The HP-filter in cross-country comparisons

Many empirical studies of business cycles have followed the practise of applying the Hodrick-Prescott filter for cross-country comparisons. The standard procedure is to set the weight \lambda, which determines the 'smoothness' of the trend equal to 1600. We show that if this value is used for against common wisdom about business cycles. As an example, we show that the long recession occurred inSpain between 1975 and 1985 goes unnotoced by the HP filter. We propose a method for adjusting \lambda by reinterpreting the HP-filter as the solution to a constrained minimization problem. We argue that the common practice of fixing \lambda across countries amounts to chankging the constraints on trend variability across countries. Our proposed method is easy to apply, retains all the virtues of the standard HP-filter and when applied to Spanish data the results are in the line with economic historian's view. Applying the method to a number of OECD countries we find that, with the exception of Spain, Italy and Japan, the standard choice of \lambda=1600 is sensible.Business cycles, cross-country comparisons, macroeconomic volatility

Quantum Rabi model for N-state atoms

A tractable N-state Rabi Hamiltonian is introduced by extending the parity symmetry of the two-state model. The single-mode case provides a few-parameter description of a novel class of periodic systems, predicting that the ground state of certain four-state atom-cavity systems will undergo parity change at strong coupling. A group-theoretical treatment provides physical insight into dynamics and a modified rotating wave approximation obtains accurate analytical energies. The dissipative case can be applied to study excitation energy transfer in molecular rings or chains.Comment: 5 pages, 3 figures + supplement (2 pages); to appear in Phys. Rev. Let

A Linear Algebra Approach to Fast DNA Mixture Analysis Using GPUs

Analysis of DNA samples is an important step in forensics, and the speed of analysis can impact investigations. Comparison of DNA sequences is based on the analysis of short tandem repeats (STRs), which are short DNA sequences of 2-5 base pairs. Current forensics approaches use 20 STR loci for analysis. The use of single nucleotide polymorphisms (SNPs) has utility for analysis of complex DNA mixtures. The use of tens of thousands of SNPs loci for analysis poses significant computational challenges because the forensic analysis scales by the product of the loci count and number of DNA samples to be analyzed. In this paper, we discuss the implementation of a DNA sequence comparison algorithm by re-casting the algorithm in terms of linear algebra primitives. By developing an overloaded matrix multiplication approach to DNA comparisons, we can leverage advances in GPU hardware and algoithms for Dense Generalized Matrix-Multiply (DGEMM) to speed up DNA sample comparisons. We show that it is possible to compare 2048 unknown DNA samples with 20 million known samples in under 6 seconds using a NVIDIA K80 GPU.Comment: Accepted for publication at the 2017 IEEE High Performance Extreme Computing conferenc