Topological Map Research Articles

The category of topological spaces and open maps does not have products

We prove that the category of topological spaces and open maps does not have binary products, thus resolving the Esakia problem in the negative. We also prove that the category of Kripke frames does not have binary products and that the category of complete Heyting algebras does not have binary coproducts.

Pressure and Temperature Prediction of Oil Pipeline Networks Based on a Mechanism-Data Hybrid Driven Method

To ensure the operational safety of oil transportation stations, it is crucial to predict the impact of pressure and temperature before crude oil enters the pipeline network. Accurate predictions enable the assessment of the pipeline’s load-bearing capacity and the prevention of potential safety incidents. Most existing studies primarily focus on describing and modeling the mechanisms of the oil flow process. However, monitoring data can be skewed by factors such as instrument aging and pipeline friction, leading to inaccurate predictions when relying solely on mechanistic or data-driven approaches. To address these limitations, this paper proposes a Temporal-Spatial Three-stream Temporal Convolutional Network (TS-TTCN) model that integrates mechanistic knowledge with data-driven methods. Building upon Temporal Convolutional Networks (TCN), the TS-TTCN model synthesizes mechanistic insights into the oil transport process to establish a hybrid driving mechanism. In the temporal dimension, it incorporates real-time operating parameters and applies temporal convolution techniques to capture the time-series characteristics of the oil transportation pipeline network. In the spatial dimension, it constructs a directed topological map based on the pipeline network’s node structure to characterize spatial features. Data analysis and experimental results show that the Three-stream Temporal Convolutional Network (TTCN) model, which uses a Tanh activation function, achieves an error rate below 5%. By analyzing and validating real-time data from the Dongying oil transportation station, the proposed hybrid model proves to be more stable, reliable, and accurate under varying operating conditions.

CATOM : Causal Topology Map for Spatiotemporal Traffic Analysis with Granger Causality in Urban Areas.

The transportation network is an important element in an urban system that supports daily activities, enabling people to travel from one place to another. One of the key challenges is the network complexity, which is composed of many node pairs distributed over the area. This spatial characteristic results in the high dimensional network problem in understanding the 'cause' of problems such as traffic congestion. Recent studies have proposed visual analytics systems aimed at understanding these underlying causes. Despite these efforts, the analysis of such causes is limited to identified patterns. However, given the intricate distribution of roads and their mutual influence, new patterns continuously emerge across all roads within urban transportation. At this stage, a well-defined visual analytics system can be a good solution for transportation practitioners. In this paper, we propose a system, CATOM (Causal Topology Map), for the cause-effect analysis of traffic patterns based on Granger causality for extracting causal topology maps. CATOM discovers causal relationships between roads through the Granger causality test and quantifies these relationships through the causal density. During the design process, the system was developed to fully utilize spatial information with visualization techniques to overcome the previous problems in the literature. We also evaluate the usability of our approach by conducting a SUS(System Usability Scale) test and traffic cause analysis with the real-world data from two study sites in collaboration with domain experts.

Participatory topological mapping: A novel approach for exploring and communicating situated knowledge of complex socio-ecological systems

Land use change impacts on Sámi reindeer husbandry are well-documented, but existing maps often fail to capture socio-ecological relationships between herders, reindeer and nature. Conventional Geographic Information Systems (GIS) simplify these relationships, lacking local context and excluding valuable knowledge due to their rigid structure. This paper introduces participatory topological mapping, a low-tech, knowledge co-production method that allows communities to share geospatial insights without advanced software. Combining hand-drawn maps with a standardised topological structure facilitates the visualisation of geographical relationships and dynamic land use systems from a local perspective. Developed and assessed through a Swedish case study in collaboration with Vittangi and Malå reindeer herding communities, the method aims to reduce barriers to knowledge exchange and enhance dialogue between Indigenous knowledge-holders, researchers and decision-makers. The paper discusses the authors’ experiences with participatory topological mapping, emphasising its potential and limitations for knowledge exchange. The method is advocated for broader use, recognising its value in articulating concerns about land use change beyond research settings and reindeer husbandry. Participatory topological mapping enables knowledge-holders to control the map and its narrative, deciding what is included or excluded. The maps and accompanying stories are valuable sources for documenting, sharing and analysing local perspectives on landscapes and the effects of land use change. The method treats mapping as a social process with the potential to affect how we understanding the world. When thoughtfully applied, it offers a valuable avenue for knowledge co-production, fostering deeper engagement, supporting informed decision-making and empowering communities.

