Angelica Pachon

Angelica Pachon
Swansea University | SWAN

Dr.

About

22
Publications
2,085
Reads
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142
Citations
Additional affiliations
October 2018 - present
University of South Wales
Position
  • Lecturer
January 2014 - present
University of Turin
Position
  • PostDoc Position
January 2012 - December 2013
Graz University of Technology
Position
  • PostDoc Position
Education
March 2006 - August 2009
University of Bielefeld
Field of study
  • Mathematics

Publications

Publications (22)
Preprint
Full-text available
We study a random graph model with preferential edge attachment and detachment through the embedding into a generalized Yule model. We show that the in-degree distribution of a vertex chosen uniformly at random follows a power law in the supercritical regime but has an exponential decay in the subcritical. We provide the corresponding asymptotics....
Preprint
Full-text available
We consider the critical inhomogeneous random graph as described in van der Hofstad [11], where edges are present independently but edge probabilities are moderated by vertex weights, and provide simpler upper bounds for the probability of observing unusually large maximal components with respect to those available in the literature. We do this by...
Preprint
Full-text available
In the last years many authors studied a class of continuous time semi-Markov processes obtained by time-changing Markov processes by hitting times of independent subordinators. Such processes are governed by integro-differential convolution equations of generalized fractional type. The aim of this paper is to develop the discrete-time version of s...
Article
Full-text available
In the classical Erd\"os-R\'enyi random graph G(n, p) there are n vertices and each of the possible edges is independently present with probability p. One of the most known results for this model is the threshold for connectedness, a phenomenon which is tightly related to the nonexistence of isolated vertices. Numerous random graphs inspired in rea...
Article
Full-text available
We consider the Maki-Thompson model for the stochastic propagation of a rumour within a population. In this model the population is made up of “spreaders”, “ignorants” and “stiflers”; any spreader attempts to pass the rumour to the other individuals via pair-wise interactions and in case the other individual is an ignorant, it becomes a spreader, w...
Article
Full-text available
Complex networks in different areas exhibit degree distributions with heavy upper tail. A preferential attachment mechanism in a growth process produces a graph with this feature. We herein investigate a variant of the simple preferential attachment model, whose modifications are interesting for two main reasons: to analyze more realistic models an...
Preprint
Full-text available
Complex networks in different areas exhibit degree distributions with heavy upper tail. A preferential attachment mechanism in a growth process produces a graph with this feature. We herein investigate a variant of the simple preferential attachment model, whose modifications are interesting for two main reasons: to analyze more realistic models an...
Preprint
We consider the Maki-Thompson model for the stochastic propagation of a rumour within a population. We extend the original hypothesis of homogenously mixed population by allowing for a small-world network embedding the model. This structure is realized starting from a $k$-regular ring and by inserting, in the average, $c$ additional links in such a...
Article
Full-text available
We prove that, via an appropriate scaling, the degree of a fixed vertex in the Barabási–Albert model appeared at a large enough time converges in distribution to a Yule process. Using this relation we explain why the limit degree distribution of a vertex chosen uniformly at random (as the number of vertices goes to infinity), coincides with the lim...
Preprint
Full-text available
We prove that the Barab\'asi-Albert model converges weakly to a set of generalized Yule models via an appropriate scaling. To pursue this aim we superimpose to its graph structure a suitable set of processes that we call the planted model and we introduce an ad-hoc sampling procedure. The use of the obtained limit process represents an alternative...
Article
Full-text available
We give a common description of Simon, Barab\'asi-Albert, and II-PA growth models, by introducing suitable random graph processes with preferential attachment mechanisms. Through the II-PA model, we prove the conditions for which the asymptotic degree distribution of the Barab\'asi-Albert model coincides with the asymptotic in-degree distribution o...
Article
Full-text available
In this paper we consider a d-dimensional scenery seen along a simple symmetric branching random walk, where at each time each particle gives the color record it is seeing. We show that we can a.s. reconstruct the scenery up to equivalence from the color record of all the particles. For this we assume that the scenery has at least 2d + 1 colors whi...
Article
Full-text available
We determine the asymptotic size of the largest component in the 2-type binomial random graph G(n, P) near criticality using a refined branching process approach. In G(n, P) every vertex has one of two types, the vector n describes the number of vertices of each type, and any edge {u, v} is present independently with a probability that is given by...
Article
Full-text available
We determine the asymptotic size of the largest component in the multi-type binomial random graph $G(\mathbf{n},P)$ near criticality using a refined branching process approach. In $G(\mathbf{n},P)$ every vertex has one of two types, the vector $\mathbf{n}$ describes the number of vertices of each type and any edge $\{u,v\}$ is present independently...
Article
Full-text available
In this article we consider a simple random walker moving on a random media. Whilst doing so, the random walker observes at each point of time the “color” of the location he is at. This process creates a sequence of observations. We consider the problem of determining when the walker is close to the origin. For this we are only given, the observati...
Article
The basic reconstruction problem lead with the general task of retrieving a scenery from observations made by a random walker. A critical factor associated with the problem is reconstructing the scenery in polynomial time. In this article, we propose a novel technique based on the modern DNA sequencing method for reconstructing a 3-color scenery of...
Conference Paper
Full-text available
Let F be a uniformly distributed random k-SAT formula with n variables and m clauses. Non-rigorous statistical mechanics ideas have inspired a message passing algorithm called Belief Propagation Guided Decimation for finding satisfying assignments of F. This algorithm can be viewed as an attempt at implementing a certain thought experiment that we...
Article
Full-text available
Suppose that to each site on the integer numbers a color from the set 0, 1,..., C -1 is assigned. This defines a coloration of Z which is called scenery. Suppose a simple random walk starts to move registering the color it sees at each time t > 0 and producing a new sequence of colors, i.e, at time t, the random walk sees the color where it is on....
Article
Full-text available
This paper exploits the long history of the minimum wage in Colombia in order to see whether it has im-proved the living conditions of low income families and reduced income inequality. This paper also ex-plores how the minimum wage may have distorted market outcomes in the process. We fi nd signifi cant negative minimum wage effects on both the li...

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