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In a population practicing consanguineous marriage, rare recessive lethal alleles (RRLA) have higher chances of affecting phenotypes. As inbreeding causes more homozygosity and subsequently more deaths, the loss of individuals with RRLA…
Molecular phenotypes are important links between genomic information and organismic functions, fitness, and evolution. Complex phenotypes, which are also called quantitative traits, often depend on multiple genomic loci. Their evolution…
The quantum-resonant evolution of the mean kinetic energy (MKE) of the kicked particle is studied in detail on different time scales for {\em general} kicking potentials. It is shown that the asymptotic time behavior of a wave-packet MKE is…
Frequency power spectra due to a super-position of uncorrelated Lorentzian pulses with a random distribution of amplitudes are considered. For pulses with constant duration, there is an exponential frequency spectrum which is independent of…
We develop an analytical framework for understanding how the generated distribution evolves during diffusion model training. Leveraging a Gaussian-equivalence principle, we solve the full-batch gradient-flow dynamics of linear and…
We study the role of phylogenetic trees on correlations in mutation processes. Generally, correlations decay exponentially with the generation number. We find that two distinct regimes of behavior exist. For mutation rates smaller than a…
In sexual population, recombination reshuffles genetic variation and produces novel combinations of existing alleles, while selection amplifies the fittest genotypes in the population. If recombination is more rapid than selection,…
The site frequency spectrum (SFS) is a widely used summary statistic of genomic data. Motivated by recent evidence for the role of neutral evolution in cancer, we investigate the SFS of neutral mutations in an exponentially growing…
In this thesis we develop minimal models of the relationship between motility, growth, and evolution of cancer cells. We utilise simple simulations of a population of individual cells in space to examine how changes in mechanical properties…
A recently developed wavelet based approach is employed to characterize the scaling behavior of spectral fluctuations of random matrix ensembles, as well as complex atomic systems. Our study clearly reveals anti-persistent behavior and…
We study a general setting of neutral evolution in which the population is of finite, constant size and can have spatial structure. Mutation leads to different genetic types ("traits"), which can be discrete or continuous. Under minimal…
Major efforts to sequence cancer genomes are now occurring throughout the world. Though the emerging data from these studies are illuminating, their reconciliation with epidemiologic and clinical observations poses a major challenge. In the…
Stronger selection implies faster evolution---that is, the greater the force, the faster the change. This apparently self-evident proposition, however, is derived under the assumption that genetic variation within a population is primarily…
Pervasive natural selection can strongly influence observed patterns of genetic variation, but these effects remain poorly understood when multiple selected variants segregate in nearby regions of the genome. Classical population genetics…
We study a simple model of DNA evolution in a growing population of cells. Each cell contains a nucleotide sequence which randomly mutates at cell division. Cells divide according to a branching process. Following typical parameter values…
Whether evolution can be predicted is a key question in evolutionary biology. Here we set out to better understand the repeatability of evolution. We explored experimentally the effect of mutation supply and the strength of selective…
Empirical substitution matrices represent the average tendencies of substitutions over various protein families by sacrificing gene-level resolution. We develop a codon-based model, in which mutational tendencies of codon, a genetic code,…
We study the evolution of asexual microorganisms with small mutation rate in fluctuating environments, and develop techniques that allow us to expand the formal solution of the evolution equations to first order in the mutation rate. Our…
We study large deviation events in the timing of disease recurrence. In particular, we are interested in modeling cancer treatment failure due to mutation-induced drug resistance. We first present a two-type branching process model of this…
We explore how the behavior of galaxy cluster scaling relations are affected by flux-limited selection biases and intrinsic covariance among observable properties. Our models presume log-normal covariance between luminosity (L) and…