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A good deal of science and technology concepts and methods rely on comparing and relating entities in quantitative terms. Among the several possible approaches, similarity indices allow some interesting features, especially the ability to quantify how much two entities resemble one another. In this work, the Jaccard similarity for comparing non-zero real-valued vectors is modified so as to estimate similarity while focusing on the distinct parts of the signals. The resulting operator, which is called partially proportional similarity index, not only allows more strict comparisons, but also paves the way to develop an adaptive approach to similarity estimation in which the size and orientation of the comparisons adapt to those of a respective calibration field expressing how the observed features are related to original counterparts. Being a particularly relevant concept in data analysis and modeling, emphasis is placed on presenting and discussing the concept of calibration field and how they can be taken into account while performing similarity comparisons. Several results are described which illustrate the potential of the reported concepts and approaches for enhancing, and even simultaneously normalizing to some extent the representation of entities in terms of their features, as frequently required in scientific modeling and pattern recognition., Comment: 46 pages, 32 figures

The Jaccard similarity index has often been employed in science and technology as a means to quantify the similarity between two sets. When modified to operate on real-valued values, the Jaccard similarity index can be applied to compare vectors, an operation which plays a central role in visualization, classification, and modeling. The present work aims at developing an analytical approach for estimating the probability density of the Jaccard similarity values as implied by set of data elements characterized by specific statistical densities, with emphasis on the uniform and normal cases. Several theoretical and practical situations can benefit directly from such an approach, as it allows several of the properties of the similarity comparisons among a given dataset to be better understood and anticipated. Situations in which the described approach can be applied include the estimation and visualization of data interrelationships in terms of similarity networks, as well as diverse problems in data analysis, pattern recognition and scientific modeling. In addition to presenting the analytical developments and results, examples are also provided in order to illustrate the potential of the approach. The work also includes extension of the reported developments to modifications of the Jaccard index intended for regularization and control of the sharpness of the implemented comparisons.

The subject of features normalization plays an important central role in data representation, characterization, visualization, analysis, comparison, classification, and modeling, as it can substantially influence and be influenced by all of these activities and respective aspects. The selection of an appropriate normalization method needs to take into account the type and characteristics of the involved features, the methods to be used subsequently for the just mentioned data processing, as well as the specific questions being considered. After briefly considering how normalization constitutes one of the many interrelated parts typically involved in data analysis and modeling, the present work addressed the important issue of feature normalization from the perspective of uniform and proportional (right skewed) features and comparison operations. More general right skewed features are also considered in an approximated manner. Several concepts, properties, and results are described and discussed, including the description of a duality relationship between uniform and proportional feature spaces and respective comparisons, specifying conditions for consistency between comparisons in each of the two domains. Two normalization possibilities based on non-centralized dispersion of features are also presented, and also described is a modified version of the Jaccard similarity index which incorporates intrinsically normalization. Preliminary experiments are presented in order to illustrate the developed concepts and methods., Comment: 31 pages, 10 figures

Pattern recognition constitutes a particularly important task underlying a great deal of scientific and technologica activities. At the same time, pattern recognition involves several challenges, including the choice of features to represent the data elements, as well as possible respective transformations. In the present work, the classification potential of the Euclidean distance and a dissimilarity index based on the coincidence similarity index are compared by using the k-neighbors supervised classification method respectively to features resulting from several types of transformations of one- and two-dimensional symmetric densities. Given two groups characterized by respective densities without or with overlap, different types of respective transformations are obtained and employed to quantitatively evaluate the performance of k-neighbors methodologies based on the Euclidean distance an coincidence similarity index. More specifically, the accuracy of classifying the intersection point between the densities of two adjacent groups is taken into account for the comparison. Several interesting results are described and discussed, including the enhanced potential of the dissimilarity index for classifying datasets with right skewed feature densities, as well as the identification that the sharpness of the comparison between data elements can be independent of the respective supervised classification performance., Comment: 25 page and 16 figures

Pattern comparison represents a fundamental and crucial aspect of scientific modeling, artificial intelligence, and pattern recognition. Three main approaches have typically been applied for pattern comparison: (i) distances; (ii) statistical joint variation; (iii) projections; and (iv) similarity indices, each with their specific characteristics. In addition to arguing for intrinsic interesting properties of multiset-based similarity approaches, the present work describes a respectively based hierarchical agglomerative clustering approach which inherits the several interesting characteristics of the coincidence similarity index -- including strict comparisons allowing distinguishing between closely similar patterns, inherent normalization, as well as substantial robustness to the presence of noise and outliers in datasets. Two other hierarchical clustering approaches are considered, namely a multiset-based method as well as the traditional Ward's approach. After characterizing uniform and proportional features spaces and presenting the main basic concepts and methods, a comparison of relative performance between the three considered hierarchical methods is reported and discussed, with several interesting and important results. In particular, though intrinsically suitable for implementing proportional comparisons, the coincidence similarity methodology also works effectively in several types of data in uniform feature spaces, Comment: 32 pages, 22 figures

The relationship between topology and dynamics of complex systems has motivated continuing interest from the scientific community. In the present work, we address this interesting topic from the perspective of simple games, involving two teams playing according to a small set of simple rules, taking place on four types of complex networks. Starting from a minimalist game, characterized by full symmetry always leading to ties, four other games are described in progressive order of complexity, taking into account the presence of neighbors as well as strategies. Each of these five games, as well as their specific changes when implemented in four types of networks, are studied in terms of statistics of the total duration of the game as well as the number of victories and ties, with several interesting results that substantiate, in some cases, the importance of the network topology on the respective dynamics. As a subsidiary result, the visualization of relationships between the data elements in terms of coincidence similarity networks allowed a more complete and direct interpretation of the obtained results., Comment: 16 pages, 8 figures

