4,959 research outputs found
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
(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 ). 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 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 , for the right value of
, the number of nodes making a wrong decision is logarithmic in . That
is, in the limit for large , 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
PVLR: Prompt-driven Visual-Linguistic Representation Learning for Multi-Label Image Recognition
Multi-label image recognition is a fundamental task in computer vision.
Recently, vision-language models have made notable advancements in this area.
However, previous methods often failed to effectively leverage the rich
knowledge within language models and instead incorporated label semantics into
visual features in a unidirectional manner. In this paper, we propose a
Prompt-driven Visual-Linguistic Representation Learning (PVLR) framework to
better leverage the capabilities of the linguistic modality. In PVLR, we first
introduce a dual-prompting strategy comprising Knowledge-Aware Prompting (KAP)
and Context-Aware Prompting (CAP). KAP utilizes fixed prompts to capture the
intrinsic semantic knowledge and relationships across all labels, while CAP
employs learnable prompts to capture context-aware label semantics and
relationships. Later, we propose an Interaction and Fusion Module (IFM) to
interact and fuse the representations obtained from KAP and CAP. In contrast to
the unidirectional fusion in previous works, we introduce a Dual-Modal
Attention (DMA) that enables bidirectional interaction between textual and
visual features, yielding context-aware label representations and
semantic-related visual representations, which are subsequently used to
calculate similarities and generate final predictions for all labels. Extensive
experiments on three popular datasets including MS-COCO, Pascal VOC 2007, and
NUS-WIDE demonstrate the superiority of PVLR.Comment: 15 pages, 8 figure
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