Related papers: On an efficient induction step with Nklt(X,D)

We further develop the description of three-dimensional quantum gravity with negative cosmological constant in terms of Virasoro TQFT formulated in our previous paper arXiv:2304.13650. We compare the partition functions computed in the…

It is shown that any smooth closed orientable manifold of dimension $2k + 1$, $k \geq 2$, admits a smooth polynomially convex embedding into $\mathbb C^{3k}$. This improves by $1$ the previously known lower bound of $3k+1$ on the possible…

We formulate an effective cone conjecture for klt Calabi--Yau pairs $(X,\Delta)$, pertaining to the structure of the cone of effective divisors $\mathrm{Eff}(X)$ modulo the action of the subgroup of pseudo-automorphisms…

A numerically efficient, accurate, and easily implemented integration scheme over convex Voronoi polyhedra (VP) is presented for use in {\it ab-initio} electronic-structure calculations. We combine a weighted Voronoi tessellation with…

Let $K$ be a convex body in $\mathbb{R}^{3}$. We denote the volume of $K$ by $Vol(K)$ and the diameter of $K$ by $Diam(K).$ In this paper we prove that there exists a linear bijection $T:\mathbb{R}^{3}\to \mathbb{R}^{3}$ such that…

We present a new construction of four dimensional $\mathcal N=3$ theories, given by M5 branes wrapping a $T^2$ in an M-theory U-fold background. The resulting setup generalizes the one used in the usual class $\mathcal S$ construction of…

In deep learning, processing multidimensional inputs (e.g., images, medical scans, and time series) is an important task that often requires flattening the inputs. We introduce $\mathit{NdLinear}$, a drop-in replacement for linear layers…

An orthogonal 16-point approximate discrete cosine transform (DCT) is introduced. The proposed transform requires neither multiplications nor bit-shifting operations. A fast algorithm based on matrix factorization is introduced, requiring…

Let $\sigma$ be an isometric representation of $\mathbb{N}^d$ on a Hilbert space $\mathcal{H}$. We induce $\sigma$ to an isometric representation $V$ of $\mathbb{R}_{+}^{d}$ on another Hilbert space $\mathcal{K}$. We show that the map…

We establish the Noether inequality for projective $3$-folds. More precisely, we prove that the inequality $${\rm vol}(X)\geq \tfrac{4}{3}p_g(X)-{\tfrac{10}{3}}$$ holds for all projective $3$-folds $X$ of general type with either…

In this note, we prove an effective linear volume growth for complete three-manifolds with non-negative Ricci curvature and uniformly positive scalar curvature. This recovers the results obtained by Munteanu-Wang. Our method builds upon…

Given an $n$-vertex 1.5D terrain $\T$ and a set $\A$ of $m<n$ viewpoints, the Voronoi visibility map $\vorvis(\T,\A)$ is a partitioning of $\T$ into regions such that each region is assigned to the closest (in Euclidean distance) visible…

We prove several results of the following type: given finite dimensional normed space V there exists another space X with log (dim X) = O(log (dim V)) and such that every subspace (or quotient) of X, whose dimension is not "too small,"…

Let $(E,\xi)={\rm ind}(E_n, \xi_n)$ be an inductive limit of a sequence $(E_n, \xi_n)_{n\in N}$ of locally convex spaces and let every step $(E_n, \xi_n)$ be endowed with a partial order by a pointed convex (solid) cone $S_n$. In the…

We show that the baker's map is a product of transpositions (particularly pleasant involutions), and conclude from this that an existing very short proof of the simplicity of Thompson's group V applies with equal brevity to the higher…

We prove that in an n-vertex graph, induced chordal and interval subgraphs with the maximum number of vertices can be found in time $O(2^{\lambda n})$ for some $\lambda<1$. These are the first algorithms breaking the trivial $2^n n^{O(1)}$…

The topological Tur\'an number $\mathrm{ex}_{\hom}(n,X)$ of a 2-dimensional simplicial complex $X$ asks for the maximum number of edges in an $n$-vertex 3-uniform hypergraph containing no triangulation of $X$ as a subgraph. We prove that…

In the Hausdorff Voronoi diagram of a set of clusters of points in the plane, the distance between a point t and a cluster P is the maximum Euclidean distance between t and a point in P. This diagram has direct applications in VLSI design.…

In this paper we present efficient algorithms for the computation of several invariant objects for Hamiltonian dynamics. More precisely, we consider KAM tori (i.e diffeomorphic copies of the torus such that the motion on them is conjugated…

This paper investigates a real-valued topological invariant of 3-manifolds called topological volume. For a given 3-manifold M it is defined as the smallest volume of the complement of a (possibly empty) hyperbolic link in M. Various…