Linear Codes Research Articles

Hybrid kinetic-MHD modeling of alpha-driven TAEs in the SPARC tokamak

Abstract As the magnetic confinement fusion community prepares for the next generation of fusion devices and burning plasmas, there is still a question of whether fast ions (FIs) will drive MHD instabilities, causing significant redistribution or even loss of FIs, thereby leading to reduced plasma performance and possibly threatening the integrity of the first wall. In this paper, we explore the existence and stability of Toroidicity-induced Alfven Eigenmodes (TAEs) in the >100 MW, Q ∼ 9 − 11 DT-fusion power “Primary Reference Discharge” (PRD) of the SPARC tokamak; the PRD has a relatively low on-axis alpha pressure, βα0 ≈ 0.6%, due to the high magnetic field strength, B0 = 12.2 T. A scan in toroidal mode number is performed in the vicinity of the estimated “most unstable” modes, n ≈ 5−20, with the linear eigenvalue code NOVA-K and nonlinear initial-value code MEGA. Both codes identify the same (even) n = 10 TAE located near q = 1 with frequency f ≈ 360 kHz and alpha drive γ/ω ≈ +0.6%. While MEGA evaluates this mode to be marginally unstable for the nominal alpha pressure, NOVA-K instead identifies a higher frequency (odd) n = 10 TAE as marginally destabilized; different evaluations of radiative damping are likely the cause of this discrepancy. These results indicate that AEs may be only marginally unstable for the highest performing SPARC PRD, at least for the q profile explored here. They also serve as a starting point for further scans, inclusion of FIs from auxiliary heating systems, and exploration of AE-induced FI transport, as well as a guide for diagnostic measurements of these n ≈ 10 AEs

Adaptive nonlinear deep coding using hybrid attention for wireless image transmission

Adaptive nonlinear deep coding using hybrid attention for wireless image transmission

Symplectic ACD codes over a non-commutative non-unitary ring

We introduce a symplectic inner product on vectors over a non-unitary non commutative ring of order 4. Linear and additive codes over that ring are explored from the standpoint of self-duality and complementarity with their duals.

A Computationally Efficient Method for the Diagnosis of Defects in Rolling Bearings Based on Linear Predictive Coding

Monitoring the condition of rolling bearings is a crucial task in many industries. An efficient tool for diagnosing bearing defects is necessary since they can lead to complete machine failure and significant economic losses. Traditional diagnosis solutions often rely on a complex artificial feature extraction process that is time-consuming, computationally expensive, and too complex to deploy in practice. In actual working conditions, however, the amount of labeled fault data available is relatively small, so a deep learning model with good generalization and high accuracy is difficult to train. This paper proposes a solution that uses a simple feedforward artificial neural network (NN) for classification and adopts the linear predictive coding (LPC) algorithm for feature extraction. The LPC algorithm finds several coefficients for a given signal segment containing information about the signal spectrum, which is sufficient for further classification. The LPC-NN solution was tested on the Case Western Reserve University (CWRU) and South Ural State University (SUSU) datasets. The results demonstrated that, in most cases, LPC-NN yielded an accuracy of 100%. The proposed method achieves higher diagnostic accuracy and stability to load changes than other advanced techniques, has a significantly improved time performance, and is conducive to real-time industrial fault diagnosis.

Effective connectivity predicts distributed neural coding of perceptual decision confidence, uncertainty, and speed

Abstract Decision making is often accompanied by a level of confidence regarding the accuracy of one’s decision. Previous studies have indicated neural activity associated with perceptual decision confidence during sensory stimulus presentation. Choice-based reaction time (RT) has been suggested as an indirect but more objective measure of decision confidence—generally faster RT for higher confidence. However, it is unclear whether choice confidence and RT are mediated by distinct neural pathways, and whether their neural correlates are encoded nonlinearly. Within a perceptual decision-making task, we applied functional magnetic resonance imaging-informed electroencephalography-based effective connectivity analysis via dynamic causal modelling (DCM) on event-related potentials and found the frontoparietal network for fast-vs-slow RT condition to be different from that of high-vs-low confidence rating condition. Furthermore, trial-by-trial DCM analysis predicted cortical layer-based, distributed, and nonlinear coding of RT, confidence or uncertainty. Collectively, our study suggests that decision confidence and speed are instantiated by different dynamical networks distributed across cortical layers.

