Mass spectra of doubly heavy tetraquarks in an improved chromomagnetic interaction model

Doubly heavy tetraquark $(QQbar qbar q)$ states are the prime candidates of tightly bound exotic systems and weakly decaying. In the framework of the improved chromomagnetic interaction (ICMI) model, we complete a systematic study on the mass spectra of the $S$-wave doubly heavy tetraquark states $QQbar{q}bar{q}$ ($q=u, d, s$ and $Q=c, b$) with different quantum numbers $J^P=0^+$, $1^+$, and $2^+$. The parameters in the ICMI model are extracted by fitting the conventional hadron spectra and used directly to predict the masses of tetraquark states. For heavy quarks, the uncertainties of the parameters are acquired by comparing the masses of doubly (triply) heavy baryons with these given by lattice QCD, QCD sum rule, and potential models. Several compact and stable bound states are found in both charm and bottom tetraquark sectors. The predicted mass of $ccbar ubar d$ state is compatible with the recent result of the LHCb collaboration.

Mass spectra and decays of open-heavy tetraquark states

Open-heavy tetraquark states, especially those contain four different quarks have drawn much attention in both theoretical and experimental fields. In the framework of the improved chromomagnetic interaction (ICMI) model, we complete a systematic study on the mass spectra and possible strong decay channels of the $S$-wave open-heavy tetraquark states, $qqbar{q}bar{Q}$ ($q=u,d,s$ and $Q=c,b$), with different quantum number $J^P=0^+$, $1^+$, and $2^+$. The parameters in the ICMI model are extracted from the conventional hadron spectra and used directly to predict the mass of tetraquark states. Several compact bound states and narrow resonances are found in both charm-strange and bottom-strange tetraquark sectors, most of them as a product of the strong coupling between the different channels. Our results show the recently discovered four different flavors tetraquark candidates $X_0(2900)$ is probably compact $udbar{s}bar{c}$ state with quantum number $J^P=0^+$. The predictions about $X_0(2900)$ and its partners are expected to be better checked with other theories and future experiments.

VisEvent: Reliable Object Tracking via Collaboration of Frame and Event Flows

Different from visible cameras which record intensity images frame by frame, the biologically inspired event camera produces a stream of asynchronous and sparse events with much lower latency. In practice, the visible cameras can better perceive texture details and slow motion, while event cameras can be free from motion blurs and have a larger dynamic range which enables them to work well under fast motion and low illumination. Therefore, the two sensors can cooperate with each other to achieve more reliable object tracking. In this work, we propose a large-scale Visible-Event benchmark (termed VisEvent) due to the lack of a realistic and scaled dataset for this task. Our dataset consists of 820 video pairs captured under low illumination, high speed, and background clutter scenarios, and it is divided into a training and a testing subset, each of which contains 500 and 320 videos, respectively. Based on VisEvent, we transform the event flows into event images and construct more than 30 baseline methods by extending current single-modality trackers into dual-modalit

Factorization of Hilbert class polynomials over prime fields

Let $D$ be a negative integer congruent to $0$ or $1bmod{4}$ and $mathcal{O}=mathcal{O}_D$ be the corresponding order of $ K=mathbb{Q}(sqrt{D})$. The Hilbert class polynomial $H_D(x)$ is the minimal polynomial of the $j$-invariant $ j_D=j(mathbb{C}/mathcal{O})$ of $mathcal{O}$ over $K$. Let $n_D=(mathcal{O}_{mathbb{Q}( j_D)}:mathbb{Z}[ j_D])$ denote the index of $mathbb{Z}[ j_D]$ in the ring of integers of $mathbb{Q}(j_D)$. Suppose $p$ is any prime. We completely determine the factorization of $H_D(x)$ in $mathbb{F}_p[x]$ if either $p mid n_D$ or $p mid D$ is inert in $K$ and the $p$-adic valuation $v_p(n_D)leq 3$. As an application, we analyze the key space of Oriented Supersingular Isogeny Diffie-Hellman (OSIDH) protocol proposed by Col`o and Kohel in 2019 which is the roots set of the Hilbert class polynomial in $mathbb{F}_{p^2}$.

