Exact properties of Frobenius numbers and fraction of the symmetric semigroups in the weak limit for n=3

We generalize and prove a hypothesis by V. Arnold on the parity of Frobenius number. For the case of symmetric semigroups with three generators of Frobenius numbers we found an exact formula, which in a sense is the sum of two Sylvester's formulaes. We prove that the fraction of the symmetric semigroups is vanishing in the weak limit

Prying into the intimate secrets of animal lives; software beyond hardware for comprehensive annotation in ‘Daily Diary’ tags

Smart tags attached to freely-roaming animals recording multiple parameters at infra-second rates are becoming commonplace, and are transforming our understanding of the way wild animals operate. However, interpretation of such data is complex and currently limits the ability of biologists to realise the value of their recorded information. This work presents a single program, FRAMEWORK 4, that uses a particular sensor constellation described in the?Daily Diary? tag (recording tri-axial acceleration, tri-axial magnetic field intensity, pressure and e.g. temperature and light intensity) to determine the 4 key elements considered pivotal within the conception of the tag. These are; animal trajectory, behaviour, energy expenditure and quantification of the environment in which the animal operates. The program takes the original data recorded by the Daily Dairy and transforms it into dead-reckoned movements,template-matched behaviours, dynamic body acceleration-derived energetics and positionlinked environmental data before outputting it all into a single file. Biologists are thus left with a single data set where animal actions and environmental conditions can be linked across time and space.Fil: Walker, James S.. Swansea University. College Of Sciences; Reino UnidoFil: Jones, Mark W.. Swansea University. College Of Sciences; Reino UnidoFil: Laramee, Robert S.. Swansea University. College Of Sciences; Reino UnidoFil: Holton, Mark D.. Swansea University; Reino UnidoFil: Shepard, Emily L. C.. Swansea University. College Of Sciences; Reino UnidoFil: Williams, Hannah J.. Swansea University. College Of Sciences; Reino UnidoFil: Scantlebury, D. Michael. The Queens University Of Belfast; IrlandaFil: Marks, Nikki, J.. The Queens University Of Belfast; IrlandaFil: Magowan, Elizabeth A.. The Queens University Of Belfast; IrlandaFil: Maguire, Iain E.. The Queens University Of Belfast; IrlandaFil: Grundy, Ed. Swansea University. College Of Sciences; Reino UnidoFil: Di Virgilio, Agustina Soledad. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Patagonia Norte. Instituto de Investigación En Biodiversidad y Medioambiente; Argentina. Universidad Nacional del Comahue; ArgentinaFil: Wilson, Rory P.. Swansea University. College Of Sciences; Reino Unid

Identification of animal movement patterns using tri-axial magnetometry

BackgroundAccelerometers are powerful sensors in many bio-logging devices, and are increasingly allowing researchers to investigate the performance, behaviour, energy expenditure and even state, of free-living animals. Another sensor commonly used in animal-attached loggers is the magnetometer, which has been primarily used in dead-reckoning or inertial measurement tags, but little outside that. We examine the potential of magnetometers for helping elucidate the behaviour of animals in a manner analogous to, but very different from, accelerometers. The particular responses of magnetometers to movement means that there are instances when they can resolve behaviours that are not easily perceived using accelerometers.MethodsWe calibrated the tri-axial magnetometer to rotations in each axis of movement and constructed 3-dimensional plots to inspect these stylised movements. Using the tri-axial data of Daily Diary tags, attached to individuals of number of animal species as they perform different behaviours, we used these 3-d plots to develop a framework with which tri-axial magnetometry data can be examined and introduce metrics that should help quantify movement and behaviour.ResultsTri-axial magnetometry data reveal patterns in movement at various scales of rotation that are not always evident in acceleration data. Some of these patterns may be obscure until visualised in 3D space as tri-axial spherical plots (m-spheres). A tag-fitted animal that rotates in heading while adopting a constant body attitude produces a ring of data around the pole of the m-sphere that we define as its Normal Operational Plane (NOP). Data that do not lie on this ring are created by postural rotations of the animal as it pitches and/or rolls. Consequently, stereotyped behaviours appear as specific trajectories on the sphere (m-prints), reflecting conserved sequences of postural changes (and/or angular velocities), which result from the precise relationship between body attitude and heading. This novel approach shows promise for helping researchers to identify and quantify behaviours in terms of animal body posture, including heading.ConclusionMagnetometer-based techniques and metrics can enhance our capacity to identify and examine animal behaviour, either as a technique used alone, or one that is complementary to tri-axial accelerometry

