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We present an alternative method for calculating likelihoods in molecular phylogenetics. Our method is based on partial likelihood tensors, which are generalizations of partial likelihood vectors, as used in Felsenstein's approach.…
The Bayesian evidence is a key tool in model selection, allowing a comparison of models with different numbers of parameters. Its use in analysis of cosmological models has been limited by difficulties in calculating it, with current…
The drive for reproducibility in the computational sciences has provoked discussion and effort across a broad range of perspectives: technological, legislative/policy, education, and publishing. Discussion on these topics is not new, but…
While large language models (LLMs) have demonstrated remarkable reasoning capabilities, they often struggle with complex tasks that require specific thinking paradigms, such as divide-and-conquer and procedural deduction, \etc Previous…
Support vector machines and kernel methods are increasingly popular in genomics and computational biology, due to their good performance in real-world applications and strong modularity that makes them suitable to a wide range of problems,…
Distance-based methods such as UPGMA (Unweighted Pair Group Method with Arithmetic Mean) continue to play a significant role in phylogenetic research. We use polyhedral combinatorics to analyze the natural subdivision of the positive…
We evaluate four computational models of explanation in Bayesian networks by comparing model predictions to human judgments. In two experiments, we present human participants with causal structures for which the models make divergent…
Construction of phylogenetic trees has traditionally focused on binary trees where all species appear on leaves, a problem for which numerous efficient solutions have been developed. Certain application domains though, such as viral…
There has been a resurgence of interest in lower bounds whose truth rests on the conjectured hardness of well known computational problems. These conditional lower bounds have become important and popular due to the painfully slow progress…
Combinatorics is a fundamental mathematical discipline as well as an essential component of many mathematical areas, and its study has experienced an impressive growth in recent years. One of the main reasons for this growth is the tight…
Smart premise selection is essential when using automated reasoning as a tool for large-theory formal proof development. A good method for premise selection in complex mathematical libraries is the application of machine learning to large…
Machine Learning methods have of late made significant efforts to solving multidisciplinary problems in the field of cancer classification using microarray gene expression data. Feature subset selection methods can play an important role in…
Scientific claims gain credibility by replicability, especially if replication under different circumstances and varying designs yields equivalent results. Aggregating results over multiple studies is, however, not straightforward, and when…
We describe a case of an interplay between human and computer proving which played a role in the discovery of an interesting mathematical result. The unusual feature of the use of computers here was that a computer generated but human…
Recent studies have suggested that Large Language Models (LLMs) could provide interesting ideas contributing to mathematical discovery. This claim was motivated by reports that LLM-based genetic algorithms produced heuristics offering new…
We consider a new approach to the description of the collective behavior of complex systems of mathematical biology based on the evolution equations for observables of such systems. This representation of the kinetic evolution seems, in…
Preference analysis is widely applied in various domains such as social choice and e-commerce. A recently proposed framework augments the relational database with a preference relation that represents uncertain preferences in the form of…
Understanding and creating mathematics using natural mathematical language - the mixture of symbolic and natural language used by humans - is a challenging and important problem for driving progress in machine learning. As a step in this…
We uncover a close relationship between combinatorial and syntactic proofs for first-order logic (without equality). Whereas syntactic proofs are formalized in a deductive proof system based on inference rules, a combinatorial proof is a…
Probabilistic models over strings have played a key role in developing methods allowing indels to be treated as phylogenetically informative events. There is an extensive literature on using automata and transducers on phylogenies to do…