Investigating the impacts of training data set length (T) and the aggregation unit size (M) on the accuracy of the self-exciting point process (SEPP) hotspot method

This study examines the impacts of two variables; the training data lengths (T) and the aggregation unit sizes (M); on the accuracy of the self-exciting point process (SEPP) model during crime prediction. A case study of three crime types in the South Chicago area is presented, in which different combinations of values of T and M are used for 100 daily consecutive crime predictions. The results showed two important points regarding the SEPP model: first is that large values of T are likely to improve the accuracy of the SEPP model and second is that, a small aggregation unit, such as a 50m x 50m grid, is better in terms of capturing local repeat and near-repeat patterns of crimes

Runtime Distributions and Criteria for Restarts

Randomized algorithms sometimes employ a restart strategy. After a certain number of steps, the current computation is aborted and restarted with a new, independent random seed. In some cases, this results in an improved overall expected runtime. This work introduces properties of the underlying runtime distribution which determine whether restarts are advantageous. The most commonly used probability distributions admit the use of a scale and a location parameter. Location parameters shift the density function to the right, while scale parameters affect the spread of the distribution. It is shown that for all distributions scale parameters do not influence the usefulness of restarts and that location parameters only have a limited influence. This result simplifies the analysis of the usefulness of restarts. The most important runtime probability distributions are the log-normal, the Weibull, and the Pareto distribution. In this work, these distributions are analyzed for the usefulness of restarts. Secondly, a condition for the optimal restart time (if it exists) is provided. The log-normal, the Weibull, and the generalized Pareto distribution are analyzed in this respect. Moreover, it is shown that the optimal restart time is also not influenced by scale parameters and that the influence of location parameters is only linear

Submonolayer Epitaxy Without A Critical Nucleus

The nucleation and growth of two--dimensional islands is studied with Monte Carlo simulations of a pair--bond solid--on--solid model of epitaxial growth. The conventional description of this problem in terms of a well--defined critical island size fails because no islands are absolutely stable against single atom detachment by thermal bond breaking. When two--bond scission is negligible, we find that the ratio of the dimer dissociation rate to the rate of adatom capture by dimers uniquely indexes both the island size distribution scaling function and the dependence of the island density on the flux and the substrate temperature. Effective pair-bond model parameters are found that yield excellent quantitative agreement with scaling functions measured for Fe/Fe(001).Comment: 8 pages, Postscript files (the paper and Figs. 1-3), uuencoded, compressed and tarred. Surface Science Letters, in press

Computational Relativistic Astrophysics With Adaptive Mesh Refinement: Testbeds

We have carried out numerical simulations of strongly gravitating systems based on the Einstein equations coupled to the relativistic hydrodynamic equations using adaptive mesh refinement (AMR) techniques. We show AMR simulations of NS binary inspiral and coalescence carried out on a workstation having an accuracy equivalent to that of a $1025^3$ regular unigrid simulation, which is, to the best of our knowledge, larger than all previous simulations of similar NS systems on supercomputers. We believe the capability opens new possibilities in general relativistic simulations.Comment: 7 pages, 16 figure

Towards a Singularity-Proof Scheme in Numerical Relativity

Progress in numerical relativity has been hindered for 30 years because of the difficulties of avoiding spacetime singularities in numerical evolution. We propose a scheme which excises a region inside an apparent horizon containing the singularity. Two major ingredients of the scheme are the use of a horizon-locking coordinate and a finite differencing which respects the causal structure of the spacetime. Encouraging results of the scheme in the spherical collapse case are given.Comment: 9 page