Topological Point Cloud Clustering

We present Topological Point Cloud Clustering (TPCC), a new method to cluster points in an arbitrary point cloud based on their contribution to global topological features. TPCC synthesizes desirable features from spectral clustering and topological data analysis and is based on considering the spectral properties of a simplicial complex associated to the considered point cloud. As it is based on considering sparse eigenvector computations, TPCC is similarly easy to interpret and implement as spectral clustering. However, by focusing not just on a single matrix associated to a graph created from the point cloud data, but on a whole set of Hodge-Laplacians associated to an appropriately constructed simplicial complex, we can leverage a far richer set of topological features to characterize the data points within the point cloud and benefit from the relative robustness of topological techniques against noise. We test the performance of TPCC on both synthetic and real-world data and compare it with classical spectral clustering

Non-isotropic Persistent Homology: Leveraging the Metric Dependency of PH

Persistent Homology is a widely used topological data analysis tool that creates a concise description of the topological properties of a point cloud based on a specified filtration. Most filtrations used for persistent homology depend (implicitly) on a chosen metric, which is typically agnostically chosen as the standard Euclidean metric on $\mathbb{R}^n$. Recent work has tried to uncover the 'true' metric on the point cloud using distance-to-measure functions, in order to obtain more meaningful persistent homology results. Here we propose an alternative look at this problem: we posit that information on the point cloud is lost when restricting persistent homology to a single (correct) distance function. Instead, we show how by varying the distance function on the underlying space and analysing the corresponding shifts in the persistence diagrams, we can extract additional topological and geometrical information. Finally, we numerically show that non-isotropic persistent homology can extract information on orientation, orientational variance, and scaling of randomly generated point clouds with good accuracy and conduct some experiments on real-world data.Comment: 30 pages, 17 figures, comments welcome

Dilution versus pollution in watercourses affected by acid mine drainage: a graphic model for the Iberian Pyrite Belt (SW Spain)

The aim of this study was to chemically characterize the water quality impacts of the 88 acid mine drainage (AMD) generating mines in the Spanish sector of the Iberian Pyrite Belt (IPB). This was necessary because the Water Framework Directive of the European Union and the hydrological plans of the Tinto, Odiel, and Piedras river basins require that water quality be improved enough to allow at least some of the rivers in the IPB to sustain healthy fish populations by 2027. The results indicate a clear decrease in metals, arsenic, and sulfate concentrations and increased pH between the AMD-sources and the river channels.info:eu-repo/semantics/publishedVersio

Effective growth of matter density fluctuations in the running LCDM and LXCDM models

We investigate the matter density fluctuations \delta\rho/\rho for two dark energy (DE) models in the literature in which the cosmological term \Lambda is a running parameter. In the first model, the running LCDM model, matter and DE exchange energy, whereas in the second model, the LXCDM model, the total DE and matter components are conserved separately. The LXCDM model was proposed as an interesting solution to the cosmic coincidence problem. It includes an extra dynamical component, the "cosmon" X, which interacts with the running \Lambda, but not with matter. In our analysis we make use of the current value of the linear bias parameter, b^2(0)= P_{GG}/P_{MM}, where P_{MM} ~ (\delta\rho/\rho)^2 is the present matter power spectrum and P_{GG} is the galaxy fluctuation power spectrum. The former can be computed within a given model, and the latter is found from the observed LSS data (at small z) obtained by the 2dF galaxy redshift survey. It is found that b^2(0)=1 within a 10% accuracy for the standard LCDM model. Adopting this limit for any DE model and using a method based on the effective equation of state for the DE, we can set a limit on the growth of matter density perturbations for the running LCDM model, the solution of which is known. This provides a good test of the procedure, which we then apply to the LXCDM model in order to determine the physical region of parameter space, compatible with the LSS data. In this region, the LXCDM model is consistent with known observations and provides at the same time a viable solution to the cosmic coincidence problem.Comment: LaTeX, 38 pages, 8 figures. Version accepted in JCA