GRID-FAST: A Grid-based Intersection Detection for Fast Semantic Topometric Mapping

This article introduces a novel approach to constructing a topometric map that allows for efficient navigation and decision-making in mobile robotics applications. The method generates the topometric map from a 2D grid-based map. The topometric map segments areas of the input map into different structural-semantic classes: intersections, pathways, dead ends, and pathways leading to unexplored areas. This method is grounded in a new technique for intersection detection that identifies the area and the openings of intersections in a semantically meaningful way. The framework introduces two levels of pre-filtering with minimal computational cost to eliminate small openings and objects from the map which are unimportant in the context of high-level map segmentation and decision making. The topological map generated by GRID-FAST enables fast navigation in large-scale environments, and the structural semantics can aid in mission planning, autonomous exploration, and human-to-robot cooperation. The efficacy of the proposed method is demonstrated through validation on real maps gathered from robotic experiments: 1) a structured indoor environment, 2) an unstructured cave-like subterranean environment, and 3) a large-scale outdoor environment, which comprises pathways, buildings, and scattered objects. Additionally, the proposed framework has been compared with state-of-the-art topological mapping solutions and is able to produce a topometric and topological map with up to 92% fewer nodes than the next best solution. The method proposed in this article has been implemented in the robotics framework ROS and is open-sourced. The code is available at: https://github.com/LTU-RAI/GRID-FAST.

NOise Reduction with DIstribution Corrected (NORDIC) principal component analysis improves brain activity detection across rodent and human functional MRI contexts.

NOise Reduction with DIstribution Corrected (NORDIC) principal component analysis (PCA) has been shown to selectively suppress thermal noise and improve the temporal signal-to-noise ratio (tSNR) in human functional magnetic resonance imaging (fMRI). However, the feasibility to improve data quality for rodent fMRI using NORDIC PCA remains uncertain. NORDIC PCA may also be particularly beneficial for improving topological brain mapping, as conventional mapping requires precise spatiotemporal signals from large datasets (ideally ~1 hour acquisition) for individual representations. In this study, we evaluated the effects of NORDIC PCA compared with "Standard" processing in various rodent fMRI contexts that range from task-evoked optogenetic fMRI to resting-state fMRI. We also evaluated the effects of NORDIC PCA on human resting-state and retinotopic mapping fMRI via population receptive field (pRF) modeling. In rodent optogenetic fMRI, apart from doubling the tSNR, NORDIC PCA resulted in a larger number of activated voxels and a significant decrease in the variance of evoked brain responses without altering brain morphology. In rodent resting-state fMRI, we found that NORDIC PCA induced a nearly threefold increase in tSNR and preserved task-free relative cerebrovascular reactivity (rCVR) across cortical depth. NORDIC PCA further improved the detection of TGN020-induced aquaporin-4 inhibition on rCVR compared with Standard processing without NORDIC PCA. NORDIC PCA also increased the tSNR for both human resting-state and pRF fMRI, and for the latter also increased activation cluster sizes while retaining retinotopic organization. This suggests that NORDIC PCA preserves the spatiotemporal precision of fMRI signals needed for pRF analysis, and effectively captures small activity changes with high sensitivity. Taken together, these results broadly demonstrate the value of NORDIC PCA for the enhanced detection of neural dynamics across various rodent and human fMRI contexts. This can in turn play an important role in improving fMRI image quality and sensitivity for translational and preclinical neuroimaging research.

Construction of Metaphorical Maps of Cyberspace Resources Based on Point‐Cluster Feature Generalization

ABSTRACTIn the digital age, the expansion of cyberspace has resulted in increasing complexity, making clear cyberspace visualization crucial for effective analysis and decision‐making. Current cyberspace visualizations are overly complex and fail to accurately reflect node importance. To address the challenge of complex cyberspace visualization, this study introduces the integrated centrality metric (ICM) for constructing a metaphorical map that accurately reflects node importance. The ICM, a novel node centrality measure, demonstrates superior accuracy in identifying key nodes compared to degree centrality (DC), k‐shell centrality (KC), and PageRank values. Through community partitioning and point‐cluster feature generalization, we extract a network's hierarchical structure to intuitively represent its community and backbone topology, and we construct a metaphorical map that offers a clear visualization of cyberspace. Experiments were conducted on four original networks and their extracted backbone networks to identify core nodes. The Jaccard coefficient was calculated considering the results of the three aforementioned centrality measures, ICM, and the SIR model. The results indicate that ICM achieved the best performance in both the original networks and all extracted backbone networks. This demonstrates that ICM can more precisely evaluate node importance, thereby facilitating the construction of metaphorical maps. Moreover, the proposed metaphorical map is more convenient than traditional topological maps for quickly comprehending the complex characteristics of networks.