Differentiable Annealed Importance Sampling and the Perils of Gradient Noise

Annealed importance sampling (AIS) and related algorithms are highly effective tools for marginal likelihood estimation, but are not fully differentiable due to the use of Metropolis-Hastings (MH) correction steps. Differentiability is a desirable property as it would admit the possibility of optimizing marginal likelihood as an objective using gradient-based methods. To this end, we propose a differentiable AIS algorithm by abandoning MH steps, which further unlocks mini-batch computation. We provide a detailed convergence analysis for Bayesian linear regression which goes beyond previous analyses by explicitly accounting for non-perfect transitions. Using this analysis, we prove that our algorithm is consistent in the full-batch setting and provide a sublinear convergence rate. However, we show that the algorithm is inconsistent when mini-batch gradients are used due to a fundamental incompatibility between the goals of last-iterate convergence to the posterior and elimination of the pathwise stochastic error. This result is in stark contrast to our experience with stochastic optimization and stochastic gradient Langevin dynamics, where the effects of gradient noise can be washed out by taking more steps of a smaller size. Our negative result relies crucially on our explicit consideration of convergence to the stationary distribution, and it helps explain the difficulty of developing practically effective AIS-like algorithms that exploit mini-batch gradients.

On the $lambda$-invariant of Selmer groups arising from certain quadratic twists of Gross curves

Let $q$ be a prime with $q equiv 7 mod 8$, and let $K=mathbb{Q}(sqrt{-q})$. Then $2$ splits in $K$, and we write $mathfrak{p}$ for either of the primes $K$ above $2$. Let $K_infty$ be the unique $mathbb{Z}_2$-extension of $K$ unramified outside $mathfrak{p}$ with $n$-th layer $K_n$. For certain quadratic extensions $F/K$, we prove a simple exact formula for the $lambda$-invariant of the Galois group of the maximal abelian 2-extension unramified outside $mathfrak{p}$ of the field $F_infty = FK_infty$. Equivalently, our result determines the exact $mathbb{Z}_2$-corank of certain Selmer groups over $F_infty$ of a large family of quadratic twists of the higher dimensional abelian variety with complex multiplication, which is the restriction of scalars to $K$ of the Gross curve with complex multiplication defined over the Hilbert class field of $K$. We also discuss computations of the associated Selmer groups over $K_n$ in the case when the $lambda$-invariant is equal to $1$.

On abelian $2$-ramification torsion modules of quadratic fields

For a number field $F$ and a prime number $p$, the $mathbb{Z}_p$-torsion module of the Galois group of the maximal abelian pro-$p$ extension of $F$ unramified outside $p$ over $F$, denoted as $mathcal{T}_p(F)$, is an important subject in abelian $p$-ramification theory. In this paper we study the group $mathcal{T}_2(F)=mathcal{T}_2(m)$ of the quadratic field $F=mathbb{Q}(sqrt{ m})$. Firstly, assuming $m>0$, we prove an explicit $4$-rank formula for $mathcal{T}_2(-m)$. Furthermore, applying this formula and exploring the connection of $mathcal{T}_2(-m)$ to the ideal class group of $mathbb{Q}(sqrt{-m})$ and the tame kernel of $mathbb{Q}(sqrt{m})$, we obtain the $4$-rank density of $mathcal{T}_2$-groups of imaginary quadratic fields. Secondly, for $l$ an odd prime, we obtain results about the $2$-divisibility of orders of $mathcal{T}_2(pm l)$ and $mathcal{T}_2(pm 2l)$. In particular we find that $#mathcal{T}_2(l)equiv 2# mathcal{T}_2(2l)equiv h_2(-2l)bmod{16}$ if $lequiv 7bmod{8}$ where $h_2(-2l)$ is the $2$-class number of $mathbb{Q}(sqrt{-2l})$. We then obtain density results for $mathcal{T}_2(pm l)$ and $mathcal{T}_2(pm 2l)$. Finally, based on our density results and numerical data, we propose distribution conjectures about $mathcal{T}_p(F)$ when $F$ varies over real or imaginary quadratic fields for any prime $p$, and about $mathcal{T}_2(pm l)$ and $mathcal{T}_2(pm 2 l)$ when $l$ varies, in the spirit of Cohen-Lenstra heuristics. Our conjecture in the $mathcal{T}_2(l)$ case is closely connected to Shanks-Sime-Washingtons speculation on the distributions of the zeros of $2$-adic $L$-functions and to the distributions of the fundamental units.

Improving Generalizability of Fake News Detection Methods using Propensity Score Matching

Recently, due to the booming influence of online social networks, detecting fake news is drawing significant attention from both academic communities and general public. In this paper, we consider the existence of confounding variables in the features of fake news and use Propensity Score Matching (PSM) to select generalizable features in order to reduce the effects of the confounding variables. Experimental results show that the generalizability of fake news method is significantly better by using PSM than using raw frequency to select features. We investigate multiple types of fake news methods (classifiers) such as logistic regression, random forests, and support vector machines. We have consistent observations of performance improvement.