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Abstract: In this paper we provide an analytical description of various classes of digital circles, spheres and in some cases hyperspheres, defined in a morphological framework. The topological properties of these objects, especially the separation of the digital space, are discussed according to the shape of the structuring element. The proposed framework is generic enough so that it encompasses most of the digital circle definitions that appear in the literature and extends them to dimension and sometimes dimension . [Copyright &y& Elsevier]

Abstract: Several tests to assess skin sensitization hazard are in peer-review for pre-validation. These tests, as well as the animal tests they aim to replace, were developed (and validated) for the testing of pure substances. However, in the cosmetic field, active ingredients are often mixtures from natural sources. It is therefore important to understand which tests could be used to evaluate their safety. Here we describe a proof-of-concept study to test whether the KeratinoSens™ assay is able to detect sensitizing constituents within botanical mixtures. Four extracts were spiked with different doses of the sensitizers citral, cinnamic aldehyde and isoeugenol. The tested extracts were negative in the test whereas they became positive in most cases when spiked with the sensitizers. Analysis of the results from the samples spiked with different doses allowed the determination of the minimal level of sensitizers being detectable. The contribution to sensitization potential of doses of 2% and above of the spiked sensitizers were reliably detected. There were limitations for an extract with high cytotoxicity, in which case detection of the artificially spiked sensitizers proved difficult. This study gives a proof of principle for testing of mixtures in the KeratinoSens™ assay and indicates how sensitive the assay is to detect minor components with sensitizing potential. [Copyright &y& Elsevier]

Abstract: In this paper, we study the relationship between Euclidean and discrete space. We study discrete operations based on Euclidean functions: discrete smooth scaling and discrete-continuous rotation. Conversely, we study Euclidean operations based on discrete functions: the discrete based simplification, the Euclidean-discrete union and the Euclidean-discrete co-refinement. These operations operate partly in discrete, and partly in continuous space. Especially for the discrete smooth scaling operation, we provide error bounds when such different operations are chained. [Copyright &y& Elsevier]

Abstract: The aim of this paper is to show that the supercover of an -flat (i.e. a Euclidean affine subspace of dimension ) in Euclidean -space is a discrete analytical object. The supercover of a Euclidean object is a discrete object consisting of all the voxels that intersect . A discrete analytical object is a set of discrete points that is defined by a finite set of inequalities. A method to determine the inequalities defining the supercover of an -flat is provided. [Copyright &y& Elsevier]

In this paper, we present a new implementation of the Ridgelet transform based on discrete analytical 2-D lines: the discrete analytical Ridgelet transform (DART). This transform uses the Fourier strategy for the computation of the associated discrete Radon transform. The innovative step of the DART is the construction of discrete analytical lines in the Fourier domain. These discrete analytical lines have a parameter called arithmetical thickness, allowing us to define a DART adapted to a specific application. Indeed, the DART representation is not orthogonal it is associated with a flexible redundancy factor. The DART has a very simple forward/inverse algorithm that provides an exact reconstruction. We apply the DART and its extension to a local-DART (with smooth windowing) to the denoising of some images. These experimental results show that the simple thresholding of the DART coefficients is competitive or more effective than the classical denoising techniques. [Copyright &y& Elsevier]

In this paper we study discretizations of objects in higher dimensions. We introduce a large class of object discretizations, called k-discretizations. This class is natural and quite general, including as special cases some known discretizations, like the standard covers and the naive discretizations. Various results are obtained in the proposed general setting. [Copyright &y& Elsevier]

We investigated the commercially available Episkin LM™ reconstructed epidermis test system as a potential 3D model for human genotoxicity assessment by cytokinesis-block micronucleus assay to mitigate limitations of the currently accepted micronucleus test. We established appropriate culture conditions for cytokinesis-block micronucleus assay in maximizing the frequency of binucleated cells by choice of culture medium and calibration of the system exposure to the cytokinesis inhibitor Cytochalasin B, without affecting the basal frequency of micronuclei in the model. We confirmed that the application of the classic solvents had no significant effect on this basal level of micronuclei. We determined the performance of cytokinesis-block micronucleus assay in Episkin LM™ reconstructed epidermis to predict in vivo genotoxins by testing the genotoxicity potential of 17 well known in vivo genotoxic, progenotoxic and non-genotoxic reference chemicals over a 48 h and 72 h exposure period. We found that cytokinesis-block micronucleus assays in Episkin™ reconstructed epidermis following the 48 h-topical regimen had a specificity of 60–75% and a sensitivity of 83–85%, resulting in an overall accuracy of 76–82% for genotoxicity assessment in tissues depending on the assessment of the reference chemicals with equivocal genotoxic profiles in the literature. The positive micronucleus test results obtained without addition of any exogenous metabolic activation system confirmed the ability of Episkin LM™ reconstructed epidermis to intrinsically bioactivate progenotoxic chemicals. The evidence showed that the 72-h exposure protocol significantly improved the detection of progenotoxins. Taken together, our data demonstrated that the Episkin LM™ reconstructed epidermis system is a relevant in vitro tool in the study of genetic toxicology. [ABSTRACT FROM AUTHOR]

• The body centered cubic grid is a viable alternative to the cubic grid. • A coordinate system provides one to one correspondence with the cubic grid. • Discrete analytical planes and spheres defined through double Diophantine inequalities. • Topological separation and connectivity properties depend on the chosen thickness. • Discrete analytical lines defined as the intersection of up to six plane. We propose a characterization of discrete analytical spheres, planes and lines in the body-centered cubic (BCC) grid, both in the Cartesian and in the recently proposed alternative compact coordinate system, in which each integer triplet addresses some voxel in the grid. We define spheres and planes through double Diophantine inequalities and investigate their relevant topological features, such as functionality or the interrelation between the thickness of the objects and their connectivity and separation properties. We define lines as the intersection of planes. The number of the planes (up to six) is equal to the number of the pairs of faces of a BCC voxel that are parallel to the line. [ABSTRACT FROM AUTHOR]

Abstract: In this article, we describe the theoretical foundations of the -arithmetization. This method provides a multi-scale discretization of a continuous function that is a solution of a differential equation. This discretization process is based on the Harthong–Reeb line . The Harthong–Reeb line is a linear space that is both discrete and continuous. This strange line stems from a nonstandard point of view on arithmetic based, in this paper, on the concept of -numbers introduced by Laugwitz and Schmieden. After a full description of this nonstandard background and of the first properties of , we introduce the -arithmetization and we apply it to some significant examples. An important point is that the constructive properties of our approach leads to algorithms which can be exactly translated into functional computer programs without uncontrolled numerical error. Afterwards, we investigate to what extent fits Bridges’s axioms of the constructive continuum. Finally, we give an overview of a formalization of the Harthong–Reeb line with the Coq proof assistant. [Copyright &y& Elsevier]

Abstract: Removal and contraction are basic operations for several methods conceived in order to handle irregular image pyramids, for multi-level image analysis for instance. We give the definitions of removal and contraction operations in the generalized maps framework. We propose a first experimentation of irregular pyramid as a basis for a discrete geometrical modeler that can handle both discrete and continuous representations of geometrical objects. This modeler is based on a pyramidal kernel with four coexisting level between the discrete and the Euclidean representations. We describe how this pyramid can be constructed and updated. [Copyright &y& Elsevier]