We determine exactly the expected number of hamilton cycles in the random graph obtained by starting with n isolated vertices and adding edges at random until each vertex degree is at least two. This complements recent work of Cooper and Frieze. There are similar results concerning expected numbers for example of perfect matchings, spanning trees, hamilton paths and directed hamilton cycles.

In the DE-STAR lab, we propose to use phased laser array with photon propellant in order to achieve significantly higher speed for the spacecraft. During the simulation, the laser is sometimes turned off to avoid cancellation of force or acceleration. However, if we shut off the laser accurately, the duration rises and drops even when the launch time is altered slightly, which makes the real im...

Introduction In UC Santa Cruz’s first ever offering of a Game Design Seminar, I had the involving experience of developing four games from scratch, participating in discussions relevant to the times, and developing my skill in computer game design. This paper documents my thinking, efforts, and analysis of mine and other’s games developed for the seminar. In the first section, I will briefly di...

We propose to approximate the unknown error density of a nonparametric regression model by a mixture of Gaussian densities with means being the individual error realizations and variance a constant parameter. This mixture density has the form of a kernel density estimator of error realizations. We derive an approximate likelihood and posterior for bandwidth parameters in the kernel–form error d...

This paper examines the out-of-sample performance of two common extensions of the Black-Scholes framework, namely a GARCH and a stochastic volatility option pricing model. The models are calibrated to intraday FTSE 100 option prices. We apply two sets of performance criteria, namely out-of-sample valuation errors and Value-at-Risk oriented measures. When we analyze the t to observed prices, GAR...

We analyzed the volatility dynamics of three developed markets (U.K., U.S. and Japan), during the period 2003-2011, by comparing the performance of several multivariate volatility models, namely Constant Conditional Correlation (CCC), Dynamic Conditional Correlation (DCC) and consistent DCC (cDCC) models. To evaluate the performance of models we used four statistical loss functions on the daily...

By exploiting the analyticity and boundary value properties of the thermal Green functions that result from the KMS condition in both time and energy complex variables, we treat the general (non–perturbative) problem of recovering the thermal functions at real times from the corresponding functions at imaginary times, introduced as primary objects in the Matsubara formalism. The key property on...