Weak elastic energy of irregular curves.

A weak notion of elastic energy for (not necessarily regular) rectifiable curves in any space dimension is proposed. Our [Formula: see text]-energy is defined through a relaxation process, where a suitable [Formula: see text]-rotation of inscribed polygons is adopted. The discrete [Formula: see text]-rotation we choose has a geometric flavour: a polygon is viewed as an approximation to a smooth curve, and hence its discrete curvature is spread out into a smooth density. For any exponent [Formula: see text] greater than 1, the [Formula: see text]-energy is finite if and only if the arc-length parametrization of the curve has a second-order summability with the same growth exponent. In that case, moreover, the energy agrees with the natural extension of the integral of the [Formula: see text]th power of the scalar curvature. Finally, a comparison with other definitions of discrete curvature is provided. This article is part of the theme issue 'Foundational issues, analysis and geometry in continuum mechanics'.

The Drosophila Polycomb group gene pleiohomeotic encodes a DNA binding protein with homology to the transcription factor YY1.

Genes of the Polycomb group (PcG) of Drosophila encode proteins necessary for the maintenance of transcriptional repression of homeotic genes. PcG proteins are thought to act by binding as multiprotein complexes to DNA through Polycomb group response elements (PREs); however, specific DNA binding has not been demonstrated for any of the PcG proteins. We have identified a sequence-specific DNA binding protein that interacts with a PRE from the Drosophila engrailed gene. This protein (PHO) is a homolog of the ubiquitous mammalian transcription factor Yin Yang-1 and is encoded by pleiohomeotic, a known member of the PcG. We propose that PHO acts to anchor PcG protein complexes to DNA.

Level of receptor-associated protein moderates cellular susceptibility to pseudomonas exotoxin A.

Pseudomonas exotoxin A (PE) enters mammalian cells via a receptor-mediated endocytic pathway. The initial step in this pathway is binding to the multiligand receptor termed the alpha 2-macroglobulin receptor/low-density lipoprotein receptor-related protein (LRP). Binding of toxin, and of the many other ligands that bind to LRP, is blocked by the addition of a 39-kDa receptor-associated protein (RAP). Here we show that approximately 40% of the cell-associated LRP is on the surface of toxin-sensitive mouse LM fibroblasts and thus accessible for toxin internalization. The remainder is located intracellularly, primarily in the Golgi region. Mammalian cells exhibit a wide range of sensitivity to PE. To investigate possible reasons for this, we examined the expression levels of both LRP and RAP. Results from a variety of cell lines indicated that there was a positive correlation between LRP expression and toxin sensitivity. In the absence of LRP, cells were as much as 200-fold more resistant to PE compared with sensitive cells. A second group of resistant cells expressed LRP but had a high level of RAP. Thus, a toxin-resistant phenotype would be expected when cells expressed either low levels of LRP or high levels of LRP in the presence of high levels of RAP. We hypothesize that RAP has a pivotal role in moderating cellular susceptibility to PE.

Emergency physician workload: a time study.

STUDY HYPOTHESIS: Physician service time varies with patient service category, length of stay, and intensity of service. DESIGN: Prospective time study of emergency physician services. Physicians recorded the beginning and ending times of each service episode offered to a patient (whether at the bedside or occurring elsewhere in the department). Each episode was defined as an "interaction," with the total service time offered to a patient being the sum of all interactions for that patient. Length of stay was the time interval from when the patient registered in the emergency department to when the patient was released. Intensity of service was calculated as service time divided by length of stay. SETTING: University-affiliated community teaching hospital. TYPE OF PARTICIPANTS: One thousand three hundred forty-seven ED patients were entered into the study for nonselected (514), walk-in (637), observation (52), laceration repair (102), or critical care (42) services. Six of 12 physicians in the group staffing the ED participated in the study. Patient data were entered onto study cards when the service was offered. Patients were entered into the study consecutively except when the physician became too busy to see one patient at a time and accurately enter time data; such interruptions occurred for 18% of the patients. RESULTS: Physician service time for nonselected service patients (24.2 minutes per patient; 95% CI, 23.1-25.3) was consistent with ACEP's findings for nonselected services offered by emergency physicians (22 minutes per patient). Physician service time did not vary significantly from the standard for laceration repair patients (25.0 minutes per patient; 95% CI, 22.6-27.4) but did vary significantly from the standard for walk-in (9.8 minutes per patient; 95% CI, 9.3-10.3; P < .05), observation (55.6 minutes per patient; 95% CI, 50.7-60.5; P < .05), and critical care patients (31.9 minutes per patient; 95% CI, 26.2-37.6; P < .05). Walk-in and laceration repair patients had a single physician-patient interaction (1.3 per patient and 1.1 per patient, respectively), consistent with a discrete service offered during episodic care. Observation and critical care patients had multiple physician-patient interactions (6.3 per patient and 2.6 per patient, respectively) over an extended period, which is consistent with additional services being offered during their period of observation/holding. CONCLUSION: Case mix of patient services affects emergency physician workload and should be considered in planning departmental staffing needs.

Decision to hospitalize: objective diagnosis-related group criteria versus clinical judgment.

Three hundred fifty patients in an observation unit attached to an emergency department received diagnostic workup of nine critical diagnostic syndromes (abdominal pain, flank pain, headache, possible cerebrovascular accident, chest pain, dizziness or syncope, head injury, seizure, multiple trauma). The decision to hospitalize for acute care after observation for 11.1 +/- 3.9 hours was examined. The objective diagnosis-related group (DRG) criteria for admission were compared retrospectively with the physician's clinical judgment of need for hospitalization. Clinical outcome was used to establish the correctness of the decision to hospitalize. Clinical judgment was compared with objective DRG criteria for reliability in predicting the presence of serious pathology necessitating acute care hospitalization; respective values were sensitivity, 100% vs 76%; specificity, 86% vs 80%; positive predictive value, 75% vs 62%; and negative predictive value, 100% vs 89%. The difference between the sensitivity of the two admission criteria was highly significant (P less than 10(-8); chi 2, 26.12). We conclude that the physician's clinical judgment outperforms DRG objective criteria in identifying which patients with critical diagnostic syndromes need acute care hospitalization for emergency medical or surgical therapy.

Use of glucagon in cholescintigraphy.

A case is presented in which intravenous administration of glucagon, presumably by relaxation of the sphincter of Oddi, facilitated the transit of a hepatobiliary radiopharmaceutical from the gallbladder into the bowel. This approach is likely more feasible than food intake and at least theoretically safer than cholecystokinin administration. Further studies are needed to assess the actual usefulness of this intervention.