The concept of node walk in graphs and complex networks has been addressed, consisting of one or more nodes that move into adjacent nodes, henceforth incorporating the respective connections. This type of dynamics is then applied to subsume complex networks. Three types of networks (Erd\'os- R\'eny, Barab\'asi-Albert, as well as a geometric model) are considered, while three node walks heuristics (uniformly random, largest degree, and smallest degree) are taken into account. Several interesting results are obtained and described, including the identification that the subsuming dynamics depend strongly on both the specific topology of the networks as well as the criteria controlling the node walks. The use of node walks as a model for studying the relationship between network topology and dynamics is motivated by this result. In addition, relatively high correlations between the initial node degree and the accumulated strength of the walking node were observed for some combinations of network types and dynamic rules, allowing some of the properties of the subsumption to be roughly predicted from the initial topology around the waking node which has been found, however, not to be enough for full determination of the subsumption dynamics. Another interesting result regards the quite distinct signatures (along the iterations) of walking node strengths obtained for the several considered combinations of network type and subsumption rules., Comment: 14 pages and 7 figures

Complex systems have motivated continuing interest from the scientific community, leading to new concepts and methods. Growing systems represent a case of particular interest, as their topological, geometrical, and also dynamical properties change along time, as new elements are incorporated into the existing structure. In the present work, an approach is the case in which systems grown radially around some straight axis of reference, such as particle deposition on electrodes, or urban expansion along avenues, roads, coastline, or rivers, among several other possibilities. More specifically, we aim at characterizing the topological properties of simulated growing structures, which are represented as graphs, in terms of a measurement corresponding to the accessibility of each involved node. The incorporation of new elements (nodes and links) is performed preferentially to the angular orientation respectively to the reference axis. Several interesting results are reported, including the tendency of structures grown preferentially to the orientation normal to the axis to have smaller accessibility., Comment: 14 pages, 8 figures

Graphs and complex networks can be successively separated into connected components associated to respective seed nodes, therefore establishing a respective hierarchical organization. In the present work, we study the properties of the hierarchical structure implied by distance-based cutting of Erd\H{o}s-R\'enyi, Barab\'asi-Albert, and a specific geometric network. Two main situations are considered regarding the choice of the seeds: non-preferential and preferential to the respective node degree. Among the obtained findings, we have the tendency of geometrical networks yielding more balanced pairs of connected components along the network progressive separation, presenting little chaining effects, followed by the Erd\H{o}s-R\'enyi and Barab\'asi-Albert types of networks. The choice of seeds preferential to the node degree tended to enhance the balance of the connected components in the case of the geometrical networks., Comment: 15 pages and 9 figures

Several interesting approaches have been reported in the literature on complex networks, random walks, and hierarchy of graphs. While many of these works perform random walks on stable, fixed networks, in the present work we address the situation in which the connections traversed by each step of a uniformly random walks are progressively removed, yielding a successively less interconnected structure that may break into two components, therefore establishing a respective hierarchy. The sizes of each of these pairs of sliced networks, as well as the permanence of each connected component, are studied in the present work. Several interesting results are reported, including the tendency of geometrical networks sometimes to be broken into two components with comparable large sizes., Comment: 16 pages and 9 figures

Bipartite networks provide an effective resource for representing, characterizing, and modeling several abstract and real-world systems and structures involving binary relations, which include food webs, social interactions, and customer-product relationships. Of particular interest is the problem of, given a specific bipartite network, to identify possible respective groups or clusters characterized by similar interconnecting patterns. The present work approaches this issue by extending and complementing a previously described coincidence similarity methodology (Bioarxiv, doi.org/10.1101/2022.07.16.500294) in several manners, including the consideration of direct and non-directed bipartite networks, the characterization of groups in those networks, as well as considering synthetic bipartite networks presenting groups as a resource for studying the performance of the described methodology. Several interesting results are described and discussed, including the corroboration of the potential of the coincidence similarity methodology for achieving enhanced separation between the groups in bipartite networks., Comment: 22 pages, 13 figures

Random walks by single-node agents have been systematically conducted on various types of complex networks in order to investigate how their topologies can affect the dynamics of the agents. However, by fitting any network node, these agents do not engage in topological interactions with the network. In the present work, we describe random walks on complex networks performed by agents that are actually small graphs. These agents can only occupy admissible portions of the network onto which they fit topologically, hence their name being taken as topologically-specific agents. These agents are also allowed to move to adjacent subgraphs in the network, which have each node adjacent to the original respective node of the agent. Two types of random walks are considered here: uniformly random and influenced by an external field. The performance of the random walks performed by three types of topologically-specific agents is studied respectively to the obtained coverage considering three types of complex networks (geometrical, Erd\H{o}s-R\'enyi, and Barab\'asi-Albert). The number of nodes displaced at each random walk step is also obtained and analyzed. Several interesting results are reported and discussed, including the fact that, despite its intrinsic node degree heterogeneity, Barab\'asi-Albert networks tend to allow relatively smooth and effective coverage by all the considered topologically-specific agents. Erd\H{o}s-R\'enyi networks were also found to yield large dispersions of node coverage. In addition, the triangle agent was found to allow more effective random walks respectively to any of the three considered networks., Comment: 17 pages, 9 figures

The arithmetic mean plays a central role in science and technology, being directly related to the concepts of statistical expectance and centrality. Yet, it is highly susceptible to the presence of outliers or biased interference in the original dataset to which it is applied. Described recently, the concept of similarity means has been preliminary found to have marked robustness to those same effects, especially when adopting the Jaccard similarity index. The present work is aimed at investigating further the properties of similarity means, especially regarding their range, translating and scaling properties, sensitivity and robustness to outliers. Several interesting contributions are reported, including an effective algorithm for obtaining the similarity mean, the analytic and experimental identification of a number of properties, as well as the confirmation of the potential stability of the similarity mean to the presence of outliers. The present work also describes an application case-example in which the Jaccard similarity is successfully employed to study cycles of sunspots, with interesting results.

