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The simplicial volume is a homotopy invariant of manifolds introduced by Gromov in his pioneering paper The first aim of this paper is to lay the foundation of the theory of multicomplexes. After setting the main definitions, we construct the singular multicomplex In the second part of this work we apply the theory of multicomplexes to the study of the bounded cohomology of topological spaces. Our constructions and arguments culminate in the complete proofs of Gromov’s Mapping Theorem (which implies in particular that the bounded cohomology of a space only depends on its fundamental group) and of Gromov’s Vanishing Theorem, which ensures the vanishing of the simplicial volume of closed manifolds admitting an amenable cover of small multiplicity. The third and last part of the paper is devoted to the study of locally finite chains on non-compact spaces, hence to the simplicial volume of open manifolds. We expand some ideas of Gromov to provide detailed proofs of a criterion for the vanishing and a criterion for the finiteness of the simplicial volume of open manifolds. As a by-product of these results, we prove a criterion for the

Context A chemical reaction can be described, from a physicochemical perspective, as a redistribution of electron density. Additionally, non-covalent interactions locally modify the electron density distribution. This study aims to characterize the modification of reactivity caused by the presence of non-covalent interactions such as hydrogen bonds, in a reaction involving the formation of two bonds and the breaking of two others: CH₃COOH + NH₂CH₃ → CH₃CONHCH₃. Methods In this work, we will follow the how a reaction mechanism involving the formation of two chemical bonds and the breaking of two other chemical bonds is affected by non-covalent interaction. To this end, the reaction force will be used to define the region of the reagents, the region of the transition state, and the region of the products. We will analyze the redistributions of electron density and electron pairs in each of the regions of the reaction mechanisms, using QTAIM and ELF, topological analyses, respectively, for the reaction between methylamine and acetic acid, in the presence of 0 to 4 water molecules. DFT calculations were carried out at the LC-ωPBE/6–311 + + G(d,p) + GD3BJ level along the intrinsic reaction coordinate of the one-step reaction leading to the formation of methylacetamide.

In this paper, time changes of the Brownian motions on generalized Sierpinski carpets including

This is the first of two volumes dedicated to the centennial of the distinguished mathematician Selim Grigorievich Krein. The companion volume is Contemporary Mathematics, Volume 734.Krein was a major contributor to functional analysis, operator theory, partial differential equations, fluid dynamics, and other areas, and the author of several influential monographs in these areas. He was a prolific teacher, graduating 83 Ph.D. students. Krein also created and ran, for many years, the annual Voronezh Winter Mathematical Schools, which significantly influenced mathematical life in the former Soviet Union.The articles contained in this volume are written by prominent mathematicians, former students and colleagues of Selim Krein, as well as lecturers and participants of Voronezh Winter Schools. They are devoted to a variety of contemporary problems in functional analysis, operator theory, several complex variables, topological dynamics, and algebraic, convex, and integral geometry.

AbstractCurrent research fields of metal-organic frameworks (MOFs), which are being developed in the last 5-10 years by Russian scientific institutions and universities, are generalized. The review encompasses the design, synthesis, topological description, and prediction of MOF properties, the development of methods for their chemical engineering and modification, their investigation by modern physicochemical techniques, and the creation of functional materials based on porous frameworks (heterogeneous catalysts, highly efficient and highly selective sorbents of the new generation, conducting materials, systems for the target drug delivery).

Morphological hierarchies constitute a rich and powerful family of graph-based structures that can be used for image modeling, processing and analysis. In this article, we focus on an important subfamily of morphological hierarchies, namely the trees that model partial partitions of the image support. This subfamily includes in particular the component-tree and the tree of shapes. In this context, we provide some new graph-based structures (one directed acyclic graph and three trees): the graph of valued shapes, the tree of valued shapes, the complete tree of shapes and the topological tree of shapes. These new objects create a continuum between the two notions of component-tree and tree of shapes. In particular, they allow to establish that these two trees (together with a third notion of adjacency tree generally considered in topological image analysis) can be defined and handled in a unified framework. In addition, this framework enables to enrich the component-tree with additional information, leading on the one hand to a topological description of grey-level images that relies on the same paradigm as persistent homology, and on the other hand to the proposal of a topological version of tree of shapes. This article provides a theoretical analysis of these new morphological hierarchies and their links with the usual ones. It also proposes an algorithmic description of two ways of building these new morphological hierarchies, and a discussion on the links that exist between these morphological hierarchies and certain topological invariants and descriptors.

The pore geometry and topology properties of pore space in rocks are significant for a better understanding of the complex hydrologic and elastic properties. However, geometry and topology information about the sandstone pore structures is not fully available. In this study, we obtained the topological and geometrical pore parameters from a representative elementary volume (REV) for fluid flow in sandstone samples. For comparison, eight types of sandstones with various porosities were studied based on the X-ray micro-computed tomography technique. In this study, the REV size was selected based on the parameters from the respective pore network models (PNM), not just the porosity. Our analysis indicates that despite different porosity, all the sandstone samples have highly triangular-shaped pores and a high degree of pore structural isotropy. The high porosity group sandstones exhibit wider ranges of pore sizes than the low porosity group sandstones. Compared to the high porosity group sandstones, the low porosity group sandstones samples showing a higher global aspect ratio, indicating some pores exist in the form of bottlenecks. The pore topological properties of different sandstones show a high dependence of the porosity. The high porosity group sandstones obtain large coordination numbers, large connectivity densities and low tortuosities. The results from this study will help better understand the complex pore structure and the fluid flow in sandstone.

