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Principles that predict reactions or properties of materials define the discipline of chemistry. In this work we derive chemical rules, based on atomic distances and chemical bond character, which predict topological materials in compounds…
The essential graph is a distinguished member of a Markov equivalence class of AMP chain graphs. However, the directed edges in the essential graph are not necessarily strong or invariant, i.e. they may not be shared by every member of the…
The paper gives an overview of recent advances in structural equation modeling. A structural equation model is a multivariate statistical model that is determined by a mixed graph, also known as a path diagram. Our focus is on the…
Predicting bioactivity and physical properties of molecules is a longstanding challenge in drug design. Most approaches use molecular descriptors based on a 2D representation of molecules as a graph of atoms and bonds, abstracting away the…
The arithmetic-geometric index is a newly proposed degree-based graph invariant in mathematical chemistry. We give a sharp upper bound on the value of this invariant for connected chemical graphs of given order and size and characterize the…
Core decomposition is an efficient building block for various graph analysis tasks such as dense subgraph discovery and identifying influential nodes. One crucial weakness of the core decomposition is its sensitivity to changes in the…
This study explores the irregularity properties of trees with prescribed degree sequences by analyzing two prominent topological indices: the Albertson index and the sigma index. With a particular emphasis on caterpillar trees -frequently…
A major practical barrier for implementing carbon-based electrode arrays with high device-packing density is to ensure large, predictable, and homogeneous sensitivities across the array. Overcoming this barrier depends on quantitative…
Basing on the molecular theory of graphene, the influence of the chemical modification of edge atoms of a graphene sheet is studied in terms of mechanochemical reactions. The mechanical behavior of graphene is shown to be not only highly…
The shape of a molecule determines its physicochemical and biological properties. However, it is often underrepresented in standard molecular representation learning approaches. Here, we propose using the Euler Characteristic Transform…
Constitutive models are fundamental to solid mechanics and materials science, underpinning the quantitative description and prediction of material responses under diverse loading conditions. Traditional phenomenological models, which are…
Optically active networks show feature-rich emission that depends on the fine details of their geometry, and find diverse applications in random lasers, sensing devices and photonics processors. In these and other systems, a thorough and…
The purpose of this review is to introduce the reader to graph kernels and the corresponding literature, with an emphasis on those with direct application to chemoinformatics. Graph kernels are functions that allow for the inference of…
We examine the role of strong nonlinearity on the topologically-robust edge state in a one-dimensional system. We consider a chain inspired from the Su-Schrieffer-Heeger model, but with a finite-frequency edge state and the dynamics…
Determining whether two graphs are isomorphic is a fundamental problem with practical applications in areas such as molecular chemistry or social network analysis, yet it remains a challenging task, with exact solutions often being…
Emergent effect is crucial to understanding the properties of complex systems that do not appear in their basic units, but there has been a lack of theories to measure and understand its mechanisms. In this paper, we consider emergence as a…
Two directed graphs are called covariance equivalent if they induce the same set of covariance matrices, up to a Lebesgue measure zero set, on the random variables of their associated linear structural equation models. For acyclic graphs,…
This work studies the limitations of uniquely identifying the structure (i.e., topology) of a networked linear system from partial measurements of its nodal dynamics. In general, many networks can be consistent with these measurements; this…
Weight-equitable partitions of graphs, which are a natural extension of the well-known equitable partitions, have been shown to be a powerful tool to weaken the regularity assumption in several well-known eigenvalue bounds. In this work we…
Strong mixing property holds for a broad class of linear and nonlinear time series models such as ARMA and GARCH models. In this article we study correlation structure of strong mixing sequences, and some asymptotic properties are…