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The study delves into the relationship between symmetry groups and automorphism groups in polyhedral graphs, emphasizing their interconnected nature and their significance in understanding the symmetries and structural properties of fullerenes. It highlights the visual importance of symmetry and its applications in architecture, as well as the mathematical structure of the automorphism group, which captures all of the symmetries of a graph. The paper also discusses the significance of groups in Abstract Algebra and their relevance to understanding the behavior of mathematical systems. Overall, the findings offer an inclusive understanding of the relationship between symmetry groups and automorphism groups, paving the way for further research in this area. [ABSTRACT FROM AUTHOR]

In this article, we introduce a new counting polynomial, namely the orbit polynomial. It is well-known that this polynomial has a unique positive zero δ in the interval [0, 1]. The aim of this paper is to study the specific properties of this polynomial and then determine the location of this root for several classes of complex networks to compare with other graphical measures. Additionally, we compare the unique positive zero measure with several well-known centrality graph measures. [ABSTRACT FROM AUTHOR]

This note is intended as a contribution to the study of quantitative measures of graph complexity that use entropy measures based on symmetry. Determining orbit sizes of graph automorphism groups is a key part of such studies. Here we focus on an extreme case where every orbit contains just a single vertex. A permutation of the vertices of a graph G is an automorphism if, and only if, the corresponding permutation matrix commutes with the adjacency matrix of G. This fact establishes a direct connection between the adjacency matrix and the automorphism group. In particular, it is known that if the eigenvalues of the adjacency matrix of G are all distinct, every non-trivial automorphism has order 2. In this note, we add a condition to the case of distinct eigenvalues that makes the graph asymmetric, i.e., reduces the automorphism group to the identity alone. In addition, we prove analogous results for the Google and Laplacian matrices. The condition is used to build an O(n3) algorithm for detecting identity graphs, and examples are given to demonstrate that it is sufficient, but not necessary. [ABSTRACT FROM AUTHOR]

Biomedical Named-Entity Recognition (BioNER) has become an essential part of text mining due to the continuously increasing digital archives of biological and medical articles. While there are many well-performing BioNER tools for entities such as genes, proteins, diseases or species, there is very little research into food and dietary constituent named-entity recognition. For this reason, in this paper, we study seven BioNER models for food and dietary constituents recognition. Specifically, we study a dictionary-based model, a conditional random fields (CRF) model and a new hybrid model, called FooDCoNER (Food and Dietary Constituents Named-Entity Recognition), which we introduce combining the former two models. In addition, we study deep language models including BERT, BioBERT, RoBERTa and ELECTRA. As a result, we find that FooDCoNER does not only lead to the overall best results, comparable with the deep language models, but FooDCoNER is also much more efficient with respect to run time and sample size requirements of the training data. The latter has been identified via the study of learning curves. Overall, our results not only provide a new tool for food and dietary constituent NER but also shed light on the difference between classical machine learning models and recent deep language models. [ABSTRACT FROM AUTHOR]

An accidental fall seriously threatens the health and safety of the elderly. The injuries caused by a fall have a lot to do with the different postures during the fall. Therefore, recognizing the posture of falling is essential for the rescue and care of the elderly. In this paper, a novel method was proposed to improve the classification and recognition accuracy of fall postures. Firstly, the wavelet packet transform was used to extract multiple features from sample data. Secondly, random forest was used to evaluate the importance of the extracted features and obtain effective features through screening. Finally, the support vector machine classifier based on the linear kernel function was used to realize the falling posture recognition. The experiment results on "Simulated Falls and Daily Living Activities Data Set" show that the proposed method can distinguish different types of fall postures and achieve 99% classification accuracy. [ABSTRACT FROM AUTHOR]

