Stewart Cole and colleagues report the genome sequence and comparative analyses of Brazilian, Indian, North American and Thai strains of Mycobacterium leprae, the etiologial agent of leprosy. They define 16 sub-types of M. leprae and examine their geographical distribution. Reductive evolution and massive pseudogene formation have shaped the 3.31-Mb genome of Mycobacterium leprae, an unculturable obligate pathogen that causes leprosy in humans. The complete genome sequence of M. leprae strain Br4923 from Brazil was obtained by conventional methods (6× coverage), and Illumina resequencing technology was used to obtain the sequences of strains Thai53 (38× coverage) and NHDP63 (46× coverage) from Thailand and the United States, respectively. Whole-genome comparisons with the previously sequenced TN strain from India revealed that the four strains share 99.995% sequence identity and differ only in 215 polymorphic sites, mainly SNPs, and by 5 pseudogenes. Sixteen interrelated SNP subtypes were defined by genotyping both extant and extinct strains of M. leprae from around the world. The 16 SNP subtypes showed a strong geographical association that reflects the migration patterns of early humans and trade routes, with the Silk Road linking Europe to China having contributed to the spread of leprosy.

Differential cross sections for protons scattered from ${\mathrm{B}}^{10}$ were measured and, combined with published differential cross sections and polarizations for protons elastically scattered from ${\mathrm{Li}}^6$, ${\mathrm{Li}}^7$, ${\mathrm{Be}}^9$, ${\mathrm{B}}^{10}$, ${\mathrm{B}}^{11}$, ${\mathrm{C}}^{12}$, ${\mathrm{C}}^{13}$, ${\mathrm{N}}^{14}$, and ${\mathrm{O}}^{16}$ at bombarding energies between 10 and 50 MeV, are analyzed in terms of the optical model. An investigation of the systematic effects observed in applying the optical model to light nuclei reveals two peculiarities. First, an examination of the effects of a nonlocal potential indicates that the radius parameter of the real central potential is energy-dependent. Second, the Thomas form usually used for the spin-orbit potential is shown to lose its surface-peaked character in the case of light nuclei; but a proposed slight modification avoids this defect. The set of parameters found to give a good description of the data over a range of incident nucleon energy and target mass was shown to be similar to the sets of parameters found to describe the nucleon scattering from heavy nuclei. Using the prescriptions for the parameters of the present study but reversing the signs of the $\frac{\mathrm{}(N-Z)\mathrm{}}{A}$ terms leads to fits of comparable quality to the differential cross sections for 14-MeV neutrons scattered from ${\mathrm{Li}}^7$, ${\mathrm{Be}}^9$, ${\mathrm{B}}^{11}$, and ${\mathrm{N}}^{14}$.

For many decades, there has been a general perception in the literature that Fourier methods are not suitable for the analysis of nonlinear and non-stationary data. In this paper, we propose a novel and adaptive Fourier decomposition method (FDM), based on the Fourier theory, and demonstrate its efficacy for the analysis of nonlinear and non-stationary time series. The proposed FDM decomposes any data into a small number of ‘Fourier intrinsic band functions’ (FIBFs). The FDM presents a generalized Fourier expansion with variable amplitudes and variable frequencies of a time series by the Fourier method itself. We propose an idea of zero-phase filter bank-based multivariate FDM (MFDM), for the analysis of multivariate nonlinear and non-stationary time series, using the FDM. We also present an algorithm to obtain cut-off frequencies for MFDM. The proposed MFDM generates a finite number of band-limited multivariate FIBFs (MFIBFs). The MFDM preserves some intrinsic physical properties of the multivariate data, such as scale alignment, trend and instantaneous frequency. The proposed methods provide a time–frequency–energy (TFE) distribution that reveals the intrinsic structure of a data. Numerical computations and simulations have been carried out and comparison is made with the empirical mode decomposition algorithms.

Significance: Leprosy was thought to be exclusively caused by infection of humans by Mycobacterium leprae . In 2008, Han et al. proposed that Mycobacterium lepromatosis , a separate unculturable species, might be responsible for a rare yet severe form of the disease called diffuse lepromatous leprosy. Here, by using comparative genomics, we show that the two species are very closely related and derived from a common ancestor that underwent genome downsizing and gene decay. Since their separation 13.9 Mya, the two species have continued to lose genes, but from different regions of the genome, and M. leprae appears to be more recent. In a phylogeographic survey, by using differential PCR, we found that M. lepromatosis was scarce and restricted to patients from Mexico.