Search Results (29)

Noisy permutation channels are applied in modeling biological storage systems and communication networks. For noisy permutation channels with strictly positive and full-rank square matrices, new achievability bounds are given in this paper, which are tighter than existing bounds. To derive this bound, we use the $ϵ$-packing with Kullback–Leibler divergence as a distance and introduce a novel way to illustrate the overlapping relationship of error events. This new bound shows analytically that for such a matrix W, the logarithm of the achievable code size with a given block n and error probability $ϵ$ is closely approximated by $\ell log\left({\displaystyle \frac{\sqrt{n}}{-{\Phi }^{-1}(ϵ/G)}}\right)+logV\left(W\right)$, where $\ell =\mathsf{rank}\left(W\right)-1$, $G=2\left({\displaystyle \genfrac{}{}{0pt}{}{\ell +1}{2}}\right)$, and $V\left(W\right)$ is a characteristic of the channel referred to as channel volume ratio. Our numerical results show that the new achievability bound significantly improves the lower bound of channel coding. Additionally, the Gaussian approximation can replace the complex computations of the new achievability bound over a wide range of relevant parameters. Full article

Federated learning (FL) enables privacy-preserving adaptation of large language models (LLMs) across distributed clients. However, deploying FL in edge environments remains challenging because of the high communication overhead of full-model updates. Recent advances in parameter-efficient fine-tuning (PEFT), particularly low-rank adaptation (LoRA), have substantially reduced update sizes by injecting lightweight trainable matrices into pretrained transformers, thereby making FL with LLMs more feasible. In this paper, we propose LoRaC-GA, a communication-aware optimization framework that dynamically determines the optimal number of clients to participate in each round under a fixed bandwidth constraint. We formulated a max-min objective to jointly maximize the model accuracy and communication efficiency and solved the resulting non-convex problem using a genetic algorithm (GA). To further reduce the overhead, we integrated a structured peer-to-peer collaboration protocol with ${log}_{2}K$ complexity, enabling scalable communication without full connectivity. The simulation results demonstrate that LoRaC-GA adaptively selects the optimal client count, achieving competitive accuracy while significantly reducing the communication cost. The proposed framework is well-suited for bandwidth-constrained edge deployments involving large-scale LLMs. Full article

Maximum Rank-Distance (MRD) codes are a class of optimal error-correcting codes that achieve the Singleton-like bound for rank metric, making them invaluable in applications such as network coding, cryptography, and distributed storage. While algebraic constructions of MRD codes (e.g., Gabidulin codes) are well-studied for specific parameters, a comprehensive theory for their existence and structure over arbitrary finite fields remains an open challenge. Recent advances have expanded MRD research to include twisted, scattered, convolutional, and machine-learning-aided approaches, yet many parameter regimes remain unexplored. This paper introduces a computational optimization framework for constructing MRD codes using Particle Swarm Optimization (PSO), a bio-inspired metaheuristic algorithm adept at navigating high-dimensional, non-linear, and discrete search spaces. Unlike traditional algebraic methods, our approach does not rely on prescribed algebraic structures; instead, it systematically explores the space of possible generator matrices to identify MRD configurations, particularly in cases where theoretical constructions are unknown. Key contributions include: (1) a tailored finite-field PSO formulation that encodes rank-metric constraints into the optimization process, with explicit parameter control to address convergence speed and global optimality; (2) a theoretical analysis of the adaptability of PSO to MRD construction in complex search landscapes, supported by experiments demonstrating its ability to find codes beyond classical families; and (3) an open-source Python toolkit for MRD code discovery, enabling full reproducibility and extension to other rank-metric scenarios. The proposed method complements established theory while opening new avenues for hybrid metaheuristic–algebraic and machine learning–aided MRD code construction. Full article

