Environmental risk factors and their footprints in vivo – a proposal for the classification of oxidative stress biomarkers

Environmental agents, including socioeconomic condition, and host factors can act as causal agents and risk factors in disease. We use biomarkers and sociomarkers to study causal factors, such as overproduction of reactive oxygen species (ROS) which could play a role in disease through oxidative stress. It is therefore important to define the exact meaning of the biomarker we measure. In this review we attempt a classification of biomarkers related to oxidative stress based on their biological meaning. We define as type zero biomarkers the direct measurement of ROS in vivo in patients. Type 1 biomarkers are the most frequently used indicators of oxidative stress, represented by oxidized lipids, proteins or nucleic acids and their bases. Type 2 biomarkers are indicators of the activation of biochemical pathways that can lead to the formation of ROS. Type 3 biomarkers are host factors such as small-molecular weight antioxidants and antioxidant enzymes, while type 4 biomarkers measure genetic factors and mutations that could modify the susceptibility of an individual to oxidative stress. We also discuss whether biomarkers are actionable or not, that is if the specific blockade of these molecules can ameliorate disease or if they are just surrogate markers. The proposed classification of biomarkers of oxidative stress based on their meaning and ambiguities, within the theoretical framework of the oxidative stress theory of disease may help identify those diseases, and individuals, where oxidative stress has a causal role, to allow targeted therapy and personalized medicine

Toroidalization of generating sequences in dimension two function fields of positive characteristic

We give a characteristic free proof of the main result of our previous paper (math.AC/0509697) concerning toroidalization of generating sequences of valuations in dimension two function fields. We show that when an extension of two dimensional algebraic regular local rings $R\subset S$ satisfies the conclusions of the Strong Monomialization theorem of Cutkosky and Piltant, the map between generating sequences in $R$ and $S$ has a toroidal structure

Adding dimensions to the analysis of the quality of health information of websites returned by Google. Cluster analysis identifies patterns of websites according to their classification and the type of intervention described.

Background and aims: Most of the instruments used to assess the quality of health information on the Web (e.g. the JAMA criteria) only analyze one dimension of information quality, trustworthiness. We try to compare these characteristics with the type of treatments the website describe, whether evidence-based medicine or note, and correlate this with the established criteria. Methods: We searched Google for “migraine cure” and analyzed the first 200 websites for: 1) JAMA criteria (authorship, attribution, disclosure, currency); 2) class of websites (commercial, health portals, professional, patient groups, no-profit); and 3) type of intervention described (approved drugs, alternative medicine, food, procedures, lifestyle, drugs still at the research stage). We used hierarchical cluster analysis to assess associations between classes of websites and types of intervention described. Subgroup analysis on the first 10 websites returned was performed. Results: Google returned health portals (44%), followed by commercial websites (31%) and journalism websites (11%). The type of intervention mentioned most often was alternative medicine (55%), followed by procedures (49%), lifestyle (42%), food (41%) and approved drugs (35%). Cluster analysis indicated that health portals are more likely to describe more than one type of treatment while commercial websites most often describe only one. The average JAMA score of commercial websites was significantly lower than for health portals or journalism websites, and this was mainly due to lack of information on the authors of the text and indication of the date the information was written. Looking at the first 10 websites from Google, commercial websites are under-represented and approved drugs over-represented. Conclusions: This approach allows the appraisal of the quality of health-related information on the Internet focusing on the type of therapies/prevention methods that are shown to the patient

On a class of vector fields with discontinuity of divide-by-zero type and its applications

We study phase portraits and singular points of vector fields of a special type, that is, vector fields whose components are fractions with a common denominator vanishing on a smooth regular hypersurface in the phase space. We assume also some additional conditions, which are fulfilled, for instance, if the vector field is divergence-free. This problem is motivated by a large number of applications. In this paper, we consider three of them in the framework of differential geometry: singularities of geodesic flows in various singular metrics on surfaces

Hausdorff volume in non equiregular sub-Riemannian manifolds

In this paper we study the Hausdorff volume in a non equiregular sub-Riemannian manifold and we compare it with a smooth volume. We first give the Lebesgue decomposition of the Hausdorff volume. Then we study the regular part, show that it is not commensurable with the smooth volume, and give conditions under which it is a Radon measure. We finally give a complete characterization of the singular part. We illustrate our results and techniques on numerous examples and cases (e.g. to generic sub-Riemannian structures)

Normal forms and invariants for 2-dimensional almost-Riemannian structures

Two-dimensional almost-Riemannian structures are generalized Riemannian structures on surfaces for which a local orthonormal frame is given by a Lie bracket generating pair of vector fields that can become collinear. Generically, there are three types of points: Riemannian points where the two vector fields are linearly independent, Grushin points where the two vector fields are collinear but their Lie bracket is not, and tangency points where the two vector fields and their Lie bracket are collinear and the missing direction is obtained with one more bracket. In this paper we consider the problem of finding normal forms and functional invariants at each type of point. We also require that functional invariants are "complete" in the sense that they permit to recognize locally isometric structures. The problem happens to be equivalent to the one of finding a smooth canonical parameterized curve passing through the point and being transversal to the distribution. For Riemannian points such that the gradient of the Gaussian curvature $K$ is different from zero, we use the level set of $K$ as support of the parameterized curve. For Riemannian points such that the gradient of the curvature vanishes (and under additional generic conditions), we use a curve which is found by looking for crests and valleys of the curvature. For Grushin points we use the set where the vector fields are parallel. Tangency points are the most complicated to deal with. The cut locus from the tangency point is not a good candidate as canonical parameterized curve since it is known to be non-smooth. Thus, we analyse the cut locus from the singular set and we prove that it is not smooth either. A good candidate appears to be a curve which is found by looking for crests and valleys of the Gaussian curvature. We prove that the support of such a curve is uniquely determined and has a canonical parametrization