In this contribution, we report the generation of 17-μJ mid-infrared (MIR) pulses with duration of 70 fs and bandwidth of 550 nm centered at 3.75 μm at 1-kHz repetition rate, by a two-stage femtosecond optical parametric amplifier utilizing 4H-silicon carbide crystal as the nonlinear medium. The crystal is selected as it processes orders of magnitude higher damage threshold than traditional MIR...

The mathematical study of genealogies has yielded important insights in population biology, such as the ability to estimate the time to the most recent common ancestor (MRCA) of a sample of genetic sequences or of a group of individuals. Here we introduce a model of cultural genealogies that is a step toward answering similar questions for cultural traits. In our model individuals can inherit f...

An important clue to the evolutionary history of an allele is the structure of the neighboring region of the genome, which we term the genomic background of the allele. Consider two copies of the allele. How similar we expect their genomic background to be is strongly influenced by the age of their most recent common ancestor (MRCA). We apply diffusion theory, first used by Motoo Kimura as a to...

The mutation process is introduced into the colored coalescent theory. The mutation process can be viewed as an independent Poisson process running on the colored genealogical random tree generated by the colored coalescent process, with the edge lengths of the random tree serving as the time scale for the mutation process. Moving backward along the colored genealogical tree, the color of verti...

The genealogies of samples of orthologous regions from multiple species can be classified by their shapes. Using a neutral coalescent model of two species, I give exact probabilities of each of four possible genealogical shapes: reciprocal monophyly, two types of paraphyly, and polyphyly. After the divergence that forms two species, each of which has population size N, polyphyly is the most lik...