Physics of Neutron Star Crusts

The physics of neutron star crusts is vast, involving many different research fields, from nuclear and condensed matter physics to general relativity. This review summarizes the progress, which has been achieved over the last few years, in modeling neutron star crusts, both at the microscopic and macroscopic levels. The confrontation of these theoretical models with observations is also briefly discussed.Comment: 182 pages, published version available at <http://www.livingreviews.org/lrr-2008-10

Increased B Cell ADAM10 in Allergic Patients and Th2 Prone Mice

ADAM10, as the sheddase of the low affinity IgE receptor (CD23), promotes IgE production and thus is a unique target for attenuating allergic disease. Herein, we describe that B cell levels of ADAM10, specifically, are increased in allergic patients and Th2 prone WT mouse strains (Balb/c and A/J). While T cell help augments ADAM10 expression, Balb WT B cells exhibit increased ADAM10 in the naïve state and even more dramatically increased ADAM10 after anti-CD40/IL4 stimulation compared C57 (Th1 prone) WT B cells. Furthermore, ADAM17 and TNF are reduced in allergic patients and Th2 prone mouse strains (Balb/c and A/J) compared to Th1 prone controls. To further understand this regulation, ADAM17 and TNF were studied in C57Bl/6 and Balb/c mice deficient in ADAM10. C57-ADAM10B-/- were more adept at increasing ADAM17 levels and thus TNF cleavage resulting in excess follicular TNF levels and abnormal secondary lymphoid tissue architecture not noted in Balb-ADAM10B-/-. Moreover, the level of B cell ADAM10 as well as Th context is critical for determining IgE production potential. Using a murine house dust mite airway hypersensitivity model, we describe that high B cell ADAM10 level in a Th2 context (Balb/c WT) is optimal for disease induction including bronchoconstriction, goblet cell metaplasia, mucus, inflammatory cellular infiltration, and IgE production. Balb/c mice deficient in B cell ADAM10 have attenuated lung and airway symptoms compared to Balb WT and are actually most similar to C57 WT (Th1 prone). C57-ADAM10B-/- have even further reduced symptomology. Taken together, it is critical to consider both innate B cell levels of ADAM10 and ADAM17 as well as Th context when determining host susceptibility to allergic disease. High B cell ADAM10 and low ADAM17 levels would help diagnostically in predicting Th2 disease susceptibility; and, we provide support for the use ADAM10 inhibitors in treating Th2 disease

Giant cell tumor of the uterus: case report and response to chemotherapy

BACKGROUND: Giant cell tumor (GCT) is usually a benign but locally aggressive primary bone neoplasm in which monocytic macrophage/osteoclast precursor cells and multinucleated osteoclast-like giant cells infiltrate the tumor. The etiology of GCT is unknown, however the tumor cells of GCT have been reported to produce chemoattractants that can attract osteoclasts and osteoclast precursors. Rarely, GCT can originate at extraosseous sites. More rarely, GCT may exhibit a much more aggressive phenotype. The role of chemotherapy in metastatic GCT is not well defined. CASE PRESENTATION: We report a case of an aggressive GCT of the uterus with rapidly growing lung metastases, and its response to chemotherapy with pegylated-liposomal doxorubicin, ifosfamide, and bevacizumab, along with a review of the literature. CONCLUSION: Aggressive metastasizing GCT may arise in the uterus, and may respond to combination chemotherapy