Related papers: The long-tail distribution function of mutations i…
We study large deviation probabilities for a sum of dependent random variables from a heavy-tailed factor model, assuming that the components are regularly varying. We identify conditions where both the factor and the idiosyncratic terms…
We characterize the class of exchangeable Feller processes evolving on partitions with boundedly many blocks. In continuous-time, the jump measure decomposes into two parts: a $\sigma$-finite measure on stochastic matrices and a collection…
In a short article submitted to ArXiv [1], Maddamsetti et al. argue that the variation in the neutral mutation rate among genes in Escherichia coli that we recently reported [2] might be explained by horizontal gene transfer (HGT). To…
Genes are not located randomly along genomes. Synteny, the conservation of their relative positions in genomes of different species, reflects fundamental constraints on natural evolution. We present approaches to infer pairs of co-localized…
T cells undergo large shape changes (morphodynamics) when migrating. While progress has been made elucidating the molecular basis of cell migration, statistical characterization of morphodynamics and migration has been limited, particularly…
The time taken for gene expression varies not least because proteins vary in length considerably. This paper uses an abstract, tuneable Boolean regulatory network model to explore gene expression time variation. In particular, it is shown…
This paper introduces a stochastic adaptive dynamics model for the interplay of several crucial traits and mechanisms in bacterial evolution, namely dormancy, horizontal gene transfer (HGT), mutation and competition. In particular, it…
We describe the time evolution of gene expression levels by using a time translational matrix to predict future expression levels of genes based on their expression levels at some initial time. We deduce the time translational matrix for…
We study the long-time behavior of the scaled walker (particle) position associated with decoupled continuous-time random walk which is characterized by superheavy-tailed distribution of waiting times and asymmetric heavy-tailed…
We model the growth of a cell population using a piecewise deterministic Markov branching tree. In this model, each cell splits into two offspring at a division rate $B(x)$, which depends on its size $x$. The size of each cell increases…
We consider a class of non-local reaction-diffusion problems, referred to as replicator-mutator equations in evolutionary genetics. For a confining fitness function, we prove well-posedness and write the solution explicitly, via some…
Fluctuation properties of the Langevin equation including a multiplicative, power-law noise and a quadratic potential are discussed. The noise has the Levy stable distribution. If this distribution is truncated, the covariance can be…
We study numerically the distributions of the length $L$ of the longest increasing subsequence (LIS) for the two cases of random permutations and of one-dimensional random walks. Using sophisticated large-deviation algorithms, we are able…
Weibull distribution is widely used in modelling health data. However, its lack of sufficient tail flexibility often results in poor fit in extreme events. We proposed another three-parameter extension of the Weibull distribution with…
Bacterial cells navigate around their environment by directing their movement along chemical gradients. This process, known as chemotaxis, can promote the rapid expansion of bacterial populations into previously unoccupied territories.…
In the growth of bacterial colonies, a great variety of complex patterns are observed in experiments, depending on external conditions and the bacterial species. Typically, existing models employ systems of reaction-diffusion equations or…
This paper considers learning deep features from long-tailed data. We observe that in the deep feature space, the head classes and the tail classes present different distribution patterns. The head classes have a relatively large spatial…
A stochastic model for the evolution of a growing population is proposed, in order to explain empirical power-law distributions in the frequency of family names as a function of the family size. Preliminary results show that the predicted…
A multiscale approach is used to simulate the translocation of DNA through a nanopore. Within this scheme, the interactions of the molecule with the surrounding fluid (solvent) are explicitly taken into account. By generating polymers of…
High precision photometry and spectroscopy of low-mass stars reveal a variety of properties standard stellar evolution cannot predict. Rotation, an essential ingredient of stellar evolution, is a step towards resolving the discrepancy…