Stability of a two-sublattice spin-glass model

We study the stability of the replica-symmetric solution of a two-sublattice infinite-range spin-glass model, which can describe the transition from antiferromagnetic to spin glass state. The eigenvalues associated with replica-symmetric perturbations are in general complex. The natural generalization of the usual stability condition is to require the real part of these eigenvalues to be positive. The necessary and sufficient conditions for all the roots of the secular equation to have positive real parts is given by the Hurwitz criterion. The generalized stability condition allows a consistent analysis of the phase diagram within the replica-symmetric approximation.Comment: 21 pages, 5 figure

Border trees of complex networks

The comprehensive characterization of the structure of complex networks is essential to understand the dynamical processes which guide their evolution. The discovery of the scale-free distribution and the small world property of real networks were fundamental to stimulate more realistic models and to understand some dynamical processes such as network growth. However, properties related to the network borders (nodes with degree equal to one), one of its most fragile parts, remain little investigated and understood. The border nodes may be involved in the evolution of structures such as geographical networks. Here we analyze complex networks by looking for border trees, which are defined as the subgraphs without cycles connected to the remainder of the network (containing cycles) and terminating into border nodes. In addition to describing an algorithm for identification of such tree subgraphs, we also consider a series of their measurements, including their number of vertices, number of leaves, and depth. We investigate the properties of border trees for several theoretical models as well as real-world networks.Comment: 5 pages, 1 figure, 2 tables. A working manuscript, comments and suggestions welcome

Analyzing Trails in Complex Networks

Even more interesting than the intricate organization of complex networks are the dynamical behavior of systems which such structures underly. Among the many types of dynamics, one particularly interesting category involves the evolution of trails left by moving agents progressing through random walks and dilating processes in a complex network. The emergence of trails is present in many dynamical process, such as pedestrian traffic, information flow and metabolic pathways. Important problems related with trails include the reconstruction of the trail and the identification of its source, when complete knowledge of the trail is missing. In addition, the following of trails in multi-agent systems represent a particularly interesting situation related to pedestrian dynamics and swarming intelligence. The present work addresses these three issues while taking into account permanent and transient marks left in the visited nodes. Different topologies are considered for trail reconstruction and trail source identification, including four complex networks models and four real networks, namely the Internet, the US airlines network, an email network and the scientific collaboration network of complex network researchers. Our results show that the topology of the network influence in trail reconstruction, source identification and agent dynamics.Comment: 10 pages, 16 figures. A working manuscript, comments and criticisms welcome

Seeking for Simplicity in Complex Networks

Complex networks can be understood as graphs whose connectivity deviates from those of regular or near-regular graphs, which are understood as being `simple'. While a great deal of the attention so far dedicated to complex networks has been duly driven by the `complex' nature of these structures, in this work we address the identification of simplicity, in the sense of regularity, in complex networks. The basic idea is to seek for subgraphs exhibiting small dispersion (e.g. standard deviation or entropy) of local measurements such as the node degree and clustering coefficient. This approach paves the way for the identification of subgraphs (patches) with nearly uniform connectivity, therefore complementing the characterization of the complexity of networks. We also performed analysis of cascade failures, revealing that the removal of vertices in `simple' regions results in smaller damage to the network structure than the removal of vertices in the heterogeneous regions. We illustrate the potential of the proposed methodology with respect to four theoretical models as well as protein-protein interaction networks of three different species. Our results suggest that the simplicity of protein interaction grows as the result of natural selection. This increase in simplicity makes these networks more robust to cascade failures.Comment: 5 pages, 3 figures, 1 table. Submitted to Physical Review Letter

Prominent effect of soil network heterogeneity on microbial invasion

Using a network representation for real soil samples and mathematical models for microbial spread, we show that the structural heterogeneity of the soil habitat may have a very significant influence on the size of microbial invasions of the soil pore space. In particular, neglecting the soil structural heterogeneity may lead to a substantial underestimation of microbial invasion. Such effects are explained in terms of a crucial interplay between heterogeneity in microbial spread and heterogeneity in the topology of soil networks. The main influence of network topology on invasion is linked to the existence of long channels in soil networks that may act as bridges for transmission of microorganisms between distant parts of soil

Use of data analysis techniques for multi-objective optimization of real problems: decision making

