Search Results (214)

This research introduces a new spectral pruning approach using the Adjacency Edge Index (AEI), which is a centrality measure from the theory of spectral graphs and first-order matrix perturbation theory. The AEI score reflects the contribution of each neuron to the network’s dynamic synchronizability via the Fiedler vector. The AEI approach thus offers a mathematically motivated saliency score in the context of data-driven neuron co-activation graphs. The proposed approach has been tested on MNIST, Fashion MNIST, KMNIST, and a real-world social network dataset. The approach has been extended to convolutional filter pruning on the CIFAR-10 dataset using spatial global average pooling. The AEI approach has been compared to magnitude-based pruning methods like L1 and L2 norms and gradient-based pruning methods like SNIP and GraSP. The robustness of the proposed approach has been established by comparing the results over five random seeds. The AEI approach is proposed as a principled, interpretable, structure-aware pruning criterion rather than an accuracy-maximising method. Spectral analysis demonstrates that AEI is the only evaluated method that systematically targets structurally peripheral neurons, whereas magnitude-based methods prune broadly across the structural spectrum and GraSP actively removes structurally central neurons, an effect most pronounced on more complex datasets and deeper architectures (CIFAR-100, ResNet-20), where it causes substantial accuracy degradation at high sparsity. The AEI approach has been extended to the Hybrid approach by combining the AEI and L2 norms. The Hybrid approach has been seen to improve the accuracy gap at 40% sparsity from 5.46 to 2.26 percentage points over the state of the art. The robustness of the proposed approach has been established by conducting ablation studies on the robustness of the approach to the selection of the graph. The approach has been seen to be moderately robust to the selection of the graph with Spearman’s $\rho$ ≈ 0.70. The accuracy gap has been seen to be less than 0.2%. Full article

Federated learning enables privacy-preserving distributed training but suffers from client drift and slow convergence under statistical data heterogeneity. Most existing federated optimization methods address client drift via parameter-space constraints or aggregation-level corrections, while fewer works directly shape the gradient covariance spectral structure of the optimization landscape. This paper analyzes the convergence problem from a spectral perspective, revealing that non-IID data causes spectral diffusion in the gradient covariance matrix and degrades convergence. Guided by random matrix theory, we propose federated spectral regularization (Fed-SR), a computationally efficient method that indirectly constrains spectral spread via gradient norm regularization. Although computing the regularizer gradient requires Hessian vector products, our optimized auto-differentiation implementation avoids storing full Hessian matrices and restricts extra computational overhead to a negligible level. Experiments on CIFAR-10, CIFAR-100, and other benchmarks show that Fed-SR outperforms baselines including FedAvg, FedProx, and SCAFFOLD in non-IID scenarios, reducing communication rounds and improving accuracy and stability. Ablation studies, spectral analysis, and controlled spectral feature manipulation experiments provide consistent empirical evidence showing a strong empirical association between the “spectral concentration” effect and performance gains, offering mechanistic interpretability consistent with our proposed theoretical framework within the tested experimental settings. Full article

Asymmetric interaction matrices encode the linear coupling structure and directed interaction patterns that arise in mathematical models of complex networks across ecology, finance, and machine learning, yet their geometric structure as points on a statistical manifold has received comparatively little systematic treatment. This paper develops a rigorous information-geometric framework for the manifold ${\mathcal{M}}_n^{+}$ of real $n\times n$ interaction matrices whose symmetric part is negative definite—equivalently, the matrices satisfying the numerical stability condition $\omega \left(A\right)={\lambda }_{\max }\left(S\left(A\right)\right)<0$. The symmetric part $S\left(A\right)=(A+A^{\mathsf{T}})/2$ and the skew-symmetric part $K\left(A\right)=(A-A^{\mathsf{T}})/2$ correspond, respectively, to the metric structure and the torsion of the induced statistical manifold. We construct the natural augmented Riemannian metric g on ${\mathcal{M}}_n^{+}$ as the sum of the Fisher–Rao pullback metric through $-S(·)$ and a Frobenius term on $K(·)$, derive explicit formulae for the sectional curvature in the mixed symmetric–skew plane, and prove that the sectional curvature vanishes if and only if A is normal. The central theoretical result is a curvature-mediated stability theorem: a Fisher–Rao stability margin, derived from the precision representative of A, provides a sharp, computationally accessible certificate for the asymptotic stability of the linear dynamical system $\dot{\mathbf{x}}=A\mathbf{x}$, with the instability boundary lying at infinite Fisher–Rao distance. We further establish an information-geometric reformulation of May’s stability criterion for random ecological networks, a curvature-based covariance regularisation scheme for financial correlation matrices, and a Jacobian stability bound for deep neural networks. All the main results are illustrated with explicit $3\times 3$ and $4\times 4$ numerical examples. Full article

