On the minimum distance of elliptic curve codes

Computing the minimum distance of a linear code is one of the fundamental problems in algorithmic coding theory. Vardy [14] showed that it is an \np-hard problem for general linear codes. In practice, one often uses codes with additional mathematical structure, such as AG codes. For AG codes of genus $0$ (generalized Reed-Solomon codes), the minimum distance has a simple explicit formula. An interesting result of Cheng [3] says that the minimum distance problem is already \np-hard (under \rp-reduction) for general elliptic curve codes (ECAG codes, or AG codes of genus $1$). In this paper, we show that the minimum distance of ECAG codes also has a simple explicit formula if the evaluation set is suitably large (at least $2/3$ of the group order). Our method is purely combinatorial and based on a new sieving technique from the first two authors [8]. This method also proves a significantly stronger version of the MDS (maximum distance separable) conjecture for ECAG codes.Comment: 13 page

Information Cascades on Arbitrary Topologies

In this paper, we study information cascades on graphs. In this setting, each node in the graph represents a person. One after another, each person has to take a decision based on a private signal as well as the decisions made by earlier neighboring nodes. Such information cascades commonly occur in practice and have been studied in complete graphs where everyone can overhear the decisions of every other player. It is known that information cascades can be fragile and based on very little information, and that they have a high likelihood of being wrong. Generalizing the problem to arbitrary graphs reveals interesting insights. In particular, we show that in a random graph $G(n,q)$, for the right value of $q$, the number of nodes making a wrong decision is logarithmic in $n$. That is, in the limit for large $n$, the fraction of players that make a wrong decision tends to zero. This is intriguing because it contrasts to the two natural corner cases: empty graph (everyone decides independently based on his private signal) and complete graph (all decisions are heard by all nodes). In both of these cases a constant fraction of nodes make a wrong decision in expectation. Thus, our result shows that while both too little and too much information sharing causes nodes to take wrong decisions, for exactly the right amount of information sharing, asymptotically everyone can be right. We further show that this result in random graphs is asymptotically optimal for any topology, even if nodes follow a globally optimal algorithmic strategy. Based on the analysis of random graphs, we explore how topology impacts global performance and construct an optimal deterministic topology among layer graphs

Thrust distribution in Higgs decays at the next-to-leading order and beyond

We present predictions for the thrust distribution in hadronic decays of the Higgs boson at the next-to-leading order and the approximate next-to-next-to-leading order. The approximate NNLO corrections are derived from a factorization formula in the soft/collinear phase-space regions. We find large corrections, especially for the gluon channel. The scale variations at the lowest orders tend to underestimate the genuine higher order contributions. The results of this paper is therefore necessary to control the perturbative uncertainties of the theoretical predictions. We also discuss on possible improvements to our results, such as a soft-gluon resummation for the 2-jets limit, and an exact next-to-next-to-leading order calculation for the multi-jets region

A supramolecular radical cation: folding-enhanced electrostatic effect for promoting radical-mediated oxidation.

We report a supramolecular strategy to promote radical-mediated Fenton oxidation by the rational design of a folded host-guest complex based on cucurbit[8]uril (CB[8]). In the supramolecular complex between CB[8] and a derivative of 1,4-diketopyrrolo[3,4-c]pyrrole (DPP), the carbonyl groups of CB[8] and the DPP moiety are brought together through the formation of a folded conformation. In this way, the electrostatic effect of the carbonyl groups of CB[8] is fully applied to highly improve the reactivity of the DPP radical cation, which is the key intermediate of Fenton oxidation. As a result, the Fenton oxidation is extraordinarily accelerated by over 100 times. It is anticipated that this strategy could be applied to other radical reactions and enrich the field of supramolecular radical chemistry in radical polymerization, photocatalysis, and organic radical battery and holds potential in supramolecular catalysis and biocatalysis

Regional Attention with Architecture-Rebuilt 3D Network for RGB-D Gesture Recognition

Human gesture recognition has drawn much attention in the area of computer vision. However, the performance of gesture recognition is always influenced by some gesture-irrelevant factors like the background and the clothes of performers. Therefore, focusing on the regions of hand/arm is important to the gesture recognition. Meanwhile, a more adaptive architecture-searched network structure can also perform better than the block-fixed ones like Resnet since it increases the diversity of features in different stages of the network better. In this paper, we propose a regional attention with architecture-rebuilt 3D network (RAAR3DNet) for gesture recognition. We replace the fixed Inception modules with the automatically rebuilt structure through the network via Neural Architecture Search (NAS), owing to the different shape and representation ability of features in the early, middle, and late stage of the network. It enables the network to capture different levels of feature representations at different layers more adaptively. Meanwhile, we also design a stackable regional attention module called dynamic-static Attention (DSA), which derives a Gaussian guidance heatmap and dynamic motion map to highlight the hand/arm regions and the motion information in the spatial and temporal domains, respectively. Extensive experiments on two recent large-scale RGB-D gesture datasets validate the effectiveness of the proposed method and show it outperforms state-of-the-art methods. The codes of our method are available at: https://github.com/zhoubenjia/RAAR3DNet.Comment: Accepted by AAAI 202