arXiv subjects

Luciano da F. Costa

Publications and source records attributed to Luciano da F. Costa.

At least 55 records · Page 3Linked to original sources

arXiv2021

An Introduction to Multisets

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.

math.GM↗

arXiv2021

An Ample Approach to Data and Modeling

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 $M^{<ε>}$ 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 $M^{<σ>}$ 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.

cs.AI↗

arXiv2021

Accessibility: A Generalization of the Node Degree (A Tutorial)

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.

physics.soc-ph↗

arXiv2021

Cost-Based Approach to Complexity: A Common Denominator?

Complexity remains one of the central challenges in science and technology. Although several approaches at defining and/or quantifying complexity have been proposed, at some point each of them seems to run into intrinsic limitations or mutual disagreement. Two are the main objectives of the present work: (i) to review some of the main approaches to complexity; and (ii) to suggest a cost-based approach that, to a great extent, can be understood as an integration of the several facets of complexity while keeping its meaning for humans in mind. More specifically, it is poised that complexity, an inherently relative and subjective concept, can be summarized as the cost of developing a model, plus the cost of its respective operation. As a consequence, complexity can vary along time and space. The proposal is illustrated respectively to several applications examples, including a real-data base situation.

cs.OH↗

arXiv2021

A pattern recognition approach for distinguishing between prose and poetry

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.

cs.CL↗

arXiv2021

On Hypercomplex Networks

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.

physics.soc-ph↗

arXiv2021

Estimating the Effects of Urban Green Regions in terms of Diffusion

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.

physics.soc-ph↗

arXiv2021

Modeling the Perspectives for Scientific Advancement

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 Erdős-Rényi (ER) and Barabási-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.

physics.soc-ph↗

arXiv2021

Complex Networks of Functions

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.

cs.DM↗

arXiv2021

Modeling how social network algorithms can influence opinion polarization

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.

cs.SI↗

arXiv2020

Spatial distribution of graffiti: A complex network approach

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.

physics.soc-ph↗

arXiv2020

Classification of abrupt changes along viewing profiles of scientific articles

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.

cs.DL↗

arXiv2020

Spacing ratio characterization of the spectra of directed random networks

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 Erdős-Rényi (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.

cond-mat.dis-nn↗

arXiv2020

Power laws in the Roman Empire: a survival analysis

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.

stat.AP↗

arXiv2020

Characterization and comparison of large directed graphs through the spectra of the magnetic Laplacian

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.

cs.SI↗

arXiv2020

Revisiting Agglomerative Clustering

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.

cs.LG↗

arXiv2020

Shortest Paths in Complex Networks: Structure and Optimization

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.

cs.SI↗

arXiv2020

Toward Generalized Clustering through an One-Dimensional Approach

After generalizing the concept of clusters to incorporate clusters that are linked to other clusters through some relatively narrow bridges, an approach for detecting patches of separation between these clusters is developed based on an agglomerative clustering, more specifically the single-linkage, applied to one-dimensional slices obtained from respective feature spaces. The potential of this method is illustrated with respect to the analyses of clusterless uniform and normal distributions of points, as well as a one-dimensional clustering model characterized by two intervals with high density of points separated by a less dense interstice. This partial clustering method is then considered as a means of feature selection and cluster identification, and two simple but potentially effective respective methods are described and illustrated with respect to some hypothetical situations.

cs.CV↗