A Fast Multi-Scale of Distributed Batch-Learning Growing Neural Gas for Multi-Camera 3D Environmental Map Building.

Biologically inspired intelligent methods have been applied to various sensing systems in order to extract features from a huge size of raw sensing data. For example, point cloud data can be applied to human activity recognition, multi-person tracking, and suspicious person detection, but a single RGB-D camera is not enough to perform the above tasks. Therefore, this study propose a 3D environmental map-building method integrating point cloud data measured via multiple RGB-D cameras. First, a fast multi-scale of distributed batch-learning growing neural gas (Fast MS-DBL-GNG) is proposed as a topological feature extraction method in order to reduce computational costs because a single RGB-D camera may output 1 million data. Next, random sample consensus (RANSAC) is applied to integrate two sets of point cloud data using topological features. In order to show the effectiveness of the proposed method, Fast MS-DBL-GNG is applied to perform topological mapping from several point cloud data sets measured in different directions with some overlapping areas included in two images. The experimental results show that the proposed method can extract topological features enough to integrate point cloud data sets, and it runs 14 times faster than the previous GNG method with a 23% reduction in the quantization error. Finally, this paper discuss the advantage and disadvantage of the proposed method through numerical comparison with other methods, and explain future works to improve the proposed method.

Transforming Two-Dimensional Carbon Allotropes into Three-Dimensional Ones through Topological Mapping: The Case of Biphenylene Carbon (Graphenylene).

In this work, we propose a new methodology for obtaining three-dimensional (3D) carbon allotrope structures from 2D ones through topological mapping. The idea is to select a 3D target structure and "slice" it along different structural directions, creating a series of 2D structures. As a proof of concept, we chose the tubulane structure 12-hexa(3,3) as a target. Tubulanes are 3D carbon allotropes based on cross-linked carbon nanotubes. One of the obtained 2D "sliced" structures was mapped into the biphenylene carbon (BPC). We showed that compressing BPC in-plane, biaxially, followed by compression along the z direction using different strain rates could generate not only the target tubulane 12-hexa(3,3) structure but also at least two others: bcc-C6 and an unreported member of the tubulane family, which we called tubulane X. The methodology proposed here is entirely general; it can be used coupled with any quantum method. Considering that the 2D biphenylene carbon network, which is closely related to BPC, has been recently synthesized, the approach proposed here opens new perspectives to obtain new 3D carbon allotropes from 2D structures.

Multi-Robot Navigation System Design Based on Proximal Policy Optimization Algorithm

The more path conflicts between multiple robots, the more time it takes to avoid each other, and the more navigation time it takes for the robots to complete all tasks. This study designs a multi-robot navigation system based on deep reinforcement learning to provide an innovative and effective method for global path planning of multi-robot navigation. It can plan paths with fewer path conflicts for all robots so that the overall navigation time for the robots to complete all tasks can be reduced. Compared with existing methods of global path planning for multi-robot navigation, this study proposes new perspectives and methods. It emphasizes reducing the number of path conflicts first to reduce the overall navigation time. The system consists of a localization unit, an environment map unit, a path planning unit, and an environment monitoring unit, which provides functions for calculating robot coordinates, generating preselected paths, selecting optimal path combinations, robot navigation, and environment monitoring. We use topological maps to simplify the map representation for multi-robot path planning so that the proposed method can perform path planning for more robots in more complex environments. The proximal policy optimization (PPO) is used as the algorithm for deep reinforcement learning. This study combines the path selection method of deep reinforcement learning with the A* algorithm, which effectively reduces the number of path conflicts in multi-robot path planning and improves the overall navigation time. In addition, we used the reciprocal velocity obstacles algorithm for local path planning in the robot, combined with the proposed global path planning method, to achieve complete and effective multi-robot navigation. Some simulation results in NVIDIA Isaac Sim show that for 1000 multi-robot navigation tasks, the maximum number of path conflicts that can be reduced is 60,375 under nine simulation conditions.