The dimensions of Galois hulls of linear codes derived from an improved propagation rule and related applications

The dimensions of Galois hulls of linear codes derived from an improved propagation rule and related applications

Effect of ply orientation on impact resistance of woven GFRP composites subjected to projectile impact

The focus of this paper is to present experimental and numerical investigations on the effect of fibre orientation on ballistic resistance and energy absorption capacity of glass fibre reinforced polymer (GFRP) panels. Experiments were conducted on three different GFRP laminates made of woven fabric with cross ply, angle ply and combination of cross ply and angle ply (hybrid) with dimensions of 140 mm ×140 mm ×1 mm (thick) subjected to projectile impact with 12 mm spherical projectile using single-stage gas gun setup. In each case of cross ply, angle ply and hybrid composite laminates, six experiments with nearly same velocities (52, 55, 58, 62.5, 65 and 68 m/s) were conducted and the experiments exhibited denting and perforation. The numerical analysis was carried out using LSDYNA non-linear finite-element code considering strain rate effects based on Cowper-Symonds relation. The residual velocity, ballistic limit, energy absorption capacity and damage area of GFRP laminates obtained from numerical analysis is compared with experimental results.

Optimization of LDPC decoding algorithm in semi-conductor storage based on artificial neural networks

ABSTRACT Low-density parity check digit is a linear block code, which is applied to semiconductor storage to achieve effective information storage. However, in semiconductor storage, the existing ways have weak decoding performance and high bit error rate. Therefore, the decoding algorithm in the existing low-density parity check digit is optimised. Then, a semiconductor storage decoding optimisation algorithm based on artificial neural networks is designed to improve decoding performance. In addition, a multi-layer perceptron neural network is introduced to construct an optimised decoding method. The experimental results showed that when the threshold was 5, the throughput of the low-density parity check decoding algorithm based on the multi-layer perceptron decreased slowly with the increase in the signal-to-noise ratio. The minimum throughput rate was 1.18. The proposed semiconductor storage decoding optimisation algorithm based on artificial neural networks has better decoding performance. In summary, the proposed decoding optimisation method for semiconductor storage has good performance, which can effectively achieve information decoding in semiconductor storage.

Proximity Gaps in Interleaved Codes

A linear error-correcting code exhibits proximity gaps if each affine line of words either consists entirely of words which are close to the code or else contains almost no such words. In this short note, we prove that for each linear code which exhibits proximity gaps within the unique decoding radius, that code's interleaved code also does. Combining our result with a recent argument of Angeris, Evans and Roh ('24), we extend those authors' sharpening of the tensor-based proximity gap of Diamond and Posen (Commun. Cryptol. '24) up to the unique decoding radius, at least in the Reed–Solomon setting.

A multi-level feature fusion artificial neural network for classification of acoustic emission signals.

In this paper, we introduce FUSION-ANN, a novel artificial neural network (ANN) designed for acoustic emission (AE) signal classification. FUSION-ANN comprises four distinct ANN branches, each housing anindependent multilayer perceptron. We extract denoised features of speech recognition such as linear predictive coding, Mel-frequency cepstral coefficient, and gammatone cepstral coefficient to represent AE signals. These features are concatenated to form a new feature called LMGC, which serves as input data for the four branches of FUSION-ANN. The network performs AE signal recognition and classification through forward propagation in each branch, utilizing multi-level feature fusion. We evaluate FUSION-ANN's performance on the ORION-AE benchmark dataset, which contains AE signals from various loading conditions simulating loosening phenomena in aeronautics, automotive, and civil engineering structures. Our results demonstrate an impressive average accuracy of 98% in AE signal classification. Additionally, FUSION-ANN boasts high training efficiency, robustness, and accuracy, making it suitable for reliable AE signal analysis. However, given the current limitations, we aim to conduct more comprehensive investigations in the future. Our plan includes further testing of the network's performance across various categories of AE signals to assess its generality. Additionally, we will select richer and more efficient feature sets to characterize these signals.

