The structure of algebraic covariant derivative curvature tensors

We use the Nash embedding theorem to construct generators for the space of algebraic covariant derivative curvature tensors

The ROCK inhibitor Fasudil prevents chronic restraint stress-induced depressive-like behaviors and dendritic spine loss in rat hippocampus

Indexación: Web of Science; Scopus.Background: Dendritic arbor simplification and dendritic spine loss in the hippocampus, a limbic structure implicated in mood disorders, are assumed to contribute to symptoms of depression. These morphological changes imply modifications in dendritic cytoskeleton. Rho GTPases are regulators of actin dynamics through their effector Rho kinase. We have reported that chronic stress promotes depressive-like behaviors in rats along with dendritic spine loss in apical dendrites of hippocampal pyramidal neurons, changes associated with Rho kinase activation. The present study proposes that the Rho kinase inhibitor Fasudil may prevent the stress-induced behavior and dendritic spine loss. Methods: Adult male Sprague-Dawley rats were injected with saline or Fasudil (i.p., 10 mg/kg) starting 4 days prior to and maintained during the restraint stress procedure (2.5 h/d for 14 days). Nonstressed control animals were injected with saline or Fasudil for 18 days. At 24 hours after treatment, forced swimming test, Golgi-staining, and immuno-western blot were performed. Results: Fasudil prevented stress-induced immobility observed in the forced swimming test. On the other hand, Fasudiltreated control animals showed behavioral patterns similar to those of saline-treated controls. Furthermore, we observed that stress induced an increase in the phosphorylation of MYPT1 in the hippocampus, an exclusive target of Rho kinase. This change was accompanied by dendritic spine loss of apical dendrites of pyramidal hippocampal neurons. Interestingly, increased pMYPT1 levels and spine loss were both prevented by Fasudil administration. Conclusion: Our findings suggest that Fasudil may prevent the development of abnormal behavior and spine loss induced by chronic stress by blocking Rho kinase activity.https://academic.oup.com/ijnp/article/20/4/336/263217

Stanilov-Tsankov-Videv Theory

We survey some recent results concerning Stanilov-Tsankov-Videv theory, conformal Osserman geometry, and Walker geometry which relate algebraic properties of the curvature operator to the underlying geometry of the manifold.Comment: This is a contribution to the Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P. Branson, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

A Non-Algebraic Patchwork

Itenberg and Shustin's pseudoholomorphic curve patchworking is in principle more flexible than Viro's original algebraic one. It was natural to wonder if the former method allows one to construct non-algebraic objects. In this paper we construct the first examples of patchworked real pseudoholomorphic curves in $\Sigma_n$ whose position with respect to the pencil of lines cannot be realised by any homologous real algebraic curve.Comment: 6 pages, 1 figur

Isotopic evidence for biogenic molecular hydrogen production in the Atlantic Ocean

Oceans are a net source of molecular hydrogen (H2) to the atmosphere. The production of marine H2 is assumed to be mainly biological by N2 fixation, but photochemical pathways are also discussed. We present measurements of mole fraction and isotopic composition of dissolved and atmospheric H2 from the southern and northern Atlantic between 2008 and 2010. In total almost 400 samples were taken during five cruises along a transect between Punta Arenas (Chile) and Bremerhaven (Germany), as well as at the coast of Mauretania. The isotopic source signatures of dissolved H2 extracted from surface water are highly deuterium-depleted and correlate negatively with temperature, showing δD values of (−629 ± 54) ‰ for water temperatures at (27 ± 3) °C and (−249 ± 88) ‰ below (19 ± 1) °C. The results for warmer water masses are consistent with biological production of H2. This is the first time that marine H2 excess has been directly attributed to biological production by isotope measurements. However, the isotope values obtained in the colder water masses indicate that beside possible biological production a significant different source should be considered. The atmospheric measurements show distinct differences between both hemispheres as well as between seasons. Results from the global chemistry transport model TM5 reproduce the measured H2 mole fractions and isotopic composition well. The climatological global oceanic emissions from the GEMS database are in line with our data and previously published flux calculations. The good agreement between measurements and model results demonstrates that both the magnitude and the isotopic signature of the main components of the marine H2 cycle are in general adequately represented in current atmospheric models despite a proposed source different from biological production or a substantial underestimation of nitrogen fixation by several authors

Random Walks Along the Streets and Canals in Compact Cities: Spectral analysis, Dynamical Modularity, Information, and Statistical Mechanics

Different models of random walks on the dual graphs of compact urban structures are considered. Analysis of access times between streets helps to detect the city modularity. The statistical mechanics approach to the ensembles of lazy random walkers is developed. The complexity of city modularity can be measured by an information-like parameter which plays the role of an individual fingerprint of {\it Genius loci}. Global structural properties of a city can be characterized by the thermodynamical parameters calculated in the random walks problem.Comment: 44 pages, 22 figures, 2 table

Leibnizian, Robinsonian, and Boolean Valued Monads

This is an overview of the present-day versions of monadology with some applications to vector lattices and linear inequalities.Comment: This is a talk prepared for the 20th St. Petersburg Summer Meeting in Mathematical Analysis, June 24-29, 201

A measure of centrality based on the spectrum of the Laplacian

We introduce a family of new centralities, the k-spectral centralities. k-Spectral centrality is a measurement of importance with respect to the deformation of the graph Laplacian associated with the graph. Due to this connection, k-spectral centralities have various interpretations in terms of spectrally determined information. We explore this centrality in the context of several examples. While for sparse unweighted networks 1-spectral centrality behaves similarly to other standard centralities, for dense weighted networks they show different properties. In summary, the k-spectral centralities provide a novel and useful measurement of relevance (for single network elements as well as whole subnetworks) distinct from other known measures.Comment: 12 pages, 6 figures, 2 table

Analysis of weighted networks

The connections in many networks are not merely binary entities, either present or not, but have associated weights that record their strengths relative to one another. Recent studies of networks have, by and large, steered clear of such weighted networks, which are often perceived as being harder to analyze than their unweighted counterparts. Here we point out that weighted networks can in many cases be analyzed using a simple mapping from a weighted network to an unweighted multigraph, allowing us to apply standard techniques for unweighted graphs to weighted ones as well. We give a number of examples of the method, including an algorithm for detecting community structure in weighted networks and a new and simple proof of the max-flow/min-cut theorem.Comment: 9 pages, 3 figure