On the sequential topological complexity of group homomorphisms

We define and develop a homotopy invariant notion for the sequential topological complexity of a map f:X→Y, denoted TCr(f), that interacts with TCr(X) and TCr(Y) in the same way Jamie Scott's topological complexity map TC(f) interacts with TC(X) and TC(Y). Furthermore, we apply TCr(f) to studying group homomorphisms ϕ:Γ→Λ.In addition, we give the characterization of cohomological dimension of group homomorphisms.

Intuitive network topology.

Topology is the branch of mathematics that seeks to understand and describe spatial relations. A number of studies have examined the human perception of topology-in particular, whether adults and young children perceive and differentiate objects based on features like closure, boundedness, and emptiness. Topology is about more than "wholes and holes," however; it also offers an efficient language for representing network structure. Topological maps, common for subway systems across the world, are an example of how effective this language can be. Inspired by this idea, here we examine "intuitive network topology." We first show that people readily differentiate objects based on several different features of topological networks. We then show that people both remember and match objects in accordance with their topology, over and above substantial variation in their surface features. These results demonstrate that humans possess an intuitive understanding for the basic topological features of networks, and hint at the possibility that topology may serve as a format for representing relations in the mind. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Railway alignment optimization in regions with densely-distributed obstacles based on semantic topological maps

Railway alignment development in a study area with densely-distributed obstacles, in which regions favorable for alignments are isolated (termed an isolated island effect, i.e., IIE), is a computation-intensive and time-consuming task. To enhance search efficiency and solution quality, an environmental suitability analysis is conducted to identify alignment-favorable regions (AFRs), focusing the subsequent alignment search on these areas. Firstly, a density-based clustering algorithm (DBSCAN) and a specific criterion are customized to distinguish AFR distribution patterns: continuously-distributed AFRs, obstructed effects, and IIEs. Secondly, a study area characterized by IIEs is represented with a semantic topological map (STM), integrating between-island and within-island paths. Specifically, between-island paths are derived through a multi-directional scanning strategy, while within-island paths are optimized using a Floyd-Warshall algorithm. To this end, the intricate alignment optimization problem is simplified into a shortest path problem, tackled with conventional shortest path algorithms (of which Dijkstra’s algorithm is adopted in this work). Lastly, the proposed method is applied to a real case in a mountainous region with karst landforms. Numerical results indicate its superior performance in both construction costs and environmental suitability compared to human designers and a prior alignment optimization method.

Antigenic cartography using variant-specific hamster sera reveals substantial antigenic variation among Omicron subvariants

Severe acute respiratory syndrome Coronavirus 2 (SARS-CoV-2) has developed substantial antigenic variability. As the majority of the population now has pre-existing immunity due to infection or vaccination, the use of experimentally generated animal immune sera can be valuable for measuring antigenic differences between virus variants. Here, we immunized Syrian hamsters by two successive infections with one of nine SARS-CoV-2 variants. Their sera were titrated against 16 SARS-CoV-2 variants, and the resulting titers were visualized using antigenic cartography. The antigenic map shows a condensed cluster containing all pre-Omicron variants (D614G, Alpha, Delta, Beta, Mu, and an engineered B.1+E484K variant) and considerably more diversity among a selected panel of Omicron subvariants (BA.1, BA.2, BA.4/BA.5, the BA.5 descendants BF.7 and BQ.1.18, the BA.2.75 descendant BN.1.3.1, the BA.2-derived recombinants XBB.2 and EG.5.1, and the BA.2.86 descendant JN.1). Some Omicron subvariants were as antigenically distinct from each other as the wildtype is from the Omicron BA.1 variant. Compared to titers measured in human sera, titers in hamster sera are of higher magnitude, show less fold change, and result in a more compact antigenic map topology. The results highlight the potential of sera from hamsters for the continued antigenic characterization of SARS-CoV-2.

