Classification in biological networks with hypergraphlet kernels

Motivation Biological and cellular systems are often modeled as graphs in which vertices represent objects of interest (genes, proteins and drugs) and edges represent relational ties between these objects (binds-to, interacts-with and regulates). This approach has been highly successful owing to the theory, methodology and software that support analysis and learning on graphs. Graphs, however, suffer from information loss when modeling physical systems due to their inability to accurately represent multiobject relationships. Hypergraphs, a generalization of graphs, provide a framework to mitigate information loss and unify disparate graph-based methodologies. Results We present a hypergraph-based approach for modeling biological systems and formulate vertex classification, edge classification and link prediction problems on (hyper)graphs as instances of vertex classification on (extended, dual) hypergraphs. We then introduce a novel kernel method on vertex- and edge-labeled (colored) hypergraphs for analysis and learning. The method is based on exact and inexact (via hypergraph edit distances) enumeration of hypergraphlets; i.e. small hypergraphs rooted at a vertex of interest. We empirically evaluate this method on fifteen biological networks and show its potential use in a positive-unlabeled setting to estimate the interactome sizes in various species. Availability and implementation https://github.com/jlugomar/hypergraphlet-kernels Supplementary information Supplementary data are available at Bioinformatics online.

Some Analytical Solitary Wave Solutions for the Generalized q-Deformed Sinh-Gordon Equation: ∂2θ/∂z∂ξ=αsinhq⁡(βθγ)p-δ

We introduce the generalized q-deformed Sinh-Gordon equation and derive analytical soliton solutions for some sets of parameters. This new defined equation could be useful for modeling physical systems with violated symmetries.

Block-Based Physical Modeling with Applications in Musical Acoustics

Block-Based Physical Modeling with Applications in Musical AcousticsBlock-based physical modeling is a methodology for modeling physical systems with different subsystems. Each subsystem may be modeled according to a different paradigm. Connecting systems of diverse nature in the discrete-time domain requires a unified interconnection strategy. Such a strategy is provided by the well-known wave digital principle, which had been introduced initially for the design of digital filters. It serves as a starting point for the more general idea of block-based physical modeling, where arbitrary discrete-time state space representations can communicate via wave variables. An example in musical acoustics shows the application of block-based modeling to multidimensional physical systems.