No abstract

We study matrix quantum mechanics at finite temperature by Monte Carlo simulation. The model is obtained by dimensionally reducing 10d U(N ) pure Yang-Mills theory to 1d. Following Aharony et al., one can view the same model as describing the high temperature regime of (1+1)d U(N ) super Yang-Mills theory on a circle. In this interpretation an analog of the deconfinement transition was conjectured to be a continuation of the black-hole/black-string transition in the dual gravity theory. Our detailed analysis in the critical regime up to N = 32 suggests the existence of the non-uniform phase, in which the eigenvalue distribution of the holonomy matrix is non-uniform but gapless. The transition to the gapped phase is of second order. The internal energy is constant (giving the ground state energy) in the uniform phase, and rises quadratically in the non-uniform phase, which implies that the transition between these two phases is of third order.

The recent results of liver resection for hepatocellular carcinoma are generally satisfactory; however, the recurrence rate is still high.

We formulate the high temperature expansion in supersymmetric matrix quantum mechanics with 4, 8 and 16 supercharges. The models can be obtained by dimensionally reducing N = 1 U(N ) super Yang-Mills theory in D = 4, 6, 10 to 1 dimension, respectively. While the non-zero frequency modes become weakly coupled at high temperature, the zero modes remain strongly coupled. We find, however, that the integration over the zero modes that remains after integrating out all the non-zero modes perturbatively, reduces to the evaluation of connected Green's functions in the bosonic IKKT model. We perform Monte Carlo simulation to compute these Green's functions, which are then used to obtain the coefficients of the high temperature expansion for various quantities up to the next-leading order. Our results nicely reproduce the asymptotic behaviors of the recent simulation results at finite temperature. In particular, the fermionic matrices, which decouple at the leading order, give rise to substantial effects at the next-leading order, reflecting finite temperature behaviors qualitatively different from the corresponding models without fermions.

Physiological angiogenesis results from the balance of angiogenesis activators and inhibitors.