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We present a method of dimensional reduction for the general Markov model of sequence evolution on a phylogenetic tree. We show that taking certain linear combinations of the associated random variables (site pattern counts) reduces the…
Theory of tree transducers provides a foundation for understanding expressiveness and complexity of analysis problems for specification languages for transforming hierarchically structured data such as XML documents. We introduce streaming…
We study quantum phase transitions by measuring the bond energy, the number density, and the half-chain entanglement entropy in the one-dimensional ionic Hubbard model. By performing the infinite density matrix renormalization group with…
Using graphical methods based on a `lookdown' and pruned version of the {\em ancestral selection graph}, we obtain a representation of the type distribution of the ancestor in a two-type Wright-Fisher population with mutation and selection,…
We observe $n$ sequences at each of $m$ sites, and assume that they have evolved from an ancestral sequence that forms the root of a binary tree of known topology and branch lengths, but the sequence states at internal nodes are unknown.…
Hidden Markov chains are widely applied statistical models of stochastic processes, from fundamental physics and chemistry to finance, health, and artificial intelligence. The hidden Markov processes they generate are notoriously…
Random forests are decision tree ensembles that can be used to solve a variety of machine learning problems. However, as the number of trees and their individual size can be large, their decision making process is often incomprehensible. In…
Rich phenomenology emerges at the intersection of non-Hermiticity and many-body dynamics, yet physically realizable implementations remain challenging. In this work, we propose a general formalism that maps non-Hermitian many-body…
Branching processes are a class of continuous-time Markov chains (CTMCs) with ubiquitous applications. A general difficulty in statistical inference under partially observed CTMC models arises in computing transition probabilities when the…
We study the continuous-time evolution of the recombination equation of population genetics. This evolution is given by a differential equation that acts on a product probability space, and its solution can be described by a Markov chain on…
We introduce an algorithm for generating a random sequence of fragmentation trees, which we call the ancestral branching algorithm. This algorithm builds on the recursive partitioning structure of a tree and gives rise to an associated…
We consider the discrete-time migration-recombination equation, a deterministic, nonlinear dynamical system that describes the evolution of the genetic type distribution of a population evolving under migration and recombination in a law of…
The maximum parsimony phylogenetic tree reconstruction problem is NP-hard, presenting a computational bottleneck for classical computing and motivating the exploration of emerging paradigms like quantum computing. To this end, we design…
Methods of phylogenetic inference use more and more complex models to generate trees from data. However, even simple models and their implications are not fully understood. Here, we investigate the two-state Markov model on a tripod tree,…
Tensor structured Markov chains are part of stochastic models of many practical applications, e.g., in the description of complex production or telephone networks. The most interesting question in Markov chain models is the determination of…
Using a newly introduced connection between the local and non-local description of open quantum system dynamics, we investigate the relationship between these two characterisations in the case of quantum semi-Markov processes. This class of…
Motivated by applications in systems biology, we seek a probabilistic framework based on Markov processes to represent intracellular processes. We review the formal relationships between different stochastic models referred to in the…
Handwritten mathematical expression recognition (HMER) is a challenging task that has many potential applications. Recent methods for HMER have achieved outstanding performance with an encoder-decoder architecture. However, these methods…
In this work, we combine an established method for open quantum systems -- the time evolving density matrix using orthogonal polynomials algorithm (TEDOPA) -- with the transfer tensors formalism (TTM), a new tool for the analysis,…
In single-cell research, tracing and analyzing high-throughput single-cell differentiation trajectories is crucial for understanding biological processes. Key to this is the robust modeling of hierarchical structures that govern cellular…