Breumkaas7963

These findings, which emerged uniformly in three different countries, among different partisan and ideological groups, and for those for whom the inductions were differently effective, underscore the stability of outgroup attitudes in contemporary America and other countries.

The online version contains supplementary material available at 10.1007/s11109-021-09701-1.

The online version contains supplementary material available at 10.1007/s11109-021-09701-1.We present an algorithm to compute all factorizations into linear factors of univariate polynomials over the split quaternions, provided such a factorization exists. Failure of the algorithm is equivalent to non-factorizability for which we present also geometric interpretations in terms of rulings on the quadric of non-invertible split quaternions. However, suitable real polynomial multiples of split quaternion polynomials can still be factorized and we describe how to find these real polynomials. Split quaternion polynomials describe rational motions in the hyperbolic plane. Factorization with linear factors corresponds to the decomposition of the rational motion into hyperbolic rotations. Since multiplication with a real polynomial does not change the motion, this decomposition is always possible. Some of our ideas can be transferred to the factorization theory of motion polynomials. These are polynomials over the dual quaternions with real norm polynomial and they describe rational motions in Euclidean kinematics. We transfer techniques developed for split quaternions to compute new factorizations of certain dual quaternion polynomials.Let M be a connected, closed, oriented three-manifold and K, L two rationally null-homologous oriented simple closed curves in M. We give an explicit algorithm for computing the linking number between K and L in terms of a presentation of M as an irregular dihedral three-fold cover of S 3 branched along a knot α ⊂ S 3 . Since every closed, oriented three-manifold admits such a presentation, our results apply to all (well-defined) linking numbers in all three-manifolds. Furthermore, ribbon obstructions for a knot α can be derived from dihedral covers of α . The linking numbers we compute are necessary for evaluating one such obstruction. This work is a step toward testing potential counter-examples to the Slice-Ribbon Conjecture, among other applications.Randomized incremental construction (RIC) is one of the most important paradigms for building geometric data structures. Clarkson and Shor developed a general theory that led to numerous algorithms which are both simple and efficient in theory and in practice. Randomized incremental constructions are usually space-optimal and time-optimal in the worst case, as exemplified by the construction of convex hulls, Delaunay triangulations, and arrangements of line segments. However, the worst-case scenario occurs rarely in practice and we would like to understand how RIC behaves when the input is nice in the sense that the associated output is significantly smaller than in the worst case. For example, it is known that the Delaunay triangulation of nicely distributed points in E d or on polyhedral surfaces in E 3 has linear complexity, as opposed to a worst-case complexity of Θ ( n ⌊ d / 2 ⌋ ) in the first case and quadratic in the second. The standard analysis does not provide accurate bounds on the complexity of such cases and we aim at establishing such bounds in this paper. More precisely, we will show that, in the two cases above and variants of them, the complexity of the usual RIC is O ( n log n ) , which is optimal. In other words, without any modification, RIC nicely adapts to good cases of practical value. At the heart of our proof is a bound on the complexity of the Delaunay triangulation of random subsets of ε -nets. Along the way, we prove a probabilistic lemma for sampling without replacement, which may be of independent interest.Given a locally finite X ⊆ R d and a radius r ≥ 0 , the k-fold cover of X and r consists of all points in R d that have k or more points of X within distance r. We consider two filtrations-one in scale obtained by fixing k and increasing r, and the other in depth obtained by fixing r and decreasing k-and we compute the persistence diagrams of both. While standard methods suffice for the filtration in scale, we need novel geometric and topological concepts for the filtration in depth. In particular, we introduce a rhomboid tiling in R d + 1 whose horizontal integer slices are the order-k Delaunay mosaics of X, and construct a zigzag module of Delaunay mosaics that is isomorphic to the persistence module of the multi-covers.We show that a convex body admits a translative dense packing in R d if and only if it admits a translative economical covering.We consider a class of sparse random matrices which includes the adjacency matrix of the Erdős-Rényi graph G ( N , p ) . We show that if N ε ⩽ N p ⩽ N 1 / 3 - ε then all nontrivial eigenvalues away from 0 have asymptotically Gaussian fluctuations. These fluctuations are governed by a single random variable, which has the interpretation of the total degree of the graph. This extends the result (Huang et al. in Ann Prob 48916-962, 2020) on the fluctuations of the extreme eigenvalues from N p ⩾ N 2 / 9 + ε down to the optimal scale N p ⩾ N ε . The main technical achievement of our proof is a rigidity bound of accuracy N - 1 / 2 - ε ( N p ) - 1 / 2 for the extreme eigenvalues, which avoids the ( N p ) - 1 -expansions from Erdős et al. (Ann Prob 412279-2375, 2013), Huang et al. (2020) and Lee and Schnelli (Prob Theor Rel Fields 171543-616, 2018). Our result is the last