This paper presents three novel sufficient and necessary conditions for the admissibility of singular fractional-order systems (FOSs), a stabilization criterion, and a solution algorithm. The strict linear matrix inequality (LMI) stability criterion for integer-order systems is generalized to singular FOSs by using column-full rank matrices. This admissibility criterion does not involve complex variables and is different from all previous results, filling a gap in this area. Based on the LMIs in the generalized condition, the improved criterion utilizes a variable substitution technique to reduce the number of matrix variables to be solved from one pair to one, reflecting the admissibility more essentially. This improved result simplifies the programming process compared to the traditional approach that requires two matrix variables. To complete the state feedback controller design, the system matrices in the generalized admissibility criterion are decoupled, but bilinear constraints still occur in the stabilization criterion. For this case, where a feasible solution cannot be found using the MATLAB LMI toolbox, a branch-and-bound algorithm (BBA) is designed to solve it. Finally, the validity of these criteria and the BBA is verified by three examples, including a real circuit model. Full article

The increasing threat of quantum computing to traditional cryptographic systems has prompted intense research into post-quantum schemes. Despite SNOVA’s potential for lightweight and secure digital signatures, its performance on embedded devices (e.g., ARMv8 platforms) remains underexplored. This research addresses this gap by presenting the optimal SNOVA implementations on embedded devices. This paper presents a performance-optimized implementation of the SNOVA post-quantum digital signature scheme on ARMv8 processors. SNOVA is a multivariate cryptographic algorithm under consideration in the NIST’s additional signature standardization. Our work targets the performance bottlenecks in the SNOVA scheme. Specifically, we employ matrix arithmetic over ${\mathbb{GF}}_{16}$ and AES-CTR-based pseudorandom number generation by exploiting the NEON SIMD extension and tailoring the computations to the matrix rank. At a low level, we develop rank-specific SIMD kernels for addition and multiplication. Rank 4 matrices (i.e., 16 bytes) are handled using fully vectorized instructions that align with 128-bit-wise registers, while rank 2 matrices (i.e., 4 bytes) are processed in batches of four to ensure full SIMD occupancy. At the high level, core routines such as key generation and signature evaluation are structurally refactored to provide aligned memory layouts for batched execution. This joint optimization across algorithmic layers reduces the overhead and enables seamless hardware acceleration. The resulting implementation supports 12 SNOVA parameter sets and demonstrates substantial efficiency improvements compared to the reference baseline. These results highlight that fine-grained SIMD adaptation is essential for the efficient deployment of multivariate cryptography on modern embedded platforms. Full article

Background and Objectives: Military capability may be reduced in hot environments with individuals at risk of exertional heat stroke (EHS). Heat tolerance testing (HTT) can be used to indicate readiness to return to duty following EHS. HTT traditionally relies on rectal core temperature (T_re) assessment via a rectal probe. This study investigated the use of gastrointestinal core temperature (T_gi) as an alternative to T_re during HTT. A secondary aim was to compare physiological factors between heat-tolerant and heat-intolerant trials. Materials and Methods: Australian Defence Force personnel undergoing HTT following known or suspected heat stroke volunteered (n = 23 cases participating in 26 trials) along with 14 controls with no known heat illness history. Confusion matrices enabled comparison of HTT outcome based on T_gi and T_re. The validity of T_gi compared to T_re during HTT was assessed using correlation and bias. Comparisons between heat-tolerant and intolerant trials were performed using non-parametric tests. Results: Although T_gi correlated closely with T_re (Spearman’s rank correlation $\rho$ = 0.893; median bias 0.2 °C) there was no consistent pattern in the differences between measures. Importantly, the two measures only agreed on heat tolerance outcome in 80% of trials with T_gi failing to detect heat intolerance identified by T_re in 6 of 8 trials. If T_gi was relied upon for diagnostic outcome, return to duty may occur before full recovery. None of the assessed covariates were related to the difference between T_re and T_gi. In addition, resting heart rate and systolic blood pressure were significantly lower and body surface area to mass ratio significantly higher in heat-tolerant compared to intolerant trials. Conclusions: It is not recommended to rely on T_gi instead of T_re during HTT. Resting heart rate and systolic blood pressure findings point to the importance of aerobic exercise in conveying heat tolerance along with body composition. Full article

