A novel, brain-like, hierarchical (affine-neuro-fuzzy-topological) control for biomechanically realistic humanoid-robot biodynamics (HB), formulated previously in [15, 16], is proposed in the form of a tensor-invariant, “meta-cybernetic” functor machine. It represents a physiologically inspired, three-level, nonlinear feedback controller of muscularlike joint actuators. On the spinal level, nom...

The pentagram map is a discrete dynamical system defined on the moduli space of polygons in the projective plane. This map has recently attracted a considerable interest, mostly because its connection to a number of different domains, such as: classical projective geometry, algebraic combinatorics, moduli spaces, cluster algebras and integrable systems. Integrability of the pentagram map was co...

Motion and deformation are common in prostate diffusion-weighted magnetic resonance imaging (DWI) during acquisition. These misalignments lead to errors in estimating an apparent diffusion coefficient (ADC) map fitted with DWI. To address this problem, we propose an image registration algorithm to align the prostate DWI and improve ADC map. First, we apply affine transformation to DWI to correc...

Let X be a rational homogeneous space and let QH(X)× loc be the group of invertible elements in the small quantum cohomology ring of X localised in the quantum parameters. We generalise results of [ChMaPe06] and realise explicitly the map π1(Aut(X)) → QH (X)× loc described in [Se97]. We even prove that this map is an embedding and realise it in the equivariant quantum cohomology ring QH T (X)× ...

̂ M of the connection ∇M to the universal cover ̂ M of M is a locally flat connection. The affine structure of ̂ M is defined by a local diffeomorphism DM : ̂ M → R called the developing map. The developing map gives rise to a representation hM : π1 M → Aff R called the holonomy. The linear part L hM of hM is the linear holonomy. The affine manifold M,∇M is complete if and only if DM is a diffeomor...

We introduce a non-iterative geometric-based method for shape matching using a novel set of geometric landmarks residing on a 2D contours. These landmarks are intrinsic and are computed from the differential geometry of the curve. We exploit the invariant properties of geometric landmarks that are local and preserved under the affine and some perspective transformation. Geometric invariant expl...

In this paper we consider generic families of 2-dimensional analytic vector fields unfolding a generic (codimension 1) saddle-node at the origin. We show that a complete modulus of orbital analytic classification for the family is given by an unfolding of the Martinet–Ramis modulus of the saddle-node. The Martinet–Ramis modulus is given by a pair of germs of diffeomorphisms, one of which is an ...

For any affine variety equipped with coordinates, there is a surjective, continuous map from its Berkovich space to its tropicalisation. Exploiting torus actions, we develop techniques for finding an explicit, continuous section of this map. In particular, we prove that such a section exists for linear spaces, Grassmannians of planes (reproving a result due to Cueto, Häbich, and Werner), matrix...

Let R be a Dedekind domain, G an affine flat R-group scheme, and B a flat R-algebra on which G acts. Let A → BG be an R-algebra map. Assume that A is Noetherian. We show that if the induced map K ⊗ A → (K ⊗ B)K⊗G is an isomorphism for any algebraically closed field K which is an R-algebra, then S ⊗A→ (S ⊗B)S⊗G is an isomorphism for any R-algebra S.