相关论文: Genetic algorithms and the Andrews-Curtis conjectu…

Providing explanations about how machine learning algorithms work and/or make particular predictions is one of the main tools that can be used to improve their trusworthiness, fairness and robustness. Among the most intuitive type of…

The Grothendieck--Serre conjecture predicts that every generically trivial torsor under a reductive group scheme $G$ over a regular local ring $R$ is trivial. We settle it in the case when $G$ is quasi-split and $R$ is unramified. Some of…

We exhibit approximately fifty Betti diagrams of free resolutions of rings of smooth, connected canonical curves of genera $9$-$14$ in prime characteristics between $2$ and $11$. Generic Green's conjecture is verified for genera $9$ and…

Let $G$ be a finite group, and let $N(G)$ be the set of sizes of its conjugacy classes. We show that if a finite group $G$ has trivial center and $N(G)$ equals to $N(Alt_n)$ or $N(Sym_n)$ for $n\geq 23$, then $G$ has a composition factor…

This paper characterizes the inherent power of evolutionary algorithms. This power depends on the computational properties of the genetic encoding. With some encodings, two parents recombined with a simple crossover operator can sample from…

Why is the genetic code the way it is? The most successful theory states that the codon assignments minimise the effects of errors arising in primordial living systems. Here a transversion is reported that leaves invariant degeneracy in the…

Adam is one of the most influential adaptive stochastic algorithms for training deep neural networks, which has been pointed out to be divergent even in the simple convex setting via a few simple counterexamples. Many attempts, such as…

In this work we employ machine learning to understand structured mathematical data involving finite groups and derive a theorem about necessary properties of generators of finite simple groups. We create a database of all 2-generated…

A graph property is elusive (or evasive) if any algorithm testing it by asking questions of the form ''Is there an edge between vertices x and y?'' must, in the worst case, examine all pairs of vertices. Elusiveness for infinite vertex sets…

The ability of Convolutional Neural Networks (CNNs) to accurately process real-time telemetry has boosted their use in safety-critical and high-performance computing systems. As such systems require high levels of resilience to errors, CNNs…

Genetic Algorithms (GA) are a class of metaheuristic global optimization methods inspired by the process of natural selection among individuals in a population. Despite their widespread use, a comprehensive theoretical analysis of these…

This paper studies a family of convolution quadratures, a numerical technique for efficient evaluation of convolution integrals. We employ the block generalized Adams method to discretize the underlying initial value problem, departing from…

Genealogical networks, also known as family trees or population pedigrees, are commonly studied by genealogists wanting to know about their ancestry, but they also provide a valuable resource for disciplines such as digital demography,…

A genetic algorithm (GA) is a search-based optimization technique based on the principles of Genetics and Natural Selection. We present an algorithm which enhances the classical GA with input from quantum annealers. As in a classical GA,…

The Grothendieck--Serre conjecture predicts that every generically trivial torsor under a reductive group scheme $G$ over a regular local ring $R$ is trivial. The mixed characteristic case of the conjecture is widely open. We consider the…

We propose a partitioning of the set of unlabelled, connected cubic graphs into two disjoint subsets named genes and descendants, where the cardinality of the descendants is much larger than that of the genes. The key distinction between…

We demonstrate how a genetic algorithm solves the problem of minimizing the resources used for network coding, subject to a throughput constraint, in a multicast scenario. A genetic algorithm avoids the computational complexity that makes…

The research community continues to seek increasingly more advanced synthetic data generators to reliably evaluate the strengths and limitations of machine learning methods. This work aims to increase the availability of datasets…

A default theory can be characterized by its sets of plausible conclusions, called its extensions. But, due to the theoretical complexity of Default Logic (Sigma_2p-complete), the problem of finding such an extension is very difficult if…

Genus Theory is a classical feature of integral binary quadratic forms. Using the author's generalization of the well-known correspondence between quadratic form classes and ideal classes of quadratic algebras, we extend it to the case when…