Generating random graphs in biased Maker-Breaker games

We present a general approach connecting biased Maker-Breaker games and problems about local resilience in random graphs. We utilize this approach to prove new results and also to derive some known results about biased Maker-Breaker games. In particular, we show that for $b=o\left(\sqrt{n}\right)$, Maker can build a pancyclic graph (that is, a graph that contains cycles of every possible length) while playing a $(1:b)$ game on $E(K_n)$. As another application, we show that for $b=\Theta\left(n/\ln n\right)$, playing a $(1:b)$ game on $E(K_n)$, Maker can build a graph which contains copies of all spanning trees having maximum degree $\Delta=O(1)$ with a bare path of linear length (a bare path in a tree $T$ is a path with all interior vertices of degree exactly two in $T$)

How unproportional must a graph be?

Let $u_k(G,p)$ be the maximum over all $k$-vertex graphs $F$ of by how much the number of induced copies of $F$ in $G$ differs from its expectation in the binomial random graph with the same number of vertices as $G$ and with edge probability $p$. This may be viewed as a measure of how close $G$ is to being $p$-quasirandom. For a positive integer $n$ and $0<p<1$, let $D(n,p)$ be the distance from $p\binom{n}{2}$ to the nearest integer. Our main result is that, for fixed $k\ge 4$ and for $n$ large, the minimum of $u_k(G,p)$ over $n$-vertex graphs has order of magnitude $\Theta\big(\max\{D(n,p), p(1-p)\} n^{k-2}\big)$ provided that $p(1-p)n^{1/2} \to \infty$

Assessing sediment yield and streamflow with SWAT model in a small sub-basin of the Cantareira System

Hydro-sedimentological models might be useful tools for investigating the effectiveness of soil and water conservation practices. However, evaluating the usefulness of such models requires that predictions are tested against observational data and that uncertainty from model parameterization is addressed. Here we aimed to evaluate the capacity of the SWAT model to simulate monthly streamflow and sediment load in the Posses creek catchment (12 km2), Southeast Brazil. The SUFI-2 algorithm from SWAT-CUP was applied for calibration, testing, uncertainty, and sensitivity analysis. The model was calibrated and initially tested using discharge and sediment load data, which were measured at the catchment outlet. Additionally, we used soil loss measurements from erosion plots within the catchment as independent data for model evaluation. Average monthly streamflow simulations obtained satisfactory results, with Nash-Sutcliffe coefficient (NSE) values of 0.75 and 0.51 for the calibration and testing periods, respectively. Sediment load simulations also displayed satisfactory results for calibration (NSE = 0.65) and testing (NSE = 0.52). However, the comparison with independent plot data revealed that SWAT severely overestimated hillslope erosion rates and compensated it with high sediment channel deposition. Moreover, the model was not sensitive to the parameters used for calculating hillslope sediment yields. Therefore, it should be used with caution for evaluating the interactions between land use, soil erosion, and sediment delivery. We found that the commonly used outlet-based approach for model calibration and testing can lead to internal misrepresentations, and models can reproduce the right answer for the wrong reasons