Evaluating whether clinical classifiers perform equitably across patient subgroups is a central requirement for the responsible deployment of machine learning in medicine. Conventional approaches test one fairness metric at a time, such as sensitivity, positive predictive value, or area under the receiver operating characteristic curve, and therefore cannot detect disparities that manifest only in the joint structure of a group-specific confusion matrix. We develop a unified hypothesis-testing framework rooted in random matrix theory that compares demographic groups through the $L^2$ distance between their joint eigenvalue densities, yielding a scalar spectral divergence that is sensitive to every cell of the $2\times 2$ confusion matrix simultaneously. We derive the closed-form spectral divergence for Gaussian-approximated eigenvalue densities, prove almost-sure consistency of the empirical estimator via the delta method, and construct an extreme-value (Gumbel) test statistic with family-wise error rate control. Monte Carlo experiments comprising $\mathrm{10,000}$ replications across balanced, moderately imbalanced, and severely imbalanced group-size regimes show that the spectral test keeps Type I errors close to its nominal level while achieving power exceeding $90\%$ in complex and multi-dimensional violation scenarios, where the best single-metric competitor reaches at most $63\%$. Three clinical benchmark datasets from the UCI Machine Learning Repository utilised include Pima Indians Diabetes ($n=768$), Cleveland Heart Disease ($n=303$), and Heart Failure Clinical Records ($n=299$). Results confirm that the spectral method detects statistically significant ($p<0.001$) performance disparities missed by all three conventional tests. These results support eigenvalue-based divergence as a practical, model-agnostic diagnostic equity tool for clinical machine learning audits. Full article

We introduce the MERI (Market Evolutionary Resilience Index), a cognitive big data framework operationalising jamming transition physics into a daily operational regime detector (low-latency inference, 8 ms per observation). Opaque models cannot be deployed in regulated environments because every automated alert must decompose into auditable feature contributions. The MERI addresses this by treating the market as a complex adaptive system whose metabolic state constitutes the primary observable. Three cognitive layers fuse heterogeneous streaming data: an EGARCH-GED econometric baseline, a Random Forest classifier on a 15-dimensional physics-derived feature space, and a TreeSHAP Gini attribution audit ensuring full prediction-level transparency. Fisher Information Gain epistemic gating restricts automated intervention to predictions exceeding 2.5 nats certainty. Evaluated on South African financial markets (2015–2025, $N=2870$ trading days, Eskom load-shedding as exogenous forcing), the MERI achieves 97.3% accuracy (AUC = 0.9973, recall = 1.000), statistically equivalent to Temporal Fusion Transformers (Model Confidence Set, 90% confidence) while delivering 85.7% high-certainty predictions versus 23.4% for deep learning. A Granger-validated 48-h early warning lead ($F=62.003$, $p<0.001$), $7.78\times$ recovery hysteresis (Cohen’s $d=2.13$), and infrastructure dominance of 78.0% (Gini) confirm that the framework is operationally feasible for daily monitoring in the South African JSE–Eskom setting. Cross-domain portability is proposed as a theoretical extension pending empirical validation. Full article

Two-dimensional (2D) intrinsic ferromagnets with perpendicular magnetic anisotropy (PMA) have been experimentally verified as promising candidates for nanoscale spintronic devices and magnetic random-access memories. In this work, we systematically investigate the stability, electronic structure, and magnetic properties of monolayer MOCl (M = Ti, V, Cr, Mo) via first-principles calculations. The results demonstrate that allshi ciju monolayers MOCl (M = Ti, V, Cr, Mo) are intrinsic ferromagnetic semiconductors, with magnetic moments of 1.0 μ_B/Ti atom, 2.0 μ_B/V atom, 2.5 μ_B/Cr atom and 3.0 μ_B/Mo atom, respectively. Notably, both monolayers TiOCl and CrOCl exhibit perpendicular magnetic anisotropic energy (MAE), which is mainly contributed by metal atoms Ti and Cr, respectively. Drawing on the second-order perturbation theory, we conduct an analysis of the density of states and the magnetic anisotropy energy (MAE) resolved by d orbitals for Ti and Cr atoms. Our analysis shows that in monolayer TiOCl, the MAE of Ti atoms mainly stems from the disparities in matrix elements between the d_yz and d_x²−y² (d_xz) orbitals. Conversely, in monolayer CrOCl, the MAE of Cr atoms is largely due to the differences in matrix elements between the d_xy (d_yz) and d_x²−y² (d_z²) orbitals. Biaxial strain can efficiently regulate the MAE of monolayer CrOCl. Specifically, when under tensile strain, the MAE of monolayer CrOCl experiences a substantial increase. Our research results indicate that both monolayers TiOCl and CrOCl have significant potential for use in spintronic devices and high-density data storage systems. Full article