The wind field is an essential factor that affects accurate homing and flare landing of parafoil systems. In order to obtain the ambient wind field during the descent of a parafoil system, a combination method of in-flight wind field identification and prediction is proposed. First, a wind identification method only using global position system information is derived based on the flight dynamics of parafoil systems. Then a wind field prediction model is constructed using the atmospheric dynamics, and the low-altitude wind field is predicted based on the identified wind field of high-altitude. Finally, simulations of wind field identification and prediction are conducted. The results demonstrate that the proposed method can identify the wind fields precisely and also predict the wind fields reasonably. This method can potentially be applied in practical parafoil systems to provide wind field information for homing tasks. [ABSTRACT FROM AUTHOR]

Intelligent cooperative multiagent systems are applied for solving a large range of real-life problems, including in domains like biology and healthcare. There are very few metrics able to make an effective measure of the machine intelligence quotient. The most important drawbacks of the designed metrics presented in the scientific literature consist in the limitation in universality, accuracy, and robustness. In this paper, we propose a novel universal metric called MetrIntSimil capable of making an accurate and robust symmetric comparison of the similarity in intelligence of any number of cooperative multiagent systems specialized in difficult problem solving. The universality is an important necessary property based on the large variety of designed intelligent systems. MetrIntSimil makes a comparison by taking into consideration the variability in intelligence in the problem solving of the compared cooperativemultiagent systems. It allows a classification of the cooperativemultiagent systems based on their similarity in intelligence. A cooperative multiagent system has variability in the problem solving intelligence, and it can manifest lower or higher intelligence in different problem solving tasks. More cooperative multiagent systems with similar intelligence can be included in the same class. For the evaluation of the proposed metric, we conducted a case study for more intelligent cooperative multiagent systems composed of simple computing agents applied for solving the Symmetric Travelling Salesman Problem (STSP) that is a class of NP-hard problems. STSP is the problem of finding the shortest Hamiltonian cycle/tour in a weighted undirected graph that does not have loops or multiple edges. The distance between two cities is the same in each opposite direction. Two classes of similar intelligence denoted IntClassA and IntClassB were identified. The experimental results show that the agent belonging to IntClassA intelligence class is less intelligent than the agents that belong to the IntClassB intelligence class. [ABSTRACT FROM AUTHOR]

In this exploratory paper, we discuss quantitative graph-theoretical measures of network aesthetics. Related work in this area has typically focused on geometrical features (e.g., line crossings or edge bendiness) of drawings or visual representations of graphs which purportedly affect an observer's perception. Here we take a very different approach, abandoning reliance on geometrical properties, and apply information-theoretic measures to abstract graphs and networks directly (rather than to their visual representaions) as a means of capturing classical appreciation of structural symmetry. Examples are used solely to motivate the approach to measurement, and to elucidate our symmetry-based mathematical theory of network aesthetics. [ABSTRACT FROM AUTHOR]

Many graph invariants have been used for the construction of entropy-based measures to characterize the structure of complex networks. The starting point has been always based on assigning a probability distribution to a network when using Shannon's entropy. In particular, Cao et al. (2014 and 2015) defined special graph entropy measures which are based on degrees powers. In this paper, we obtain some lower and upper bounds for these measures and characterize extremal graphs. Moreover we resolve one part of a conjecture stated by Cao et al. [ABSTRACT FROM AUTHOR]

Shannon entropies for networks have been widely introduced. However, entropies for weighted graphs have been little investigated. Inspired by the work due to Eagle et al., we introduce the concept of graph entropy for special weighted graphs. Furthermore, we prove extremal properties by using elementary methods of classes of weighted graphs, and in particular, the one due to Bollobás and Erdös, which is also called the Randic weight. As a result, we derived statements on dendrimers that have been proven useful for applications. Finally, some open problems are presented. [ABSTRACT FROM AUTHOR]

This paper demonstrates properties of Hosoya entropy, a quantitative measure of graph complexity based on a decomposition of the vertices linked to partial Hosoya polynomials. Connections between the information content of a graph and Hosoya entropy are established, and the special case of Hosoya entropy of trees is investigated. [ABSTRACT FROM AUTHOR]

