Being its major component, aggregate can occupy up to three-quarter of the volume of concrete. The structure of aggregate formed in hardened state impacts largely on mechanical and durability properties of concrete. On another hand, physical characteristics of aggregate are primarily assumed to be relevant to granular behavior of aggregate. Therefore, characterization of aggregate is of high re...

Cubical type theory provides a constructive justification of homotopy theory. A crucial ingredient cubical is path lifting operation which explained computationally by induction on the involving several non-canonical choices. We present in this article two canonicity results, both proved sconing argument: result, every natural number equal to numeral, even if we take away equations defining str...

We present a cubical type theory based on the Cartesian cube category (faces, degeneracies, symmetries, diagonals, but no connections or reversal) with univalent universes, each containing Π, Σ, path, identity, natural number, boolean, pushout, and glue (equivalence extension) types. The type theory includes a syntactic description of a uniform Kan operation, along with judgemental equality rul...

In homotopy type theory (HoTT), higher inductive types provide a means of defining and reasoning about higher-dimensional objects such as circles and tori. The formulation of a schema for such types remains a matter of current research. We investigate the question in the context of cubical type theory, where the homotopical structure implicit in HoTT is made explicit in the judgmental apparatus...

We present two methods for non-rigid shape matching. Both methods formulate shape matching as an energy minimization problem, where the energy measures distortion of the metric defined on the shapes in one case, or directly describes the physical deformation relating the two shapes in the other case. The first method considers a parametrized relaxation of the widely adopted quadratic assignment...

We associate to any (strict) multiple category C three homology theories : the rst one is called the globular homology and it contains the oriented loops of C ; both other ones are called corner homology, the negative one and the positive one, which contain the corners included in C. We make explicit the link between these homology theories and the homotopy of paths in multiple category. We con...

Cohomology groups and the cohomology ring of threedimensional (3D) objects are topological invariants that characterize holes and their relations. Cohomology ring has been traditionally computed on simplicial complexes. Nevertheless, cubical complexes deal directly with the voxels in 3D images, no additional triangulation is necessary. This could facilitate efficient algorithms for the computat...

We introduce a deformed product construction for simple polytopes in terms of lowertriangular block matrix representations. We further show how Gale duality can be employed for the construction and for the analysis of deformed products such that specified faces (e.g. all the k-faces) are “strictly preserved” under projection. Thus, starting from an arbitrary neighborly simplicial (d−2)-polytope...

We propose a new shape-based modeling technique for applications in imaging problems. Given a collection of shape priors (a shape dictionary), we define our problem as choosing the right dictionary elements and geometrically composing them through basic set operations to characterize desired regions in an image. This is a combinatorial problem solving which requires an exhaustive search among a...