Sensitivity analysis of initial value problems with mixed odes and algebraic equations

An efficient method is described for sensitivity analysis of nonlinear initial value problems, which may include algebraic equations as well as ordinary differential equations.The linearity of the sensitivity equations is utilized to solve them directly via the local Jacobian of the state equations. The method is implemented with the implicit integrator DASSL and is demonstrated on a stiff industrial reaction model.     

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.     

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.     

Human papillomavirus-specific serologic response in vulvar neoplasia

We describe a case of positional dyspnea due to compression of the tracheobronchial tree by an extensive thoracic aneurysm. In a 77-year-old woman with long-standing systemic hypertension, intermittent anterior chest pain gradually developed over several years. She had no history of asthma or thoracic trauma. She was admitted to our hospital because of sudden, severe shortness of breath. The breathlessness was markedly worse when she lay on her back or on her right side. On physical examination, she was in acute respiratory distress with cyanosis, severe hypertension (180/110 mmHg), tachycardia, and inspiratory stridor. A chest X-ray film showed loss of volume and nearly complete radiopacity of the left hemithorax. Arterial blood gas analysis revealed an arterial oxygen partial pressure of 54.8 mmHg, a carbon dioxide partial pressure of 39.8 mmHg, and an oxygen saturation of 84.5 percent on room air. Computed tomographic examination of the thorax showed dilation of the aortic arch and descending aorta, and marked compression of the trachea and the left main bronchus. Examination with a fiberoptic bronchoscope revealed extrinsic compression of the trachea just proximal to the carina. The patient's symptoms stabilized. However, she did not undergo surgery because of her age and because of the size of the aneurysm. She died due to rupture of the aneurysm.     

The partial testing design: a less costly way to test equivalence for sensitivity and specificity

We propose a new, less costly, design to test the equivalence of digital versus analogue mammography in terms of sensitivity and specificity. Because breast cancer is a rare event among asymptomatic women, the sample size for testing equivalence of sensitivity is larger than that for testing equivalence of specificity. Hence calculations of sample size are based on sensitivity. With the proposed design it is possible to achieve the same power as a completely paired design by increasing the number of less costly analogue mammograms and not giving the more expensive digital mammograms to some randomly selected subjects who are negative on the analogue mammogram. The key idea is that subjects who are negative on the analogue mammogram are unlikely to have cancer and hence contribute less information for estimating sensitivity than subjects who are positive on the analogue mammogram. To ascertain disease state among subjects not biopsied, we propose another analogue mammogram at a later time determined by a natural history model. The design differs from a double sampling design because it compares two imperfect tests instead of combining information from a perfect and imperfect test.