A large number of real and abstract systems involve the transformation of some basic resource into respective products under the action of multiple processing agents, which can be understood as multiple-agent production systems (MAP). At each discrete time instant, for each agent, a fraction of the resources is assumed to be kept, forwarded to other agents, or converted into work with some efficiency. The present work describes a systematic study of nine basic MAP architectures subdivided into two main groups, namely parallel and sequential distribution of resources from a single respective source. Several types of interconnections among the involved processing agents are also considered. The resulting MAP architectures are studied in terms of the total amount of work, the dispersion of the resources (states) among the agents, and the transition times from the start of operation until the respective steady state. Several interesting results are obtained and discussed, including the observation that some of the parallel designs were able to yield maximum work and minimum state dispersion, achieved at the expense of the transition time and use of several interconnections between the source and the agents. The results obtained for the sequential designs indicate that relatively high performance can be obtained for some specific cases., Comment: 21 pages, 12 figures

Complex networks can be used to represent and model an ample diversity of abstract and real-world systems and structures. A good deal of the research on these structures has focused on specific topological properties, including node degree, shortest paths, and modularity. In the present work, we develop an approach aimed at identifying and characterizing simple bundles of interconnections between pairs of nodes (source and destination) in complex networks. More specifically, simple bundles can be understood as corresponding to the bundle of paths obtained while traveling through successive neighborhoods after departing from a given source node. Because no node appears more than once along a given bundle, these structures have been said to be simple, in analogy to the concept of a simple path. In addition to describing simple bundles and providing a possible methodology for their identification, we also consider how their respective effective width can be estimated in terms of diffusion flow and exponential entropy of transition probabilities. The potential of the concepts and methods described in this work is then illustrated respectively to the characterization and analysis of model-theoretic networks, with several interesting results., Comment: 29 pages, 21 figures

Though performed almost effortlessly by humans, segmenting 2D gray-scale or color images into respective regions of interest (e.g.~background, objects, or portions of objects) constitutes one of the greatest challenges in science and technology as a consequence of several effects including dimensionality reduction(3D to 2D), noise, reflections, shades, and occlusions, among many other possibilities. While a large number of interesting related approaches have been suggested along the last decades, it was mainly thanks to the recent development of deep learning that more effective and general solutions have been obtained, currently constituting the basic comparison reference for this type of operation. Also developed recently, a multiset-based methodology has been described that is capable of encouraging image segmentation performance combining spatial accuracy, stability, and robustness while requiring little computational resources (hardware and/or training and recognition time). The interesting features of the multiset neurons methodology mostly follow from the enhanced selectivity and sensitivity, as well as good robustness to data perturbations and outliers, allowed by the coincidence similarity index on which the multiset approach to supervised image segmentation is founded. After describing the deep learning and multiset neurons approaches, the present work develops comparison experiments between them which are primarily aimed at illustrating their respective main interesting features when applied to the adopted specific type of data and parameter configurations. While the deep learning approach confirmed its potential for performing image segmentation, the alternative multiset methodology allowed for enhanced accuracy while requiring little computational resources., Comment: 38 pages, 19 figures

Knowledge networks have become increasingly important as a changing repository of data which can be represented, studied and modeled by using complex networks concepts and methodologies. Here we report a study of knowledge networks corresponding to the areas of Physics and Theology, obtained from the Wikipedia and taken at two different dates separated by 4 years. The respective two versions of these networks were characterized in terms of their respective cross-relation signatures, being summarized in terms of modification indices obtained for each of the nodes that are preserved among the two versions. The proposed methodology is first evaluated on Erdos-Renyi (ER) and Barabasi-Albert model (BA) networks, before being tested on the knowledge networks obtained from the Wikipedia respectively to the areas of Physics and Theology. In the former study, it has been observed that the nodes at the core and periphery of both types of theoretical models yielded similar modification indices within these two groups of nodes, but with distinct values when taken across these two groups. The study of the Physics and Theology networks indicated that these two networks have signatures respectively similar to those of the BA and ER models, as well as that higher modification values being obtained for the periphery nodes, as compared to the respective core nodes., Comment: 23 pages, 15 figures

Artistic pieces can be studied from several perspectives, one example being their reception among readers over time. In the present work, we approach this interesting topic from the standpoint of literary works, particularly assessing the task of predicting whether a book will become a best seller. Dissimilarly from previous approaches, we focused on the full content of books and considered visualization and classification tasks. We employed visualization for the preliminary exploration of the data structure and properties, involving SemAxis and linear discriminant analyses. Then, to obtain quantitative and more objective results, we employed various classifiers. Such approaches were used along with a dataset containing (i) books published from 1895 to 1924 and consecrated as best sellers by the Publishers Weekly Bestseller Lists and (ii) literary works published in the same period but not being mentioned in that list. Our comparison of methods revealed that the best-achieved result - combining a bag-of-words representation with a logistic regression classifier - led to an average accuracy of 0.75 both for the leave-one-out and 10-fold cross-validations. Such an outcome suggests that it is unfeasible to predict the success of books with high accuracy using only the full content of the texts. Nevertheless, our findings provide insights into the factors leading to the relative success of a literary work.

The study of neuronal morphology is important not only for its potential relationship with neuronal dynamics, but also as a means to classify diverse types of cells and compare than among species, organs, and conditions. In the present work, we approach this interesting problem by using the concept of coincidence similarity, as well as a respectively derived method for mapping datasets into networks. The coincidence similarity has been found to allow some specific interesting properties which have allowed enhanced performance (selectivity and sensitivity) concerning several pattern recognition tasks. Several combinations of 20 morphological features were considered, and the respective networks were obtained by maximizing the literal modularity (in supervised manner) respectively to the involved parameters. Well-separated groups were obtained that provide a rich representation of the main similarity interrelationships between the 735 considered neuronal cells. A sequence of network configurations illustrating the progressive merging between cells and groups was also obtained by varying one of the coincidence parameters.

