Hyperbolicity Measures "Democracy" in Real-World Networks

We analyze the hyperbolicity of real-world networks, a geometric quantity that measures if a space is negatively curved. In our interpretation, a network with small hyperbolicity is "aristocratic", because it contains a small set of vertices involved in many shortest paths, so that few elements "connect" the systems, while a network with large hyperbolicity has a more "democratic" structure with a larger number of crucial elements. We prove mathematically the soundness of this interpretation, and we derive its consequences by analyzing a large dataset of real-world networks. We confirm and improve previous results on hyperbolicity, and we analyze them in the light of our interpretation. Moreover, we study (for the first time in our knowledge) the hyperbolicity of the neighborhood of a given vertex. This allows to define an "influence area" for the vertices in the graph. We show that the influence area of the highest degree vertex is small in what we define "local" networks, like most social or peer-to-peer networks. On the other hand, if the network is built in order to reach a "global" goal, as in metabolic networks or autonomous system networks, the influence area is much larger, and it can contain up to half the vertices in the graph. In conclusion, our newly introduced approach allows to distinguish the topology and the structure of various complex networks

Fast approximation of centrality and distances in hyperbolic graphs

We show that the eccentricities (and thus the centrality indices) of all vertices of a $\delta$-hyperbolic graph $G=(V,E)$ can be computed in linear time with an additive one-sided error of at most $c\delta$, i.e., after a linear time preprocessing, for every vertex $v$ of $G$ one can compute in $O(1)$ time an estimate $\hat{e}(v)$ of its eccentricity $ecc_G(v)$ such that $ecc_G(v)\leq \hat{e}(v)\leq ecc_G(v)+ c\delta$ for a small constant $c$. We prove that every $\delta$-hyperbolic graph $G$ has a shortest path tree, constructible in linear time, such that for every vertex $v$ of $G$, $ecc_G(v)\leq ecc_T(v)\leq ecc_G(v)+ c\delta$. These results are based on an interesting monotonicity property of the eccentricity function of hyperbolic graphs: the closer a vertex is to the center of $G$, the smaller its eccentricity is. We also show that the distance matrix of $G$ with an additive one-sided error of at most $c'\delta$ can be computed in $O(|V|^2\log^2|V|)$ time, where $c'< c$ is a small constant. Recent empirical studies show that many real-world graphs (including Internet application networks, web networks, collaboration networks, social networks, biological networks, and others) have small hyperbolicity. So, we analyze the performance of our algorithms for approximating centrality and distance matrix on a number of real-world networks. Our experimental results show that the obtained estimates are even better than the theoretical bounds.Comment: arXiv admin note: text overlap with arXiv:1506.01799 by other author

High Auxin and High Phosphate Impact on RSL2 Expression and ROS-Homeostasis Linked to Root Hair Growth in Arabidopsis thaliana

Root hair size determines the surface area/volume ratio of the whole roots exposed to the nutrient and water pools, thereby likely impacting nutrient and water uptake rates. The speed at which they grow is determined both by cell-intrinsic factors like hormones (e.g., auxin) and external environmental signals like nutrient availability in the soil (e.g., phosphate). Overall root hair growth is controlled by the transcription factors RSL4 and RSL2. While high levels of auxin promote root hair growth, high levels of inorganic phosphate (Pi) in the media are able to strongly repress RSL4 and RSL2 expression linked to a decreased polar growth. In this work, we inquired the mechanism used by root hairs to integrate conflicting growth signals like the repressive signal of high Pi levels and a concomitant high auxin exposure that promotes growth and questioned whether these complex signals might activate known molecular players in root hair polar growth. Under these conditions, RSL2 expression (but not RSL4) is activated linked to ROS production and root hair growth. On the other hand, by blocking ROS production derived from the NADPH Oxidase C (or RBOHC for RESPIRATORY BURST OXIDASE HOMOLOG C) and ROS production from Secreted type-III Peroxidases (PERs), it was possible to repress the auxin growth-promoting effect. This study identifies a new layer of complexity between auxin, Pi nutrient availability and RSL2/RSL4 transcription factors all acting on ROS homeostasis and growth at the root hair level

