A generalization of bounds for cyclic codes, including the HT and BS bounds

We use the algebraic structure of cyclic codes and some properties of the discrete Fourier transform to give a reformulation of several classical bounds for the distance of cyclic codes, by extending techniques of linear algebra. We propose a bound, whose computational complexity is polynomial bounded, which is a generalization of the Hartmann-Tzeng bound and the Betti-Sala bound. In the majority of computed cases, our bound is the tightest among all known polynomial-time bounds, including the Roos bound

Distil the informative essence of loop detector data set: Is network-level traffic forecasting hungry for more data?

Network-level traffic condition forecasting has been intensively studied for decades. Although prediction accuracy has been continuously improved with emerging deep learning models and ever-expanding traffic data, traffic forecasting still faces many challenges in practice. These challenges include the robustness of data-driven models, the inherent unpredictability of traffic dynamics, and whether further improvement of traffic forecasting requires more sensor data. In this paper, we focus on this latter question and particularly on data from loop detectors. To answer this, we propose an uncertainty-aware traffic forecasting framework to explore how many samples of loop data are truly effective for training forecasting models. Firstly, the model design combines traffic flow theory with graph neural networks, ensuring the robustness of prediction and uncertainty quantification. Secondly, evidential learning is employed to quantify different sources of uncertainty in a single pass. The estimated uncertainty is used to "distil" the essence of the dataset that sufficiently covers the information content. Results from a case study of a highway network around Amsterdam show that, from 2018 to 2021, more than 80\% of the data during daytime can be removed. The remaining 20\% samples have equal prediction power for training models. This result suggests that indeed large traffic datasets can be subdivided into significantly smaller but equally informative datasets. From these findings, we conclude that the proposed methodology proves valuable in evaluating large traffic datasets' true information content. Further extensions, such as extracting smaller, spatially non-redundant datasets, are possible with this method.Comment: 13 pages, 5 figure

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Cloud-Chamber Observations of Some Unusual Neutral V Particles Having Light Secondaries

From six cloud-chamber photographs of unusual V0 decay events, the following conclusions are drawn: (1) there is a neutral V particle that decays into two particles lighter than κ mesons with a Q value too small to be consistent with a θ0(π, π, 214 Mev) particle; (2) some of these events cannot be explained in terms of the decay of a τ0(π0, π-, π+, Q∼80 Mev) particle; (3) these events can be explained by any one of a number of three-body decay schemes, but two different types of V particles must be postulated if two-body decays are assumed

Sibling Rivalry among Paralogs Promotes Evolution of the Human Brain

Geneticists have long sought to identify the genetic changes that made us human, but pinpointing the functionally relevant changes has been challenging. Two papers in this issue suggest that partial duplication of SRGAP2, producing an incomplete protein that antagonizes the original, contributed to human brain evolution

Complete Solving for Explicit Evaluation of Gauss Sums in the Index 2 Case

Let $p$ be a prime number, $q=p^f$ for some positive integer $f$, $N$ be a positive integer such that $\gcd(N,p)=1$, and let \k be a primitive multiplicative character of order $N$ over finite field \fq. This paper studies the problem of explicit evaluation of Gauss sums in "\textsl{index 2 case}" (i.e. f=\f{\p(N)}{2}=[\zn:\pp], where \p(\cd) is Euler function). Firstly, the classification of the Gauss sums in index 2 case is presented. Then, the explicit evaluation of Gauss sums G(\k^\la) (1\laN-1) in index 2 case with order $N$ being general even integer (i.e. N=2^{r}\cd N_0 where $r,N_0$ are positive integers and $N_03$ is odd.) is obtained. Thus, the problem of explicit evaluation of Gauss sums in index 2 case is completely solved

On the Exact Evaluation of Certain Instances of the Potts Partition Function by Quantum Computers

We present an efficient quantum algorithm for the exact evaluation of either the fully ferromagnetic or anti-ferromagnetic q-state Potts partition function Z for a family of graphs related to irreducible cyclic codes. This problem is related to the evaluation of the Jones and Tutte polynomials. We consider the connection between the weight enumerator polynomial from coding theory and Z and exploit the fact that there exists a quantum algorithm for efficiently estimating Gauss sums in order to obtain the weight enumerator for a certain class of linear codes. In this way we demonstrate that for a certain class of sparse graphs, which we call Irreducible Cyclic Cocycle Code (ICCC_\epsilon) graphs, quantum computers provide a polynomial speed up in the difference between the number of edges and vertices of the graph, and an exponential speed up in q, over the best classical algorithms known to date