Lyn is a multifunctional Src-family kinase (SFK) that regulates immune signaling and has been implicated in diverse types of cancer. Unlike other SFKs, its full-length structure and regulatory dynamics remain poorly characterized. In this study, we present the first long-timescale molecular dynamics analysis of full-length Lyn, including the SH3, SH2, and SH1 domains, across wildtype, ligand-bound, and cancer-associated mutant states. Using principal component analysis, dynamic cross-correlation matrices, and network-based methods, we show that ATP binding stabilizes the kinase core and promotes interdomain coordination, while the ATP-competitive inhibitor dasatinib and specific mutations (e.g., E290K, I364N) induce conformational decoupling and weaken long-range communication. We identify integration modules and develop an interface-weighted scoring scheme to rank dynamically central residues. This analysis reveals 44 allosteric hubs spanning SH3, SH2, SH1, and interdomain regions. Finally, a random forest classifier trained on 16 MD-derived features highlights key interdomain descriptors, distinguishing functional states with an AUC of 0.98. Our results offer a dynamic and network-level framework for understanding Lyn regulation and identify potential regulatory hotspots for structure-based drug design. More broadly, our approach demonstrates the value of integrating full-length MD simulations with network and machine learning techniques to probe allosteric control in multidomain kinases. Full article

This paper proposes a class of randomized Kaczmarz and Gauss–Seidel-type methods for solving the matrix equation $AXB=C$, where the matrices A and B may be either full-rank or rank deficient and the system may be consistent or inconsistent. These iterative methods offer high computational efficiency and low memory requirements, as they avoid costly matrix–matrix multiplications. We rigorously establish theoretical convergence guarantees, proving that the generated sequences converge to the minimal Frobenius-norm solution (for consistent systems) or the minimal Frobenius-norm least squares solution (for inconsistent systems). Numerical experiments demonstrate the superiority of these methods over conventional matrix multiplication-based iterative approaches, particularly for high-dimensional problems. Full article

The problem of determining the conditions under which a random rectangular matrix is of full rank is a fundamental question in random matrix theory, with significant implications for coding theory, cryptography, and combinatorics. In this paper, we study the probability of full rank for a $K\times N$ random matrix over the finite field ${\mathbb{F}}_q$, where q is a prime power, under the assumption that the rows of the matrix are sampled independently from a probability distribution $\mathcal{P}$ over ${\mathbb{F}}_q^N$. We demonstrate that the probability of full rank attains a local maximum when the distribution $\mathcal{P}$ is uniform over ${\mathbb{F}}_q^N\setminus \left\{0\right\}$, for any $K⩽N$ and prime power q. Moreover, we establish that this local maximum is also a global maximum in the special case where $K=2$. These results highlight the optimality of the uniform distribution in maximizing full rank and represent a significant step toward solving the broader problem of maximizing the probability of full rank for random matrices over finite fields. Full article

This paper introduces an efficient approach for implementing the Four-Dimensional Variational Ensemble Kalman Filter (4D-EnKF) for non-linear data assimilation, leveraging a modified Cholesky decomposition (4D-EnKF-MC). In this method, control spaces at observation times are represented by full-rank square root approximations of background error covariance matrices, derived using the modified Cholesky decomposition. To ensure global convergence, we integrate line-search optimization into the filter formulation. The performance of the 4D-EnKF-MC is evaluated through experimental tests using the Lorenz 96 model, and its accuracy is compared to that of a 4D-Var extension of the Maximum-Likelihood Ensemble Filter (4D-MLEF). Through Root Mean Square Error (RMSE) analysis, we demonstrate that the proposed method outperforms the 4D-MLEF across a range of ensemble sizes and observational network configurations, providing a robust and scalable solution for non-linear data assimilation in complex systems. Full article

