracranial pressure. This introduces the concept of developing targeted disease-modifying therapeutic strategies for IIH. CONCLUSIONS This review will discuss the possible role of the adipose/gut/brain metabolism axis in IIH and speculate how this may impact the pathogenesis of IIH and therapeutic opportunities