New results on q-positivity

In this paper we discuss symmetrically self-dual spaces, which are simply real vector spaces with a symmetric bilinear form. Certain subsets of the space will be called q-positive, where q is the quadratic form induced by the original bilinear form. The notion of q-positivity generalizes the classical notion of the monotonicity of a subset of a product of a Banach space and its dual. Maximal q-positivity then generalizes maximal monotonicity. We discuss concepts generalizing the representations of monotone sets by convex functions, as well as the number of maximally q-positive extensions of a q-positive set. We also discuss symmetrically self-dual Banach spaces, in which we add a Banach space structure, giving new characterizations of maximal q-positivity. The paper finishes with two new examples.Comment: 18 page

Algal-fungal mutualism: cell recognition and maintenance of the symbiotic status of lichens

Lichens are specific symbiotic associations between photosynthetic algae or cyanobacteria and heterotrophic fungi forming a double entity in which both components coexist. Specificity required for the lichen establishment can be defined in this context as the preferential, but not exclusive, association of a biont with another, since the algal factor susceptible to be recognized is an inducible protein. Recognition of compatible algal cells is performed by specific lectins produced and secreted by the potential mycobiont. Some lectins from phycolichens and cyanolichens are glycosylated arginases which bind to an algal cell wall receptor, identified as a a-1, 4-polygalactosylated urease. However, other ligands exist which bind other lectins specific for mannose or glucose. This implies that, after recognition of a potential, compatible partner, other fungal lectins could determine the final success of the association. Since the fungus can parasitize non - recognized partners during the development of the association, the success after the first contact needs of a set of algal cells, the number of which was sufficient to prevent that the death of a certain number of them makes fail the symbiosis. Fungal lectins act as chemo tactic factors in such a way that algae and cyanobacteria move towards the hyphae, to acquire that critical size of the colony, by means of successive contractions and relaxation of the actomyosin cytoskeleton in absence of any motile appendages

UVB radiation induced effects on cells studied by FTIR spectroscopy

We have made a preliminary analysis of the results about the eVects on tumoral cell line (lymphoid T cell line Jurkat) induced by UVB radiation (dose of 310 mJ/cm^2) with and without a vegetable mixture. In the present study, we have used two techniques: Fourier transform infrared spectroscopy (FTIR) and flow cytometry. FTIR spectroscopy has the potential to provide the identiWcation of the vibrational modes of some of the major compounds (lipid, proteins and nucleic acids) without being invasive in the biomaterials. The second technique has allowed us to perform measurements of cytotoxicity and to assess the percentage of apoptosis. We already studied the induction of apoptotic process in the same cell line by UVB radiation; in particular, we looked for correspondences and correlations between FTIR spetroscopy and flow cytometry data finding three highly probable spectroscopic markers of apoptosis (Pozzi et al. in Radiat Res 168:698-705, 2007). In the present work, the results have shown significant changes in the absorbance and spectral pattern in the wavenumber protein and nucleic acids regions after the treatments

Closedness type regularity conditions for surjectivity results involving the sum of two maximal monotone operators

In this note we provide regularity conditions of closedness type which guarantee some surjectivity results concerning the sum of two maximal monotone operators by using representative functions. The first regularity condition we give guarantees the surjectivity of the monotone operator $S(\cdot + p)+T(\cdot)$, where $p\in X$ and $S$ and $T$ are maximal monotone operators on the reflexive Banach space $X$. Then, this is used to obtain sufficient conditions for the surjectivity of $S+T$ and for the situation when $0$ belongs to the range of $S+T$. Several special cases are discussed, some of them delivering interesting byproducts.Comment: 11 pages, no figure

An additive subfamily of enlargements of a maximally monotone operator

We introduce a subfamily of additive enlargements of a maximally monotone operator. Our definition is inspired by the early work of Simon Fitzpatrick. These enlargements constitute a subfamily of the family of enlargements introduced by Svaiter. When the operator under consideration is the subdifferential of a convex lower semicontinuous proper function, we prove that some members of the subfamily are smaller than the classical $\epsilon$-subdifferential enlargement widely used in convex analysis. We also recover the epsilon-subdifferential within the subfamily. Since they are all additive, the enlargements in our subfamily can be seen as structurally closer to the $\epsilon$-subdifferential enlargement

