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We establish a new on-diagonal lower estimate of continuous-time heat kernels for large time on graphs. To achieve the goal, we first introduce an upper estimate of heat kernels in natural graph metric, then use the upper estimate and the volume growth condition to show the validity of the on-diagonal lower estimate. [ABSTRACT FROM AUTHOR]

The decomposition of aquatic plant residues changes by the invasive algal organic matter in eutrophic lakes, however, the driving mechanisms of these biogeochemistry processes are still far from clear. In this study, a series of microcosms was constructed to simulate the mixed decomposition processes of aquatic plant residues with invasive algae as long as 205 days. Three aquatic plants (Potamogeton malaianus, Nymphoides peltatum, and Phragmites australis) and algae were collected from a typical eutrophic lake. The addition of algae promoted the decomposition of three plant residues based on the mass loss, and the positive co-metabolism effect was produced. The co-metabolism intensity was 8%–25% on the water surface and 19%–45% on the water-sediment interface, respectively. In addition, the response of three aquatic plant residues to the algal organic matter was different with their co-metabolism intensities in the order of P. australis > P. malaianus > N. peltatum on both the water surface and water-sediment interface. The phylum number of bacteria attached to the surface of plant residues increased from 27 to 52. The abundance of Bacteroidetes, which had the function of decomposing refractory organic matter, increased most significantly at the final incubation. At present, shallow lakes are under the double pressure of eutrophication and global warming, and the intensity and duration of algal blooms are increasing. Therefore, the co-metabolism effect of the residue decomposition process described here may change the carbon cycle strength and increase the greenhouse gas emissions of lakes and need to be taken into account in future lake management. [Display omitted] • Decomposition of aquatic plants mediated by algal organic matter was studied. • The invasive algal organic matter was associated with the mass loss of aquatic plant. • The water surface was more favorable for the decomposition of aquatic plant. • Co-metabolism effect was closely related to the bacterial action of Bacteroidetes. • Co-metabolism effect in plant decomposition of eutrophic lakes should not be ignored. [ABSTRACT FROM AUTHOR]