Perturbations in the relaxation mechanism for a large cosmological constant

Recently, a mechanism for relaxing a large cosmological constant (CC) has been proposed [arxiv:0902.2215], which permits solutions with low Hubble rates at late times without fine-tuning. The setup is implemented in the LXCDM framework, and we found a reasonable cosmological background evolution similar to the LCDM model with a fine-tuned CC. In this work we analyse analytically the perturbations in this relaxation model, and we show that their evolution is also similar to the LCDM model, especially in the matter era. Some tracking properties of the vacuum energy are discussed, too.Comment: 18 pages, LaTeX; discussion improved, accepted by CQ

FRCM-to-masonry bonding behaviour in the case of curved surfaces: Experimental investigation

Fabric-reinforced cementitious matrix (FRCM) are composite materials more and more used for the reinforcement of masonry structures. The combination of high tensile strength fabrics (or meshes) with cementitious matrices, having good thixotropic capabilities and vapour permeability, makes such composites suitable for reinforcing a large number of masonry structures, including the one belonging to the historic heritage. FRCMs are bonded to the outer surfaces of structural masonry elements and, thanks to their adhesive capacity, bear much of the tensile stresses that unreinforced masonry cannot withstand. The effectiveness of such reinforcements, which is highly dependent on their ability to adhere to the masonry substrate, is generally investigated throughout specific experimental investigations (shear tests). Almost all the papers in the literature devoted to bond-slip analysis refer to the case of flat bonding surfaces, although these reinforcements are also widely used on curved structural elements such as arches and vaults. Therefore, this paper reports and examines the results of an extensive experimental program concerning the behavior of FRCM systems applied on curved masonry specimens. The results point out the influence of both curvature and reinforcement position (intrados or extrados) on the response of specimens in terms of bearing capacity, failure mode and post-peak response

Different formation routes of pore structure in aluminum powder metallurgy alloy

In powder metallurgy (PM), severe plastic deformation (SPD) is a well-known technological solution to achieve interesting properties. However, the occurrence of pores in the final product may limit these properties. Also, for a given type of microstructure, the stereometric parameters of the pore structures, such as shape (represented by Aspect and Dcircle) and distribution (fshape, and fcircle), decisively affect the final properties. The influence of different processing routes (pressing, sintering and equal channel angular pressing (ECAP)) on pore structures in an aluminum PMalloy is discussed. The nature of porosity, porosity evolution and its behavior is explored. The correlation between pore size and morphology is also considered. The final pore structure parameters (Aspect, Dcircle, fshape, and fcircle) of studied aluminum alloys produced by different processing routes depends on the different formation routes

The operationalized psychodynamic diagnostics system. Clinical relevance, reliability and validity

In this paper, we present a multiaxial system for psychodynamic diagnosis, which has attained wide usage in Germany in the last 10 years. First we will discuss the 4 operationalized psychodynamic diagnostics (OPD) axes: illness experience and treatment assumptions, relationships, mental conflicts, and structure, then clinical applications will be outlined. Focus psychodynamic formulations can be employed both with inpatients and with outpatients. Studies show good reliability in a research context and acceptable reliability for clinical purposes. Validity will be separately summarized as content, criterion, and construct validity. Validity studies indicate good validity for the individual axes. Numerous studies on the OPD indicate areas of possible improvement, for example for clinical purposes the OPD should be more practically formulated

Signal Processing on Product Spaces

We establish a framework for signal processing on product spaces of simplicial and cellular complexes. For simplicity, we focus on the product of two complexes representing time and space, although our results generalize naturally to products of simplicial complexes of arbitrary dimension. Our framework leverages the structure of the eigenmodes of the Hodge Laplacian of the product space to jointly filter along time and space. To this end, we provide a decomposition theorem of the Hodge Laplacian of the product space, which highlights how the product structure induces a decomposition of each eigenmode into a spatial and temporal component. Finally, we apply our method to real world data, specifically for interpolating trajectories of buoys in the ocean from a limited set of observed trajectories