A combinatorial approach to knot recognition

This is a report on our ongoing research on a combinatorial approach to knot recognition, using coloring of knots by certain algebraic objects called quandles. The aim of the paper is to summarize the mathematical theory of knot coloring in a compact, accessible manner, and to show how to use it for computational purposes. In particular, we address how to determine colorability of a knot, and propose to use SAT solving to search for colorings. The computational complexity of the problem, both in theory and in our implementation, is discussed. In the last part, we explain how coloring can be utilized in knot recognition

30 inch Roll-Based Production of High-Quality Graphene Films for Flexible Transparent Electrodes

We report that 30-inch scale multiple roll-to-roll transfer and wet chemical doping considerably enhance the electrical properties of the graphene films grown on roll-type Cu substrates by chemical vapor deposition. The resulting graphene films shows a sheet resistance as low as ~30 Ohm/sq at ~90 % transparency which is superior to commercial transparent electrodes such as indium tin oxides (ITO). The monolayer of graphene shows sheet resistances as low as ~125 Ohm/sq with 97.4% optical transmittance and half-integer quantum Hall effect, indicating the high-quality of these graphene films. As a practical application, we also fabricated a touch screen panel device based on the graphene transparent electrodes, showing extraordinary mechanical and electrical performances

Pediatric supracondylar fractures of the distal humerus

Supracondylar fractures of the humerus are a common pediatric elbow injury that are historically associated with morbidity due to malunion, neurovascular complications, and compartment syndrome. True anteroposterior and lateral radiographs are essential not only for an accurate diagnosis, but also for creating a treatment plan for these injuries. A staging system (based on the lateral radiograph) for classifying the severity of the fracture helps guide definitive management. Nondisplaced fractures are treated initially with a posterior splint, followed by a long-arm casting. Closed reduction and percutaneous pinning is the preferred treatment for displaced or unstable fractures. If there is any question about fracture stability, patients should be seen within 5 days postoperatively for repeat radiographs to ensure that the reduction and pin fixation has been maintained. Understanding the anatomy, radiographic findings, management options, and complications associated with this fracture allow physicians to limit the morbidity associated with this relatively common pediatric injury

Prenatal hypoxia induces increased cardiac contractility on a background of decreased capillary density.

Background: Chronic hypoxia in utero (CHU) is one of the most common insults to fetal development and may be associated with poor cardiac recovery from ischaemia-reperfusion injury,yet the effects on normal cardiac mechanical performance are poorly understood. Methods: Pregnant female wistar rats were exposed to hypoxia (12% oxygen, balance nitrogen)for days 10–20 of pregnancy. Pups were born into normal room air and weaned normally. At 10 weeks of age, hearts were excised under anaesthesia and underwent retrograde 'Langendorff' perfusion. Mechanical performance was measured at constant filling pressure (100 cm H2O) with intraventricular balloon. Left ventricular free wall was dissected away and capillary density estimated following alkaline phosphatase staining. Expression of SERCA2a and Nitric Oxide Synthases (NOS) proteins were estimated by immunoblotting. Results: CHU significantly increased body mass (P < 0.001) compared with age-matched control rats but was without effect on relative cardiac mass. For incremental increases in left ventricular balloon volume, diastolic pressure was preserved. However, systolic pressure was significantly greater following CHU for balloon volume = 50 μl (P < 0.01) and up to 200 μl (P < 0.05). For higher balloon volumes systolic pressure was not significantly different from control. Developed pressures were correspondingly increased relative to controls for balloon volumes up to 250 μl (P < 0.05).Left ventricular free wall capillary density was significantly decreased in both epicardium (18%; P <0.05) and endocardium (11%; P < 0.05) despite preserved coronary flow. Western blot analysis revealed no change to the expression of SERCA2a or nNOS but immuno-detectable eNOS protein was significantly decreased (P < 0.001) in cardiac tissue following chronic hypoxia in utero. Conclusion: These data offer potential mechanisms for poor recovery following ischaemia, including decreased coronary flow reserve and impaired angiogenesis with subsequent detrimental effects of post-natal cardiac performance

History of sentinel node and validation of the technique

Sentinel node biopsy is a minimally invasive technique to select patients with occult lymph node metastases who may benefit from further regional or systemic therapy. The sentinel node is the first lymph node reached by metastasising cells from a primary tumour. Attempts to remove this node with a procedure based on standard anatomical patterns did not become popular. The development of the dynamic technique of intraoperative lymphatic mapping in the 1990s resulted in general acceptance of the sentinel node concept. This hypothesis of sequential tumour dissemination seems to be valid according to numerous studies of sentinel node biopsy with confirmatory regional lymph node dissection. This report describes the history and the validation of the technique, with particular reference to breast cancer

A Novel Liquid Multi-Phytonutrient Supplement Demonstrates DNA-Protective Effects

This study explored the DNA protective (anti-mutagenic) effects of an oral, liquid, multi-phytonutrient dietary supplement containing a proprietary blend of fruits, vegetables and aloe vera concentrated components in addition to a proprietary catechin complex from green tea (VIBE Cardiac & Life, Eniva Nutraceuticals, Anoka, MN; herein described as “VIBE”). This study tested the hypothesis that VIBE would reduce DNA damage in skin cells exposed to UVR. Human epidermal cells, from the cell line A431NS, were treated with 0% (control), 0.125%, 0.5%, 1% and 2% VIBE, and then exposed to 240 J/m2 UVR. The amount of DNA damage was assessed using the COMET assay. At each concentration tested, a significantly smaller amount of DNA damage was measured by the COMET assay for the VIBE treated cells compared to the control cells exposed to UVR without VIBE. The dose response curves showed a maximal response at 0.5% VIBE with a threefold reduction in COMET tail density compared to the control samples without VIBE (p < 0.001). Additional research is warranted in human clinical trials to further explore the results of this study which demonstrated the DNA protective and anti-mutagenic effects of VIBE for human skin cells exposed to UVR-induced DNA damage