Periodic dynamics of coupled cell networks I: rigid patterns of synchrony and phase relations

It has recently been proved by Golubitsky and coworkers that in any network of coupled dynamical systems, the possible 'rigid' patterns of synchrony of hyperbolic equilibria are determined by purely combinatorial properties of the network, known as 'balanced equivalence relations'. A pattern is 'rigid' if it persists under small 'admissible' perturbations of the differential equation — ones that respect the network structure. We discuss a natural generalisation of these ideas to time-periodic states, and motivate two basic conjectures, the Rigid Synchrony Conjecture and the Rigid Phase Conjecture. These conjectures state that for rigid hyperbolic time-periodic patterns, cells with synchronous dynamics must have synchronous input cells, and cells with phase-related dynamics must have input cells that have the same phase relations. We provide evidence supporting the two conjectures, by proving them for a special class of periodic orbits, which we call 'tame', under strong assumptions on the network architecture and the symmetries of the periodic state. The discussion takes place in the formal setting of coupled cell networks. We prove that rigid patterns of synchrony are balanced, together with the analogous result for rigid patterns of phase relations. The assumption on the network architecture simplifies the geometry of admissible vector fields, while tameness rules out patterns with non-trivial local or multilocal symmetry. The main idea is to perturb an admissible vector field in a way that retains sufficient control over the associated perturbed periodic orbit. We present two techniques for constructing these perturbations, both using a general theorem on groupoid-symmetrisation of vector fields, which has independent interest. In particular we introduce a method of 'patching' that makes local changes to an admissible vector field. Having established these results for all-to-all coupled networks and tame periodic orbits we prove more general versions that require these assumptions only on a suitable quotient network. These conditions are weaker and encompass a larger class of networks and periodic orbits. We give an example to show that rigidity cannot be relaxed to hyperbolicity. We also prove, without any technical assumptions, that rigidly synchronous or phase-related cells must be input-isomorphic, a necessary precondition for the two conjectures to hold.     

Abnormal mucosal glycoprotein synthesis in inflammatory bowel diseases is not related to cigarette smoking

Patients with ulcerative colitis are usually non- or ex-smokers in contrast to Crohn's disease where smoking is common. Abnormalities of quantity and quality of intestinal mucus have been postulated in the pathogenesis of these diseases. It is possible that smoking habit may exert its effects via changes in mucus in inflammatory bowel disease. We have therefore studied incorporation of N-acetylglucosamine into synthesized colonic mucin in explants from 85 controls with normal colonoscopic appearances and histology, including 27 smokers and 58 nonsmokers, 36 patients with ulcerative colitis and 19 with ileocolonic Crohn's disease over 24 h in tissue culture. Incorporation of N-acetylglucosamine into normal explants was 31.3 +/- (SD) 7.1 dpm/microgram biopsy protein, incorporation was increased in patients with active Crohn's disease (mean 41.2 +/- (SD) 10.4 dpm/microgram biopsy protein, p = 0.003), decreased in inactive ulcerative colitis (mean 24.1 +/- 7.8 dpm/microgram biopsy protein, p = 0.0006) but normal in active ulcerative colitis (mean 35.0 +/- 13.8 dpm/microgram biopsy protein, p = 0.44). No significant relationship was found between cigarette smoking habits and mucus synthesis in controls with normal mucosa (nonsmokers, n = 58, mean 31.0 +/- (SD) 7.52 dpm/microgram biopsy protein; smokers, n = 27, mean 31.8 +/- (SD) 6.1 dpm/microgram biopsy protein, p = 0.9). This study shows that mucus glycoprotein synthesis is reduced in inactive ulcerative colitis, rising to normal levels in active disease and that synthesis is increased in Crohn's disease. There is no effect of smoking on mucus synthesis by control biopsies suggesting that the differences seen in inflammatory bowel disease are not related to cigarette smoking.     

