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The expansion of a graph $F$, denoted by $F^3$, is the $3$-graph obtained from $F$ by adding a new vertex to each edge such that different edges receive different vertices. For large $n$, we establish tight upper bounds for: The maximum number of edges in an $n$-vertex $3$-graph that does not contain $T^3$ for certain class $\mathcal{T}$ of trees, sharpening (partially) a result of Kostochka--Mubayi--Verstra\"{e}te. The minimum number of colors needed to color the complete $n$-vertex $3$-graph to ensure the existence of a rainbow copy of $F^3$ when $F$ is a graph obtained from some tree $T\in \mathcal{T}$ by adding a new edge, extending anti-Ramsey results on $P_{2t}^3$ by Gu--Li--Shi and $C_{2t}^3$ by Tang--Li--Yan. The maximum number of edges in an $n$-vertex $3$-graph whose shadow does not contain the shadow of $C_{k}^3$ or $T^3$ for $T\in \mathcal{T}$, answering a question of Lv \etal on generalized Tur\'{a}n problems., Comment: 33 pages + appendix, comments are welcome

The anti-Ramsey number $\mathrm{ar}(n,F)$ of an $r$-graph $F$ is the minimum number of colors needed to color the complete $n$-vertex $r$-graph to ensure the existence of a rainbow copy of $F$. We prove a general upper bound for $\mathrm{ar}(n,F)$ when $F$ is the expansion of a hypergraph with smaller uniformality, which refines the general bound $\mathrm{ar}(n,F) = \mathrm{ex}(n,F_{-}) + o(n^r)$ by Erd{\H o}s--Simonovits--S{\' o}s. Here $F_{-}$ is the family of $r$-graphs obtained from $F$ by removing one edge. We also determine the exact value of $\mathrm{ar}(n,F)$ for large $n$ when $F$ is the expansion of a complete graph, extending a result of Erd{\H o}s--Simonovits--S{\' o}s from graphs to hypergraphs., Comment: fixed a minor mistake in the proof of Claim 3.5

At the millimeter scale and in the intermediate Reynolds number (Re) regime, the midge and mosquito larvae can reach swimming speeds of more than one body length per cycle performing a "figure-of-8" gait, in which their elongated bodies periodically bend nearly into circles and then fully unfold. To elucidate the propulsion mechanism of this cycle of motion, we conducted a 3D numerical study which investigates the hydrodynamics of undergoing the prescribed kinematics. Novel propulsion mechanisms, such as modulating the body deformation rate to dynamically increase the maximum net propulsion force, using asymmetric kinematics to generate torque and the appropriate rotation, and controlling the radius of the curled body to manipulate the moment of inertia. The figure-of-8 gait is found to achieve propulsion at a wide range of Re, but is most effective at intermediate Re. The results were further validated experimentally, via the development of a soft millimeter-sized robot that can reach comparable speeds using the figure-of-8 gait., Comment: 12pages,11 figures, 2 tables

A hole is an induced cycle of length at least 4, and an odd hole is a hole of odd length. A full house is a graph composed by a vertex adjacent to both ends of an edge in $K_4$ . Let $H$ be the complement of a cycle on 7 vertices. Chudnovsky et al [6] proved that every (odd hole, $K_4$)-free graph is 4-colorable and is 3-colorable if it does not has $H$ as an induced subgraph. In this paper, we use the proving technique of Chudnovsky et al to generalize this conclusion to (odd hole, full house)-free graphs, and prove that for (odd hole, full house)-free graph $G$, $\chi(G)\le \omega(G)+1$, and the equality holds if and only if $\omega(G)=3$ and $G$ has $H$ as an induced subgraph.

In undulatory swimming of fish, muscles contract sequentially along the body to generate a bending wave that pushes against the water and produces thrust. Here, we use a 3D computational fluid dynamics model coupled to the motion of the fish with prescribed deformation to study the basic mechanical quantities along the fish's body: force, torque, and power. We find that forces on the bodies of both the anguilliform swimmer and the carangiform swimmer are dominated by reactive forces; furthermore, the force on the caudal fin of the carangiform swimmer is dominated by drag-like forces. The torque exhibits a wave pattern that travels faster than the curvature wave in both the anguilliform and carangiform swimmers, but the wave speed is even higher for the carangiform swimmer. The power output for the anguilliform swimmer is concentrated on the anterior half of the body and is significantly negative on the posterior side of the body. In contrast, most of the power is generated by the posterior part of the body before the peduncle for the carangiform swimmer. The results explain the differences in the observed electromyography patterns in fish with different swimming modes and explain the tendon function in carangiform swimmers.