The structural properties and thermal stability of Si-doped amorphous indium oxide (ISO) were investigated via experimental characterization and computational modeling techniques. The total structure factors, S ( Q ), and reduced pair distribution functions, G ( r ), were calculated for both annealed and pristine ISO samples, revealing the distinct structural features induced by Si doping and thermal treatment. Although the pristine ISO samples exhibited halo patterns indicative of an amorphous structure, annealing at 600 °C led to pronounced Bragg peaks, suggesting that the sample was crystallized. However, an ISO with a higher Si content (20 at%) retained its amorphous structure even after annealing, highlighting the role of Si-doping in enhancing the thermal stability. Classical molecular dynamics–reverse Monte Carlo simulations were employed to elucidate the structure of pristine ISO samples, revealing good agreement with the experimental data. Furthermore, the partial structure factors, S ij ( Q ), and partial pair distribution functions, g ij ( r ) demonstrate the influence of Si doping on atomic correlations and density changes in the ISO. Polyhedral connectivity analysis suggests that the fraction changes of edge sharing due to Si doping affect the thermal stability of ISO and that SiO 4 tetrahedra play a crucial role in inhibiting crystallization.

Expert determination of the third molar maturity index (I3M) constitutes one of the most common approaches for dental age estimation. This work aimed to investigate the technical feasibility of creating a decision-making tool based on I3M to support expert decision-making. Methods: The dataset consisted of 456 images from France and Uganda. Two deep learning approaches (Mask R-CNN, U-Net) were compared on mandibular radiographs, leading to a two-part instance segmentation (apical and coronal). Then, two topological data analysis approaches were compared on the inferred mask: one with a deep learning component (TDA-DL), one without (TDA). Regarding mask inference, U-Net had a better accuracy (mean intersection over union metric (mIoU)), 91.2% compared to 83.8% for Mask R-CNN. The combination of U-Net with TDA or TDA-DL to compute the I3M score revealed satisfying results in comparison with a dental forensic expert. The mean ± SD absolute error was 0.04 ± 0.03 for TDA, and 0.06 ± 0.04 for TDA-DL. The Pearson correlation coefficient of the I3M scores between the expert and a U-Net model was 0.93 when combined with TDA and 0.89 with TDA-DL. This pilot study illustrates the potential feasibility to automate an I3M solution combining a deep learning and a topological approach, with 95% accuracy in comparison with an expert.

•The dynamic functional network framework overlooks the continuous impact of non-dynamic dependencies, which dominants the fluctuations of regional correlations, within its connection measurements resulting in a relatively stable spatiotemporal pattern to model the communication process in the human brain.•We propose the activation network framework based on the functional connectivity activity, capturing the potential time-specific dependency fluctuations, to establish a new spatiotemporal pattern of brain network.•The activation network reveals a different spatiotemporal connection mode that presents a more effective connectivity pattern with temporal evolution, largely invisible to the dynamic functional network.•The successful application of this approach to autism spectrum disorders and coronavirus disease classification demonstrates its feasibility for extracting communication dynamics. Dynamic functional networks (DFN) have considerably advanced modelling of the brain communication processes. The prevailing implementation capitalizes on the system and network-level correlations between time series. However, this approach does not account for the continuous impact of non-dynamic dependencies within the statistical correlation, resulting in relatively stable connectivity patterns of DFN over time with limited sensitivity for communication dynamic between brain regions. Here, we propose an activation network framework based on the activity of functional connectivity (AFC) to extract new types of connectivity patterns during brain communication process. The AFC captures potential time-specific fluctuations associated with the brain communication processes by eliminating the non-dynamic dependency of the statistical correlation. In a simulation study, the positive correlation (r=0.966,p<0.001) between the extracted dynamic dependencies and the simulated \"ground truth\" validates the method's dynamic detection capability. Applying to autism spectrum disorders (ASD) and COVID-19 datasets, the proposed activation network extracts richer topological reorganization information, which is largely invisible to the DFN. Detailed, the activation network exhibits significant inter-regional connections between function-specific subnetworks and reconfigures more efficiently in the temporal dimension. Furthermore, the DFN fails to distinguish between patients and healthy controls. However, the proposed method reveals a significant decrease (p<0.05) in brain information processing abilities in patients. Finally, combining two types of networks successfully classifies ASD (83.636 % ± 11.969 %,mean±std) and COVID-19 (67.333 % ± 5.398 %). These findings suggest the proposed method could be a potential analytic framework for elucidating the neural mechanism of brain dynamics.