Related papers: Geometrical morphology
This paper gives two different proofs to a structural theorem of decreasing minimization (lexicographic optimization) on integrally convex sets. The theorem states that the set of decreasingly minimal elements of an integrally convex set…
Despite encouraging recent progresses in ensemble approaches, classification methods seem to have reached a plateau in development. Further advances depend on a better understanding of geometrical and topological characteristics of point…
Morphogenesis emerges from dynamic feedback among geometry, mechanics, and chemistry; however, disentangling these contributions in living systems remains challenging. Here, we focus on the interplay between geometry and mechanics by…
Language models exhibit strong robustness to paraphrasing, suggesting that semantic information may be encoded through stable internal representations, yet the structure and origin of such invariance remain unclear. We propose a local…
Given a compact smooth manifold $M$ with non-empty boundary and a Morse function, a pseudo-gradient Morse-Smale vector field adapted to the boundary allows one to build a Morse complex whose homology is isomorphic to the (absolute or…
Modern work on the cross-linguistic computational modeling of morphological inflection has typically employed language-independent data splitting algorithms. In this paper, we supplement that approach with language-specific probes designed…
This paper studies the effect of discretizing the parametrization of a dictionary used for Matching Pursuit decompositions of signals. Our approach relies on viewing the continuously parametrized dictionary as an embedded manifold in the…
We describe a procedure for constructing morphisms in additive categories, combining Auslander's concept of a morphism determined by an object with the existence of flat covers. Also, we show how flat covers are turned into projective…
Mathematical morphology provides a nonlinear framework for image and spatial data processing and analysis. Although there have been many successful applications of mathematical morphology to vector-valued images, such as color and…
It it shown that geometric morphisms between elementary toposes can be represented as adjunctions between the corresponding categories of locales. These adjunctions are characterised as those that preserve the order enrichment, commute with…
Given a finite Borel measure $\mu$ on R n and basic semi-algebraic sets $\Omega$\_i $\subset$ R n , i = 1,. .. , p, we provide a systematic numerical scheme to approximate as closely as desired $\mu$(\cup\_i $\Omega$\_i), when all moments…
Persistent homology, a technique from computational topology, has recently shown strong empirical performance in the context of graph classification. Being able to capture long range graph properties via higher-order topological features,…
The analytic implicit function theorem is extended. The function f of the theorem is integrated with respect to the dependent variable of the implicit function. A geometrical interpretation is given for the sub-geometry of the integral…
It is well known that the SU(2)-gauge invariant phase space of loop gravity can be represented in terms of twisted geometries. These are piecewise-linear-flat geometries obtained by gluing together polyhedra, but the resulting geometries…
We give an algebraic characterisation of first-order logic with the neighbour relation, on finite words. For this, we consider languages of finite words over alphabets with an involution on them. The natural algebras for such languages are…
Interferometric closure invariants encode calibration-independent details of an object's morphology. Excepting simple cases, a direct backward transformation from closure invariants to morphologies is not well established. We demonstrate…
We study a class of complex polynomial equations on a finite graph with a view to understanding how holistic phenomena emerge from combinatorial structure. Particular solutions arise from orthogonal projections of regular polytopes,…
A piecewise constant curvature manifold is a triangulated manifold that is assigned a geometry by specifying lengths of edges and stipulating that for a chosen background geometry (Euclidean, hyperbolic, or spherical), each simplex has an…
This paper investigates type isomorphism in a lambda-calculus with intersection and union types. It is known that in lambda-calculus, the isomorphism between two types is realised by a pair of terms inverse one each other. Notably,…
Persistent homology analysis provides means to capture the connectivity structure of data sets in various dimensions. On the mathematical level, by defining a metric between the objects that persistence attaches to data sets, we can…