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In this paper, we give a formula for the proper class number of a binary quadratic polynomial assuming that the conductor ideal is sufficiently divisible at dyadic places. This allows us to study the growth of the proper class numbers of totally positive binary quadratic polynomials. As an application, we prove finiteness results on totally positive binary quadratic polynomials with a fixed quadratic part and a fixed proper class number., Comment: 14 pages

In this paper, we prove formulas for local densities of quadratic polynomials over non-dyadic fields and over unramified dyadic fields., Comment: 17 pages, revised Lemma 2.3, Lemma 4.9, and Theorem 4.12

In this paper, we consider a version of the bias conjecture for second moments in the setting of elliptic curves over finite fields whose trace of Frobenius lies in an arbitrary fixed arithmetic progression. Contrary to the classical setting of reductions of one-parameter families over the rationals, where it is conjectured by Steven J. Miller that the bias is always negative, we prove that in our setting the bias is positive for a positive density of arithmetic progressions and negative for a positive density of arithmetic progressions. Along the way, we obtain explicit formulas for moments of traces of Frobenius of elliptic curves over finite fields in arithmetic progressions and related moments of Hurwitz class numbers in arithmetic progressions, the distribution of which are of independent interest.

In this paper, we study universal sums of triangular numbers and squares. Specifically, we prove that a sum of triangular numbers and squares is universal if and only if it represents $1,2,3,4,5,6,7,8,10,13,14,15,18,19,20,23,27,28,34,41,47$, and $48$., Comment: 12 pages

In this paper, we consider mixed sums of generalized polygonal numbers. Specifically, we obtain a finiteness condition for universality of such sums; this means that it suffices to check representability of a finite subset of the positive integers in order to conclude that the sum of generalized polygonal numbers represents every positive integer. The sub-class of sums of generalized polygonal numbers which we consider is those sums of $m_j$-gonal numbers for which $\operatorname{lcm}(m_1-2,\dots,m_{r}-2)\leq \mathfrak{M}$ and we obtain a bound on the asymptotic growth of a constant $\Gamma_{\mathfrak{M}}$ such that it suffices to check the representability condition for $n\leq \Gamma_{\mathfrak{M}}$.

We present Ru $L_3$-edge resonant inelastic x-ray scattering (RIXS) measurements of spin-orbit and d-d excitations in exfoliated nanolayers of the Kitaev spin-liquid candidate RuCl$_3$. Whereas the spin-orbit excitations are independent of thickness, we observe a pronounced red-shift and broadening of the d-d excitations in layers with thickness below $\sim$7 nm. Aided by model calculations, we attribute these effects to distortions of the RuCl$_6$ octahedra near the surface. Our study paves the way towards RIXS investigations of electronic excitations in various other 2D materials and heterostructures.

Weakly-supervised temporal action localization (WTAL) in untrimmed videos has emerged as a practical but challenging task since only video-level labels are available. Existing approaches typically leverage off-the-shelf segment-level features, which suffer from spatial incompleteness and temporal incoherence, thus limiting their performance. In this paper, we tackle this problem from a new perspective by enhancing segment-level representations with a simple yet effective graph convolutional network, namely action complement graph network (ACGNet). It facilitates the current video segment to perceive spatial-temporal dependencies from others that potentially convey complementary clues, implicitly mitigating the negative effects caused by the two issues above. By this means, the segment-level features are more discriminative and robust to spatial-temporal variations, contributing to higher localization accuracies. More importantly, the proposed ACGNet works as a universal module that can be flexibly plugged into different WTAL frameworks, while maintaining the end-to-end training fashion. Extensive experiments are conducted on the THUMOS'14 and ActivityNet1.2 benchmarks, where the state-of-the-art results clearly demonstrate the superiority of the proposed approach., Comment: Accepted to AAAI 2022

We present a comparative study of magnetic excitations in the first two Ruddlesden-Popper members of the Hg-family of high-temperature superconducting cuprates, which are chemically nearly identical and have the highest critical temperature ($T_\mathrm{c}$) among all cuprate families. Our inelastic photon scattering experiments reveal that the two compounds' paramagnon spectra are nearly identical apart from an energy scale factor of $\sim130\%$ that matches the ratio of $T_\mathrm{c}$'s, as expected in magnetic Cooper pairing theories. By relating our observations to other cuprates, we infer that the strength of magnetic interactions determines how high $T_\mathrm{c}$ can reach. Our finding can be viewed as a magnetic analogue of the isotope effect, thus firmly supporting models of magnetically mediated high-temperature superconductivity., Comment: 6 pages, 4 figures, SM available via link in pdf

