相关论文: Genetic algorithms and the Andrews-Curtis conjectu…
The reconstruction of a central tendency `species tree' from a large number of conflicting gene trees is a central problem in systematic biology. Moreover, it becomes particularly problematic when taxon coverage is patchy, so that not all…
A graph property is said to be elusive ( evasive) if every algorithm testing this property by asking questions of the form "is there an edge between vertices x and y" requires, in the worst case, to ask about all pairs of vertices. The…
Convolutional neural networks often dominate fully-connected counterparts in generalization performance, especially on image classification tasks. This is often explained in terms of 'better inductive bias'. However, this has not been made…
The deterministic selection-recombination equation describes the evolution of the genetic type composition of a population under selection and recombination in a law of large numbers regime. So far, an explicit solution has seemed out of…
The statement ``no nonabelian simple group can be obtained from a nonsimple group by adding one generator and one relator" 1) is equivalent to the Kervaire--Laudenbach conjecture; 2) becomes true under the additional assumption that the…
In this paper, a simple explanation for the Goldbach Conjecture is given. We have shown that the probability of violating the conjecture not only for the prime numbers, but also for any subset of natural numbers whose distribution is…
This manuscript contains an outline of lectures course "Evolutionary Algorithms" read by the author. The course covers Canonic Genetic Algorithm and various other genetic algorithms as well as evolutionary strategies, genetic programming,…
Counterfactual explanations elucidate algorithmic decisions by pointing to scenarios that would have led to an alternative, desired outcome. Giving insight into the model's behavior, they hint users towards possible actions and give grounds…
Although degree bounds and algorithms for the generators of various invariant rings have been known for decades, little is known about the cardinality of minimal generating sets. Estimates of such would provide lower bounds for the runtime…
Generalised Probabilistic Theories (GPTs) provide a unifying framework encompassing classical theories, quantum theories, as well as hypothetical alternatives. We investigate the problem of extending a system with a finite set of…
Multi-model inference covers a wide range of modern statistical applications such as variable selection, model confidence set, model averaging and variable importance. The performance of multi-model inference depends on the availability of…
A first step in exploring population structure in crop plants and other organisms is to define the number of subpopulations that exist for a given data set. The genetic marker data sets being generated have become increasingly large over…
The genetic code has been shown to be very error robust compared to randomly selected codes, but to be significantly less error robust than a certain code found by a heuristic algorithm. We formulate this optimisation problem as a Quadratic…
According to the Tits conjecture proved by Crisp and Paris, [CP], the subgroups of the braid group generated by proper powers of the Artin elements are presented by the commutators of generators which are powers of commuting elements. Hence…
We present two related conjectures, arising in work on i-matchings in random r-regular bipartite graphs. The conjectures themselves are easily stated and involve only basic properties of convergent power series. One formulation involves…
Genetic Programming is an evolutionary algorithm that generates computer programs, or mathematical expressions, to solve complex problems. In this Guide, we demonstrate how to use Genetic Programming to develop surrogate models to mitigate…
We consider the evolution of populations under the joint action of mutation and differential reproduction, or selection. The population is modelled as a finite-type Markov branching process in continuous time, and the associated…
We present methods for inference about relationships between contributors to a DNA mixture and other individuals of known genotype: a basic example would be testing whether a contributor to a mixture is the father of a child of known…
Mounting evidence suggests that natural populations can harbor extensive fitness diversity with numerous genomic loci under selection. It is also known that genealogical trees for populations under selection are quantifiably different from…
We explore the Collatz conjecture and its variants through the lens of termination of string rewriting. We construct a rewriting system that simulates the iterated application of the Collatz function on strings corresponding to mixed…