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Statistical consistency in phylogenetics has traditionally referred to the accuracy of estimating phylogenetic parameters for a fixed number of species as we increase the number of characters. However, as sequences are often of fixed length…
The Promise Constraint Satisfaction Problem (PCSP for short) is a generalization of the well-studied Constraint Satisfaction Problem (CSP). The PCSP has its roots in such classic problems as the Approximate Graph Coloring and the…
Approximate message passing (AMP) type algorithms have been widely used in the signal reconstruction of certain large random linear systems. A key feature of the AMP-type algorithms is that their dynamics can be correctly described by state…
A Burling graph is an induced subgraph of some graph in Burling's construction of triangle-free high-chromatic graphs. Equivalently, a Burling graph is a graph that admits a so-called strict frame representation. We provide a…
The mapping between biological genotypes and phenotypes is central to the study of biological evolution. Here we introduce a rich, intuitive, and biologically realistic genotype-phenotype (GP) map, that serves as a model of self-assembling…
This paper deals with the complexity of some natural graph problems when parametrized by {measures that are restrictions of} clique-width, such as modular-width and neighborhood diversity. The main contribution of this paper is to introduce…
We present a new recursive generation algorithm for prefix normal words. These are binary strings with the property that no substring has more 1s than the prefix of the same length. The new algorithm uses two operations on binary strings,…
Longest Run Subsequence is a problem introduced recently in the context of the scaffolding phase of genome assembly (Schrinner et al., WABI 2020). The problem asks for a maximum length subsequence of a given string that contains at most one…
Motivated by applications in in-vivo DNA storage, we study codes for correcting duplications. A reverse-complement duplication of length $k$ is the insertion of the reversed and complemented copy of a substring of length $k$ adjacent to its…
Phylogenetic comparative methods (PCMs) are widely used to study trait evolution. However, many evolutionary histories involve reticulate evolutionary scenarios, such as hybridization, that violate core assumptions of these methods. In this…
A common problem in phylogenetics is to try to infer a species phylogeny from gene trees. We consider different variants of this problem. The first variant, called Unrestricted Minimal Episodes Inference, aims at inferring a species tree…
We consider the low rank matrix completion problem over finite fields. This problem has been extensively studied in the domain of real/complex numbers, however, to the best of authors' knowledge, there exists merely one efficient algorithm…
The binary Constraint Satisfaction Problem (CSP) is to decide whether there exists an assignment to a set of variables which satisfies specified constraints between pairs of variables. A binary CSP instance can be presented as a labelled…
Recent studies of genotype-phenotype (GP) maps have reported universally enhanced phenotypic robustness to genotype mutations, a feature essential to evolution. Virtually all of these studies make a simplifying assumption that each genotype…
In this paper, we propose an effective face completion algorithm using a deep generative model. Different from well-studied background completion, the face completion task is more challenging as it often requires to generate semantically…
Obtaining meaningful solutions for inverse problems has been a major challenge with many applications in science and engineering. Recent machine learning techniques based on proximal and diffusion-based methods have shown promising results.…
The statistical estimation of phylogenies is always associated with uncertainty, and accommodating this uncertainty is an important component of modern phylogenetic comparative analysis. The birth-death polytomy resolver is a method of…
Many classical theorems in combinatorics establish the emergence of substructures within sufficiently large collections of objects. Well-known examples are Ramsey's theorem on monochromatic subgraphs and the Erd\H{o}s-Rado sunflower lemma.…
In this paper, a fully compressed pattern matching problem is studied. The compression is represented by straight-line programs (SLPs), i.e. a context-free grammars generating exactly one string; the term fully means that both the pattern…
In lifelong learning, tasks (or classes) to be learned arrive sequentially over time in arbitrary order. During training, knowledge from previous tasks can be captured and transferred to subsequent ones to improve sample efficiency. We…