Protocols to evaluate turfgrass quality rely on visual ratings that, depending on the rater’s expertise, can be subjective and susceptible to positive and negative drifts. We developed seasonal (spring, summer and fall) as well as inter-seasonal machine learning predictive models of turfgrass quality using multispectral and thermal imagery collected using unmanned aerial vehicles for two years as a proof-of-concept. We chose ordinal regression to develop the models instead of conventional classification to account for the ranked nature of the turfgrass quality assessments. We implemented a fuzzy correction of the resulting confusion matrices to ameliorate the probable drift of the field-based visual ratings. The best seasonal predictions were rendered by the fall (multi-class AUC: 0.774, original kappa 0.139, corrected kappa: 0.707) model. However, the best overall predictions were obtained when observation across seasons and years were used for model fitting (multi-class AUC: 0.872, original kappa 0.365, corrected kappa: 0.872), clearly highlighting the need to integrate inter-seasonal variability to enhance models’ accuracies. Vegetation indices such as the NDVI, GNDVI, RVI, CGI and the thermal band can render as much information as a full array of predictors. Our protocol for modeling turfgrass quality can be followed to develop a library of predictive models that can be used in different settings where turfgrass quality ratings are needed. Full article

In the present paper, we introduce the concept of idempotent-aided factorization (I.-A. factorization) of a regular element of a semigroup, which can be understood as a semigroup-theoretical extension of full-rank factorization of matrices over a field. I.-A. factorization of a regular element d is defined by means of an idempotent e from its Green’s $\mathcal{D}$-class as decomposition into the product $d=uv$, so that the element u belongs to the Green’s $\mathcal{R}$-class of the element d and the Green’s $\mathcal{L}$-class of the idempotent e, while the element v belongs to the Green’s $\mathcal{L}$-class of the element d and the Green’s $\mathcal{R}$-class of the idempotent e. The main result of the paper is a theorem which states that each regular element of a semigroup possesses an I.-A. factorization with respect to each idempotent from its Green’s $\mathcal{D}$-class. In addition, we prove that when one of the factors is given, then the other factor is uniquely determined. I.-A. factorizations are then used to provide new existence conditions and characterizations of group inverses and $(b,c)$-inverses in a semigroup. In our further research, these factorizations will be applied to matrices with entries in a field, and efficient algorithms for realization of such factorizations will be provided. Full article

A rigorous perturbation analysis is presented for the singular value decomposition (SVD) of a real matrix with full column rank. It is proved that the SVD perturbation problem is well posed only when the singular values are distinct. The analysis involves the solution of symmetric coupled systems of linear equations. It produces asymptotic (local) componentwise perturbation bounds on the entries of the orthogonal matrices participating in the decomposition of the given matrix and on its singular values. Local bounds are derived for the sensitivity of the singular subspaces measured by the angles between the unperturbed and perturbed subspaces. Determining the asymptotic bounds of the orthogonal matrices and the sensitivity of singular subspaces requires knowing only the norm of the perturbation of the given matrix. An iterative scheme is described to find global bounds on the respective perturbations, and results from numerical experiments are presented. Full article

A randomized block Kaczmarz method and a randomized extended block Kaczmarz method are proposed for solving the matrix equation $AXB=C$, where the matrices A and B may be full-rank or rank-deficient. These methods are iterative methods without matrix multiplication, and are especially suitable for solving large-scale matrix equations. It is theoretically proved that these methods converge to the solution or least-square solution of the matrix equation. The numerical results show that these methods are more efficient than the existing algorithms for high-dimensional matrix equations. Full article

The Toeplitz matrix reconstruction methods are capable of resolving coherent signals, playing a crucial role in the direction-of-arrival (DOA) estimation of acoustic sources. However, the decoherence processing sacrifices the array aperture and further results in a reduced resolution capability for the number of identifiable sources. To solve this issue, we propose an enhanced method using the Khatri–Rao subspace to resolve more coherent sources than that of the existing Toeplitz matrix reconstruction methods. Firstly, a full set of Toeplitz matrices with full rank is obtained. Then, the virtual array aperture can be obtained using the Khatri–Rao product of the array response, and the degree of freedom provided inherently in the virtual array structure is about twice the size of that of the existing Toeplitz methods. Next, linear processing is further used to achieve complexity reduction without losing the effective degree of freedom. Finally, the DOA estimation for more coherent sources can be achieved by combining it with conventional methods. Numerical simulations verify the superiority of the proposed method. Full article