There is a crescent use of enzymes in multiple industries and sciences, ranging from materials and fuel synthesis to pharmaceutical and food production. Their applicability in this variety of fields depends not only on their biochemical function but also on their physicochemical properties. In the present work, we describe how the coincidence methodology can be employed to construct similarity networks of seventy well-studied enzymes of the Glycoside Hydrolase Family 13 and to identify communities of physicochemically related enzymes. More specifically, each of the selected enzymes is mapped into a network node, while the links between pairs of enzymes are determined by the coincidence similarity between selected physicochemical features of interest. The obtained networks have modularity and number of isolated nodes optimized respectively to two parameters involved in the coincidence methodology, resulting in highly modular networks. In order to investigate the effect of the considered physicochemical features on the enzymes relationships, the coincidence-based method also is applied to create a meta-network, in which the enzymes similarity networks obtained by the combination of every possible feature becomes nodes of a feature combination network, and the coincidence similarity between those networks defines the respective links. The obtained feature combination network systematically and comprehensively indicates the impact of the selected physicochemical features on enzyme similarity. Several interesting results are reported and discussed, including the identification of subgroups of enzymes with similar physicochemical features within catalytical classes, providing important information for the selection and design of enzymes for targeted biotechnological applications., Comment: 27 pages, 8 figures, 2 tables, 55 references (preprint)

Several natural and theoretical networks can be broken down into smaller portions, or subgraphs corresponding to neighborhoods. The more frequent of these neighborhoods can then be understood as motifs of the network, being therefore important for better characterizing and understanding of the overall structure. Several developments in network science have relied on this interesting concept, with ample applications in areas including systems biology, computational neuroscience, economy and ecology. The present work aims at reporting an unsupervised methodology capable of identifying motifs respective to streets networks, the latter corresponding to graphs obtained from city plans by considering street junctions and terminations as nodes while the links are defined by the streets. Remarkable results are described, including the identification of nine stable and informative motifs, which have been allowed by three critically important factors: (i) adoption of five hierarchical measurements to locally characterize the neighborhoods of nodes in the streets networks; (ii) adoption of an effective coincidence methodology for translating datasets into networks; and (iii) definition of the motifs in statistical terms by using community finding methodology. The nine identified motifs are characterized and discussed from several perspective, including their mutual similarity, visualization, histograms of measurements, and geographical adjacency in the original cities. Also presented is the analysis of the effect of the adopted features on the obtained networks as well as a simple supervised learning method capable of assigning reference motifs to cities., Comment: 34 pages, 16 figures, 3 tables, preprint

Several real-world and abstract structures and systems are characterized by marked hierarchy to the point of being expressed as trees. Because the study of these entities often involves sampling (or discovering) the tree nodes in a specific order that may not correspond to that originally shaping the tree, reconstruction errors can be obtained. The present work addresses this important problem based on two main resources: (i) the adoption of a simple model of trees, involving a single parameter; and (ii) the use of the coincidence similarity as the means to quantify the errors by comparing the original and reconstructed structures considering diverse sampling error probability and extent. Several interesting results are described and discussed, including the fact that the average and standard deviation values of the reconstruction errors depend only moderately on the extent of the errors as well as on the types of trees. At the same time, it is identified that the relative reconstruction accuracy substantially decreases markedly with the error probability, with larger reconstructions accuracy relative variations being observed for the smallest values of that probability.

Characterizing the structure of cities constitutes an important task since the identification of similar cities can promote sharing of respective experiences. In the present work, we consider 20 European cities from 5 respective countries and with comparable populations, each of which characterized in terms of four topological as well as one geometrical feature. These cities are then mapped into respective networks by considering their pairwise similarity as gauged by the coincidence methodology, which consists of combining the Jaccard and interiority indices. The methodology incorporates a parameter alpha that can control the relative contribution of features with the same or opposite signs to the overall similarity. Interestingly, the maximum modularity cities network is obtained for a non-standard parameter configuration, showing that it could not be obtained were not for the adoption of the parameter alpha. The network with maximum modularity presents four communities that can be directly related to four of the five considered countries, corroborating not only the effectiveness of the adopted features and similarity methodology, but also indicating a surprising tendency of the cities from a same country of being similar, while differing from cities from other countries. The coincidence methodology was then applied in order to investigate the effect of several features combinations on the respectively obtained networks, leading to a highly modular features network containing four main communities that can be understood as the main possible models for the considered cities.

Several complex systems are characterized by presenting intricate characteristics taking place at several scales of time and space. These multiscale characterizations are used in various applications, including better understanding diseases, characterizing transportation systems, and comparison between cities, among others. In particular, texts are also characterized by a hierarchical structure that can be approached by using multi-scale concepts and methods. The multiscale properties of texts constitute a subject worth further investigation. In addition, more effective approaches to text characterization and analysis can be obtained by emphasizing words with potentially more informational content. The present work aims at developing these possibilities while focusing on mesoscopic representations of networks. More specifically, we adopt an extension to the mesoscopic approach to represent text narratives, in which only the recurrent relationships among tagged parts of speech (subject, verb and direct object) are considered to establish connections among sequential pieces of text (e.g., paragraphs). The characterization of the texts was then achieved by considering scale-dependent complementary methods: accessibility, symmetry and recurrence signatures. In order to evaluate the potential of these concepts and methods, we approached the problem of distinguishing between literary genres (fiction and non-fiction). A set of 300 books organized into the two genres was considered and were compared by using the aforementioned approaches. All the methods were capable of differentiating to some extent between the two genres. The accessibility and symmetry reflected the narrative asymmetries, while the recurrence signature provided a more direct indication about the non-sequential semantic connections taking place along the narrative.

Several natural and artificial structures and systems are somehow optimized for performing specific functionalities. The structure and topology of cities is no exception, as it is critically important to ensure effective access to the several resources as well as overall mobility. The present work addresses the important subject of improving the plan of a given city through the incorporation of avenues and other express ways such as bridges and tunnels. More specifically, we start with the topology of a real city and consider the incorporation of a express way between any two locations in the city, keeping one location fixed and varying the angle of the other. The whole city area is covered in this manner, which allows us to derive a respective energy surface indicating the gain obtained regarding the average shortest path length for each of the possible situations. These surfaces therefore provide a complete picture of how much each city can be improved regarding minimal distances. Quite distinct surfaces have been obtained for 18 considered European cities. These surfaces are then characterized in terms of the number of local extrema and respective spatial complexity, expressed in terms of a raggedness measurement. Measurements are also obtained respectively to the geometry and topology of the considered cities. It is shown that the shortest path gain depends strongly on some of the considered measurements, especially lacunarity and transitivity. Interestingly, the intricacy of the energy surfaces resulted in relatively little correlation with the topological and geometrical measurements.