Every $ \mathbb{F}_q $-linear code is equivalent to a multi-twisted code

Every $ \mathbb{F}_q $-linear code is equivalent to a multi-twisted code

Eigenvalue Sensitivity Computations for Linear Stability Theory

To realize the drag reduction benefit of boundary-layer transition control strategies, it is crucial to integrate transition prediction into the vehicle design through an optimization process. The integration of transition prediction based on linear stability analysis into adjoint-based design optimization requires coupling an adjoint-enabled computational fluid dynamics (CFD) solver with an adjoint-enabled linear stability code. In particular, the boundary-layer transition location is often predicted using the N-factor method based on linear stability theory (LST). Thus, the sensitivity of the linear-stability eigenvalues constitutes an essential building block for optimizing the laminar flow performance. The present paper describes an implementation of LST eigenvalue sensitivity analysis that can be easily coupled with a CFD solver. Specifically, we describe a discrete adjoint formulation for the transition location prediction based on the N-factor method. The verification of this formulation is carried out by comparing the adjoint-based sensitivity of the local growth rate of a given instability mode with respect to the disturbance frequency and the adjoint-based sensitivity of the transition location with respect to the spanwise wavenumber with those sensitivities computed using a finite-difference approximation. Finally, the adjoint LST formulation is applied to flat-plate boundary-layer flows at transonic, supersonic, and hypersonic conditions to determine the behavior and sensitivities of the transition location with respect to a range of disturbance spanwise wavenumbers.

Weight distributions and weight hierarchies of a class of binary linear codes with a few weights

Weight distributions and weight hierarchies of a class of binary linear codes with a few weights

A Mass Formula for Linear Codes With Prescribed Hull Dimension and Related Classification

A Mass Formula for Linear Codes With Prescribed Hull Dimension and Related Classification

Construction of linear codes with various Hermitian hull dimensions and related EAQECCs

Construction of linear codes with various Hermitian hull dimensions and related EAQECCs

Minimal linear codes constructed from hierarchical posets with two levels

Minimal linear codes constructed from hierarchical posets with two levels

The weight distributions of several classes of few-weight linear codes

The weight distributions of several classes of few-weight linear codes

The support designs of several families of lifted linear codes

The support designs of several families of lifted linear codes

Using Skew Cyclic Codes Over R = R<sub>1</sub>×R<sub>2</sub>×R<sub>3</sub> to Detect Skew Cyclic Codes Over F<sub>q</sub>

This article investigates linear codes over the ring , focusing on the properties and structure of skew cyclic codes within this framework. We explore various algebraic features of these codes, highlighting their distinctivenessfrom traditional cyclic codes. In addition, we examine the utility ofskew cyclic codes over in the context of identifying skew cyclic codes over the finite field with optimal parameters. The findings offer fresh perspectives on developing efficient and high-performing coding systems, which could benefit error correction and data transmission applications.

Advantage distillation for quantum key distribution

Abstract Quantum key distribution promises information-theoretically secure communication, with data post-processing playing a vital role in extracting secure keys from raw data. While hardware advancements have significantly improved practical implementations, optimizing post-processing techniques offers a cost-effective avenue to enhance performance. Advantage distillation, which extends beyond standard information reconciliation and privacy amplification, has proven instrumental in various post-processing methods. However, the optimal post-processing remains an open question. Therefore, it is important to develop a comprehensive framework to encapsulate and enhance these existing methods. In this work, we propose an advantage distillation framework for quantum key distribution, generalizing and unifying existing key distillation protocols. Inspired by entanglement distillation, our framework not only integrates current techniques but also improves upon them. Notably, by employing classical linear codes, we achieve higher key rates, particularly in scenarios where one-time pad encryption is not used for post-processing. Our approach provides insights into existing protocols and offers a systematic way for further enhancements in quantum key distribution.