Related papers: The converse problem for the multipotentialisation…

The inverse problem is studied in multi-body systems with nonlinear dynamics representing, e.g., phase-locked wave systems, standard multimode and random lasers. Using a general model for four-body interacting complex-valued variables we…

We investigate a multi-locus evolutionary model which is based on the DNA shuffling protocol widely applied in \textit{in vitro} directed evolution. This model incorporates selection, recombination and point mutations. The simplicity of the…

Set-valued prediction is a well-known concept in multi-class classification. When a classifier is uncertain about the class label for a test instance, it can predict a set of classes instead of a single class. In this paper, we focus on…

The usual superposition formulas for Baecklund transformations of (2+1)-dimensional integrable systems include quadratures unlike the well known case of (1+1)-dimensional inegrable systems where the fourth solution is found with algebraic…

Multi-label classification consists in classifying an instance into two or more classes simultaneously. It is a very challenging task present in many real-world applications, such as classification of biology, image, video, audio, and text.…

Population-based evolutionary algorithms have great potential to handle multiobjective optimisation problems. However, these algorithms depends largely on problem characteristics, and there is a need to improve their performance for a wider…

We exhibit a class of classical or tropical posynomial systems which can be solved by reduction to linear or convex programming problems. This relies on a notion of colorful vectors with respect to a collection of Newton polytopes. This…

Evidences have suggested that counting representations are sometimes tractable even when the corresponding classification problem is almost impossible, or "wild" in a precise sense. Such counting problems are directly related to matrix…

The human visual system is able to recognize objects despite transformations that can drastically alter their appearance. To this end, much effort has been devoted to the invariance properties of recognition systems. Invariance can be…

Two meta-evolutionary optimization strategies described in this paper accelerate the convergence of evolutionary programming algorithms while still retaining much of their ability to deal with multi-modal problems. The strategies, called…

We assess an emerging simulation research method -- Inverse Generative Social Science (IGSS) \citep{Epstein23a} -- that harnesses the power of evolution by natural selection to model and explain complex targets. Drawing on a review of…

While attention has been empirically shown to improve model performance, it lacks a rigorous mathematical justification. This short paper establishes a novel connection between attention mechanisms and multinomial regression. Specifically,…

Higher order tensor inversion is possible for even order. We have shown that a tensor group endowed with the Einstein (contracted) product is isomorphic to the general linear group of degree $n$. With the isomorphic group structures, we…

We obtain the complete Lie point symmetry algebras of two sequences of odd-order evolution equations. This includes equations that are fully-nonlinear, i.e. nonlinear in the highest derivative. Two of the equations in the sequences have…

We consider systems of diffusion equations that have considerable interest in Soil Science and Mathematical Biology and focus upon the problem of finding those forms of this class that can be linearized. In particular we use the equivalence…

Real-world optimization problems often involve stochastic and dynamic components. Evolutionary algorithms are particularly effective in these scenarios, as they can easily adapt to uncertain and changing environments but often uncertainty…

Generative learning generates high dimensional data based on low dimensional conditions, also called prompts. Therefore, generative learning algorithms are eligible for solving (Bayesian) inverse problems. In this article we compare a…

In many tasks, in particular in natural science, the goal is to determine hidden system parameters from a set of measurements. Often, the forward process from parameter- to measurement-space is a well-defined function, whereas the inverse…

We establish global convergence of the (1+1) evolution strategy, i.e., convergence to a critical point independent of the initial state. More precisely, we show the existence of a critical limit point, using a suitable extension of the…

This paper introduces a multi-level (m-lev) mechanism into Evolution Strategies (ESs) in order to address a class of global optimization problems that could benefit from fine discretization of their decision variables. Such problems arise…