Singular manifolds of proteomic drivers to model the evolution of inflammatory bowel disease status

The conditions used to describe the presence of an immune disease are often represented by interaction graphs. These informative, but intricate structures are susceptible to perturbations at different levels. The mode in which that perturbation occurs is still of utmost importance in areas such as cell reprogramming and therapeutics models. In this sense, module identification can be useful to well characterise the global graph architecture. To help us with this identification, we perform topological overlap-related measures. Thanks to these measures, the location of highly disease-specific module regulators is possible. Such regulators can perturb other nodes, potentially causing the entire system to change behaviour or collapse. We provide a geometric framework explaining such situations in the context of inflammatory bowel diseases (IBD). IBD are severe chronic disorders of the gastrointestinal tract whose incidence is dramatically increasing worldwide. Our approach models different IBD status as Riemannian manifolds defined by the graph Laplacian of two high throughput proteome screenings. It also identifies module regulators as singularities within the manifolds (the so-called singular manifolds). Furthermore, it reinterprets the characteristic nonlinear dynamics of IBD as compensatory responses to perturbations on those singularities. Then, particular reconfigurations of the immune system could make the disease status move towards an innocuous target state.

Singular manifolds of proteomic drivers to model the evolution of inflammatory bowel disease status

The conditions who denotes the presence of an immune disease are often represented by interaction graphs. These informative, but complex structures are susceptible to being perturbed at different levels. The mode in which that perturbation occurs is still of utmost importance in areas such as reprogramming therapeutics. In this sense, the overall graph architecture is well characterise by module identification. Topological overlap-related measures make possible the localisation of highly specific module regulators that can perturb other nodes, potentially causing the entire system to change behaviour or collapse. We provide a geometric framework explaining such situations in the context of inflammatory bowel diseases (IBD). IBD are important chronic disorders of the gastrointestinal tract which incidence is dramatically increasing worldwide. Our approach models different IBD status as Riemannian manifolds defined by the graph Laplacian of two high throughput proteome screenings. Identifies module regulators as singularities within the manifolds (the so-called singular manifolds). And reinterprets the characteristic IBD nonlinear dynamics as compensatory responses to perturbations on those singularities. Thus, we could control the evolution of the disease status by reconfiguring particular setups of immune system to an innocuous target state.

Recent developments on pseudo-differential operators (II)

The analysis on manifolds with singularities is a rapidly developing field of research, with new achievements and compelling challenges. We present here elements of an iterative approach to building up pseudo-differential structures. Those participate in operator algebras on singular manifolds and reflect the properties of parametrices of elliptic operators, including boundary value problems.