In this work we describe and compare the classic inner product and Pearson correlation coefficient as well as the recently introduced real-valued Jaccard and coincidence indices. Special attention is given to diverse schemes for taking into account the signs of the operands, as well as on the study of the geometry of the scalar field surface related to the generalized multiset binary operations underling the considered similarity indices. The possibility to split the classic inner product, cross-correlation, and Pearson correlation coefficient is also described., Comment: 9 pages, 8 figure. A preprint

Mathematical models represent one of the fundamental ways of studying nature. In special, epidemic models have shown to be particularly useful in the understanding of the course of diseases and in the planning effective control policies. A particular type of epidemic model considers the individuals divided into populations. When studied in graphs, it is already known that the graph topology can play an important role in the evolution of the disease. At the same time, one may want to study the effect of the presence of an underlying \emph{attraction landscape} of the vertices, apart from the respectively underlying topology. In this work, we study metapopulations with small number of individuals in the presence of an attraction landscape. Individuals move across populations and get infected according to the SIS compartmental model. By using a Markov chain approach, we provide a numerical approximation to the prediction of the long-term prevalence of the disease. More specifically, an approach that combines two binomial distributions for mobility, with appropriate assumptions, is proposed to approximate the model. The problem setting is simulated through Monte-Carlo experiments and the obtained results are compared to the mathematic-analytical approach. Substantial agreement is observed between both approaches, which corroborates the effectiveness of the reported numerical approach. In addition, we also study the impact of different levels of attraction landscapes, as well as propagation on the local scale of the entire population. All in all, this study proposes a potentially effective approach to a mostly unexplored setting of disease transmission.

The present work reports a comparative performance of artificial neurons obtained in terms of the real-valued Jaccard and coincidence similarity indices and respectively derived functionals. The interiority index and classic cross-correlation are also included for comparison purposes. After presenting the basic concepts related to real-valued multisets and the adopted similarity metrics, including the generalization of the real-valued Jaccard and coincidence indices to higher orders, we proceed to studying the response of a single neuron, not taking into account the output non-linearity (e.g.~sigmoid), respectively to the detection of gaussian two-dimensional stimulus in presence of displacement, magnification, intensity variation, noise and interference from additional patterns. It is shown that the real-valued Jaccard and coincidence approaches are substantially more robust and effective than the interiority index and the classic cross-correlation. The coincidence-based neurons are shown to have the best overall performance respectively to the considered type of data and perturbations. The potential of the multiset neurons is further illustrated with respect to the challenging problem of image segmentation, leading to impressive cost/benefit performance. The reported concepts, methods, and results, have substantial implications not only for pattern recognition and machine learning, but also regarding neurobiology and neuroscience., Comment: 21 pages, 32 figures. A preprint of a work submitted to a scientific journal (first revision)

Multisets are an intuitive extension of the traditional concept of sets that allow repetition of elements, with the number of times each element appears being understood as the respective multiplicity. Recent generalizations of multisets to real-valued functions, accounting for possibly negative values, have paved the way to a number of interesting implications and applications, including respective implementations as electronic systems. The basic multiset operations include the set complementation (sign change), intersection (minimum between two values), union (maximum between two values), difference and sum (identical to the algebraic counterparts). When applied to functions or signals, the sign and conjoint sign functions are also required. Given that signals are functions, it becomes possible to effectively translate the multiset and multifunction operations to analog electronics, which is the objective of the present work. It is proposed that effective multiset operations capable of high performance self and cross-correlation can be obtained with relative simplicity in either discrete or integrated circuits. The problem of switching noise is also briefly discussed. The present results have great potential for applications and related developments in analog and digital electronics, as well as for pattern recognition, signal processing, and deep learning., Comment: 7 pages, 8 figures. A preprint of a work submitted to a scientific journal

The real-valued Jaccard and coincidence indices, in addition to their conceptual and computational simplicity, have been verified to be able to provide promising results in tasks such as template matching, tending to yield peaks that are sharper and narrower than those typically obtained by standard cross-correlation, while also attenuating substantially secondary matchings. In this work, the multiset-based correlations based on the real-valued multiset Jaccard and coincidence indices are compared from the perspective of template matching, with encouraging results which have implications for pattern recognition, deep learning, and scientific modeling in general. The multiset-based correlation methods, and especially the coincidence index, presented remarkable performance characterized by sharper and narrower peaks while secondary peaks were attenuated, which was maintained even in presence of intense levels of noise. In particular, the two methods derived from the coincidence index led to particularly interesting results. The cross correlation, however, presented the best robustness to symmetric additive noise, which suggested a new combination of the considered approaches. After a preliminary investigation of the relative performance of the multiset approaches, as well as the classic cross-correlation, a systematic comparison framework is proposed and applied for the study of the aforementioned methods. Several results are reported, including the confirmation, at least for the considered type of data, of the coincidence correlation as providing enhanced performance regarding detection of narrow, sharp peaks while secondary matches are duly attenuated. The combined method also resulted promising for dealing with signals in presence of intense additive noise., Comment: 13 pages, 8 figures. A preprint

for representing, characterizing, and modeling an ample range of structures and phenomena from both theoretical and applied perspectives. The present work describes the application of the recently introduced real-valued Jaccard and coincidence similarity indices for building complex networks from datasets. More specifically, two nodes are linked whenever their similarity is greater than a given threshold. Weighted networks can also be obtained by taking the similarity indices as weights. It is shown that the proposed approach allows substantially enhanced performance when compared to cosine distance-based approaches, yielding a detailed description of the specific patterns of connectivity between the nodes. The impressive ability of the proposed methodology to emphasize the modular structure of networks is also illustrated with respect to the iris dataset and C.~elegans neuronal network connectivity data with remarkable results. The reported methodology and results pave the way to a significant number of possible theoretical and applied developments., Comment: 10 pages, 8 figures

The objective quantification of similarity between two mathematical structures constitutes a recurrent issue in science and technology. In the present work, we developed a principled approach that took the Kronecker's delta function of two scalar values as the prototypical reference for similarity quantification and then derived for more yielding indices, three of which bound between 0 and 1. Generalizations of these indices to take into account the sign of the scalar values were then presented and developed to multisets, vectors, and functions in real spaces. Several important results have been obtained, including the interpretation of the Jaccard index as a yielding implementation of the Kronecker's delta function. When generalized to real functions, the four described similarity indices become respective functionals, which can then be employed to obtain associated operations of convolution and correlation., Comment: 9 pages, 6 figures