Self-organizing maps for exploration and classification of nuclear magnetic resonance spectra for untargeted metabolomics of breast cancer

Metabolomics has emerged as a powerful tool for identifying biomarkers of disease, and nuclear magnetic resonance (NMR) spectroscopy allows for the simultaneous detection of a wide range of metabolites. However, due to complex interactions within metabolic networks, metabolites often exhibit high correlation and collinearity. To address this challenge, self-organizing maps (SOMs) of Kohonen maps and counter propagation-artificial neural networks (CP-ANN) were employed in this study to model proton nuclear magnetic resonance spectroscopic (1HNMR) data from control samples and breast cancer (BC) patients. Blood serum samples from a control group (n=24) and BC patients (n=18) were used to extract metabolites using methanol and chloroform solvents in optimum extraction conditions. The 1HNMR data was preprocessed by performing phase, baseline, and shift corrections. Subsequently, the preprocessed data was modeled using Kohonen network as an unsupervised technique and CP-ANN as a supervised technique. In this regard, the model built with CP-ANN successfully distinguished between the two classes with an accuracy of 100 % for both group and sensitivity of 96 % and 100 % for control group and BC patients, respectively. Additionally, CP-ANN algorithm demonstrated predictive capabilities by accurately classifying test samples with 90 % sensitivity, 98 % specificity, and 96 % accuracy for control group and 100 % sensitivity, 90 % specificity, and 96 % accuracy for BC patients. Furthermore, analysis of the resulting topological map revealed 14 significant variables (biomarkers) such as sarcosine, lysine, trehalose, tryptophan, and betaine that effectively differentiated between healthy individuals and BC patients.

Multi-threshold image segmentation using new strategies enhanced whale optimization for lupus nephritis pathological images

Lupus Nephritis (LN) has been considered as the most prevalent form of systemic lupus erythematosus. Medical imaging plays an important role in diagnosing and treating LN, which can help doctors accurately assess the extent and extent of the lesion. However, relying solely on visual observation and judgment can introduce subjectivity and errors, especially for complex pathological images. Image segmentation techniques are used to differentiate various tissues and structures in medical images to assist doctors in diagnosis. Multi-threshold Image Segmentation (MIS) has gained widespread recognition for its direct and practical application. However, existing MIS methods still have some issues. Therefore, this study combines non-local means, 2D histogram, and 2D Renyi’s entropy to improve the performance of MIS methods. Additionally, this study introduces an improved variant of the Whale Optimization Algorithm (GTMWOA) to optimize the aforementioned MIS methods and reduce algorithm complexity. The GTMWOA fusions Gaussian Exploration (GE), Topology Mapping (TM), and Magnetic Liquid Climbing (MLC). The GE effectively amplifies the algorithm’s proficiency in local exploration and quickens the convergence rate. The TM facilitates the algorithm in escaping local optima, while the MLC mechanism emulates the physical phenomenon of MLC, refining the algorithm’s convergence precision. This study conducted an extensive series of tests using the IEEE CEC 2017 benchmark functions to demonstrate the superior performance of GTMWOA in addressing intricate optimization problems. Furthermore, this study executed an experiment using Berkeley images and LN images to verify the superiority of GTMWOA in MIS. The ultimate outcomes of the MIS experiments substantiate the algorithm’s advanced capabilities and robustness in handling complex optimization problems.

A DWT-Based Approach with Gradient Analysis for Robust and Blind Medical Image Watermarking

The growing adoption of telemedicine necessitates robust security measures for medical images during transmission. This paper proposes a novel blind watermarking system for medical images that utilizes both image gradients and the Discrete Wavelet Transform (DWT). Image gradients, acting as spatial derivatives, provide a “topological map” of the image, aiding in the identification of areas susceptible to disruption. The DWT, with its multi-resolution analysis, offers a favorable balance between robustness and imperceptibility. The proposed method embeds the watermark within the low–low band (LL) of the DWT-decomposed image, specifically in 3 × 3 block regions selected based on gradient information. The mathematical relationships between the gradient’s direction and magnitude are employed to extract the corresponding blocks and their codes adequately. These codes are then XORed with the watermark and embedded into the chosen blocks using the least significant bit (LSB) technique. Extensive experimentation on a medical image dataset evaluates the system’s performance against some attacks like filtering, noise, and scaling. The results demonstrate the efficacy of the proposed approach in hiding information while ensuring the security and integrity of watermarked medical images.