A variety of problems in, e.g., discrete mathematics, computer science, information theory, statistics, chemistry, biology, etc., deal with inferring and characterizing relational structures by using graph measures. In this sense, it has been proven that information-theoretic quantities representing graph entropies possess useful properties such as a meaningful structural interpretation and uniqueness. As classical work, many distance-based graph entropies, e.g., the ones due to Bonchev et al. and related quantities have been proposed and studied. Our contribution is to explore graph entropies that are based on a novel information functional, which is the number of vertices with distance k to a given vertex. In particular, we investigate some properties thereof leading to a better understanding of this new information-theoretic quantity. [ABSTRACT FROM AUTHOR]

The paper puts the emphasis on surveying information-theoretic network measures for analyzing the structure of networks. In order to apply the quantities interdisciplinarily, we also discuss some of their properties such as their structural interpretation and uniqueness. [ABSTRACT FROM AUTHOR]

Prognostic biomarkers can have an important role in the clinical practice because they allow stratification of patients in terms of predicting the outcome of a disorder. Obstacles for developing such markers include lack of robustness when using different data sets and limited concordance among similar signatures. In this paper, we highlight a new problem that relates to the biological meaning of already established prognostic gene expression signatures. Specifically, it is commonly assumed that prognostic markers provide sensible biological information and molecular explanations about the underlying disorder. However, recent studies on prognostic biomarkers investigating 80 established signatures of breast and prostate cancer demonstrated that this is not the case. We will show that this surprising result is related to the distinction between causal models and predictive models and the obfuscating usage of these models in the biomedical literature. Furthermore, we suggest a falsification procedure for studies aiming to establish a prognostic signature to safeguard against false expectations with respect to biological utility. [ABSTRACT FROM AUTHOR]

To ensure the safe operation of an interconnected power system, it is necessary to maintain the stability of the frequency and the tie-line exchanged power. This is one of the hottest issues in the power system field and is usually called load frequency control. To overcome the influences of load disturbances on multi-source power systems containing thermal power plants, hydropower plants, and gas turbine plants, we design a linear active disturbance rejection control (LADRC) based on the tie-line bias control mode. For LADRC, the parameter selection of the controller directly affects the response performance of the entire system, and it is usually not feasible to manually adjust parameters. Therefore, to obtain the optimal controller parameters, we use the Soft Actor-Critic algorithm in reinforcement learning to obtain the controller parameters in real time, and we design the reward function according to the needs of the power system. We carry out simulation experiments to verify the effectiveness of the proposed method. Compared with the results of other proportional–integral–derivative control techniques using optimization algorithms and LADRC with constant parameters, the proposed method shows significant advantages in terms of overshoot, undershoot, and settling time. In addition, by adding different disturbances to different areas of the multi-source power system, we demonstrate the robustness of the proposed control strategy. [ABSTRACT FROM AUTHOR]

The definition of orbit polynomial is based on the size of orbits of a graph which is O G (x) = ∑ i x | O i | , where O 1 , ... , O k are all orbits of graph G. It is a well-known fact that according to Descartes' rule of signs, the new polynomial 1 − O G (x) has a positive root in (0 , 1) , which is unique and it is a relevant measure of the symmetry of a graph. In the current work, several bounds for the unique and positive zero of modified orbit polynomial 1 − O G (x) are investigated. Besides, the relation between the unique positive root of O G in terms of the structure of G is presented. [ABSTRACT FROM AUTHOR]

The size of the orbits or similar vertices of a network provides important information regarding each individual component of the network. In this paper, we investigate the entropy or information content and the symmetry index for several classes of graphs and compare the values of this measure with that of the symmetry index of certain graphs. [ABSTRACT FROM AUTHOR]

