Related papers: $\beta$-diversity and Graph Sheaf Laplacians
The standard notion of the Laplacian of a graph is generalized to the setting of a graph with the extra structure of a ``transmission`` system. A transmission system is a mathematical representation of a means of transmitting…
We consider an evolution algebra which corresponds to a bisexual population with a set of females partitioned into finitely many different types and the males having only one type. We study basic properties of the algebra. This algebra is…
We make a case for "planetary computing" -- infrastructure to handle the ingestion, transformation, analysis and publication of global data products for furthering environmental science and enabling better informed policy-making. We draw on…
The increasing volume of ecologically and biologically relevant data has revealed a wide collection of emergent patterns in living systems. Analyzing different datasets, ranging from metabolic gene-regulatory to species interaction…
This paper presents an assessment of global economic energy potentials for all major natural energy resources. This work is based on both an extensive literature review and calculations using natural resource assessment data. Economic…
We apply bio-inspired methods for the analysis of different dynamic bibliometric networks (linking papers by citation, authors, and keywords, respectively). Biological species are clusters of individuals defined by widely different criteria…
The singularities of the electromagnetic field are derived to include all the point-like multipoles representing an electric charge and current distribution. We show that for higher orders, it is more efficient to have fields represented in…
We propose a new approach towards determining the distribution of mechanical and acoustic wave energy in complex built-up structures. The technique interpolates between standard Statistical Energy Analysis (SEA) and full ray tracing…
Diversity represents a key concept in ecology, and there are various methods of assessing it. The multitude of diversity indices are quite puzzling and sometimes difficult to compute for a large volume of data. This paper promotes a…
In this paper, we introduce a graph structure called linear dependence graph of a finite dimensional vector space over a finite field. Some basic properties of the graph like connectedness, completeness, planarity, clique number, chromatic…
Motivated by discrete Laplacian differential operators with various accuracy orders in numerical analysis, we introduce new matrices attached to a simple graph that can be considered graph Laplacians with higher accuracy. In particular, we…
Accelerating global biodiversity loss has highlighted the role of complex relationships and shared patterns among species in determining their responses to environmental changes. The structure of an ecological community, represented by…
We study the orbital effect of a strong magnetic field parallel to the layers on the energy spectrum of the Bernal-stacked graphene bilayer and multilayers, including graphite. We consider the minimal model with the electron tunneling…
Because of the significant increase in size and complexity of the networks, the distributed computation of eigenvalues and eigenvectors of graph matrices has become very challenging and yet it remains as important as before. In this paper…
Many real-world systems studied are governed by complex, nonlinear dynamics. By modeling these dynamics, we can gain insight into how these systems work, make predictions about how they will behave, and develop strategies for controlling…
We discuss the relevance of studying ecology within the framework of Complexity Science from a statistical mechanics approach. Ecology is concerned with understanding how systems level properties emerge out of the multitude of interactions…
Typically, graph structures are represented by one of three different matrices: the adjacency matrix, the unnormalised and the normalised graph Laplacian matrices. The spectral (eigenvalue) properties of these different matrices are…
We present a mainly analytical study of the entanglement spectrum of Bernal-stacked graphene bilayers in the presence of trigonal warping in the energy spectrum. Upon tracing out one layer, the entanglement spectrum shows qualitative…
This chapter explores dynamical structural equation models (DSEMs) and their nonlinear generalizations into sheaves of dynamical systems. It demonstrates these two disciplines on part of the food web in the Bering Sea. The translation from…
The Laplacian energy of a graph is the sum of the distances of the eigenvalues of the Laplacian matrix of the graph to the graph's average degree. The maximum Laplacian energy over all graphs on $n$ nodes and $m$ edges is conjectured to be…