Ruben Sanchez-Garcia

• PhD
• Lecturer at University of Southampton

We study the synchronization properties of a generic networked dynamical system, and show that, under a suitable approximation, the transition to synchronization can be predicted with the only help of eigenvalues and eigenvectors of the graph Laplacian matrix. The transition comes out to be made of a well defined sequence of events, each of which c...

Networks have provided extremely successful models of data and complex systems. Yet, as combinatorial objects, networks do not have in general intrinsic coordinates and do not typically lie in an ambient space. The process of assigning an embedding space to a network has attracted lots of interest in the past few decades, and has been efficiently a...

We study the synchronization properties of a generic networked dynamical system, and show that, under a suitable approximation, the transition to synchronization can be predicted with the only help of eigenvalues and eigenvectors of the graph Laplacian matrix. The transition comes out to be made of a well defined sequence of events, each of which c...

Complex systems of intracellular biochemical reactions have a central role in regulating cell identities and functions. Biochemical reaction systems are typically studied using the language and tools of graph theory. However, graph representations only describe pairwise interactions between molecular species, and so are not well suited to modelling...

Adult tissues in multicellular organisms typically contain a variety of stem, progenitor and differentiated cell types arranged in a lineage hierarchy that regulates healthy tissue turnover. Lineage hierarchies in disparate tissues often exhibit common features, yet the general principles regulating their architecture are not known. Here, we provid...

Complex systems of intracellular biochemical reactions have a central role in regulating cell identities and functions. Biochemical reaction systems are typically studied using the language and tools of graph theory. However, graph representations only describe pairwise interactions between molecular species, and so are not well suited to modelling...

Single-cell sequencing (sc-Seq) experiments are producing increasingly large data sets. However, large data sets do not necessarily contain large amounts of information. Here, we introduce a formal framework for assessing that amount of information obtained from a sc-Seq experiment, which can be used throughout the sc-Seq analysis pipeline, includi...

We compute the equivariant $K$-homology of the classifying space for proper actions, for compact 3-dimensional hyperbolic reflection groups. This coincides with the topological $K$-theory of the reduced $C^\ast$-algebra associated to the group, via the Baum-Connes conjecture. We show that, for any such reflection group, the associated $K$-theory gr...

A power transmission system can be represented by a network with nodes and links representing buses and electrical transmission lines, respectively. Each line can be given a weight, representing some electrical property of the line, such as line admittance or average power flow at a given time. We use a hierarchical spectral clustering methodology...

Intentional controlled islanding is an effective corrective approach to minimise the impact of cascading outages leading to large-area blackouts. This paper proposes a novel methodology, based on constrained spectral clustering, that is computationally very efficient and determines an islanding solution with minimal power flow disruption, while ens...

Research endeavours require the collaborative effort of an increasing number of individuals. International scientific collaborations are particularly important for HIV and HPV co-infection studies, since the burden of disease is rising in developing countries, but most experts and research funds are found in developed countries, where the prevalenc...

Network representations are useful for describing the structure of a large variety of complex systems. Although most studies of networks suppose that nodes are connected by only a single type of edge, most real and engineered systems are multiplex because they include multiple subsystems and layers of connectivity. This new paradigm has attracted a...

We consider groups G which have a cocompact, 3-manifold model for the classifying space \underline{E}G. We provide an algorithm for computing the rationalized equivariant K-homology of \underline{E}G. Under the additional hypothesis that the quotient 3-orbifold \underline{E}G/G is geometrizable, the rationalized K-homology groups coincide with the...

These notes evolved from the lecture notes of a minicourse given in Swisk, the Sedano Winter School on K theory held in Sedano, Spain, during the week January 22 to 27 of 2007, and from those of a longer course given in the University of Buenos Aires, during the second half of 2006.

We present a model of adaptive regulatory networks consisting of a simple biologically-motivated rewiring procedure coupled to an elementary stability criterion. The resulting networks exhibit a characteristic stationary heavy-tailed degree distribution, show complex structural microdynamics and self-organize to a dynamically critical state. We sho...

In our earlier article we described a power series formula for the Borel regulator evaluated on the odd-dimensional homology of the general linear group of a number field and, concentrating on dimension three for simplicity, described a computer algorithm which calculates the value to any chosen degree of accuracy. In this sequel we give an algorit...

We present an infinite series formula based on the Karoubi-Hamida integral, for the universal Borel class evaluated on H_{2n+1}(GL(\mathbb{C})). For a cyclotomic field F we define a canonical set of elements in K_3(F) and present a novel approach (based on a free differential calculus) to constructing them. Indeed, we are able to explicitly constru...

Many real-world complex networks contain a significant amount of structural redundancy, in which multiple vertices play identical topological roles. Such redundancy arises naturally from the simple growth processes which form and shape many real-world systems. Since structurally redundant elements may be permuted without altering network structure,...

Many real-world complex networks contain a significant amount of structural redundancy, in which multiple vertices play identical topological roles. Such redundancy arises naturally from the simple growth processes which form and shape many real-world systems. Since structurally redundant elements may be permuted without altering network structure,...

We consider the size and structure of the automorphism groups of a variety of empirical ‘real-world’ networks and find that, in contrast to classical random graph models, many real-world networks are richly symmetric. We construct a practical network automorphism group decomposition, relate automorphism group structure to network topology and discu...

Ben MacArthur and Rubén Sánchez-García contributed equally to this work. We consider the size and structure of the automorphism groups of a variety of empirical ‘realworld’ networks and find that, in contrast to classical random graph models, many real-world networks – including a variety of biological networks and technological networks such as th...

We obtain the equivariant K-homology of the classifying space ESL(3, Z) from the computation of its Bredon homology with respect to finite sub- groups and coefficients in the representation ring. We also obtain the corresponding results for GL(3, Z). Our calculations give therefore the topological side of the Baum-Connes conjecture for these groups...

We consider the size and structure of the automorphism groups of a variety of empirical `real-world' networks and find that, in contrast to classical random graph models, many real-world networks are richly symmetric. We relate automorphism group structure to network topology and discuss generic forms of symmetry and their origin in real-world netw...

We obtain the equivariant K-homology of the classifying space \underline{E}W for W a right-angled or, more generally, an even Coxeter group. The key result is a formula for the relative Bredon homology of \underline{E}W in terms of Coxeter cells. Our calculations amount to the K-theory of the reduced C^*-algebra of W, via the Baum-Connes assembly m...

These notes are based on a lecture course given by the first author in the Sedano Winter School on K theory held in Sedano, Spain, on January 22,27th of 2007. They aim at introducing K theory of C*algebras, equivariant K homology and KK-theory in the context of the Baum Connes conjecture.