This article aims to be a further contribution to the research on structural complexity networks. Here, we emphasize measures to determine symmetry. The so-called "orbit polynomial" is defined by O G (x) = ∑ i a i x i , where a i is the number of orbits of size i. Furthermore, the graph polynomial 1 − O G (x) has a unique positive root in the interval (0 , 1) , which can be considered as a relevant measure of the symmetry of a graph. In the present paper, we studied some properties of the orbit polynomial with respect to the stabilizer elements of each vertex. Furthermore, we constructed graphs with a small number of orbits and characterized some classes of graphs in terms of calculating their orbit polynomials. We studied the symmetry structure of well-known real-world networks in terms of the orbit polynomial. [ABSTRACT FROM AUTHOR]

Suppose ai indicates the number of orbits of size i in graph G. A new counting polynomial, namely an orbit polynomial, is defined as OG(x) = ∑i aixi. Its modified version is obtained by subtracting the orbit polynomial from 1. In the present paper, we studied the conditions under which an integer polynomial can arise as an orbit polynomial of a graph. Additionally, we surveyed graphs with a small number of orbits and characterized several classes of graphs with respect to their orbit polynomials. [ABSTRACT FROM AUTHOR]

This paper considers commuting graphs over the semidihedral group S D 8 n . We compute their eigenvalues and obtain that these commuting graphs are not hyperenergetic for odd n ≥ 15 or even n ≥ 2 . We further compute the Laplacian spectrum, the Laplacian energy and the number of spanning trees of the commuting graphs over S D 8 n . We also discuss vertex connectivity, planarity, and minimum disconnecting sets of these graphs and prove that these commuting graphs are not Hamiltonian. [ABSTRACT FROM AUTHOR]

If G is a graph and P is a partition of V (G) , then the partition distance of G is the sum of the distances between all pairs of vertices that lie in the same part of P. A colored distance is the dual concept of the partition distance. These notions are motivated by a problem in the facility location network and applied to several well-known distance-based graph invariants. In this paper, we apply an extended cut method to induce the partition and color distances to some subsets of vertices which are not necessary a partition of V (G) . Then, we define a two-dimensional weighted graph and an operator to prove that the induced partition and colored distances of a graph can be obtained from the weighted Wiener index of a two-dimensional weighted quotient graph induced by the transitive closure of the Djoković–Winkler relation as well as by any partition that is coarser. Finally, we utilize our main results to find some upper bounds for the modified Wiener index and the number of orbits of partial cube graphs under the action of automorphism group of graphs. [ABSTRACT FROM AUTHOR]

The orbit polynomial is a new graph counting polynomial which is defined as O G (x) = ∑ i = 1 r x | O i | , where O 1 , ..., O r are all vertex orbits of the graph G. In this article, we investigate the structural properties of the automorphism group of a graph by using several novel counting polynomials. Besides, we explore the orbit polynomial of a graph operation. Indeed, we compare the degeneracy of the orbit polynomial with a new graph polynomial based on both eigenvalues of a graph and the size of orbits. [ABSTRACT FROM AUTHOR]

Erratum: Liu, W.; Ban, J.; Feng, L.; Cheng, T.; Emmert-Streib, F.; Dehmer, M. The Maximum Hosoya Index of Unicyclic Graphs with Diameter at Most Four. [Extracted from the article]

Symmetry is an important visual feature for humans and its application in architecture is completely evident. This paper aims to investigate the role of symmetry in the aesthetics judgment of residential building façades and study the pattern of eye movement based on the expertise of subjects in architecture. In order to implement this in the present paper, we have created images in two categories: symmetrical and asymmetrical façade images. The experiment design allows us to investigate the preference of subjects and their reaction time to decide about presented images as well as record their eye movements. It was inferred that the aesthetic experience of a building façade is influenced by the expertise of the subjects. There is a significant difference between experts and non-experts in all conditions, and symmetrical façades are in line with the taste of non-expert subjects. Moreover, the patterns of fixational eye movements indicate that the horizontal or vertical symmetry (mirror symmetry) has a profound influence on the observer's attention, but there is a difference in the points watched and their fixation duration. Thus, although symmetry may attract the same attention during eye movements on façade images, it does not necessarily lead to the same preference between the expert and non-expert groups. [ABSTRACT FROM AUTHOR]

