A new algorithm for recognizing the unknot

The topological underpinnings are presented for a new algorithm which answers the question: `Is a given knot the unknot?' The algorithm uses the braid foliation technology of Bennequin and of Birman and Menasco. The approach is to consider the knot as a closed braid, and to use the fact that a knot is unknotted if and only if it is the boundary of a disc with a combinatorial foliation. The main problems which are solved in this paper are: how to systematically enumerate combinatorial braid foliations of a disc; how to verify whether a combinatorial foliation can be realized by an embedded disc; how to find a word in the the braid group whose conjugacy class represents the boundary of the embedded disc; how to check whether the given knot is isotopic to one of the enumerated examples; and finally, how to know when we can stop checking and be sure that our example is not the unknot.Comment: 46 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol2/paper9.abs.htm

Phase Transitions from Saddles of the Potential Energy Landscape

The relation between saddle points of the potential of a classical many-particle system and the analyticity properties of its thermodynamic functions is studied. For finite systems, each saddle point is found to cause a nonanalyticity in the Boltzmann entropy, and the functional form of this nonanalytic term is derived. For large systems, the order of the nonanalytic term increases unboundedly, leading to an increasing differentiability of the entropy. Analyzing the contribution of the saddle points to the density of states in the thermodynamic limit, our results provide an explanation of how, and under which circumstances, saddle points of the potential energy landscape may (or may not) be at the origin of a phase transition in the thermodynamic limit. As an application, the puzzling observations by Risau-Gusman et al. on topological signatures of the spherical model are elucidated.Comment: 5 pages, no figure

The influence of self-citation corrections on Egghe's g index

The g index was introduced by Leo Egghe as an improvement of Hirsch's index h for measuring the overall citation record of a set of articles. It better takes into account the highly skewed frequency distribution of citations than the h index. I propose to sharpen this g index by excluding the self-citations. I have worked out nine practical cases in physics and compare the h and g values with and without self-citations. As expected, the g index characterizes the data set better than the h index. The influence of the self-citations appears to be more significant for the g index than for the h index.Comment: 9 pages, 2 figures, submitted to Scientometric

Oxygen Concentration Flammability Thresholds of Selected Aerospace Materials Considered for the Constellation Program

Materials selection for spacecraft is based on an upward flammability test conducted in a quiescent environment in the highest expected oxygen concentration environment. The test conditions and its pass/fail test logic do not provide sufficient quantitative materials flammability information for an advanced space exploration program. A modified approach has been suggested determination of materials self-extinguishment limits. The flammability threshold information will allow NASA to identify materials with increased flammability risk from oxygen concentration and total pressure changes, minimize potential impacts, and allow for development of sound requirements for new spacecraft and extraterrestrial landers and habitats. This paper provides data on oxygen concentration self-extinguishment limits under quiescent conditions for selected materials considered for the Constellation Program

Optimization of Drug Prescription and Medication Management in Older Adults with Cardiovascular Disease

Cardiovascular disease increases incrementally with age and elderly patients concomitantly sustain multimorbidities, with resultant prescription of multiple medications. Despite conforming with disease-specific cardiovascular clinical practice guidelines, this polypharmacy predisposes many elderly individuals with cardiovascular disease to adverse drug events and non-adherence. Patient-centered care requires that the clinician explore with each patient his or her goals of care and that this shared decision-making constitutes the basis for optimization of medication management. This approach to aligning therapies with patient preferences is likely to promote patient satisfaction, to limit morbidity, and to favorably affect healthcare costs

A regularisation approach to causality theory for C^{1,1}Lorentzian metrics

We show that many standard results of Lorentzian causality theory remain valid if the regularity of the metric is reduced to C^{1,1}. Our approach is based on regularisations of the metric adapted to the causal structure

The Incidence and Health Economic Burden of Ischemic Amputation in Minnesota, 2005-2008

Critical limb ischemia (CLI) is the most severe manifestation of peripheral artery disease (PAD), is associated with high rates of myocardial infarction, stroke, and amputation, and has a high health economic cost. The objective of this study was to estimate the incidence of lower limb amputation, the most serious consequence of CLI, and to create a surveillance methodology for the incidence of ischemic amputation in Minnesota

Nonanalyticities of the entropy induced by saddle points of the potential energy landscape

The relation between saddle points of the potential of a classical many-particle system and the analyticity properties of its Boltzmann entropy is studied. For finite systems, each saddle point is found to cause a nonanalyticity in the Boltzmann entropy, and the functional form of this nonanalytic term is derived for the generic case of potentials having the Morse property. With increasing system size the order of the nonanalytic term grows unboundedly, leading to an increasing differentiability of the entropy. Nonetheless, a distribution of an unboundedly growing number of saddle points may cause a phase transition in the thermodynamic limit. Analyzing the contribution of the saddle points to the density of states in the thermodynamic limit, conditions on the distribution of saddle points and their curvatures are derived which are necessary for a phase transition to occur. With these results, the puzzling absence of topological signatures in the spherical model is elucidated. As further applications, the phase transitions of the mean-field XY model and the mean-field k-trigonometric model are shown to be induced by saddle points of vanishing curvature.Comment: 24 pages, 2 figure

Electrical cortical stimulation can impair production of the alphabet without impairing counting

Neurosurgery has the potential to cure patients with drug-resistant focal epilepsy, but carries the risk of permanent language impairment when surgery involves the dominant hemisphere of the brain. This risk can be estimated and minimized using electrical stimulation mapping (ESM), which uses cognitive and linguistic tasks during cortical ESM to differentiate "eloquent" and "resectable" areas in the brain. One such task, counting, is often used to screen and characterize language during ESM in patients whose language abilities are limited. Here we report a patient with drug-resistant epilepsy arising from the language-dominant hemisphere using fMRI. Our patient experienced loss of the ability to recite or write the alphabet, but not to count, during ESM of the dominant left posterior superior temporal gyrus. This selective impairment extended to both spoken and written production. We suggest the need for caution when using counting as a sole means to screen language function and as a method of testing low functioning patients using ESM