REPLY: In the letter of Chmielewski and Snyder-Mackler, the authors pointed out that the clinical classification scheme used in their studies is not comparable to ours to separate anterior cruciate ligament (ACL) patients without “giving-way symptoms” (copers) from ACL patients with giving-way symptoms (noncopers). In contrast to their comprehensive screening protocol that included issues of di...

The nonperturbative aspects of string theory are explored for noncritical string in two distinct formulations, loop equations and matrix models. The effects corresponding to the D-brane in these formulations are especially investigated in detail. It is shown that matrix models can universally yield a definite value of the chemical potential for an instanton while loop equations cannot. This imp...

We announce and sketch the rigorous proof of a new kind of anomalous (or sub-ballistic) Lieb-Robinson (LR) bound for an isotropic XY chain in a quasiperiodic transversal magnetic field. Instead of the usual effective light cone |x|≤v|t|, we obtain |x|≤v|t|α for some 0<α<1. We can characterize the allowed values of α exactly as those exceeding the upper transport exponent αu+ of a one-body Schrö...

The nonperturbative aspects of string theory are explored for noncritical string in two distinct formulations, loop equations and matrix models. The effects corresponding to the D-brane in these formulations are especially investigated in detail. It is shown that matrix models can universally yield a definite value of the chemical potential for an instanton while loop equations cannot. This imp...