Generating functions of non-backtracking walks on weighted digraphs: radius of convergence and Ihara's theorem

It is known that the generating function associated with the enumeration of non-backtracking walks on finite graphs is a rational matrix-valued function of the parameter; such function is also closely related to graph-theoretical results such as Ihara's theorem and the zeta function on graphs. In [P. Grindrod, D. J. Higham, V. Noferini, The deformed graph Laplacian and its application to network centrality analysis, SIAM J. Matrix Anal. Appl. 39(1), 310--341, 2018], the radius of convergence of the generating function was studied for simple (i.e., undirected, unweighted and with no loops) graphs, and shown to depend on the number of cycles in the graph. In this paper, we use technologies from the theory of polynomial and rational matrices to greatly extend these results by studying the radius of convergence of the corresponding generating function for general, possibly directed and/or weighted, graphs. We give an analogous characterization of the radius of convergence for directed unweighted graphs, showing that it depends on the number of cycles in the undirectization of the graph. For weighted graphs, we provide for the first time an exact formula for the radius of convergence, improving a previous result that exhibited a lower bound. Finally, we consider also backtracking-downweighted walks on unweighted digraphs, and we prove a version of Ihara's theorem in that case

Dbl oncogene expression in MCF-10 A epithelial cells disrupts mammary acinar architecture, induces EMT and angiogenic factor secretion.

The proteins of the Dbl family are guanine nucleotide exchange factors (GEFs) of Rho GTPases and are known to be involved in cell growth regulation. Alterations of the normal function of these proteins lead to pathological processes such as developmental disorders, neoplastic transformation, and tumor metastasis. We have previously demonstrated that expression of Dbl oncogene in lens epithelial cells modulates genes encoding proteins involved in epithelial-mesenchymal-transition (EMT) and induces angiogenesis in the lens. Our present study was undertaken to investigate the role of Dbl oncogene in epithelial cells transformation, providing new insights into carcinoma progression. To assess how Dbl oncogene can modulate EMT, cell migration, morphogenesis, and expression of pro-apoptotic and angiogenic factors we utilized bi- and three-dimensional cultures of MCF-10░A cells. We show that upon Dbl expression MCF-10░A cells undergo EMT. In addition, we found that Dbl overexpression sustain

Enigmatic persistence of dissolved organic matter in the ocean

Marine dissolved organic matter (DOM) contains more carbon than the combined stocks of Earth’s biota. Organisms in the ocean continuously release a myriad of molecules that become food for microheterotrophs, but, for unknown reasons, a residual fraction persists as DOM for millennia. In this Perspective, we discuss and compare two concepts that could explain this persistence. The long-standing ‘intrinsic recalcitrance’ paradigm attributes DOM stability to inherent molecular properties. In the ‘emergent recalcitrance’ concept, DOM is continuously transformed by marine microheterotrophs, with recalcitrance emerging on an ecosystems level. Both concepts are consistent with observations in the modern ocean, but they imply very different responses of the DOM pool to climate-related changes. To better understand DOM persistence, we propose a new overarching research strategy — the ecology of molecules — that integrates the concepts of intrinsic and emergent recalcitrance with the ecological and environmental context

Biofilm Structure Promotes Coexistence of Phage-Resistant and Phage-Susceptible Bacteria

Encounters among bacteria and their viral predators (bacteriophages) are among the most common ecological interactions on Earth. These encounters are likely to occur with regularity inside surface-bound communities that microbes most often occupy in natural environments. Such communities, termed biofilms, are spatially constrained: interactions become limited to near neighbors, diffusion of solutes and particulates can be reduced, and there is pronounced heterogeneity in nutrient access and physiological state. It is appreciated from prior theoretical work that phage-bacteria interactions are fundamentally different in spatially structured contexts, as opposed to well-mixed liquid culture. Spatially structured communities are predicted to promote the protection of susceptible host cells from phage exposure, and thus weaken selection for phage resistance. The details and generality of this prediction in realistic biofilm environments, however, are not known. Here, we explore phage-host interactions using experiments and simulations that are tuned to represent the essential elements of biofilm communities. Our simulations show that in biofilms, phage-resistant cells-as their relative abundance increases-can protect clusters of susceptible cells from phage exposure, promoting the coexistence of susceptible and phage-resistant bacteria under a large array of conditions. We characterize the population dynamics underlying this coexistence, and we show that coexistence is recapitulated in an experimental model of biofilm growth measured with confocal microscopy. Our results provide a clear view into the dynamics of phage resistance in biofilms with single-cell resolution of the underlying cell-virion interactions, linking the predictions of canonical theory to realistic models and in vitro experiments of biofilm growth. IMPORTANCE In the natural environment, bacteria most often live in communities bound to one another by secreted adhesives. These communities, or biofilms, play a central role in biogeochemical cycling, microbiome functioning, wastewater treatment, and disease. Wherever there are bacteria, there are also viruses that attack them, called phages. Interactions between bacteria and phages are likely to occur ubiquitously in biofilms. We show here, using simulations and experiments, that biofilms will in most conditions allow phage-susceptible bacteria to be protected from phage exposure, if they are growing alongside other cells that are phage resistant. This result has implications for the fundamental ecology of phage-bacteria interactions, as well as the development of phage-based antimicrobial therapeutics

An overlooked new species of Desmodium (Fabaceae, Papilionoideae) from Argentina.

More than seventy years ago Arturo Burkart transferred Meimomia riedelii to Desmodium riedelii and confirmed the occurrence of this species in Argentina. His position was based only on the original description and a photo of one of the syntypes. Fieldwork in northeastern Argentina and central Brazil and examination of all syntypes of Meibomia riedelii revealed that these are not conspecific with Argentinean specimens and a new species, Desmodium burkartii, is described here. This new species is restricted to grasslands in the Province of Corrientes in northeastern Argentina and is promptly differentiated from D. riedelii by shape of leaflets, shape and number of articles of loments, besides quantitative traitsFil: Lima, Laura C. P.. Universidade Estadual de Feira de Santana; BrasilFil: Vanni, Ricardo Oscar. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Nordeste. Instituto de Botánica del Nordeste (i); ArgentinaFil: de Queiroz, Luciano P.. Universidade Estadual de Feira de Santana; BrasilFil: Tozzi, Ana M. G. A.. Universidade Estadual de Campinas; Brasi