Dynamic community detection algorithm based on hyperbolic graph convolution

PurposeCommunity detection is a key factor in analyzing the structural features of complex networks. However, traditional dynamic community detection methods often fail to effectively solve the problems of deep network information loss and computational complexity in hyperbolic space. To address this challenge, a hyperbolic space-based dynamic graph neural network community detection model (HSDCDM) is proposed.Design/methodology/approachHSDCDM first projects the node features into the hyperbolic space and then utilizes the hyperbolic graph convolution module on the Poincaré and Lorentz models to realize feature fusion and information transfer. In addition, the parallel optimized temporal memory module ensures fast and accurate capture of time domain information over extended periods. Finally, the community clustering module divides the community structure by combining the node characteristics of the space domain and the time domain. To evaluate the performance of HSDCDM, experiments are conducted on both artificial and real datasets.FindingsExperimental results on complex networks demonstrate that HSDCDM significantly enhances the quality of community detection in hierarchical networks. It shows an average improvement of 7.29% in NMI and a 9.07% increase in ARI across datasets compared to traditional methods. For complex networks with non-Euclidean geometric structures, the HSDCDM model incorporating hyperbolic geometry can better handle the discontinuity of the metric space, provides a more compact embedding that preserves the data structure, and offers advantages over methods based on Euclidean geometry methods.Originality/valueThis model aggregates the potential information of nodes in space through manifold-preserving distribution mapping and hyperbolic graph topology modules. Moreover, it optimizes the Simple Recurrent Unit (SRU) on the hyperbolic space Lorentz model to effectively extract time series data in hyperbolic space, thereby enhancing computing efficiency by eliminating the reliance on tangent space.

The Art of Internet Mapping: A Comprehensive Guide to Regional Internet Topology Mapping at the Autonomous System Level

Background: Internet topology is studied more by researchers on global internet coverage compared to limited regional coverage. However, some studies also see the importance of studying internet topology in certain countries or regions. The internet performance of a country or region can be influenced by the structure of its internet topology, and research on internet topology can contribute to improving internet topology in that region. Objective: This research initially carried out internet topology mapping in a limited region, then used experience from each step in conducting internet topology mapping to create a comprehensive guide on procedures for internet topology mapping at the autonomous system (AS) level in certain regional areas. Methods: Internet topology mapping is carried out by inferring relationships between ASes through an inference process against border gateway protocol (BGP) table dumps, while the internet topology mapping method chosen is passive mapping. Results: The entire series of steps involved in the regional internet topology mapping process have been successfully outlined in a detailed guide as a result of this research. Evaluation of the research results was carried out by implementing the application of this comprehensive guide and also through assessments from experts in related fields regarding the results of this research. The results of both evaluations showed that the research results were appropriate. Conclusion: This research provides a comprehensive guide for mapping internet topology in specific regional areas, consisting of nine sequential steps grouped into four major steps. This guide can be used to assist similar research efforts in other regional areas as well as provide further knowledge regarding studies in this field. This research is different from previous studies, because it provides a comprehensive guide to the internet topology mapping process, which has not been available in previous studies. Keywords: Internet Topology Mapping, Regional Internet Topology, Autonomous System, Border Gateway Protocol

Sieci neuronowe do mapowania archeologicznych artefaktów litowych

An analytical non-destructive strategy to chemically characterize lithic artefacts has been developed. Around 100 archaeological lithic materials found in Neolithic-Chalcolithic sites in the Mediterranean region of the Iberian Peninsula and nowadays stored in different museums of the Valencian Community (Spain), were studied. The materials belong to different typologies of rock (diabase, sillimanite, ophite and amphibolite) and were analysed employing portable energy dispersive X-ray fluorescence spectroscopy (pXRF) directly in the rock surface. The obtained data were processed through neural networks protocol, specifically the so-called Kohonen networks or Self Organised Maps (SOM), to map the geologic samples. This self-organized topological feature maps are suitable to deal with multidimensional representations and map them in a two-dimensional space of neurons, following an unsupervised learning protocol. SOM is used to reduce multidimensional data onto lower-dimensional spaces and clustering procedures. As a result, SOM create spatially organized representations, which enhance the discovery of correlations between data. In this case the method has enabled the evaluation of elemental markers related to each rock type behaving as a fine hidden pattern detector and so understand the possible advantages and disadvantages of the analytical method employed to define provenance issues. The attribution suggested by statistics is mainly driven by the composition of rocks essential minerals which are linked to the different petrogenetic conditions. The results showed that in most of the cases the distribution and dispersion of the chemical profile depend of the kind of rock, and clearly suggest that a good way to identify stone tools raw material procurement is to look for elemental markers, being the prior step to create an approximation to ancient exchange networks and their evolution in a diachronic axis.