An elementary proof of Franks' lemma for geodesic flows

Given a Riemannian manifold $(M,g)$ and a geodesic $\gamma$, the perpendicular part of the derivative of the geodesic flow $\phi_g^t: SM \rightarrow SM$ along $\gamma$ is a linear symplectic map. We give an elementary proof of the following Franks' lemma, originally found in [G. Contreras and G. Paternain, 2002] and [G. Contreras, 2010]: this map can be perturbed freely within a neighborhood in $Sp(n)$ by a $C^2$-small perturbation of the metric $g$ that keeps $\gamma$ a geodesic for the new metric. Moreover, the size of these perturbations is uniform over fixed length geodesics on the manifold. When $\dim M \geq 3$, the original metric must belong to a $C^2$--open and dense subset of metrics

Minimal free resolutions of complete bipartite graph ideals

Abstract. This paper gives an explicit construction for the minimal free resolution of a complete bipartite graph ideal. This yields a combinatorial formula for the Betti numbers and projective dimension of complete bipartite graph ideals. The question of how to compute the minimal free resolution of an ideal in a polynomial ring R = k[x 1 , ..., x n ] and the information it provides are very important in commutative algebra. It is theoretically possible, via algorithmic methods, to compute any free resolution with the computer program Macaulay2. We are interested, however, in finding an explicit construction of the minimal free resolution for ideals that have a combinatorial nature. Using results from [BS], this paper presents such a construction for complete bipartite graph ideals. This paper gives an explicit description of the minimal free resolution of complete bipartite graph ideals by providing a topological cell complex whose corresponding cellular complex is minimal (this topological cell complex is not simplicial and so is not the usual cell complex associated to monomial ideals). This approach not only gives a simple explicit description of the minimal free resolution but provides, as a corollary, a combinatorial description of the betti numbers for these ideals. In independent work, Sean Jacques Graph ideals are monomial, square-free ideals generated by quadrics that have a natural correspondence to combinatorial graphs. Let G be a graph with vertex se

Variation in VKORC1 is associated with vascular dementia

BACKGROUND: The genetic variant rs9923231 (VKORC1) is associated with differences in the coagulation of blood and consequentially with sensitivity to the drug warfarin. Variation in VKORC1 has been linked in a gene-based test to dementia/Alzheimer’s disease in the parents of participants, with suggestive evidence for an association for rs9923231 (p = 1.8×10(–7)), which was included in the genome-wide significant KAT8 locus. OBJECTIVE: Our study aimed to investigate whether the relationship between rs9923231 and dementia persists only for certain dementia sub-types, and if those taking warfarin are at greater risk. METHODS: We used logistic regression and data from 238,195 participants from UK Biobank to examine the relationship between VKORC1, risk of dementia, and the interplay with warfarin use. RESULTS: Parental history of dementia, APOE variant, atrial fibrillation, diabetes, hypertension, and hypercholesterolemia all had strong associations with vascular dementia (p < 4.6×10(–6)). The T-allele in rs9923231 was linked to a lower warfarin dose (β(perT - allele) = –0.29, p < 2×10(–16)) and risk of vascular dementia (OR = 1.17, p = 0.010), but not other dementia sub-types. However, the risk of vascular dementia was not affected by warfarin use in carriers of the T-allele. CONCLUSION: Our study reports for the first time an association between rs9923231 and vascular dementia, but further research is warranted to explore potential mechanisms and specify the relationship between rs9923231 and features of vascular dementia

Microbial Diversity in Sediment Ecosystems (Evaporites Domes, Microbial Mats, and Crusts) of Hypersaline Laguna Tebenquiche, Salar de Atacama, Chile

We combined nucleic acid-based molecular methods, biogeochemical measurements, and physicochemical characteristics to investigate microbial sedimentary ecosystems of Laguna Tebenquiche, Atacama Desert, Chile. Molecular diversity, and biogeochemistry of hypersaline microbial mats, rhizome-associated concretions, and an endoevaporite were compared with: The V4 hypervariable region of the 16S rRNA gene was amplified by pyrosequencing to analyze the total microbial diversity (i.e., bacteria and archaea) in bulk samples, and in addition, in detail on a millimeter scale in one microbial mat and in one evaporite. Archaea were more abundant than bacteria. Euryarchaeota was one of the most abundant phyla in all samples, and particularly dominant (97% of total diversity) in the most lithified ecosystem, the evaporite. Most of the euryarchaeal OTUs could be assigned to the class Halobacteria or anaerobic and methanogenic archaea

Review of additive manufactured tissue engineering scaffolds: relationship between geometry and performance

Material extrusion additive manufacturing has rapidly grown in use for tissue engineering research since its adoption in the year 2000. It has enabled researchers to produce scaffolds with intricate porous geometries that were not feasible with traditional manufacturing processes. Researchers can control the structural geometry through a wide range of customisable printing parameters and design choices including material, print path, temperature, and many other process parameters. Currently, the impact of these choices is not fully understood. This review focuses on how the position and orientation of extruded filaments, which sometimes referred to as the print path, lay-down pattern, or simply "scaffold design", affect scaffold properties and biological performance. By analysing trends across multiple studies, new understanding was developed on how filament position affects mechanical properties. Biological performance was also found to be affected by filament position, but a lack of consensus between studies indicates a need for further research and understanding. In most research studies, scaffold design was dictated by capabilities of additive manufacturing software rather than free-form design of structural geometry optimised for biological requirements. There is scope for much greater application of engineering innovation to additive manufacture novel geometries. To achieve this, better understanding of biological requirements is needed to enable the effective specification of ideal scaffold geometries

Prokaryotic diversity and biogeochemical characteristics of benthic microbial ecosystems at La Brava, a hypersaline lake at Salar de Atacama, Chile

Benthic microbial ecosystems of Laguna La Brava, Salar de Atacama, a high altitude hypersaline lake, were characterized in terms of bacterial and archaeal diversity, biogeochem-istry, (including O2 and sulfide depth profiles and mineralogy), and physicochemical characteristics. La Brava is one of several lakes in the Salar de Atacama where microbial communities are growing in extreme conditions, including high salinity, high solar insolation, and high levels of metals such as lithium, arsenic, magnesium, and calcium. Evaporation creates hypersaline conditions in these lakes and mineral precipitation is a characteristic geomicrobiological feature of these benthic ecosystems. In this study, the La Brava non-lithifying microbial mats, microbialites, and rhizome-associated concretions were compared to each other and their diversity was related to their environmental conditions. All the ecosystems revealed an unusual community where Euryarchaeota, Crenarchaeota, Acetothermia, Firmicutes and Planctomycetes were the most abundant groups, and cyanobacteria, typically an important primary producer in microbial mats, were relatively insignificant or absent. This suggests that other microorganisms, and possibly novel pathways unique to this system, are responsible for carbon fixation. Depth profiles of O2 and sulfide showed active production and respiration. The mineralogy composition was calcium carbonate (as aragonite) and increased from mats to microbialites and rhizome-associated concretions. Halite was also present. Further analyses were performed on representative microbial mats and microbialites by layer. Different taxonomic compositions were observed in the upper layers, with Archaea dominating the non-lithifying mat, and Planctomycetes the microbialite. The bottom layers were similar, with Euryarchaeota, Crenarchaeota and Planctomycetes as dominant phyla. Sequences related to Cyanobacteria were very scarce. These systems may contain previously uncharacterized community metabolisms, some of which may be contributing to net mineral precipitation. Further work on these sites might reveal novel organisms and metabolisms of biotechnological interest.Centro de Investigaciones Geológica