Non-affine response: jammed packings versus spring networks

We compare the elastic response of spring networks whose contact geometry is derived from real packings of frictionless discs, to networks obtained by randomly cutting bonds in a highly connected network derived from a well-compressed packing. We find that the shear response of packing-derived networks, and both the shear and compression response of randomly cut networks, are all similar: the elastic moduli vanish linearly near jamming, and distributions characterizing the local geometry of the response scale with distance to jamming. Compression of packing-derived networks is exceptional: the elastic modulus remains constant and the geometrical distributions do not exhibit simple scaling. We conclude that the compression response of jammed packings is anomalous, rather than the shear response.Comment: 6 pages, 6 figures, submitted to ep

Unlabeled sample compression schemes and corner peelings for ample and maximum classes

We examine connections between combinatorial notions that arise in machine learning and topological notions in cubical/simplicial geometry. These connections enable to export results from geometry to machine learning. Our first main result is based on a geometric construction by Tracy Hall (2004) of a partial shelling of the cross-polytope which can not be extended. We use it to derive a maximum class of VC dimension 3 that has no corners. This refutes several previous works in machine learning from the past 11 years. In particular, it implies that all previous constructions of optimal unlabeled sample compression schemes for maximum classes are erroneous. On the positive side we present a new construction of an unlabeled sample compression scheme for maximum classes. We leave as open whether our unlabeled sample compression scheme extends to ample (a.k.a. lopsided or extremal) classes, which represent a natural and far-reaching generalization of maximum classes. Towards resolving this question, we provide a geometric characterization in terms of unique sink orientations of the 1-skeletons of associated cubical complexes

A very efficient RCS data compression and reconstruction technique, volume 4

A very efficient compression and reconstruction scheme for RCS measurement data was developed. The compression is done by isolating the scattering mechanisms on the target and recording their individual responses in the frequency and azimuth scans, respectively. The reconstruction, which is an inverse process of the compression, is granted by the sampling theorem. Two sets of data, the corner reflectors and the F-117 fighter model, were processed and the results were shown to be convincing. The compression ratio can be as large as several hundred, depending on the target's geometry and scattering characteristics

The stochastic geometry of unconstrained one-bit data compression

A stationary stochastic geometric model is proposed for analyzing the data compression method used in one-bit compressed sensing. The data set is an unconstrained stationary set, for instance all of $\mathbb{R}^n$ or a stationary Poisson point process in $\mathbb{R}^n$. It is compressed using a stationary and isotropic Poisson hyperplane tessellation, assumed independent of the data. That is, each data point is compressed using one bit with respect to each hyperplane, which is the side of the hyperplane it lies on. This model allows one to determine how the intensity of the hyperplanes must scale with the dimension $n$ to ensure sufficient separation of different data by the hyperplanes as well as sufficient proximity of the data compressed together. The results have direct implications in compressive sensing and in source coding.Comment: 29 page

Coding and Compression of Three Dimensional Meshes by Planes

The present paper suggests a new approach for geometric representation of 3D spatial models and provides a new compression algorithm for 3D meshes, which is based on mathematical theory of convex geometry. In our approach we represent a 3D convex polyhedron by means of planes, containing only its faces. This allows not to consider topological aspects of the problem (connectivity information among vertices and edges) since by means of the planes we construct the polyhedron uniquely. Due to the fact that the topological data is ignored this representation provides high degree of compression. Also planes based representation provides a compression of geometrical data because most of the faces of the polyhedron are not triangles but polygons with more than three vertices.Comment: 10 pages, 7 figure

The ring compression test: Analysis of dimensions and canonical geometry

The compression ring test is universally accepted as a perfectly valid method by which determine simply and reliably the adhesion friction factor in a plastic deformation process. Its methodology is based on the application of geometric changes as both the reduction in thickness as the decrease in bore inner diameter in the strained ring itself. In this paper the performance of that test is the basis for establishing the coefficient of friction on a forging process so that, given this, its application to Upper Bound Theorem (UBT) by model Triangular Rigid Zones (TRZ), enable the establishment an intercomparison with empirical force, reaching a cuasivalidation of this Theorem in a certain range.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tec