Estructura genética de poblaciones de Phytophthora capsici en el noreste de la provincia de Buenos Aires, Argentina

Phytophthora capsici causa enfermedades destructivas en todo el mundo. El patógeno es heterotálico y los dos tipos de apareamiento (TAs) son requeridos para la reproducción sexual. La razón de TAs varía entre regiones geográficas y por lo tanto también la chance para reproducirse sexualmente. Si se toma en cuenta que la durabilidad de las medidas de control depende de la variación genética, es aconsejable considerar la cantidad y la distribución de variación genética dentro y entre poblaciones de especies, es decir, la estructura genética. Esta está determinada por factores que influencian la evolución poblacional como la mutación, la deriva genética, el flujo genético, el sistema de reproducción y de selección. En este sentido, poco se conoce sobre las poblaciones de P. capsici en Argentina. El objetivo fue evaluar la variabilidad genética de aislamientos de P. capsici de tres sitios de producción hortícola del NE de Buenos Aires. Sesenta y un aislamientos de P. capsici colectados de cultivos de Capsicum annuum, Solanum melongena, Solanum lycopersicum y Cucurbita spp. fueron identificados morfológicamente y analizados por tipo de reproducción. Los aislamientos fueron identificados por técnicas moleculares basadas en las secuencias de las regiones ITS1-5.8S e ITS2 del ADNr. Se definieron los haplotipos para cada aislamiento y los parámetros poblacionales fueron estimados por zona geográfica y por especie hospedante junto con el número mínimo de eventos de recombinación. Las desviaciones de la coalescencia básica fueron estimadas a través de Tajima´s D.; la estructura genética fue evaluada subsecuentemente a través de pruebas de AMOVA y de estimadores de Fst. La reconstrucción de redes filogenéticas fue analizada con la intención de evaluar las relaciones genealógicas entre haplotipos. Todos los aislamientos mostraron características morfológicas y genéticas típicas de P. capsici y pertenecieron al TA A1. No se evidenció una estructura genética cuando fueron incluidas como criterio de partición las especies hospedantes. Sin embargo, la partición geográfica permitió evidenciar alguna estructuración entre poblaciones, con la excepción de Exaltación de La Cruz que resultó el sitio más contrastante con respecto a ambos estimadores de índices de fijación. Al mismo tiempo, esta ubicación redituó los estimadores más bajos de diversidad, lo que probablemente refleja su origen reciente como zona hortícola. Dos a tres eventos de recombinación fueron detectados, lo que sugiere que la reproducción sexual podría haber influido sobre el proceso de diversificación en esta área. La estructura genética y los niveles de variación en esta región son opuestos a los resultados obtenidos por otros investigadores en la región centro oeste de Argentina y podría significar una amenaza para esta área de cultivo, al presente.Phytophthora capsici causes destructive diseases worldwide. The pathogen is heterothallic and the two mating types (MTs) are required for sexual reproduction. MTs rates vary amongst geographical regions and so does the chance for sexual reproduction. Taking into account that the durability of control measures depends upon genetic variation, it is advisable to consider its structure within and between populations. The objective of the present paper was to evaluate the genetic variability of P. capsici isolates from three horticultural production areas of the Northeast of Buenos Aires. Sixty one isolates of P. capsici collected from Capsicum annuum, Solanum melongena, Solanum lycopersicum and Cucurbita spp. crops were morphologically identified and analyzed for MTs. The isolates were further identified via molecular techniques based on the sequences of the ITS1 - 5.8S - ITS2 region of the ADNr. Haplotypes were defined for every isolate, and population parameterts were estimated both for geographic and hostspecies partitions, along with the minimum number of recombination events. Departures from the basic coalescent were estimated through Tajima´s D; the genetic structure was subsequently evaluated through AMOVA tests and Fst estimations. Phylogenetic network reconstruction was analysed in an attempt to assess genealogical relationships amongst haplotypes. All isolates showed morphological and genetic characteristics of P. capsici and belonged to the A1 MT. No genetic structure was detected when host-species was taken as a criterion for partition; on the other hand, geographic partition detected some structure among populations, with Exaltación de La Cruz resulting in the most contrasting site with regards to both fixation index estimates. At the same time, this location yielded the lowest estimates of diversity, probably reflecting its recent horticultural origin. Two to three recombination events were detected, suggesting that sexual reproduction could have been part of the diversification process in this area. The genetic structure and levels of variation in the region is opposite to what other researchers have found in Northwestern Argentina and could mean a threat to that breeding area now.Gerencia de Comunicación e Imagen InstitucionalFil: Iribarren, Maria Josefina. Universidad Nacional de Luján; ArgentinaFil: Borassi, C. Universidad Nacional de Luján; ArgentinaFil: Ferri, Andrea Matilde. Instituto Nacional de Tecnología Agropecuaria (INTA). Instituto de Genética; ArgentinaFil: González, B. Universidad Nacional de Luján; ArgentinaFil: Steciow, M. Universidad Nacional de La Plata; ArgentinaFil: Guillin, Eduardo Alejandro. Instituto Nacional de Tecnología Agropecuaria (INTA). Instituto de Genética; Argentin

