Related papers: Autoregressive Modeling of Coding Sequence Lengths…
Autoregressive models capture stochastic processes in which past realizations determine the generative distribution of new data; they arise naturally in a variety of industrial, biomedical, and financial settings. A key challenge when…
We study a minimal model for genome evolution whose elementary processes are single site mutation, duplication and deletion of sequence regions and insertion of random segments. These processes are found to generate long-range correlations…
We consider the problem of defining and fitting models of autoregressive time series of probability distributions on a compact interval of $\mathbb{R}$. An order-$1$ autoregressive model in this context is to be understood as a Markov…
The coding and noncoding length sequences constructed from a complete genome are characterised by multifractal analysis. The dimension spectrum $D_{q}$ and its derivative, the 'analogous' specific heat $C_{q}$, are calculated for the coding…
The nature of the alignment with gaps corresponding to a longest common subsequence (LCS) of two independent iid random sequences drawn from a finite alphabet is investigated. It is shown that such an optimal alignment typically matches…
Studies of disordered heterogeneous media and galaxy cosmology share a common goal: analyzing the distribution of particles at `microscales' to predict physical properties at `macroscales', whether for a liquid, composite material, or…
Autoregressive networks can achieve promising performance in many sequence modeling tasks with short-range dependence. However, when handling high-dimensional inputs and outputs, the huge amount of parameters in the network lead to…
For integrated sensing and communications, an intriguing question is whether information-bearing channel-coded signals can be reused for sensing - specifically ranging. This question forces the hitherto non-overlapping fields of channel…
We develop a new methodology for the fitting of nonstationary time series that exhibit nonlinearity, asymmetry, local persistence and changes in location scale and shape of the underlying distribution. In order to achieve this goal, we…
In this article we review classical and recent results in anomalous diffusion and provide mechanisms useful for the study of the fundamentals of certain processes, mainly in condensed matter physics, chemistry and biology. Emphasis will be…
Time series observations are ubiquitous in astronomy, and are generated to distinguish between different types of supernovae, to detect and characterize extrasolar planets and to classify variable stars. These time series are usually…
Coarse-graining offers a means to extend the achievable time and length scales of molecular dynamics simulations beyond what is practically possible in the atomistic regime. Sampling molecular configurations of interest can be done…
A series of simulations aimed at elucidating the self-assembly dynamics of spherical virus capsids is described. This little-understood phenomenon is a fascinating example of the complex processes that occur in the simplest of organisms.…
Consider two independent random strings having same length and taking values uniformly in a common finite alphabet. We study the order of the variance of the length of the longest common subsequences (LCS) of these strings when long blocks,…
By analyzing the spacing of genes on chromosomes, we find that transcriptional and RNA-processing regulatory sequences outside coding regions leave footprints on the distribution of intergenic distances. Using analogies between genes on…
Rearrangements of bacterial chromosomes can be studied mathematically at several levels, most prominently at a local, or sequence level, as well as at a topological level. The biological changes involved locally are inversions, deletions,…
Genome sequencing is the basis for many modern biological and medicinal studies. With recent technological advances, metagenomics has become a problem of interest. This problem entails the analysis and reconstruction of multiple DNA…
Transformers generate valid and diverse chemical structures, but little is known about the mechanisms that enable these models to capture the rules of molecular representation. We present a mechanistic analysis of autoregressive…
We investigate the Susceptible-Infectious-Recovered contagion dynamics in a system of self-propelled particles with polar alignment. Using agent-based simulations, we analyze the outbreak process for different combinations of the spatial…
Linear autoregressive models serve as basic representations of discrete time stochastic processes. Different attempts have been made to provide non-linear versions of the basic autoregressive process, including different versions based on…