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.     

High Throughput Primer Walking of cDNA Clones

Primer walking of cloned DNA is a standard research tool. It has been used in the past to determine the sequence of individual clones of interest. With the expansion of DNA sequencing capacity the need to be able to walk larger numbers of clones has become necessary. Our laboratory is a mid-sized genomics facility. In conjunction with the Advanced Biomedical Computing Center (ABCC) we have developed methods for automating the primer selection, DNA sequencing, contig assembly and sequence analysis for clones arrayed in microtiter format. This approach has allowed us to walk 475 clones (five microtiter plates) selected from a cDNA library.     

Alcoholism: independent predictor of survival in patients with head and neck cancer

BACKGROUND: Despite recognition of the high prevalence of alcoholism among patients with head and neck cancer, the prognostic importance of alcoholism has not been evaluated adequately. Previous investigators have speculated that alcoholic patients may have a poorer prognosis than nonalcoholic patients because of more advanced stage of cancer, the immunosuppressive effects of alcohol, and an increased rate of death due to other alcohol-related diseases. PURPOSE: The goal of this population-based study was to identify the features of alcoholism that are associated with survival for patients with head and neck cancer and to develop an alcoholic severity staging system from a composite of the independent features of alcoholism. METHODS: This prospective study included 649 patients who were diagnosed with cancer of the oral cavity, oropharynx, hypopharynx, or larynx during the period from September 1, 1983, through February 28, 1987, in a three-county area of western Washington state that participates in the Surveillance, Epidemiology, and End Results Program of the U.S. National Cancer Institute. Details on lifetime alcohol consumption, treatment for alcoholism, abstinence from alcohol prior to the diagnosis of cancer, and alcohol-related health problems were ascertained through in-person interviews near the time of diagnosis. Patients were classified as either nonalcoholics or alcoholics according to their responses to questions from the Michigan Alcoholism Screening Test. The measures of alcohol consumption and abuse that were found to be independently associated with 5-year survival by logistic regression analysis were combined using conjunctive consolidation to create a final composite variable, called an alcoholic severity stage. Cox proportional hazards regression analysis was done to estimate the relative risk (R) of death within 5 years due to specific causes of death for each of the alcoholic severity stages. RESULTS: Alcoholism (RR = 2.06; 95% confidence interval [CI] = 1.43-2.98) and a history of alcohol-related systemic health problems (i.e., liver disease, pancreatitis, delirium tremens, or seizures) (RR = 2.76; 95% CI = 1.69-4.49) were associated with an increased risk of death, whereas abstinence (i.e., the consumption of fewer than one drink per week at 1 year prior to the diagnosis of cancer) (RR = 0.62; 95% CI = 0.39-0.97) was associated with a decreased risk of death. These associations were independent of age, site of cancer, anatomical stage, histopathologic grade, smoking, and type of antineoplastic treatment. Patients in the two worst alcoholic severity stages had an increased risk of dying not only of head and neck cancer but also of cardiovascular disease, pulmonary disease, and other alcohol-related causes. CONCLUSIONS: Alcohol abuse, measured by alcohol consumption, functional impairment, a history of alcohol-related health problems, or abstinence, can provide important prognostic information for patients with head and neck cancer. Our results suggest that sobriety among alcoholic patients can lead to prolonged survival.     

Endothelin-1 concentrations and optimisation of arterial oxygenation and venous admixture by selective pulmonary artery infusion of prostaglandin E1 during thoracotomy

PURPOSE: To demonstrate a superselective intraarterial chemotherapy as a therapeutic alternative in the treatment of previously treated recurrent lymph node metastases in breast cancer. METHODS: 14 patients with recurrent lymph node metastases in cases of breast cancer were presented to be treated by intraarterial chemotherapy of 25 mg mitoxantrone/m2 over a period of 24 hours. In two patients with superclavicular lymph node involvement an intraarterial therapy could not be carried out because of a vascular connection to the anterior spinal artery. Involved lymph stations could be reached in superselective technique by side branches of the subclavian artery. Heparin coverage was given intravenously. Every patient had had surgery, radiation, systemic chemo- and hormonal therapy before and was now graded as inoperable. Therapy indication was given by local tumour-induced symptoms. RESULTS: In the 12 treated cases complete remission was seen in three, partial remission in 4, a steady state in two and a progressive disease in three. There were no complications or severe side effects. CONCLUSION: Intraarterial chemotherapy is an effective and well tolerated treatment in recurrent lymph node metastases in cases of breast cancer even if conventional therapies can no longer be used.     

Ex vivo expansion with stem cell factor and interleukin-11 augments both short-term recovery posttransplant and the ability to serially transplant marrow

The characterization of many cytokines involved in the control of hematopoiesis has led to intense investigation into their potential use in ex vivo culture to expand progenitor numbers. We have established the optimum ex vivo culture conditions that allow substantial amplification of transient engrafting murine stem cells and which, simultaneously, augment the ability to sustain serial bone marrow transplantation (BMT). Short-term incubation of unfractionated BM cells in liquid culture with stem cell factor (SCF) and interleukin-11 (IL-11) produced a 50-fold amplification of clonogenic multipotential progenitors (CFU-A). Following such ex vivo expansion, substantially fewer cells were required to rescue lethally irradiated mice. When transplanted in cell doses above threshold for engraftment, BM cells expanded ex vivo resulted in significantly more rapid hematopoietic recovery. In a serial transplantation model, unmanipulated BM was only able to consistently sustain secondary BMT recipients, but BM expanded ex vivo has sustained quaternary BMT recipients that remain alive and well more than 140 days after 4th degree BMT. These results show augmentation of both short-term recovery posttransplant and the ability to serially transplant marrow by preincubation in culture with SCF and IL-11.     

Convection in a concentric annulus with heat generating porous media and a permeable inner boundary

The effects of a permeable inner boundary on the maximum temperature and the convective flows were investigated numerically for a two-dimensional horizontal annulus containing a uniformly heat generating porous media. The time-dependent governing equations were nondimensionalized and put into an explicit finite difference numerical form. The finite difference equations were obtained from truncated Taylor series expansions using a central differencing scheme. Nondimensional temperatures and streamlines were obtained for heat generation rates ranging from 20 to 1,500 W/m³ corresponding to a range of modified Rayleigh numbers of 324 to 24,340 and for several combinations of isothermally heated wall conditions for annuli of radius ratio of 2. It was found that multi-cellular flows occur at the highest Rayleigh numbers investigated.