missing piece, added to Erdős et al. (Commun Math Phys 314587-640, 2012), He (Bulk eigenvalue fluctuations of sparse random matrices. arXiv1904.07140), Huang et al. (2020) and Lee and Schnelli (2018), of a complete description of the eigenvalue fluctuations of sparse random matrices for N p ⩾ N ε .Schramm-Loewner evolution ( SLE κ ) is classically studied via Loewner evolution with half-plane capacity parametrization, driven by κ times Brownian motion. This yields a (half-plane) valued random field γ = γ ( t , κ ; ω ) . (Hölder) regularity of in γ ( · , κ ; ω ), a.k.a. SLE trace, has been considered by many authors, starting with Rohde and Schramm (Ann Math (2) 161(2)883-924, 2005). Subsequently, Johansson Viklund et al. (Probab Theory Relat Fields 159(3-4)413-433, 2014) showed a.s. Hölder continuity of this random field for κ less then 8 ( 2 - 3 ) . In this paper, we improve their result to joint Hölder continuity up to κ less then 8 / 3 . Moreover, we show that the SLE κ trace γ ( · , κ ) (as a continuous path) is stochastically continuous in κ at all κ ≠ 8 . Our proofs rely on a novel variation of the Garsia-Rodemich-Rumsey inequality, which is of independent interest.The bead process introduced by Boutillier is a countable interlacing of the Sine 2 point processes. We construct the bead process for general Sine β processes as an infinite dimensional Markov chain whose transition mechanism is explicitly described. We show that this process is the microscopic scaling limit in the bulk of the Hermite β corner process introduced by Gorin and Shkolnikov, generalizing the process of the minors of the Gaussian Unitary and Orthogonal Ensembles. In order to prove our results, we use bounds on the variance of the point counting of the circular and the Gaussian beta ensembles, proven in a companion paper (Najnudel and Virág in Some estimates on the point counting of the Circular and the Gaussian Beta Ensemble, 2019).Makespan minimization on identical machines is a fundamental problem in online scheduling. The goal is to assign a sequence of jobs to m identical parallel machines so as to minimize the maximum completion time of any job. Already in the 1960s, Graham showed that Greedy is ( 2 - 1 / m ) -competitive. The best deterministic online algorithm currently known achieves a competitive ratio of 1.9201. No deterministic online strategy can obtain a competitiveness smaller than 1.88. In this paper, we study online makespan minimization in the popular random-order model, where the jobs of a given input arrive as a random permutation. It is known that Greedy does not attain a competitive factor asymptotically smaller than 2 in this setting. We present the first improved performance guarantees. Specifically, we develop a deterministic online algorithm that achieves a competitive ratio of 1.8478. The result relies on a new analysis approach. We identify a set of properties that a random permutation of the input jobs satisfies with high probability. see more Then we conduct a worst-case analysis of our algorithm, for the respective class of permutations. The analysis implies that the stated competitiveness holds not only in expectation but with high probability. Moreover, it provides mathematical evidence that job sequences leading to higher performance ratios are extremely rare, pathological inputs. We complement the results by lower bounds, for the random-order model. We show that no deterministic online algorithm can achieve a competitive ratio smaller than 4/3. Moreover, no deterministic online algorithm can attain a competitiveness smaller than 3/2 with high probability.Let C and D be hereditary graph classes. Consider the following problem given a graph G ∈ D , find a largest, in terms of the number of vertices, induced subgraph of G that belongs to C . We prove that it can be solved in 2 o ( n ) time, where n is the number of vertices of G, if the following conditions are satisfiedthe graphs in C are sparse, i.e., they have linearly many edges in terms of the number of vertices;the graphs in D admit balanced separators of size governed by their density, e.g., O ( Δ ) or O ( m ) , where Δ and m denote the maximum degree and the number of edges, respectively; andthe considered problem admits a single-exponential fixed-parameter algorithm when parameterized by the treewidth of the input graph. This leads, for example, to the following corollaries for specific classes C and D a largest induced forest in a P t -free graph can be found in 2 O ~ ( n 2 / 3 ) time, for every fixed t; anda largest induced planar graph in a string graph can be found in 2 O ~ ( n 2 / 3 ) time.Given a k-node pattern graph H and an n-node host graph G, the subgraph counting problem asks to compute the number of copies of H in G. In this work we address the following question can we count the copies of H faster if G is sparse? We answer in the affirmative by introducing a novel tree-like decomposition for directed acyclic graphs, inspired by the classic tree decomposition for undirected graphs. This decomposition gives a dynamic program for counting the homomorphisms of H in G by exploiting the degeneracy of G, which allows us to beat the state-of-the-art subgraph counting algorithms when G is sparse enough. For example, we can count the induced copies of any k-node pattern H in time 2 O ( k 2 ) O ( n 0.25 k + 2 log n ) if G has bounded degeneracy, and in time 2 O ( k 2 ) O ( n 0.625 k + 2 log n ) if G has bounded average degree. These bounds are instantiations of a more general result, parameterized by the degeneracy of G and the structure of H, which generalizes classic bounds on counting cliques and complete bipartite graphs.