Correlations involving modulae and cross-polarization time constants for a series of polyurethane elastomers

Correlations between the macroscopic bulk polymer properties storage modulus (E′) and loss modulus (E″) and the microscopic property of cross-polarization as represented by the time constant T_CH have been established for a series of polyurethane elastomers. The dependence of E′, E″, and T_CH as a function of molecular weight, rigid domain concentration, and temperature are graphically presented as a series of log plots. An experimental relationship is presented that shows that the distribution of motions of the flexible domains appears to be the major factor in the success of these correlations.     

PMMA tacticity and alumina powder dispersion stability

Summary Sedimentation experiments and X-ray photoelectron spectroscopy (XPS or ESCA) analyses have been used to study the effect of poly(methylmethacrylate) (PMMA) tacticity on aluminum oxide powder dispersion stability in a common solvent medium. The relative trends from sedimentation densities, and from surface analyses after solvent washing show that (PMMA) adsorption is greatest with isotactic polymer, where isotactic>atactic>syndiotactic adsorption. These results suggest that surface adsorption and hence dispersion stability can be influenced by polymer chain configuration as well as by chain conformation.     

THC-induced place and taste aversions in Lewis and Sprague-Dawley rats.

The hedonic properties of delta-9-tetrahydrocannabinol (THC) were assessed in place and taste conditioning paradigms in both Lewis and Sprague-Dawley rat strains. THC produced place avoidance, taste avoidance, and aversive taste reactivity responses in both strains. The Lewis strain displayed more aversive taste reactions and a stronger taste avoidance when conditioned with lower doses of THC than did the Sprague-Dawley strain of rats. THC is an anomalous drug of abuse that appears to be aversive to rats when assessed by these measures. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Benzoquinones, a homoisoflavanone and other constitutents from Polygonatum alte-lobatum

From the rhizomes of Polygonatum alte-lobatum, two new homologous series of 1,4-benzoquinones, polygonaquinones A and B, a novel homoisoflavanone, a new gentrogenin glycoside and 13 known compounds were isolated and characterized. The structures of the new compounds were determined as two homologous series of three 2,5-dihydroxy-3-methyl-6-alkyl-1,4-benzoquinones and three 2-hydroxy-3-methyl-6-alkyl-1,4-benzoquinones, with chain lengths C21 to C23, and 4',5,7-trihydroxy-6,8-dimethylhomoisoflavanone and gentrogenin 3-O-beta-D-glucopyranosyl(1-->2)-[beta-D-xylopyranosyl(1-->3)] -beta-D-glucopyranosyl(1-->4)-beta-D-galactopyranoside.     

Expression of INK4 inhibitors of cyclin D-dependent kinases during mouse brain development

In situ hybridization of mouse embryo sections demonstrated expression of mRNAs encoding two polypeptide inhibitors (p18INK4c and p19INK4d) of cyclin D-dependent kinase (CDK) 4 and CDK6 in the central nervous system. No expression of two other INK4 members, p16INK4a and p15INK4b, was observed. The p19INK4d and p18INK4c proteins formed complexes with either CDK4 or CDK6 in a temporal pattern consistent with the results of in situ hybridization. Expression of INK4c was observed at embryonic day 13.5 in neuroepithelial zones of the developing brain, being restricted to dividing neuroblasts but absent from differentiating postmitotic neurons. In the neocortex, p18INK4c was expressed precisely at those developmental stages when neuroblasts switch from a symmetric to an asymmetric pattern of cell division with concomitant increases in their G1 interval. INK4d RNA was detected from embryonic day 11.5 onward, at higher levels than INK4c and with a distinctly different spatial and temporal pattern. Marked INK4d expression was seen in dorsal root ganglia, spinal cord, and focally throughout the brain, but primarily in postmitotic neurons. Neural expression of INK4d continued postnatally into adulthood in postmitotic cells of the dentate gyrus, the pyramidal layer of the hippocampus, and in discrete regions of the cerebral cortex, cerebellum, thalamus, and brainstem. Downregulation of p19INK4d in the dentate gyrus after kainic acid-induced seizures indicated that its expression could also be modified in nondividing cells by excitotoxic stress. Therefore, p19INK4d may contribute to maintaining the quiescent state, acting as a buffer to prevent reactivation of cyclin D-dependent kinases in terminally differentiated cells.     

