Related papers: Symmetries of vector fields: the diffeomorphism ce…

As the theory is subject to a section condition, coordinates in double field theory do not represent physical points in an injective manner. We argue that a physical point should be rather one-to-one identified with a `gauge orbit' in the…

Let $f$ be a dominant endomorphism of the projective line, which is not conjugate to a power map $z\mapsto z^{\pm d}$. We consider the centralizers of the iterates of $f$,…

Continuous normalizing flows (CNFs) can model data distributions with expressive infinite-length architectures. But this modeling involves computationally expensive process of solving an ordinary differential equation (ODE) during maximum…

It is known that $C^r$ Morse-Smale vector fields form an open dense subset in the space of vector fields on orientable closed surfaces and are structurally stable for any $r \in \mathbb{Z}_{>0}$. In particular, $C^r$ Morse vector fields…

It is expected that the $D$-topology makes every diffeological vector space into a topological vector space. We show that it is the case for a large class of diffeological vector spaces via $k_\omega$-space theory, but not so in general.…

Deforming a two dimensional conformal field theory on one side of a trivial defect line gives rise to a defect separating the original theory from its deformation. The Casimir force between these defects and other defect lines or boundaries…

Let $F$ be a smooth vector field defined in a neighborhood of the origin in $\mathbb{R}^n$, $F(O)=0$, and let $F_t$ be its local flow. Denote by $E$ the set of germs of diffeomorphisms $h:\mathbb{R}^n \to \mathbb{R}^n$ preserving orbits of…

An embedding of chaotic data into a suitable phase space creates a diffeomorphism of the original attractor with the reconstructed attractor. Although diffeomorphic, the original and reconstructed attractors may not be topologically…

We introduce combinatorial multivector fields, associate with them multivalued dynamics and study their topological features. Our combinatorial multivector fields generalize combinatorial vector fields of Forman. We define isolated…

We point out that double categories provide a natural setting for modular functors obtained by a (bicategorical) string-net construction: The source of the modular functor -- which is now a double functor -- is a symmetric monoidal double…

We propose to study homomorphisms of connectome graphs. Homomorphisms can be studied as sequences of elementary homomorphisms - folds, which identify pairs of vertices. Several fold types are defined. Initial computation results for some…

Scalarization method is an important tool in the study of vector optimization as corresponding solutions of vector optimization problems can be found by solving scalar optimization problems. This is applied by Du (2010) [A note on cone…

For some full measure subset B of the set of iet's (i.e. interval exchange transformations) the following is satisfied: Let X be a $C^r$, $1\le r\le \infty$, vector field, with finitely many singularities, on a compact orientable surface M.…

In this work, we propose a new evolving geometric flow (called translating mean curvature flow) for the translating solitons of hypersurfaces in $R^{n+1}$. We study the basic properties, such as positivity preserving property, of the…

Randomly connected tensor networks (RCTN) are the dynamical systems defined by summing over all the possible networks of tensors. Because of the absence of fixed lattice structure, RCTN is not expected to have renormalization procedures. In…

We study the approximation properties of a wide class of finite element differential forms on curvilinear cubic meshes in n dimensions. Specifically, we consider meshes in which each element is the image of a cubical reference element under…

Clustering is an important facet of explorative data mining and finds extensive use in several fields. In this paper, we propose an extension of the classical Fuzzy C-Means clustering algorithm. The proposed algorithm, abbreviated as VFC,…

Let $X$ be a Hamiltonian vector field defined on a symplectic manifold $(M,\omega)$, $g$ a nowhere vanishing smooth function defined on an open dense subset $M^0$ of $M$. We will say that the vector field $Y = gX$ is conformally…

We treat Mechanics as a 1-dimensional general-relativistic gauge field theory, Mechanical Field Theory (MFT), introducing what we call the Mechanical Field Space (MFS) and exploiting its bundle geometry. The diffeomorphism covariance of MFT…

We fully develop the concept of causal symmetry introduced in Class. Quant. Grav. 20 (2003) L139. A causal symmetry is a transformation of a Lorentzian manifold (V,g) which maps every future-directed vector onto a future-directed vector. We…