Multisets are sets that allow repetition of elements. As such, multisets pave the way to a number of interesting possibilities of theoretical and applied nature. In the present work, after revising the main aspects of traditional sets, we introduce some of the main concepts and characteristics of multisets, followed by their generalization to take into account vectors and matrices. An approach is also proposed in which the real, negative multiplicities are allowed, implying the multiset universe to become finite and well-defined, corresponding to the multiset with null multiplicities. The complement operation in multisets is then defined, which allows properties involving complement -- including the De Morgan theorem -- to be recovered in multisets. In addition, it becomes possible to extend multisets to functions (which become multifunctions), scalar fields and other continuous mathematical structure, therefore achieving an enhanced space endowed with all algebraic operations plus set theoretical operations including union, intersection, and complementation. The possibility to define a set operation between mfunctions, namely the common product, that is analogous to the traditional inner product is also proposed, paving the way to obtaining respective mfunction transformations, and it is argued that the Walsh functions provide an orthogonal basis for the mfunctions space under the common product. This result also allowed the proposal of performing integrated signal processing operations on mset mfunctions, including filtering and enhanced template matching. Relationships between the cosine similarity index and the Jaccard index are also identified, including the presentation of an intersection-based variation of the cosine index. The potential of multisets in pattern recognition and deep learning is also briefly characterized and illustrated., Comment: 14 pages, 9 figures. A working manuscript

Quantifying the similarity between two mathematical structures or datasets constitutes a particularly interesting and useful operation in several theoretical and applied problems. Aimed at this specific objective, the Jaccard index has been extensively used in the most diverse types of problems, also motivating some respective generalizations. The present work addresses further generalizations of this index, including its modification into a coincidence index capable of accounting also for the level of relative interiority between the two compared entities, as well as respective extensions for sets in continuous vector spaces, the generalization to multiset addition, densities and generic scalar fields, as well as a means to quantify the joint interdependence between two random variables. The also interesting possibility to take into account more than two sets has also been addressed, including the description of an index capable of quantifying the level of chaining between three structures. Several of the described and suggested eneralizations have been illustrated with respect to numeric case examples. It is also posited that these indices can play an important role while analyzing and integrating datasets in modeling approaches and pattern recognition activities, including as a measurement of clusters similarity or separation and as a resource for representing and analyzing complex networks., Comment: 15 pages, 13 figures, a preprint

Robust and comprehensive characterization of the topological properties of complex networks requires the adoption of several respective measurements, among which the node degree has special importance. In the present work, we provide an introduction to one of these measurements, namely the accessibility of a node, which can be understood as a generalization of the concept of node degree not only to incorporate successive neighborhoods of that node, but also to reflect specific types of dynamics unfolding in the network. After discussing the node degree and its hierarchical extension, we present the concepts of random walk, entropy, and then the accessibility. Several examples of its numeric calculation are provided, as well as some experimental results indicating that it can effectively complement the information provided by other topological measurements of four types of complex networks, namely Erdos-Renyi, Watts-Strogatz, Barabasi-Albert, and Geometric. We also describe how a recently developed toolbox can be used for the calculation of accessibility in relatively large networks.

In the present work, we describe a framework for modeling how models can be built that integrates concepts and methods from a wide range of fields. The information schism between the real-world and that which can be gathered and considered by any individual information processing agent is characterized and discussed, followed by the presentation of a series of the adopted requisites while developing the modeling approach. The issue of mapping from datasets into models is subsequently addressed, as well as some of the respectively implied difficulties and limitations. Based on these considerations, an approach to meta modeling how models are built is then progressively developed. First, the reference M* meta model framework is presented, which relies critically in associating whole datasets and respective models in terms of a strict equivalence relation. Among the interesting features of this model are its ability to bridge the gap between data and modeling, as well as paving the way to an algebra of both data and models which can be employed to combine models into hierarchical manner. After illustrating the M* model in terms of patterns derived from regular lattices, the reported modeling approach continues by discussing how sampling issues, error and overlooked data can be addressed, leading to the $M^{<\epsilon>}$ variant, illustrated respectively to number theory. The situation in which the data needs to be represented in terms of respective probability densities is treated next, yielding the $M^{<\sigma>}$ meta model, which is then illustrated respectively to a real-world dataset (iris flowers data). Several considerations about how the developed framework can provide insights about data clustering, complexity, collaborative research, deep learning, and creativity are then presented, followed by overall conclusions., Comment: 33 pages, 24 figures. A working manuscript

Poetry and prose are written artistic expressions that help us to appreciate the reality we live. Each of these styles has its own set of subjective properties, such as rhyme and rhythm, which are easily caught by a human reader's eye and ear. With the recent advances in artificial intelligence, the gap between humans and machines may have decreased, and today we observe algorithms mastering tasks that were once exclusively performed by humans. In this paper, we propose an automated method to distinguish between poetry and prose based solely on aural and rhythmic properties. In other to compare prose and poetry rhythms, we represent the rhymes and phones as temporal sequences and thus we propose a procedure for extracting rhythmic features from these sequences. The classification of the considered texts using the set of features extracted resulted in a best accuracy of 0.78, obtained with a neural network. Interestingly, by using an approach based on complex networks to visualize the similarities between the different texts considered, we found that the patterns of poetry vary much more than prose. Consequently, a much richer and complex set of rhythmic possibilities tends to be found in that modality.

The interaction between cities and their respective green regions corresponds to an interesting issue that has received growing attention over the last decades. These relationships have multiple natures, ranging from providing habitat for animal life to temperature and humidity dynamics. Several methods based on area, size, shape, and distance have been considered in the literature. Given that several important contributions of green regions to urban areas involve temperature, humidity and gases (e.g.~oxygen) exchanges, which are intrinsically related to physical diffusion, it becomes particularly interesting to simulate the diffusion of green effects over urban areas as a means of better understanding the respective influences. The present work reports a related approach. Once the green regions of a given city are automatically identified by semantic segmentation and have eventual artifacts eliminated, successive convolutions are applied as a means to obtain the unfolding of the diffusion of the green effects along time. As illustrated, the diffusion dynamics is intrinsically interesting because it can be strongly affected by the spatial distribution of the green mass. In particular, we observed that smaller green regions could substantially contribute to the diffusion. The reported approach has been illustrated with respect to the Brazilian city of Ribeirao Preto, whose small and medium-sized green regions were found to complement in an effective manner the diffusion of the green effects as inferred from the performed simulations under specific parameter settings.

