Related papers: On Kernel of the regulator map
We prove that if a unimodular random graph is almost surely planar and has finite expected degree, then it has a combinatorial embedding into the plane which is also unimodular. This implies the claim in the title immediately by a theorem…
We identify a set of quantum graphs with unique and precisely defined spectral properties called {\it regular quantum graphs}. Although chaotic in their classical limit with positive topological entropy, regular quantum graphs are…
We discuss several approaches to motivic complexes and explicit constructions of the regulator maps from the motivic complexes to Deligne complexes.
We prove that infinite regular and chiral maps take place on surfaces with at most one end. Moreover, we prove that an infinite regular or chiral map on an orientable surface with genus can only be realized on the Loch Ness monster, that…
A theoretical framework is established for explicitly calculating rigid kernels of self-similar regular branch groups. This is applied to a new infinite family of branch groups in order to provide the first examples of self-similar, branch…
Let $C$ be a smooth irreducible projective curve of genus $g$ and $L$ a line bundle of degree $d$ generated by a linear subspace $V$ of $H^0(L)$ of dimension $n+1$. We prove a conjecture of D. C. Butler on the semistability of the kernel of…
We introduce a method to numerically compute equilibrium measures for problems with attractive-repulsive power law kernels of the form $K(x-y) = \frac{|x-y|^\alpha}{\alpha}-\frac{|x-y|^\beta}{\beta}$ using recursively generated banded and…
Controlled topology is one of the main tools for proving the isomorphism conjecture concerning the algebraic $K$-theory of group rings. In this article we dive into this machinery in two examples: when the group is infinite cyclic and when…
Kernel matrices are a key quantity in kernel-based approximation, and important properties such as stability and algorithmic convergence can be analyzed with their help. In this work we refine a multivariate Ingham-type theorem, which is…
The regulator theorem states that, under certain conditions, any optimal controller must embody a model of the system it regulates, grounding the idea that controllers embed, explicitly or implicitly, internal models of the controlled. This…
No quantum circuit can turn a completely unknown unitary gate into its coherently controlled version. Yet, coherent control of unknown gates has been realised in experiments, making use of a different type of initial resources. Here, we…
We define a regulator map from the weight n polylogarithmic motivic complex to the weight n Deligne complex of an algebraic variety X. The regulator map is constructed explicitly via the classical polylogarithms with some funny combinations…
For an infinite field $F$, we study the kernel of the map $H_{n}(\mathrm{GL}_{n-1}(F),\mathbb{Z}\Big[\frac{1}{(m-2)!}\Big]) \to H_{n}(\mathrm{GL}_{n}(F),\mathbb{Z}\Big[\frac{1}{(m-2)!}\Big])$ and the cokernel of…
A geometric setup for control theory is presented. The argument is developed through the study of the extremals of action functionals defined on piecewise differentiable curves, in the presence of differentiable non-holonomic constraints.…
We consider regulated curves in a Banach bundle whose projection on the basis is continuous with regulated derivative. We build a Banach manifold structure on the set of such curves. This result was previously obtained for the case of…
We study the asymptotics of certain measures on partitions (the so-called z-measures and their relatives) in two different regimes: near the diagonal of the corresponding Young diagram and in the intermediate zone between the diagonal and…
We study in this work different $(0, 1)$-codings of points from the unit interval $[0, 1]$ in the relation with the treatment of continuous unimodal maps.
Let $C$ be a smooth and projective curve over the truncated polynomial ring $k_m:=k[t]/(t^m), $ where $k$ is a field of characteristic 0. Using a candidate for the motivic cohomology group ${\rm H}^{3}_{\pazocal{M}}(C,\mathbb{Q}(3))$ based…
In this paper, we focus on an indefinite structure lying behind the Bergman kernel on the open unit disk. In particular, an invariant distance, birational maps and an indefinite kernel are constructed from the Bergman kernel, and we deal…
Let $E \subset \C$ be a Borel set with finite length, that is, $0<\mathcal{H}^1 (E)<\infty$. By a theorem of David and L\'eger, the $L^2 (\mathcal{H}^1 \lfloor E)$-boundedness of the singular integral associated to the Cauchy kernel (or…