The Graovac–Pisanski (GP) index of a graph is a modified version of the Wiener index based on the distance between each vertex x and its image α (x) , where α is an automorphism of graph. The aim of this paper is to compute the automorphism group of some classes of cubic polyhedral graphs and then we determine their Wiener index. In addition, we investigate the GP-index of these classes of graphs. [ABSTRACT FROM AUTHOR]

A fullerene is a cubic three-connected graph whose faces are entirely composed of pentagons and hexagons. Entropy applied to graphs is one of the significant approaches to measuring the complexity of relational structures. Recently, the research on complex networks has received great attention, because many complex systems can be modelled as networks consisting of components as well as relations among these components. Information—theoretic measures have been used to analyze chemical structures possessing bond types and hetero-atoms. In the present article, we reviewed various entropy-based measures on fullerene graphs. In particular, we surveyed results on the topological information content of a graph, namely the orbit-entropy Ia(G), the symmetry index, a degree-based entropy measure Iλ(G), the eccentric-entropy Ifσ(G) and the Hosoya entropy H(G). [ABSTRACT FROM AUTHOR]

Every three-connected simple planar graph is a polyhedral graph and a cubic polyhedral graph with pentagonal and hexagonal faces is called as a classical fullerene. The aim of this paper is to survey some results about the symmetry group of cubic polyhedral graphs. We show that the order of symmetry group of such graphs divides 240. [ABSTRACT FROM AUTHOR]

This paper presents a proof of the existence of connected, undirected graphs with prescribed orbit structure, giving an explicit construction procedure for these graphs. Trees with prescribed orbit structure are also investigated. [ABSTRACT FROM AUTHOR]

This paper introduces a variant of entropy measures based on vertex eccentricity and applies it to all graphs representing the isomers of octane. Taking into account the vertex degree as well (degree-ecc-entropy), we find a good correlation with the acentric factor of octane isomers. In particular, we compute the degree-ecc-entropy for three classes of dendrimer graphs. [ABSTRACT FROM AUTHOR]

In this paper we extend earlier results on Hosoya entropy (H-entropy) of graphs, and establish connections between H-entropy and automorphisms of graphs. In particular, we determine the H-entropy of graphs whose automorphism group has exactly two orbits, and characterize some classes of graphs with zero H-entropy. [ABSTRACT FROM AUTHOR]

The Hosoya index of a graph is defined by the total number of the matchings of the graph. In this paper, we determine the maximum Hosoya index of unicyclic graphs with n vertices and diameter 3 or 4. Our results somewhat answer a question proposed by Wagner and Gutman in 2010 for unicyclic graphs with small diameter. [ABSTRACT FROM AUTHOR]

In this paper, we present four product operations to construct cryptographic boolean functions from smaller ones with predictable Walsh spectrum. A lot of cryptographic properties of boolean functions can be presented by their Walsh spectrum. In our method, we use the product of Cayley graphs to present new boolean functions with desired Walsh spectrum and investigate their non-linearity, algebraic and correlation immunity. [ABSTRACT FROM AUTHOR]

In this paper, we study several distance-based entropy measures on fullerene graphs. These include the topological information content of a graph I a (G) , a degree-based entropy measure, the eccentric-entropy I f σ (G) , the Hosoya entropy H (G) and, finally, the radial centric information entropy H e c c . We compare these measures on two infinite classes of fullerene graphs denoted by A 12 n + 4 and B 12 n + 6 . We have chosen these measures as they are easily computable and capture meaningful graph properties. To demonstrate the utility of these measures, we investigate the Pearson correlation between them on the fullerene graphs. [ABSTRACT FROM AUTHOR]