Fermat-Euler quotients arose from the study of the first case of Fermats Last Theorem, and have numerous applications in number theory. Recently they were studied from the cryptographic aspects by constructing many pseudorandom binary sequences, whos
e linear complexities and trace representations were calculated. In this work, we further study their correlation measures by using the approach based on Dirichlet characters, Ramanujan sums and Gauss sums. Our results show that the $4$-order correlation measures of these sequences are very large. Therefore they may not be suggested for cryptography.
We perform a systematic exploration of the possible doubly charmed molecular pentaquarks composed of $Sigma_c^{(*)}D^{(*)}$ with the one-boson-exchange potential model. After taking into account the $S-D$ wave mixing and the coupled channel effects,
we predict several possible doubly charmed molecular pentaquarks, which include the $Sigma_cD$ with $I(J^P) = 1/2(1/2^-)$, $Sigma_c^*D$ with $1/2(3/2^-)$, and $Sigma_cD^*$ with $1/2(1/2^-)$, $1/2(3/2^-)$. The $Sigma_cD$ state with $3/2(1/2^-)$ and $Sigma_cD^*$ state with $3/2(1/2^-)$ may also be suggested as candidates of doubly charmed molecular pentaquarks. The $Sigma_cD$ and $Sigma_c^*D$ states can be searched for by analyzing the $Lambda_cDpi$ invariant mass spectrum of the bottom baryon and $B$ meson decays. The $Sigma_cD^*$ states can be searched for in the invariant mass spectrum of $Lambda_cD^*pi$, $Lambda_cDpipi$ and $Lambda_cDpigamma$. Since the width of $Sigma_c^*$ is much larger than that of $D^*$, $Sigma_c^*Drightarrow Lambda_cDpi$ will be the dominant decay mode. We sincerely hope these candidates for the doubly charmed molecular pentaqurks will be searched by LHCb or BelleII collaboration in the near future.
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.
With the emergence of light field imaging in recent years, the compression of its elementary image array (EIA) has become a significant problem. Our coding framework includes modeling and reconstruction. For the modeling, the covariance-matrix form o
f the 4-D Epanechnikov kernel (4-D EK) and its correlated statistics were deduced to obtain the 4-D Epanechnikov mixture models (4-D EMMs). A 4-D Epanechnikov mixture regression (4-D EMR) was proposed based on this 4-D EK, and a 4-D adaptive model selection (4-D AMLS) algorithm was designed to realize the optimal modeling for a pseudo video sequence (PVS) of the extracted key-EIA. A linear function based reconstruction (LFBR) was proposed based on the correlation between adjacent elementary images (EIs). The decoded images realized a clear outline reconstruction and superior coding efficiency compared to high-efficiency video coding (HEVC) and JPEG 2000 below approximately 0.05 bpp. This work realized an unprecedented theoretical application by (1) proposing the 4-D Epanechnikov kernel theory, (2) exploiting the 4-D Epanechnikov mixture regression and its application in the modeling of the pseudo video sequence of light field images, (3) using 4-D adaptive model selection for the optimal number of models, and (4) employing a linear function-based reconstruction according to the content similarity.
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 stu
dy 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.
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 text
ure 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
The aortic vessel tree is composed of the aorta and its branching arteries, and plays a key role in supplying the whole body with blood. Aortic diseases, like aneurysms or dissections, can lead to an aortic rupture, whose treatment with open surgery
is highly risky. Therefore, patients commonly undergo drug treatment under constant monitoring, which requires regular inspections of the vessels through imaging. The standard imaging modality for diagnosis and monitoring is computed tomography (CT), which can provide a detailed picture of the aorta and its branching vessels if combined with a contrast agent, resulting in a CT angiography (CTA). Optimally, the whole aortic vessel tree geometry from consecutive CTAs, are overlaid and compared. This allows to not only detect changes in the aorta, but also more peripheral vessel tree changes, caused by the primary pathology or newly developed. When performed manually, this reconstruction requires slice by slice contouring, which could easily take a whole day for a single aortic vessel tree and, hence, is not feasible in clinical practice. Automatic or semi-automatic vessel tree segmentation algorithms, on the other hand, can complete this task in a fraction of the manual execution time and run in parallel to the clinical routine of the clinicians. In this paper, we systematically review computing techniques for the automatic and semi-automatic segmentation of the aortic vessel tree. The review concludes with an in-depth discussion on how close these state-of-the-art approaches are to an application in clinical practice and how active this research field is, taking into account the number of publications, datasets and challenges.
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}/m
athcal{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 $mathbb{F}_{p^2}$.
In 2012, we investigated the possible molecular states composed of two charmed mesons [Phys.Rev. D 88, 114008 (2013), arXiv:1211.5007 [hep-ph](2012)]. The $D^*D$ system with the quantum numbers of $I(J^P)=0(1^+)$ was found to be a good candidate of t
he loosely bound molecular state. This state is very close to the $D^*D$ threshold with a binding energy around 0.47 MeV. This prediction was confirmed by the new LHCb observation of $T_{cc}^+$ [see Franz Muheims talk at the European Physical Society conference on high energy physics 2021].
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 pr
operty 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.