Most, if not all, real optimization problems can be seen as multi-objective since several objectives are to be satisfied concurrently and are often conflicting. Also, due to the high computation times usually required by the numerical modelling routines available to calculate the values of the objective function, as a function of the decision variables, it is necessary to develop alternative optimization methodologies able to reduce the number of solutions to be evaluated, i.e., if compared with the procedures typically employed, such as evolutionary algorithms. Moreover, in a multi-objective environment, it is also necessary at the end of the optimization process to select a single solution from the pool of optimal non-dominated solutions obtained. Real industrial processes can be characterized by different types of data that can influence assertively its performance. For example, in the industrial process studied here, polymer processing, variables related to operating conditions of the machine, polymer properties and system geometry affect its operation since the thermomechanical environment developed allows obtaining mathematical relationships between these design variables and the objectives to be accomplished. This enables the direct process optimization using those routines to evaluate the solutions proposed by the optimization algorithms. However, this routine must be run several times, implying high computation times due to the sophistication of the numerical codes This work aims to apply Artificial Intelligence based on a data analysis technique, designated by DAMICORE, to surpass those limitations, improve the optimization process and help the selection of the best-equilibrated solution at the end. An example from single screw polymer extrusion is used to illustrate the efficient use of a methodology proposed, with a focus on decision making. Solving Multi-Objective Optimization Problems (MOOP) requires some interaction with a DM, for example, an expert in the field. The aim is to use data analysis techniques to reduce and improve the quality of those interactions, which can be done by integrating optimization methodologies with data analysis tools, i.e., the use of data to drive the optimization. At least, two different possibilities can be applied by data-driven optimization: i) replacement of the original method of calculating the objectives by a metamodel or surrogate, and 2) helping the computer in deciding about the best solutions to the problem. The aim here is to use the DAMICORE framework to facilitate the optimization taking into account the limitations/characteristics referred to above. The DAMICORE structure is based on the estimation of distances by compression algorithms called Normalized Compression Distance (NCD). Then, a Feature Sensitivity Optimization based on Phylogram Analysis (FS-OPA) is used to find the set of principal features related to the real problem environment. The present study focus on two levels of learning, which will be used to study an industrial case study using real data: First-level learning – the aim is to find clusters of variables sharing information, designated by clades, each representing the set of variables with important interactions. The result of this level is a table with a list of variables with a cluster per row. Second-level learning – the application of FS-OPA allows the estimation of the contribution of each clade of variables to the objectives, which is made by determining the distance between the clades of objectives (oclade) to each variable clade (vclade) using the phylogram obtained. These distances are an estimation of the influence of a clade to improve an objective. The results of this level are two different matrices, one with the phylogram distances from vclades to oclades and the second with the relative phylograms distances from each variable to each objective. From a practical point of view, the application of this method to the data of each population of solutions previously obtained during the multi-objective optimization using evolutionary algorithms will allow capturing the interactions between the decision variables and the objectives and, in the end, select the most important objectives to the process. Therefore, the multi-dimensional space, that results from the six objectives existent in the problem solved, can be reduced, which will help the decision maker in selecting in an easy way the solution to be applied in real practice. The results obtained for this practical example are in agreement with the expected thermomechanical behaviour of the process, which demonstrated that AI techniques can be useful in solving practical engineering problems

Application of artificial intelligence techniques in the optimization of single screw polymer extrusion

As with most real optimization problems, polymer processing technologies can be seen as multi-objective optimization problems. Due to the high computation times required by the numerical modelling routines usually available to calculate the values of the objective function, as a function of the decision variables, it is necessary to develop alternative optimization methodologies able to reduce the number of solutions to be evaluated, when compared with the technics normally employed, such as evolutionary algorithms. Therefore, in this work is proposed the use of artificial intelligence based on a data analysis technique designated by DAMICORE surpasses those limitations. An example from single screw polymer extrusion is used to illustrate the efficient use of a methodology proposed.This research was partially funded by NAWA-Narodowa Agencja Wymiany Akademickiej, under grant PPN/ULM/2020/1/00125 and European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No 734205–H2020-MSCA-RISE-2016. The authors also acknowledge the funding by FEDER funds through the COMPETE 2020 Programme and National Funds through FCT (Portuguese Foundation for Science and Technology) under the projects UIDB/05256/2020, and UID-P/05256/2020, the Center for Mathematical Sciences Applied to Industry (CeMEAI) and the support from the São Paulo Research Foundation (FAPESP grant No 2013/07375-0, the Center for Artificial Intelligence (C4AI-USP), the support from the São Paulo Research Foundation (FAPESP grant No 2019/07665-4) and the IBM Corporation