Convolutional neural networks have gained a remarkable success in computer vision. However, most usable network architectures are hand-crafted and usually require expertise and elaborate design. In this paper, we provide a block-wise network generation pipeline called BlockQNN which automatically builds high-performance networks using the Q-Learning paradigm with epsilon-greedy exploration strategy. The optimal network block is constructed by the learning agent which is trained to choose component layers sequentially. We stack the block to construct the whole auto-generated network. To accelerate the generation process, we also propose a distributed asynchronous framework and an early stop strategy. The block-wise generation brings unique advantages: (1) it yields state-of-the-art results in comparison to the hand-crafted networks on image classification, particularly, the best network generated by BlockQNN achieves 2.35% top-1 error rate on CIFAR-10. (2) it offers tremendous reduction of the search space in designing networks, spending only 3 days with 32 GPUs. A faster version can yield a comparable result with only 1 GPU in 20 hours. (3) it has strong generalizability in that the network built on CIFAR also performs well on the larger-scale dataset. The best network achieves very competitive accuracy of 82.0% top-1 and 96.0% top-5 on ImageNet., Comment: 14 pages, 18 figures

Many image processing tasks can be formulated as translating images between two image domains, such as colorization, super resolution and conditional image synthesis. In most of these tasks, an input image may correspond to multiple outputs. However, current existing approaches only show very minor diversity of the outputs. In this paper, we present a novel approach to synthesize diverse realistic images corresponding to a semantic layout. We introduce a diversity loss objective, which maximizes the distance between synthesized image pairs and links the input noise to the semantic segments in the synthesized images. Thus, our approach can not only produce diverse images, but also allow users to manipulate the output images by adjusting the noise manually. Experimental results show that images synthesized by our approach are significantly more diverse than that of the current existing works and equipping our diversity loss does not degrade the reality of the base networks., Comment: 10 pages, 11 figures

We investigate the optimal quantum state reconstruction from cloud to many spatially separated users by measure-broadcast-prepare scheme without the availability of quantum channel. The quantum state equally distributed from cloud to arbitrary number of users is generated at each port by ensemble of known quantum states with assistance of classical information of measurement outcomes by broadcasting. The obtained quantum state for each user is optimal in the sense that the fidelity universally achieves the upper bound. We present the universal quantum state distribution by providing physical realizable measurement bases in the cloud as well as the reconstruction method for each user. The quantum state reconstruction scheme works for arbitrary many identical pure input states in general dimensional system., Comment: 7 pages, 1 figure

Recently, learning equivariant representations has attracted considerable research attention. Dieleman et al. introduce four operations which can be inserted into convolutional neural network to learn deep representations equivariant to rotation. However, feature maps should be copied and rotated four times in each layer in their approach, which causes much running time and memory overhead. In order to address this problem, we propose Deep Rotation Equivariant Network consisting of cycle layers, isotonic layers and decycle layers. Our proposed layers apply rotation transformation on filters rather than feature maps, achieving a speed up of more than 2 times with even less memory overhead. We evaluate DRENs on Rotated MNIST and CIFAR-10 datasets and demonstrate that it can improve the performance of state-of-the-art architectures.

The group IV-VI compound SnSe, with an orthorhombic lattice structure, has recently attracted particular interest due to its unexpectedly low thermal conductivity and high power factor, showing great promise for thermoelectric applications. SnSe displays intriguing anisotropic properties due to the puckered low-symmetry in-plane lattice structure. Low-dimensional materials have potential advantages in improving the efficiency of thermoelectric conversion, due to the increased power factor and decreased thermal conductivity. A complete study of the optical and electrical anisotropies of SnSe nanostructures is a necessary prerequisite in taking advantage of the material properties for high performance devices. Here, we synthesize the single crystal SnSe nanoplates (NPs) by chemical vapor deposition. The angular dependence of the polarized Raman spectra of SnSe NPs shows anomalous anisotropic light-mater interaction. The angle-resolved charge transport of the SnSe NPs expresses a strong anisotropic conductivity behavior. These studies elucidate the anisotropic interactions which will be of use for future ultrathin SnSe in electronic, thermoelectric and optoelectronic devices., Comment: 25 pages, 9 figures, 3 tables