Macroscopic Loop Amplitudes in Two-Dimensional Dilaton Gravity

Macroscopic loop amplitudes are obtained for the dilation gravity in two-dimensions. The dependence on the macroscopic loop length $l$ is completely determined by using the Wheeler-DeWitt equation in the mini-superspace approximation. The dependence on the cosmological constant $\Lambda$ is also determined by using the scaling argument in addition.Comment: 23 pages, LaTeX, TIT/HEP-21

Monitoring Cascading Changes of Resources in the Kubernetes Control Plane

Kubernetes is a container management system that has many automated functionalities. Those functionalities are managed by configuring objects and resources in the control plane. Since most objects change their state depending on other objects' states, a change propagates to other objects in a chain. As cluster availability is influenced by the time required for these cascading changes, it is essential to make the propagations measurable and shed light on the behavior of the Kubernetes control plane. However, it is not easy because each object constantly monitors other objects' status and acts autonomously in response to their changes to play its role. In this paper, we propose a measurement system that outputs objects' change logs published from the API server in the control plane and assists in analyzing the time of cascading changes between objects by utilizing the relationships among resources. With a practical change scenario, our system is confirmed that it can measure change propagation times within a cascading change. Also, measurements on the system itself showed it has a small CPU and memory footprint

Generating Functions in Two Dimensional Quantum Gravity

We solve general 1-matrix models without taking the double scaling limit. A method of computing generating functions is presented. We calculate the generating functions for a simple and double torus. Our method is also applicable to more higher genus. Each generating function can be expressed by a ``specific heat'' function for sphere. Universal terms, which are survived in the double scaling limit can be easily picked out from our exact solutions. We also find that the regular part of the spherical generating function is at most bilinear in coupling constants of source terms.Comment: 43 pages, 3 encapsulated postscript figures, uses latex and epsf.st

An efficient method for computing genus expansions and counting numbers in the Hermitian matrix model

We present a method to compute the genus expansion of the free energy of Hermitian matrix models from the large N expansion of the recurrence coefficients of the associated family of orthogonal polynomials. The method is based on the Bleher-Its deformation of the model, on its associated integral representation of the free energy, and on a method for solving the string equation which uses the resolvent of the Lax operator of the underlying Toda hierarchy. As a byproduct we obtain an efficient algorithm to compute generating functions for the enumeration of labeled k-maps which does not require the explicit expressions of the coefficients of the topological expansion. Finally we discuss the regularization of singular one-cut models within this approach

Factorization in 2D String Theory

We show the factorization of correlation functions of tachyon operators in 2D string theory using the discretized approach of Moore. Our demonstration of the factorization is more general than that of the paper of Sakai and Tanii. We obtain the rules for the factorization of tachyon amplitudes. Our results can be understood in terms of the operator product expansion of tachyon operators. We also give a systematic way of computing correlation functions of tachyon operators and succeed in summarizing the results of the computation in compact form for some simple cases. We confirm that these tachyon amplitudes indeed satisfy our factorization rule.Comment: 10 pages, LaTeX, TIT/HEP-22