The development of science constitutes itself an important subject of scientific investigation.Indeed, better knowledge about this intricate dynamical system can provide subsidies for enhancing the manners in which science progresses. Recently, a network science-based approach was reported aimed at characterizing and studying the prospects for scientific advancement assuming that new pieces of knowledge are incorporated in a uniformly random manner. A surprising result was reported in the sense that quite similar advancements were observe for both Erd\H{o}s-R\'enyi (ER) and Barab\'asi-Albert (BA) knowledge networks. In the present work, we develop a systematic complementation of that preliminary investigation, considering an additional network model, the random geometric graph (GR) as well as several other manners to incorporating knowledge, namely preferential to node degree, preferential to closer or adjacent nodes, as well as taking into account the betweenness centrality of the unknown nodes. Several interesting results were obtained and discussed, including: the uniform strategy led to the best expansion in the GR model, the results of the degree and betweenness expansion for the ER and GR models were similar to those obtained using uniformity method in those same models. Surprisingly, the BA model led to just a slightly faster expansion than in the uniform case. Though qualitatively similar, strategies based on the degree and betweenness yielded distinct results as a consequence of them not being linearly related.

Functions correspond to one of the key concepts in mathematics and science, allowing the representation and modeling of several types of signals and systems. The present work develops an approach for characterizing the coverage and interrelationship between discrete signals that can be fitted by a set of reference functions, allowing the definition of transition networks between the considered discrete signals. While the adjacency between discrete signals is defined in terms of respective Euclidean distances, the property of being adjustable by the reference functions provides an additional constraint leading to a surprisingly diversity of transition networks topologies. First, we motivate the possibility to define transitions between parametric continuous functions, a concept that is subsequently extended to discrete functions and signals. Given that the set of all possible discrete signals in a bound region corresponds to a finite number of cases, it becomes feasible to verify the adherence of each of these signals with respect to a reference set of functions. Then, by taking into account also the Euclidean proximity between those discrete signals found to be adjustable, it becomes possible to obtain a respective transition network that can be not only used to study the properties and interrelationships of the involved discrete signals as underlain by the reference functions, but which also provide an interesting complex network theoretical model on itself, presenting a surprising diversity of topological features, including modular organization coexisting with more uniform portions, tails and handles, as well as hubs. Examples of the proposed concepts and methodologies are provided respectively with respect to three case examples involving power, sinusoidal and polynomial functions., Comment: 15 pages, 14 figures, a working paper

Among different aspects of social networks, dynamics have been proposed to simulate how opinions can be transmitted. In this study, we propose a model that simulates the communication in an online social network, in which the posts are created from external information. We considered the nodes and edges of a network as users and their friendship, respectively. A real number is associated with each user representing its opinion. The dynamics starts with a user that has contact with a random opinion, and, according to a given probability function, this individual can post this opinion. This step is henceforth called post transmission. In the next step, called post distribution, another probability function is employed to select the user's friends that could see the post. Post transmission and distribution represent the user and the social network algorithm, respectively. If an individual has contact with a post, its opinion can be attracted or repulsed. Furthermore, individuals that are repulsed can change their friendship through a rewiring. These steps are executed various times until the dynamics converge. Several impressive results were obtained, which include the formation of scenarios of polarization and consensus of opinions. In the case of echo chambers, the possibility of rewiring probability is found to be decisive. However, for particular network topologies, with a well-defined community structure, this effect can also happen. All in all, the results indicate that the post distribution strategy is crucial to mitigate or promote polarization.

Despite the great differences among cities, they face similar challenges regarding social inequality, politics and criminality. Urban art express these feelings from the citizen point-of-view. In particular, the drawing and painting of public surfaces may carry rich information about the time and region it was made. Existing studies have explored the spatial distribution of graffiti, but most of them considered graffiti as a whole, with no separation among the types. Also, the analyses rarely take into account the city topology. In this work, we propose to categorize the graffiti into three types: simple scribbles, complex scribbles, canvases. We analyze the spatial distribution and identify the spatial bias of each type. To further analyze the spatial distribution of the types, we apply concepts from complex networks. First, regions (communities) defined by the connectivity profiles of the city network are obtained and the prevalence of each type of graffiti over these regions are analyzed. Next, a measure based on the dynamics of the network (accessibility) is calculated and compared to the distribution of the graffiti types. A case study is performed in the analysis of three different categories of graffiti in the city of Sao Paulo, Brazil. The results showed that the categories present characteristic spatial distributions. The ratio of each type per community of the network, though, does not pose significant deviations. Finally, a small positive correlation was observed between the locations of each graffiti type and the accessibility., Comment: To be submitted to EPL

The concept of 'complexity' plays a central role in complex network science. Traditionally, this term has been taken to express heterogeneity of the node degrees of a therefore complex network. However, given that the degree distribution is not enough to provide an invertible representation of a given network, additional complementary measurements of its topology are required in order to complement its characterization. In the present work, we aim at obtaining a new model of complex networks, called hypercomplex networks - HC, that are characterized by heterogeneity not only of the degree distribution, but also of a relatively complete set of complementary topological measurements including node degree, shortest path length, clustering coefficient, betweenness centrality, matching index, Laplacian eigenvalue and hierarchical node degree. The proposed model starts with uniformly random networks, namely Erdos-Renyi structures, and then applies optimization so as to increase an index of the overall complexity of the networks. An optimization approach has been considered in terms of gradient descent. The complexity index expresses the dispersion of the several considered measurements. Several interesting results are reported and discussed, including the fact that the HC networks define, as the optimization proceeds, a trajectory in the principal component space of the measurements that tends to depart from the considered theoretical models (Erdos-Renyi, Barabasi-Albert, Waxman, Random Geometric Graph and Watts-Strogatz), heading to a previously empty space (low density of cases). We observed that, after a considerably large number of optimization steps, peripheral branching tends to appear that further enhances the complexity of these networks., Comment: 8 pages, 7 figures

