Epidemic model on a network: analysis and applications to COVID-19

We analyze an epidemic model on a network consisting of susceptible-infected-recovered equations at the nodes coupled by diffusion using a graph Laplacian. We introduce an epidemic criterion and examine different vaccination/containment strategies: we prove that it is most effective to vaccinate a node of highest degree. The model is also useful to evaluate deconfinement scenarios and prevent a so-called second wave. The model has few parameters enabling fitting to the data and the essential ingredient of importation of infected; these features are particularly important for the current COVID-19 epidemic

Comet and close-approach asteroid mission study. volume 1- summary report final report

Comet and close-approach asteroid mission stud

A family of Nikishin systems with periodic recurrence coefficients

Suppose we have a Nikishin system of $p$ measures with the $k$th generating measure of the Nikishin system supported on an interval \Delta_k\subset\er with $\Delta_k\cap\Delta_{k+1}=\emptyset$ for all $k$. It is well known that the corresponding staircase sequence of multiple orthogonal polynomials satisfies a $(p+2)$-term recurrence relation whose recurrence coefficients, under appropriate assumptions on the generating measures, have periodic limits of period $p$. (The limit values depend only on the positions of the intervals $\Delta_k$.) Taking these periodic limit values as the coefficients of a new $(p+2)$-term recurrence relation, we construct a canonical sequence of monic polynomials $\{P_{n}\}_{n=0}^{\infty}$, the so-called \emph{Chebyshev-Nikishin polynomials}. We show that the polynomials $P_{n}$ themselves form a sequence of multiple orthogonal polynomials with respect to some Nikishin system of measures, with the $k$th generating measure being absolutely continuous on $\Delta_{k}$. In this way we generalize a result of the third author and Rocha \cite{LopRoc} for the case $p=2$. The proof uses the connection with block Toeplitz matrices, and with a certain Riemann surface of genus zero. We also obtain strong asymptotics and an exact Widom-type formula for the second kind functions of the Nikishin system for $\{P_{n}\}_{n=0}^{\infty}$.Comment: 30 pages, minor change

Effects of Eye-phase in DNA unzipping

The onset of an "eye-phase" and its role during the DNA unzipping is studied when a force is applied to the interior of the chain. The directionality of the hydrogen bond introduced here shows oscillations in force-extension curve similar to a "saw-tooth" kind of oscillations seen in the protein unfolding experiments. The effects of intermediates (hairpins) and stacking energies on the melting profile have also been discussed.Comment: RevTeX v4, 9 pages with 7 eps figure

Partitioning Edge-Colored Hypergraphs into Few Monochromatic Tight Cycles

Confirming a conjecture of Gy´arf´as, we prove that, for all natural numbers k and r, the vertices of every r-edge-colored complete k-uniform hypergraph can be partitioned into a bounded number (independent of the size of the hypergraph) of monochromatic tight cycles. We further prove that, for all natural numbers p and r, the vertices of every r-edge-colored complete graph can be partitioned into a bounded number of pth powers of cycles, settling a problem of Elekes, Soukup, Soukup, and Szentmikl´ossy [Discrete Math., 340 (2017), pp. 2053–2069]. In fact we prove a common generalization of both theorems which further extends these results to all host hypergraphs of bounded independence number

Reproductive phenology of Pouteria splendens (Sapotaceae)

Indexación: Web of Science; ScieloPouteria splendens (A.DC.) Kuntze (lúcumo silvestre, palo colorado) es un arbusto endémico con problemas de conservación de Chile central. Es la única especie representante de la familia Sapotaceae en el país y se conoce muy poco de su ciclo de vida. Se estudió su fenología reproductiva durante la primavera y verano, desde septiembre 2007 hasta abril 2008, en la población remanente más grande, localizada en Los Molles (V Región de Valparaíso). Se encontró un incremento en la producción de yemas florales, flores y frutos desde septiembre a febrero, decayendo en marzo. Al igual que en otras especies de ambientes mediterráneos, el máximo en la formación de botones florales, flores y frutos ocurrió en época de verano, durante febrero. También detectamos una alta sincronía en la fenología entre los individuos en la población estudiada. PALABRAS CLAVE: Planta amenazada, floración, fructificación, lúcumo silvestre.Pouteria splendens (A.DC.) Kuntze (lúcumo silvestre, palo colorado) is an endemic and in dangered tree from Central Chile. It's the only member of the Sapotaceae family in the country and little is known about his life cycle. We studied the reproductive phenology during Spring and Summer, from September 2007 to April 2008, on the biggest remained population of P. splendens, located in Los Molles (V Región Valparaíso). We recorded an increase in the production of flower buds, flowers and fruits from September to February, decaying in March. According with other species from Mediterranean environments, the peak of flower buds, flowers and fruits was recorded during Summer, in February. We also detected a high synchrony in the phenology among the individuals within the population. KEYWORDS: Endangered plant, flowering, fructification, lúcumo silvestre.http://ref.scielo.org/k9sbc

Seedling distribution and seed germination of chilean lucumo (Pouteria splendens) in Los Molles, Chile

Indexación: Web of Science; Scielo.Pouteria splendens (lúcumo chileno, palo colorado) es un árbol endémico de Chile central con problemas de conservación. Es la única especie representante de la familia Sapotaceae en el país y se conoce muy poco de su ciclo de vida. En este trabajo describimos el patrón de distribución espacial de plántulas en la población remanente de mayor tamaño de la especie, e investigamos el efecto de la disponibilidad de agua, la presencia de pericarpo en las semillas y de la hojarasca en la capacidad de germinación. La densidad de plántulas fue mayor bajo el dosel de las plantas madres, que fuera de estas. Solo la disponibilidad de agua tuvo un efecto significativo sobre la germinación. La especie tiene el potencial de regenerar, en futuros planes de conservación y restauración de la especie hay que aprovechar el efecto nodriza que estaría ejerciendo el dosel.Pouteria splendens (Chilean lucumo, red wood) is an endemic and endangered tree from Central Chile. It is the only member of the Sapotaceae family in the country and little is known about his life cycle. In this work we described the spatial distribution of seedlings in the biggest remained population of the species, and we investigated the effect of the water availability, presence of pericarp in the seeds and the leaf litter on the capacity of germination in the species. Seedling density was higher under the canopy of mother plants, than outside its. Only water availability had a significant effect on the germination. The species has the potential to regenerate, in future plans of conservation and restoration of the species must take advantage the nurse effect of the canopy.http://ref.scielo.org/wt65f