Cedarville University is a private Baptist university in Cedarville, Ohio. It is chartered by the state of Ohio, approved by the Ohio Board of Regents, and accredited by the Higher Learning Commission.Established in 1887, the school was originally affiliated with the conservative Reformed Presbyterian Church in North America, General Synod, now known as the Presbyterian Church in America. Today, Cedarville is an independent Baptist school that is endorsed by the State Convention of Baptists in Ohio.
The sense-assess-respond feedback loop is a critical aspect of intelligence in both living and material systems. Physical reservoir computing is a strategy toward embodying intelligence into a system by leveraging nonlinear dynamics to perform nonlinear computations. While mechanical reservoirs typically produce nonlinear dynamics due to some material nonlinearity, geometric nonlinearity can also produce nonlinear dynamics due to the finite displacements and rotations in the network. This study examines the effect of both network node degree and geometry on the nonlinear computing performance of simulated mass-spring-damper systems comprised of linear springs. Smaller node degrees and sharper equilibrium angles in the network tended to produce greater nonlinear frequency content. However, the equilibrium geometry is not sufficient to characterize the reservoir performance as the dynamic variation in the spring angles also significantly correlates with nonlinear frequency content. This study highlights the significance of both network topology and dynamic geometry on the performance of mechanical reservoir computers.
A direct proof based on commuting finite-dimensional flows and local polynomial invariants is given for a sharp upper bound on the amplitudes of finite-gap solutions of the modified Korteweg-de Vries (mKdV) equation. The maximal amplitude is the sum of the imaginary parts of the upper-half-plane square roots of the roots of the invariant polynomial of the finite-gap solution of the focusing mKdV equation. An analogous formula is established for a bounded class of solutions of the defocusing mKdV equation. The upper bounds are sharp and are explicitly attained by suitable initial data.
This paper explores an understudied area of soccer development: the minor league or semi-professional level. As North America prepares to host the 2026 Men's FIFA World Cup, the impact of the minor league/semi-professional level towards respectability is studied through three qualitative methods: self-ethnography of the present author as a former semi-professional soccer player, informal interviews with other semi-professional and professional players, and descriptive statistics of the 2022 United States' Men's National Team (USMNT) and the 2022 Canadian Men's National Team (CMNT). Of the 52 players on the 2022 USMNT and CMNT World Cup squads, 27 of them played in the minor league/semi-professional system of North America - as such, the development of players between the youth, collegiate and professional levels is important in creating players for both national teams.
