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[Submitted on 11 Apr 2016 (v1), last revised 30 May 2023 (this version, v4)] Download the PDF of the paper entitled Untwisting information from Heegaard Floer Homology by Kenan Ince. Download PDF overview: The unknot number of a knot is the minimum number of crossings that must be changed to turn that knot into an unknot. We use Mathieu-Domergue’s generalization of the number to untie the knot and call it the untie number. The p untwisting number is the minimum number of full twists (in all views of the knot) of up to 2p strands of a knot, with half…

We use numerically exact diagonalization to study the correlated Haldane-Hubbard model in the presence of dissipation. Such dissipation can be quickly modeled by dynamics governed by an effective non-Hermitian Hamiltonian, and we present its complete characterization. If the dissipation corresponds to the two-body loss, the repulsive interaction of the effective Hamiltonian acquires an imaginary component. Competition between the formation of charge-ordered Mott insulator states and topological insulators ensues, but non-Hermitian contributions help stabilize the topologically non-trivial region and delay the onset of formation of the local order parameter. Finally, we analyze the robustness of the ordered phase by tracking the…

[Submitted on 1 Jan 2022 (v1), last revised 30 May 2023 (this version, v2)] Download the PDF of the paper entitled “Partial symmetries of iterated plethysms” by “Alvaro Guti” errez and Mercedes H. Rosas. Download PDF overview: This study highlights the presence of partial symmetry in a large family of repeated plethystic coefficients. The associated plethystic coefficients are obtained from the extension of the iterated plethysm of the Schur function indexed by the one-row partition with the Schur basis. Partial symmetry is described in terms of involutions over partitions, or flip involutions, which generalize the ubiquitous $\omega$ involutions. Surreal symmetric…

[Submitted on 30 May 2023] Download the PDF of the paper titled Bayesian Joint quantile autoregression by Jorge Castillo-Mateo (1) and five other authors. Download PDF overview: Quantile regression continues to grow in usage and provides a useful alternative to conventional mean regression. First-order implementations take the form of so-called multi-quantile regression, creating a separate regression for each quantile of interest. Recently, however, joint quantile regression has progressed to provide quantile functions that avoid regression crossovers between quantiles. Here we turn to quantile autoregression (QAR), which provides a full Bayesian version. We extend the initial quantile regression work of Koenker…

We study the quench dynamics of bosonic fractional quantum Hall systems in small lattices with cylindrical boundary conditions and low particle densities. The states studied have quasi-holes or quasi-particles compared to boson laflin states in half-filling. A pinning potential is placed at an edge site (or a site close to the edge) and then turned off. Since the edges of the fractional quantum Hall system host chiral edge modes, chiral dynamics with one-directional motion for positive potentials fixing quasi-holes and opposite motion for negative potentials fixing quasi-particles is expected. We numerically show that chiral motion of the density distribution is…

Our main results have topological, combinatorial, and computational flavors. This is motivated by the basic conjecture that computing the Kovanov homology of a closed braid of a fixed number of strands has a polynomial time complexity. The independent simple complex $I(w)$ (and thus the Kovanov spectrum at the extreme quantum order) associated with the quadruplet $w$ is contractible or homotopy with either a sphere or a wedge of two spheres. Indicates equality. (possibly different dimensions), or a wedge of 3 spheres (at least 2 of the same dimension), or a wedge of 4 spheres (at least 3 of the same…

[Submitted on 5 Oct 2021 (v1), last revised 27 May 2023 (this version, v2)] Download the PDF of the paper entitled “Missing $g$-mass: Investigating the Missing Parts of Distributions” by Prafulla Chandra and Andrew Thangaraj. Download PDF overview: \textit{iid} Estimating the underlying distribution from a sample is a classic and important problem in statistics. If the alphabet size is large relative to the number of samples, it is more likely that some parts of the distribution will not be observed or will be sparsely observed. The missing mass and the Good Turing estimator of the missing mass, defined as the…

We explore a method to investigate the energy spectrum of synthetic lattices, analogous to scanning tunneling microscopy. We explore this spectroscopy approach using one-dimensional synthetic lattices of atomic-momentum bound states, and qualitatively analyze between measured and simulated energy spectra of small two-site and three-site lattices, and homogeneous multisite lattices. Observe the match. Finally, through simulations, we show that this technique enables exploration of the topological bands and fractal energy spectra of Hofstadter models realized on synthetic lattices. Source link

[Submitted on 26 Mar 2018 (v1), last revised 29 May 2023 (this version, v6)] Download the PDF of Yu-Wei Fan’s paper titled “Systolic Inequalities of K3 Surfaces via Stability Conditions” Download PDF overview: We introduce the concept of categorical systole and categorical volume of the Bridgeland stability condition in the triangular category. For any projective K3 surface, there is a constant C such that $$\mathrm{sys}(\sigma)^2\leq C\cdot\mathrm{vol that depends only on the rank and discriminant of its Picard group prove it exists. }(\sigma)$$ holds for any stability condition on the derived category of coherent layers on the K3 surface. This is…

[Submitted on 28 Oct 2021 (v1), last revised 29 May 2023 (this version, v3)] Download the PDF of the paper titled MMD Aggregated Two-Sample Test by Antonin Schrab, Ilmun Kim, M\’elisande Albert, B\’eatrice Laurent, Benjamin Guedj, and Arthur Gretton. Download PDF overview: We propose two new nonparametric two-sample kernel tests based on maximum mean divergence (MMD). First, for fixed kernels, we construct MMD tests using either permutation or wild bootstrapping, two common numerical procedures for determining test thresholds. We prove that this test non-asymptotically controls the probability of type I errors. Thus, unlike his previous MMD test, which only asymptotically…