Mean Curvature Flow on Ricci Solitons

We study monotonic quantities in the context of combined geometric flows. In particular, focusing on Ricci solitons as the ambient space, we consider solutions of the heat type equation integrated over embedded submanifolds evolving by mean curvature flow and we study their monotonicity properties. This is part of an ongoing project with Magni and Mantegazzawhich will treat the case of non-solitonic backgrounds \cite{a_14}.Comment: 19 page

Integrable boundary interaction in 3D target space: the "pillow-brane" model

We propose a model of boundary interaction, with three-dimensional target space, and the boundary values of the field {\vec X}\in R^3 constrained to lay on a two-dimensional surface of the "pillow" shape. We argue that the model is integrable, and suggest that its exact solution is described in terms of certain linear ordinary differential equation.Comment: 28 pages, 4 figure

Pampean-grassland heterogeneity on the intersection of science, art, and culture

Since prehistoric times, temperate grasslands have provided favorable habitat for human subsistence. Ease of exploitation, however, has caused that temperate grasslands are among the most destroyed terrestrial ecosystems. The region known as the Pampas or Rio de la PlataGrasslands, extending over some 750,000 sq. km in central eastern Argentina, Uruguay and southern Brazil, comprises the largest temperate grassland area in the southern hemisphere. Flat topography, humid temperate climate, grassy natural vegetation, and absence of large native herbivores have conditioned multiple aspects of human life in the region, like patterns of population settlement, techniques for acquisition and transportation of goods, aesthetic preferences, and social structure. In this article, we present some writers inspired by the Pampas, we briefly summarize the main results of scientific research on the drivers of vegetation physiognomy and heterogeneity in the Pampas, based on the invaluable floristic database compiled by Professor Rolando J. C. León, and we sketch one of Professor León´s scientific-historic tours to the Pampas. Finally, we call attention to currently threats to the persistence of Pampean Grassland.Fil: Perelman, S.B.. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigaciones Fisiológicas y Ecológicas Vinculadas a la Agricultura. Universidad de Buenos Aires. Facultad de Agronomía. Instituto de Investigaciones Fisiológicas y Ecológicas Vinculadas a la Agricultura; ArgentinaFil: Omacini, Marina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigaciones Fisiológicas y Ecológicas Vinculadas a la Agricultura. Universidad de Buenos Aires. Facultad de Agronomía. Instituto de Investigaciones Fisiológicas y Ecológicas Vinculadas a la Agricultura; ArgentinaFil: Tognetti, Pedro Maximiliano. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigaciones Fisiológicas y Ecológicas Vinculadas a la Agricultura. Universidad de Buenos Aires. Facultad de Agronomía. Instituto de Investigaciones Fisiológicas y Ecológicas Vinculadas a la Agricultura; ArgentinaFil: Batista, William B.. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigaciones Fisiológicas y Ecológicas Vinculadas a la Agricultura. Universidad de Buenos Aires. Facultad de Agronomía. Instituto de Investigaciones Fisiológicas y Ecológicas Vinculadas a la Agricultura; Argentin

Secretion of Food Allergen Proteins in Saliva

RATIONALE: Peanut proteins were found to be secreted in 50% of lactating women’s breast milk. We wanted to develop a testing method to predict the secretion of peanut protein in breast milk. The secretion of food protein in saliva was hypothesized to be a possible predictor of secretion of foods in breast milk following ingestion. METHODS: Non-allergic volunteers, some lactating, ingested 50 grams of either whole peanuts, peanut milk or cow’s milk and various immunoassays were utilized to analyze for the presence of peanut or cow’s milk proteins in saliva and breast milk. Saliva and breast milk samples were subjected to SDS-PAGE, Western blot and ELISA analysis with anti-raw and roasted peanut and anti-alpha-casein antibodies and pooled serum IgE from peanut allergic individuals. RESULTS: Peanut protein levels in breast milk were undetectable using Western blot analysis and inconsistent with ELISA analysis. However, peanut proteins around 20 and 30 kDa that reacted with anti-roasted peanut antibody were detected, 6-18 hours following ingestion, in saliva of different individuals. An 18 KDa band that reacts with anti-alpha casein antibody was also detected in saliva 6-18 hours following ingestion. CONCLUSIONS: Secretion of food allergen proteins or peptides in saliva several hours following ingestion may have important implications for delayed allergic reaction by sensitive patients. Also, due to the fact that these proteins or peptides survive digestive enzymes, become absorbed into the blood stream and are subsequently secreted in biological fluids may indicate that they are most likely the sensitizing or tolerizing agent within an allergic food. Funding: National Peanut Board, USD

Ricci flow and black holes

Gradient flow in a potential energy (or Euclidean action) landscape provides a natural set of paths connecting different saddle points. We apply this method to General Relativity, where gradient flow is Ricci flow, and focus on the example of 4-dimensional Euclidean gravity with boundary S^1 x S^2, representing the canonical ensemble for gravity in a box. At high temperature the action has three saddle points: hot flat space and a large and small black hole. Adding a time direction, these also give static 5-dimensional Kaluza-Klein solutions, whose potential energy equals the 4-dimensional action. The small black hole has a Gross-Perry-Yaffe-type negative mode, and is therefore unstable under Ricci flow. We numerically simulate the two flows seeded by this mode, finding that they lead to the large black hole and to hot flat space respectively, in the latter case via a topology-changing singularity. In the context of string theory these flows are world-sheet renormalization group trajectories. We also use them to construct a novel free energy diagram for the canonical ensemble.Comment: 31 pages, 14 color figures. v2: Discussion of the metric on the space of metrics corrected and expanded, references adde

Diffusion of particles moving with constant speed

The propagation of light in a scattering medium is described as the motion of a special kind of a Brownian particle on which the fluctuating forces act only perpendicular to its velocity. This enforces strictly and dynamically the constraint of constant speed of the photon in the medium. A Fokker-Planck equation is derived for the probability distribution in the phase space assuming the transverse fluctuating force to be a white noise. Analytic expressions for the moments of the displacement $$ along with an approximate expression for the marginal probability distribution function $P(x,t)$ are obtained. Exact numerical solutions for the phase space probability distribution for various geometries are presented. The results show that the velocity distribution randomizes in a time of about eight times the mean free time ($8t^*$) only after which the diffusion approximation becomes valid. This factor of eight is a well known experimental fact. A persistence exponent of $0.435 \pm 0.005$ is calculated for this process in two dimensions by studying the survival probability of the particle in a semi-infinite medium. The case of a stochastic amplifying medium is also discussed.Comment: 9 pages, 9 figures(Submitted to Phys. Rev. E

Formal matched asymptotics for degenerate Ricci flow neckpinches

Gu and Zhu have shown that Type-II Ricci flow singularities develop from nongeneric rotationally symmetric Riemannian metrics on $S^m$, for all $m\geq 3$. In this paper, we describe and provide plausibility arguments for a detailed asymptotic profile and rate of curvature blow-up that we predict such solutions exhibit