Formal Graphs Research Articles

The Formal, Tonal, and Harmonic Logic of L. Van Beethoven’s An Die Ferne Geliebte (To the Distant Beloved) (Op. 98) Song Cycle

"This paper is an analysis of Beethoven's song cycle An die ferne Geliebte (To the Distant Beloved), op. 98, formally, tonally and harmonically. After a brief introduction, the author takes the songs in order, describing them analytically, placing the interesting and idiosyncratic arrangements in the light of the lyrics. She draws dramaturgical parallels between the text and the musical arrangements. Finally, she illustrates her analysis with formal and tonal summary tables and graphs, thus helping to understand and summarise the songs. Keywords: Beethoven, An die ferne Geliebte, To the Distant Beloved, op. 98, harmony, musical forms, tonal logic "

A Hetero-Functional Graph Resilience Analysis of the Future American Electric Power System

As climate change takes hold in the $21^{st}$ century, it places an impetus to decarbonize the American Electric Power System with renewable energy resources. There is a broad technical consensus that these renewable energy resources cannot be integrated alone but rather require a host of profound changes in the electric grid’s architecture; including meshed distribution lines, and energy storage solutions. One question that arises is whether these three types of mitigation measures required by decarbonization will also serve as adaptation measures when the climate changes and extreme weather phenomena become more prevalent. Consequently, this paper presents a structural resilience analysis of the American electric power system that incrementally incorporates these architectural changes in the future. Building upon a preliminary study, the analysis draws on an emerging hetero-functional graph theory based upon the inter-connectedness of a system’s capabilities. The hetero-functional graph analysis confirms our formal graph understandings from network science in terms of cumulative degree distributions and traditional attack vulnerability measures. The paper goes on to show that hetero-functional graphs relative to formal graphs more precisely describe the changes in functionality associated with the addition of distributed generation and energy storage as the grid evolves to a decarbonized architecture. Finally, it demonstrates that the addition of all three types of mitigation measures enhance the grid’s structural resilience; even in the presence of disruptive random and targeted attacks. The paper concludes that there is no structural trade-off between grid sustainability and resilience enhancements and that these strategic goals can be pursued simultaneously.

Understanding physics and physical chemistry using formal graphs

Understanding physics and physical chemistry using formal graphs

Simple and direct interpretation of phase angles or derivation degrees in term of energy conservation vs. dissipation with Formal Graphs

With the help of a new theory using the notion of path in a graph, a physical interpretation and meaning can be given to electroanalytical measurements, without recourse to mathematical treatments. The frequency dependence of impedances measured by ac techniques, or the scan rate dependence of current vs. potential characterizations in large signal techniques (cyclic voltammetry), can be interpreted through this approach as a determination of the proportion of conserved energy vs. total energy involved in a mechanism. This total energy includes the energy which is lost by dissipation, i.e., converted into heat. This new way of thinking sheds an interesting light on the difference between normal and anomalous or fractal diffusion and provides to the analyst a simple and immediate tool for interpreting experimental data.

Toward a Uniform Functional Model of Payment and Securities Settlement Systems

The aim of this paper is to provide a uniform representation of functional concepts used in the field of payment and securities settlement systems. The framework developed here is encompassing the whole field while using as few elements as possible. It provides a basic functional model for analyzing and tracing the life cycle of the financial legs of a transaction. In line with the network properties of the field the model is based on formal graphs. The visualization of these graphs can be considered as a symbolic language. It is shown on the basis of a number of examples that the framework is capable of representing basic notions of payment and securities settlement systems.

Analysis of biological networks

Analysis of biological networks

Universal current–potential relationship for mass-transfer through Formal Graph approach

The Formal Graph theory, a new language able to model graphically instead of algebraically most of basic equations used in physics and chemistry, is applied to mass-transfer occurring in electrochemical reactions. The integral admittance used in electrodynamics is generalized to all domains where energy is defined. Associated with the concept of energy coupling, this leads to very simple relationships between variables and operators describing processes in a system containing several energy varieties. The paradox of two different forms for the electric capacitance, linear in electrostatics and exponential in electrified materials, is treated and understood. The concept of energetic path brings physical meaning into mathematical models by attributing to each link a role in the conservation or dissipation of the energy. Normal transient diffusion, featured by an exponent 1/2, conserves half of energy, while anomalous diffusion, featured by an exponent p different from 1/2, conserves only 100 p%. The principle of every electrochemical measurement is represented in a simple and clear way by associating two Formal Graphs. The use of a mass-transfer operator generalizing all kinds of mass-transfer (diffusion, convection, thin layer, etc.) and for all geometric situations, allows the characterization of unknown process without previous knowledge of an algebraic model.

Introduction to Formal Graphs, a new approach to the classical formalism

The creation of a purely graphic language called Formal Graphs for modelling many physical and physico-chemical systems is described. It represents an improvement over traditional equivalent circuits used for modelling systems made of individual components and over bond graphs used mainly in physico-chemistry. In contradistinction with these graphs, which represent graphically only mounting equations and maintain algebraic equations for describing components behaviour, a formal graph is an oriented graph incorporating all the information contained in a usual algebraic model. Combination of paths considerably extends use to domains that were not accessible to quantitative graphs, such as relaxation processes, chemical reactivity or mass-transfer. Moreover, inclusion of space derivation allows representing graphically every physical law describing a process involving energy conservation or dissipation, such as particle diffusion. Physical meaning can be deduced from paths in a graph that can be followed by processes, as illustrated by the exponent of fractional derivation, which appears as bearing the information on the proportion of conserved versus dissipated energy. The numerous examples given in this introduction address several domains, electrodynamics, mechanics, thermodynamics, and physico-chemistry. They show common graph structures that reveal a striking unity of our classical formalism, bringing transversal insight and opening a new route towards unification. Differences also appear that are subjects of interrogation.

Epigenesis and Dynamic Similarity in Two Regulatory Networks in Pseudomonas Aeruginosa

Mucoidy and cytotoxicity arise from two independent modifications of the phenotype of the bacterium Pseudomonas aeruginosa that contribute to the mortality and morbidity of cystic fibrosis. We show that, even though the transcriptional regulatory networks controlling both processes are quite different from a molecular or mechanistic point of view, they may be identical from a dynamic point of view: epigenesis may in both cases be the cause of the acquisition of these new phenotypes. This was highlighted by the identity of formal graphs modelling these networks. A mathematical framework based on formal methods from computer science was defined and implemented with a software environment. It allows an easy and rigorous validation and certification of these models and of the experimental methods that can be proposed to falsify or validate the underlying hypothesis.

Strain energy modeling of simple and crowded aliphatic ketones: spectroscopic properties

Abstract

Modular lattices and abelian categories

A concept of “abelian lattice” is defined by adding a certain existence axiom to the modular lattice axioms. From an abelian lattice L, a small abelian category A L can be constructed. The construction is based upon identification of specified elements of L as formal graphs of morphisms of A L . The objects of A L correspond to the intervals [ x, y] for x ⊂ y in L. The subobject and quotient object lattices of [ x, y] as an object of A L are isomorphic to the interval sublattice [ x, y] of L. Two objects of A L are isomorphic if and only if the corresponding intervals are projective in L. The construction can be extended to a functor from the category of abelian lattices and lattice homomorphisms to the category of small abelian categories and exact functors. A method of constructing an abelian lattice from an abelian group is displayed. It is proved that a lattice can be embedded in an interval sublattice of an abelian lattice if and only if it can be embedded in the lattice of subgroups of some abelian group.