Intermediate-term outcome of cervical spinal cord-injured patients older than 50 years of age

STUDY DESIGN: This study retrospectively reviewed the intermediate-term clinical outcome of patients who were 50 years of age or older at the time they experienced their cervical spinal cord injury. OBJECTIVES: To establish reasonable expectations for the functional outcome in the older patient with cervical spinal cord injury. BACKGROUND DATA: The long-term morbidity and mortality of large groups of patients with spinal cord injury have been reported. The specific functional ability, disposition, morbidity, and mortality of this group of older patients injured after 50 years of age, however, have been less well defined. METHODS: Forty-one consecutive patients older than 50 years of age at the time of cervical cord injury were studied, and functional abilities, independence, need for assistance in activities of daily living, disposition, morbidity, and mortality were assessed. All patients had more than 2 years of follow-up examinations (mean, 5.5 years) by the same spine injury service. RESULTS: There were 13 complete and 28 incomplete cervical cord lesions. The mean age of the patients at follow-up examination was 67.5 years. The average follow-up period was 5.5 years after injury. None of the patients with complete cord injury improved, and all required extensive care. Twenty-one (80%) of 26 of the patients with incomplete cord injury were able to ambulate with some assistance. Nineteen of 26 patients had independent or near-independent abilities with activities of daily living. Twenty (77%) of 26 were able to return home. All patients with complete cord injury (13 of 13) had died by the time of the follow-up visit. Seventy-seven percent (10 of 13) of this patient group had died within the first year. Those surviving lived an average of 3.5 years after their injury. Fourteen of 28 patients with incomplete cord injury (50%) had died by the time of the follow-up visit. Six (43%) of the 14 deaths were attributed to complications of their spinal cord injury. CONCLUSION: The functional outcome of the person older than 50 years with a complete cervical cord injury is poor. Of the 14% who survived the first year, all required extensive attendant care, and no neurologic improvement was seen. The patient with an incomplete cord injury has an overall good outcome regarding ambulation and returning to home.     

Atrial fibrillation in Wolff-Parkinson-White syndrome. Development and therapy

In patients with Wolff-Parkinson-White syndrome the accessory pathway may participate in various tachyarrhythmias thereby influencing symptoms and prognosis. Atrial fibrillation occurs in 10 to 32% of patients and may have life-threatening consequences by precipitating ventricular fibrillation in patients with rapid conduction due to an accessory pathway with short anterograde refractory period (< 250 ms). Pathogenesis of atrial fibrillation in the WPW syndrome and therapeutic options are reviewed in this presentation. Spontaneous degeneration of atrioventricular reentrant tachycardia has been reported to represent the most frequent mode of initiation of atrial fibrillation during electrophysiologic study (up to 64% of episodes). Hemodynamic changes during tachycardia may lead to increased sympathetic tone, hypoxemia or increased tension of the atrial wall, thus, triggering atrial fibrillation. Induction of reentrant tachycardia during electrophysiologic study also has shown to be strongly correlated to its clinical prevalence and is inducible in up to 77% of patients with atrial fibrillation. The pathogenesis and high incidence of atrial fibrillation in patients with WPW syndrome is related to presence and functional properties of the accessory pathway. After surgical excision or catheter ablation more than 90% of patients are free of this arrhythmia. Anterograde conduction properties of the pathway appear to be more important than retrograde properties. High incidence of atrial fibrillation is related to short anterograde refractory periods, and of note, this arrhythmia is rare (3%) in patients with concealed pathways. With intracardiac recordings, Jackman et al. could demonstrate atrial fibrillation due to micro-reentry originating in accessory pathway networks.(ABSTRACT TRUNCATED AT 250 WORDS)