A cell surface arabinogalactan-peptide influences root hair cell fate

Indexación: Scopus.Root hairs (RHs) develop from specialized epidermal trichoblast cells, whereas epidermal cells that lack RHs are known as atrichoblasts. The mechanism controlling RH cell fate is only partially understood. RH cell fate is regulated by a transcription factor complex that promotes the expression of the homeodomain protein GLABRA 2 (GL2), which blocks RH development by inhibiting ROOT HAIR DEFECTIVE 6 (RHD6). Suppression of GL2 expression activates RHD6, a series of downstream TFs including ROOT HAIR DEFECTIVE 6 LIKE-4 (RSL4) and their target genes, and causes epidermal cells to develop into RHs. Brassinosteroids (BRs) influence RH cell fate. In the absence of BRs, phosphorylated BIN2 (a Type-II GSK3-like kinase) inhibits a protein complex that regulates GL2 expression. Perturbation of the arabinogalactan peptide (AGP21) in Arabidopsis thaliana triggers aberrant RH development, similar to that observed in plants with defective BR signaling. We reveal that an O-glycosylated AGP21 peptide, which is positively regulated by BZR1, a transcription factor activated by BR signaling, affects RH cell fate by altering GL2 expression in a BIN2-dependent manner. Changes in cell surface AGP disrupts BR responses and inhibits the downstream effect of BIN2 on the RH repressor GL2 in root epidermis. © 2020 The Authors. New Phytologist © 2020 New Phytologist Trusthttps://nph-onlinelibrary-wiley-com.recursosbiblioteca.unab.cl/doi/10.1111/nph.1648

Hyperbolicity measures democracy in real-world networks

In this work, we analyze the hyperbolicity of real-world networks, a geometric quantity that measures if a space is negatively curved. We provide two improvements in our understanding of this quantity: first of all, in our interpretation, a hyperbolic network is "aristocratic", since few elements "connect" the system, while a non-hyperbolic network has a more "democratic" structure with a larger number of crucial elements. The second contribution is the introduction of the average hyperbolicity of the neighbors of a given node. Through this definition, we outline an "influence area" for the vertices in the graph. We show that in real networks the influence area of the highest degree vertex is small in what we define "local" networks (i.e., social or peer-to-peer networks), and large in "global" networks (i.e., power grid, metabolic networks, or autonomous system networks)

8-Chloro-6-phenyl-4H-[1,2,4]triazolo[4,3-a][1,5]benzodiazepin-5(6H)-one

The title compound, C16H11ClN4O, is an anticonvulsant agent. In the crystal, a particularly short C-H...N intermolecular hydrogen bond is noted [H...N 2.22 (2) \uc5]. The diazepine ring has a boat conformation