Related papers: $\beta$-diversity and Graph Sheaf Laplacians
We present a new and exploratory approach to determine the $\Delta\beta(\beta)$-shift in the $O(3)$ nonlinear $\sigma$-model. The method is based on a scaling hypothesis for a free energy difference, which is assumed to be valid in a…
Averting the impending harms of climate change requires to replace fossil fuels with renewables as a primary source of energy. Non-electric renewable potential being limited, this implies extending the use of electricity generated from wind…
Networks with a prescribed power-law scaling in the spectrum of the graph Laplacian can be generated by evolutionary optimization. The Laplacian spectrum encodes the dynamical behavior of many important processes. Here, the networks are…
The magnetic Laplacian (also called the line bundle Laplacian) on a connected weighted graph is a self-adjoint operator wherein the real-valued adjacency weights are replaced by unit complex-valued weights $\{\omega_{xy}\}_{xy\in E}$,…
It is basic question in biology and other fields to identify the char- acteristic properties that on one hand are shared by structures from a particular realm, like gene regulation, protein-protein interaction or neu- ral networks or…
Graphs with diverse structural characteristics play a central role in modelling and optimization tasks. The ability to generate different types of graphs that exhibit shared properties is likewise essential for algorithm selection and…
In this paper, we compute Laplacian energy of the non-commuting graphs of some classes of finite non-abelian groups.
In this paper, we obtain energy, Laplacian energy and signless Laplacian energy of the commuting graphs of some families of finite non-abelian groups.
Studies on distribution, abundance and diversity of species revealed fascinating universalities in macroecology. Many of these patterns, like the species-area and range-abundance relationship or the year-to-year fluctuations in population…
In this paper we present new L-borderenergetic graphs, this is, graphs which are L-noncospectral with Kn but have the same Laplacian energy. We also present some graphs which are noncospectral to respective normalized Laplacian energy and…
Systems evolving according to the standard concept of biological or technological evolution are often described by catalytic evolution equations. We study the structure of these equations and find a deep relationship to classical…
A thermodynamic device placed outdoors, or a local ecosystem, is subject to a variety of different temperatures given by short-tem (daily) and long-term (seasonal) variations. In the long term a superstatistical description makes sense,…
Systems of interacting species, such as biological environments or chemical reactions, are often described mathematically by sets of coupled ordinary differential equations. While a large number $\beta$ of species may be involved in the…
Let $G$ be a finite non-abelian group and ${\Gamma}_{nc}(G)$ be its non-commuting graph. In this paper, we compute spectrum and energy of ${\Gamma}_{nc}(G)$ for certain classes of finite groups. As a consequence of our results we construct…
Recently various types of topological Laplacians have been studied from the perspective of data analysis. The spectral theory of these Laplacians has significantly extended the scope of algebraic topology and data analysis. Inspired by the…
We analyze several florae (collections of plant species populating specific areas) in different geographic and climatic regions. For every list of species we produce a taxonomic classification tree and we consider its statistical…
The spectrum of the normalized graph Laplacian yields a very comprehensive set of invariants of a graph. In order to understand the information contained in those invariants better, we systematically investigate the behavior of this…
An analytic theory of species abundance patterns (SAPs) in biological networks is presented. The theory is based on multispecies replicator dynamics equivalent to the Lotka-Volterra equation, with diverse interspecies interactions. Various…
Understanding the behaviors of ecological systems is challenging given their multi-faceted complexity. To proceed, theoretical models such as Lotka-Volterra dynamics with random interactions have been investigated by the dynamical…
We generalize the definition and enumeration of spanning trees from the setting of graphs to that of arbitrary-dimensional simplicial complexes $\Delta$, extending an idea due to G. Kalai. We prove a simplicial version of the Matrix-Tree…