Individual variability in cardiac biomarker release after 30 min of high-intensity rowing in elite and amateur athletes

This study had two objectives: (i) to examine individual variation in the pattern of cardiac troponin I (cTnI) and N-terminal pro-brain natriuretic peptide (NT-proBNP) release in response to high-intensity rowing exercise, and (ii) to establish whether individual heterogeneity in biomarker appearance was influenced by athletic status (elite vs. amateur). We examined cTnI and NT-proBNP in 18 elite and 14 amateur rowers before and 5 min, 1, 3, 6, 12, and 24 h after a 30-min maximal rowing test. Compared with pre-exercise levels, peak postexercise cTnI (pre: 0.014 ± 0.030 μg·L–1; peak post: 0.058 ± 0.091 μg·L–1; p = 0.000) and NT-proBNP (pre: 15 ± 11 ng·L–1; peak post: 31 ± 19 ng·L–1; p = 0.000) were elevated. Substantial individual heterogeneity in peak and time-course data was noted for cTnI. Peak cTnI exceeded the upper reference limit (URL) in 9 elite and 3 amateur rowers. No rower exceeded the URL for NT-proBNP. Elite rowers had higher baseline (0.019 ± 0.038 vs. 0.008 ± 0.015 μg·L–1; p = 0.003) and peak postexercise cTnI (0.080 ± 0.115 vs. 0.030 ± 0.029 μg·L–1; p = 0.022) than amateur rowers, but the change with exercise was similar between groups. There were no significant differences in baseline and peak postexercise NT-proBNP between groups. In summary, marked individuality in the cTnI response to a short but high-intensity rowing bout was observed. Athletic status did not seem to affect the change in cardiac biomarkers in response to high-intensity exercise

Set optimization - a rather short introduction

Recent developments in set optimization are surveyed and extended including various set relations as well as fundamental constructions of a convex analysis for set- and vector-valued functions, and duality for set optimization problems. Extensive sections with bibliographical comments summarize the state of the art. Applications to vector optimization and financial risk measures are discussed along with algorithmic approaches to set optimization problems

General models in min-max continous location

In this paper, a class of min-max continuous location problems is discussed. After giving a complete characterization of th stationary points, we propose a simple central and deep-cut ellipsoid algorithm to solve these problems for the quasiconvex case. Moreover, an elementary convergence proof of this algorithm and some computational results are presented

Best approximation by downward sets with applications

We develop a theory of downward sets for a class of normed ordered spaces. We study best approximation in a normed ordered space X by elements of downward sets, and give necessary and sufficient conditions for any element of best approximation by a closed downward subset of X. We also characterize strictly downward subsets of X, and prove that a downward subset of X is strictly downward if and only if each its boundary point is Chebyshev. The results obtained are used for examination of some Chebyshev pairs (W,x), where x E X and W is a closed downward subset of X.C

A convergent algorithm for the hybrid problem of reconstructing conductivity from minimal interior data

We consider the hybrid problem of reconstructing the isotropic electric conductivity of a body $\Omega$ from interior Current Density Imaging data obtainable using MRI measurements. We only require knowledge of the magnitude $|J|$ of one current generated by a given voltage $f$ on the boundary $\partial\Omega$. As previously shown, the corresponding voltage potential u in $\Omega$ is a minimizer of the weighted least gradient problem $$u=\hbox{argmin} \{\int_{\Omega}a(x)|\nabla u|: u \in H^{1}(\Omega), \ \ u|_{\partial \Omega}=f\},$$ with $a(x)= |J(x)|$. In this paper we present an alternating split Bregman algorithm for treating such least gradient problems, for $a\in L^2(\Omega)$ non-negative and $f\in H^{1/2}(\partial \Omega)$. We give a detailed convergence proof by focusing to a large extent on the dual problem. This leads naturally to the alternating split Bregman algorithm. The dual problem also turns out to yield a novel method to recover the full vector field $J$ from knowledge of its magnitude, and of the voltage $f$ on the boundary. We then present several numerical experiments that illustrate the convergence behavior of the proposed algorithm