Previous literature on random matrix and network science has traditionally employed measures derived from nearest-neighbor level spacing distributions to characterize the eigenvalue statistics of random matrices. This approach, however, depends crucially on eigenvalue unfolding procedures, which in many situations represent a major hindrance due to constraints in the calculation, specially in the case of complex spectra. Here we study the spectra of directed networks using the recently introduced ratios between nearest- and next-to-nearest eigenvalue spacing, thus circumventing the shortcomings imposed by spectral unfolding. Specifically, we characterize the eigenvalue statistics of directed Erd\H{o}s-R\'enyi (ER) random networks by means of two adjacency matrix representations; namely (i) weighted non-Hermitian random matrices and (ii) a transformation on non-Hermitian adjacency matrices which produces weighted Hermitian matrices. For both representations, we find that the distribution of spacing ratios becomes universal for a fixed average degree, in accordance with undirected random networks. Furthermore, by calculating the average spacing ratio as a function of the average degree, we show that the spectral statistics of directed ER random networks undergoes a transition from Poisson to Ginibre statistics for model (i) and from Poisson to Gaussian Unitary Ensemble statistics for model (ii). Eigenvector delocalization effects of directed networks are also discussed.

The Roman Empire shaped Western civilization, and many Roman principles are embodied in modern institutions. Although its political institutions proved both resilient and adaptable, allowing it to incorporate diverse populations, the Empire suffered from many internal conflicts. Indeed, most emperors died violently, from assassination, suicide, or in battle. These internal conflicts produced patterns in the length of time that can be identified by statistical analysis. In this paper, we study the underlying patterns associated with the reign of the Roman emperors by using statistical tools of survival data analysis. We consider all the 175 Roman emperors and propose a new power-law model with change points to predict the time-to-violent-death of the Roman emperors. This model encompasses data in the presence of censoring and long-term survivors, providing more accurate predictions than previous models. Our results show that power-law distributions can also occur in survival data, as verified in other data types from natural and artificial systems, reinforcing the ubiquity of power law distributions. The generality of our approach paves the way to further related investigations not only in other ancient civilizations but also in applications in engineering and medicine., Comment: 18 pages, 6 figures

In this paper we investigated the possibility to use the magnetic Laplacian to characterize directed graphs (a.k.a. networks). Many interesting results are obtained, including the finding that community structure is related to rotational symmetry in the spectral measurements for a type of stochastic block model. Due the hermiticity property of the magnetic Laplacian we show here how to scale our approach to larger networks containing hundreds of thousands of nodes using the Kernel Polynomial Method (KPM). We also propose to combine the KPM with the Wasserstein metric in order to measure distances between networks even when these networks are directed, large and have different sizes, a hard problem which cannot be tackled by previous methods presented in the literature. In addition, our python package is publicly available at \href{https://github.com/stdogpkg/emate}{github.com/stdogpkg/emate}. The codes can run in both CPU and GPU and can estimate the spectral density and related trace functions, such as entropy and Estrada index, even in directed or undirected networks with million of nodes., Comment: Accepted for publication. This work represents the first part (with extension for large graphs) of the previous one that is available in arXiv:1812.02160

An important issue in clustering concerns the avoidance of false positives while searching for clusters. This work addressed this problem considering agglomerative methods, namely single, average, median, complete, centroid and Ward's approaches applied to unimodal and bimodal datasets obeying uniform, gaussian, exponential and power-law distributions. A model of clusters was also adopted, involving a higher density nucleus surrounded by a transition, followed by outliers. This paved the way to defining an objective means for identifying the clusters from dendrograms. The adopted model also allowed the relevance of the clusters to be quantified in terms of the height of their subtrees. The obtained results include the verification that many methods detect two clusters in unimodal data. The single-linkage method was found to be more resilient to false positives. Also, several methods detected clusters not corresponding directly to the nucleus. The possibility of identifying the type of distribution was also investigated.

With the expansion of electronic publishing, a new dynamics of scientific articles dissemination was initiated. Nowadays, many works are widely disseminated even before publication, in the form of preprints. Another important new element concerns the views of published articles. Thanks to the availability of respective data by some journals, such as PLoS ONE, it became possible to develop investigations on how scientific works are viewed along time, often before the first citations appear. This provides the main theme of the present work. More specifically, our research was motivated by preliminary observations that the view profiles along time tend to present a piecewise linear nature. A methodology was then delineated in order to identify the main segments in the view profiles, which allowed several related measurements to be derived. In particular, we focused on the inclination and length of each subsequent segment. Basic statistics indicated that the inclination can vary substantially along subsequent segments, while the segment lengths resulted more stable. Complementary joint statistics analysis, considering pairwise correlations, provided further information about the properties of the views. In order to better understand the view profiles, we performed respective multivariate statistical analysis, including principal component analysis and hierarchical clustering. The results suggest that a portion of the polygonal views are organized into clusters or groups. These groups were characterized in terms of prototypes indicating the relative increase or decrease along subsequent segments. Four respective distinct models were then developed for representing the observed segments. It was found that models incorporating joint dependencies between the properties of the segments provided the most accurate results among the considered alternatives.

Among the several topological properties of complex networks, the shortest path represents a particularly important characteristic because of its potential impact not only on other topological properties, but mainly for its influence on several dynamical processes taking place on the network. In addition, several practical situations, such as transit in cities, can benefit by modifying a network so as to reduce the respective shortest paths. In the present work, we addressed the problem of trying to reduce the average shortest path of several theoretical and real-world complex networks by adding a given number of links according to different strategies. More specifically, we considered: placing new links between nodes with relatively low and high degrees; to enhance the degree regularity of the network; preferential attachment according to the degree; linking nodes with relatively low and high betweenness centrality; and linking nodes with relatively low/low, low/high, and high/high accessibilities. Several interesting results have been obtained, including the identification of the accessibility-based strategies as providing the largest reduction of the average shortest path length. Another interesting finding is that, for several types of networks, the degree-based methods tend to provide improvements comparable to those obtained by using the much more computationally expensive betweenness centrality measurement.