Geometric description of C-vectors and real L\"osungen

We introduce real Loesungen as an analogue of real roots. For each mutation sequence of an arbitrary skew-symmetrizable matrix, we define a family of reflections along with associated vectors which are real Loesungen and a set of curves on a Riemann surface. The matrix consisting of these vectors is called L-matrix. We explain how the L-matrix naturally arises in connection with the C-matrix. Then we conjecture that the L-matrix depends (up to signs of row vectors) only on the seed, and that the curves can be drawn without self-intersections, providing a new combinatorial/geometric description of c-vectors

A Combinatorial Formula for Certain Elements of Upper Cluster Algebras

We develop an elementary formula for certain non-trivial elements of upper cluster algebras. These elements have positive coefficients. We show that when the cluster algebra is acyclic these elements form a basis. Using this formula, we show that each non-acyclic skew-symmetric cluster algebra of rank 3 is properly contained in its upper cluster algebra

Hypoglossal schwannoma masquerading as a carotid body tumor.

Study Objective. To describe the clinical presentation, evaluation, and treatment of a hypoglossal schwannoma. Methods. We report an unusual case of a hypoglossal schwannoma presenting as a pulsatile level II neck mass at the bifurcation of the external and internal carotid arteries, mimicking a carotid body tumor. Radiologic findings are reviewed in detail. Results. A 59-year-old female presented to a tertiary care medical center with complaints of a pulsatile right-sided neck mass. An MRA of the neck was obtained demonstrating a 5 cm mass located at the carotid artery bifurcation and causing splaying of the internal and external carotids. Based on clinical presentation and imaging, a diagnosis of a carotid body tumor was conferred and the patient scheduled for excision. Intraoperatively, the mass was noted to arise from the hypoglossal nerve, remaining independent of the carotid artery. On histopathologic analysis, the mass was determined to be consistent with hypoglossal schwannoma. Conclusion. Though rare, the hypoglossal schwannoma should remain a consideration in the evaluation of a parapharyngeal space mass. As this report demonstrates, the clinical and radiologic presentation of a hypoglossal schwannoma may closely mimic that of the more common carotid body tumor

Civic Community Theory and Rates of Violence: A Review of Literature on an Emergent Theoretical Perspective

Civic community theory has emerged in the last 10 years as a middle range theory to explain community variation in rates of crime. It has proven to be particularly powerful for explaining variations in violent crime across rural communities in the U.S. This essay provides a review of the available published literature testing components of the theory. The three main conceptual dimensions of the civic community thesis are outlined, and the nature of the empirical evidence is evaluated. The essay concludes with several suggestions for future research

Free-Energy Calculations Highlight Differences in Accuracy between X-Ray and NMR Structures and Add Value to Protein Structure Prediction

AbstractBackground: While X-ray crystallography structures of proteins are considerably more reliable than those from NMR spectroscopy, it has been difficult to assess the inherent accuracy of NMR structures, particularly the side chains.Results: For 15 small single-domain proteins, we used a molecular mechanics-/dynamics-based free-energy approach to investigate native, decoy, and fully extended alpha conformations. Decoys were all less energetically favorable than native conformations in nine of the ten X-ray structures and in none of the five NMR structures, but short 150 ps molecular dynamics simulations on the experimental structures caused them to have the lowest predicted free energy in all 15 proteins. In addition, a strong correlation exists (r2 = 0.86) between the predicted free energy of unfolding, from native to fully extended conformations, and the number of residues.Conclusions: This work suggests that the approximate treatment of solvent used in solving NMR structures can lead NMR model conformations to be less reliable than crystal structures. This conclusion was reached because of the considerably higher calculated free energies and the extent of structural deviation during aqueous dynamics simulations of NMR models compared to those determined by X-ray crystallography. Also, the strong correlation found between protein length and predicted free energy of unfolding in this work suggests, for the first time, that a free-energy function can allow for identification of the native state based on calculations on an extended state and in the absence of an experimental structure

Mathematical modelling of tissue-engineering angiogenesis

We present a mathematical model for the vascularisation of a porous scaffold following implantation in vivo. The model is given as a set of coupled non-linear ordinary differential equations (ODEs) which describe the evolution in time of the amounts of the different tissue constituents inside the scaffold. Bifurcation analyses reveal how the extent of scaffold vascularisation changes as a function of the parameter values. For example, it is shown how the loss of seeded cells arising from slow infiltration of vascular tissue can be overcome using a prevascularisation strategy consisting of seeding the scaffold with vascular cells. Using certain assumptions it is shown how the system can be simplified to one which is partially tractable and for which some analysis is given. Limited comparison is also given of the model solutions with experimental data from the chick chorioallantoic membrane (CAM) assay

Peri-urban wild dogs : diet and movements in north-eastern Australia

Knowledge of peri-urban dingo or wild dog ecology can assist management agencies in developing management approaches that alleviate human-wildlife conflicts. Here we summarise (1) the food and dietary items identified in wild dog scats and (2) wild dog movement ecology in urban areas. Individual prey species commonly observed in scats included agile wallabies, northern brown bandicoots and swamp wallabies. Dietary overlap analyses indicated that wild dogs ate the same types or sizes of prey in different regions. In general, wild dogs occupied small fragments of bushland within an urban matrix, were active at all times of the day, and lived within a few hundred meters of houses and humans at all times. These data suggest that urban wild dog management strategies should focus on the mitigation of impacts at the individual or group level, and not population-level reductions in numbers