Related papers: Paterson compactifications, inverse limits and sha…
In this paper we deduce a local deformation lemma for uniform embeddings in a metric covering space over a compact manifold from the deformation lemma for embeddings of a compact subspace in a manifold. This implies the local…
Transverse linearization-based approaches have become among the most prominent methods for orbitally stabilizing feedback design in regards to (periodic) motions of underactuated mechanical systems. Yet, in an $n$-dimensional state-space,…
This work introduces topological regularization as a framework for handling ultraviolet divergences in quantum field theory, reinterpreting infinities as topological obstructions at spacetime boundaries. Through geometric compactification…
Recently, we introduced a symmetry on the structure of angular momentum which interchanges internal and external degrees of freedom. The spin-orbit duality is a holographic map that projects a massive theory in four-dimensional flat…
We study the properties of topological spaces $(X,\tau)$, where $X$ is a definable set in an o-minimal structure and the topology $\tau$ on $X$ has a basis that is (uniformly) definable. Examples of such spaces include the canonical…
The scaling properties of quantum gravity are discussed by employing a class of proper-time regulators in the functional flow equation for the conformal factor within the formalism of the background field method. Renormalization group…
In the absence of the Axiom of Choice, necessary and sufficient conditions for a locally compact Hausdorff space to have all non-empty second-countable compact Hausdorff spaces as remainders are given in $\mathbf{ZF}$. Among other…
We study a one-parameter family of time-reversible Hamiltonian vector fields in $\mathbb{R}^4$, which has received great attention in the literature. On the one hand, it is due to the role it plays in the context of certain applications in…
The paper introduces a Poisson-type problem on a mixed-dimensional structure combining a Euclidean domain and a lower-dimensional self-similar component touching a compact surface (interface). The lower-dimensional piece is a so-called…
We consider the problem of topological linearization of smooth (C infinity or real analytic) control systems, i.e. of their local equivalence to a linear controllable system via point-wise transformations on the state and the control…
We prove dynamical local limits for the singular numbers of $p$-adic random matrix products at both the bulk and edge. The limit object which we construct, the reflecting Poisson sea, may thus be viewed as a $p$-adic analogue of line…
We describe the duality between the gravitating $c=1$ (compact) Sine-Gordon model and a normal matrix model. From a two-dimensional quantum gravity perspective and due to the periodic nature of the potential, this model admits both anti-de…
Matrix configurations define noncommutative spaces endowed with extra structure including a generalized Laplace operator, and hence a metric structure. Made dynamical via matrix models, they describe rich physical systems including…
In this paper we show that the group of automorphisms of a non-recurrent tent map inverse limit is very simple by demonstrating that every homeomorphism of such a space is isotopic to a power of the induced shift homeomorphism.
The kinematical phase space of classical gravitational field is flat (affine) and unbounded. Because of this, field variables may tend to infinity leading to appearance of singularities, which plague Einstein's theory of gravity. The…
We consider an empty (4+1) dimensional Kaluza-Klein universe with a negative cosmological constant and a Robertson-Walker type metric. It is shown that the solutions to Einstein field equations have degenerate metric and exhibit…
We construct a continuum of non-homeomorphic compact subspaces of the real line R without singleton components. Thus from the purely topological point of view the real line contains not only more closed sets than open sets but also more…
In this paper, we study a flag complex which is naturally associated to the Thurston theory of surface diffeomorphisms for compact connected orientable surfaces with boundary. The various pieces of the Thurston decomposition of a surface…
The inverse design of metasurfaces faces inherent challenges due to the nonlinear and highly complex relationship between geometric configurations and their electromagnetic behavior. Traditional optimization approaches often suffer from…
In this work we introduce Deforming Autoencoders, a generative model for images that disentangles shape from appearance in an unsupervised manner. As in the deformable template paradigm, shape is represented as a deformation between a…