I am a lecturer in the Department of Mathematics at Swansea University. Previously, from October 2018 to August 2023, I was a lecturer in mathematics at the University of South Wales, UK.
My research can be defined as a crossover between Probability, Combinatorics and Statistics. My areas of expertise are “scenery reconstruction” and “random graphs models and complex networks”.
Personal website: http://www.angelicapachon.eu/
I undertake research in scenery reconstruction, and in random graphs.
Scenery Reconstruction
The simplest scenery reconstruction problem considers a colouring ξ: Z → {1, 2, . . . , κ} of the integers Z. To ξ one refers as the scenery and to κ as the number of colours of ξ. Furthermore, a particle moves according to a recurrent random walk S on Z and at each instant of time t observes the colour χt := ξ(St ) at its current position St , see the example in Figure 1 where, following the path above on ξ we obtain the sequence of observations χ=02020101001.
The original scenery reconstruction problem is formulated through the following question:
From a colour record χ = χ0 χ1 χ2 ..., can one reconstruct the scenery ξ?
My research has primarily focussed on studying:
• scenery reconstruction with special branching random walk.
• Use of techniques of DNA reconstruction for reconstructing 3-color scenery.
• Multidimensional scenery reconstruction with a branching random walk.
Random graphs
During the last few decades, increasing attention in the field of random graphs has been devoted to find models that describe the complexity of real-world networks. A random graph is a graph where nodes or edges or both are created by some random procedure. The subject of random graphs began in 1959-1960 with the papers “On random graphs I” and “On the evolution of random graphs” by Erdős and Rényi. In the classical Erdős and Rényi model G(n,m), a graph is chosen uniformly at random from the collection of all graphs which have exactly n nodes and m edges. There exist a close relation between G(n,m) and a variant of this model introduced by Gilbert at about the same time and denoted by G(n,p), where each edge is included in the graph with probability p independent from every other edge.
My research has primarily focussed on studying properties on:
• inhomogeneous random graphs and
• preferential attachment models.