Rainfall-induced delayed instability of fractured rock slopes is strongly affected by fracture preferential flow, hydro-mechanical coupling, and spatial matrix heterogeneity. However, the coupled influence of stress-dependent fracture aperture evolution and heterogeneous matrix properties on delayed slope deformation remains insufficiently quantified. In this study, a two-dimensional discrete fracture network (DFN)–equivalent continuum coupled model was established using spectral random field theory and a representative Monte Carlo-generated fracture geometry. The spectral exponent β = 1.0–2.5 was adopted to characterize different degrees of matrix heterogeneity, and rainfall infiltration–stress coupling simulations were conducted under an extreme rainfall scenario followed by drainage. The results indicate that the wetting front advances irregularly in the heterogeneous matrix, while fracture preferential flow accelerates rainwater infiltration and promotes local pore-pressure accumulation near the phreatic surface. After rainfall cessation, water stored in fractures continues to recharge the deep matrix, leading to delayed pore-pressure increase and post-rainfall deformation. The simulated fracture aperture shows an initial closure followed by gradual dilation, which is controlled by the competition between saturation-induced stress redistribution and pore-pressure-driven effective stress reduction. Under a common strength reduction factor of FOS = 1.4, stronger matrix heterogeneity results in more pronounced plastic strain concentration and larger displacement amplitude along the potential slip zone. These findings suggest that fracture aperture evolution and matrix heterogeneity jointly influence delayed deformation and potential failure-zone development in rainfall-affected fractured rock slopes. The conclusions should be interpreted within the scope of a two-dimensional DFN–equivalent continuum numerical framework with prescribed rainfall conditions and representative fracture/random-field realizations. Full article

There is a lack of knowledge concerning the interlaminar fracture toughness of 3D-printed composite materials using both commercial filament composites and fused deposition modeling (FDM) technology from Markforged^®. In this investigation, additive manufacturing (AM) continuous fiber-reinforced thermoplastic (cFRT) specimens have been tested to characterize the initiation and propagation of interlaminar fracture toughness in mode I (G_I). Unidirectional glass fiber (GF)-reinforced polyamide 6 (PA) laminates were characterized by means of the double cantilever beam (DCB) test. These specimens were manufactured using a MarkTwo^® printer and tested without doublers, following a laminate configuration selected according to appropriate experimental findings reported in the state of the art, ensuring reliable fracture characterization. The experimental results exhibited repeatability and strong agreement between the modified compliance calibration (MCC) and modified beam theory (MBT) reduction methods. The resistance curve (R-curve) indicated a progressive increase in fracture resistance during crack propagation. To analyze the experienced failure mechanism during testing, the fracture surfaces of representative post-mortem DCB specimens were observed using a scanning electron microscope (SEM), revealing characteristic morphological features at two magnification levels. Moreover, representative cross-sections of the tested DCB specimens were electronically observed to analyze the interlaminar morphologies, showing an irregular and random distribution of the matrix, fiber, and voids between consecutive plies and adjacent deposited rasters. Compared with previously reported Markforged^® continuous fiber-reinforced systems, the GF/PA composite material exhibited intermediate initiation fracture toughness but lower propagation toughness. This study contributes to filling the existing gap in fracture toughness data for glass fiber-reinforced additively manufactured composites. Full article

We are interested in determining the physics bound for the detection of signals in modern digital radio frequency (RF) hardware. Classical signal theory (Kalman filters) requires that the signal-to-noise power ratio (SNR) $>10$, but this is not the physics bound. Instead, the physics bound is much more complicated. Because an important application is radar, we ask whether, in a time interval of 1 $\mathsf{\mu }$s, a signal is present within the noise of the receiver baseband. For radar, this would be the pulse return reflection. For our analysis, we use the Keysight Technologies UXR_25 oscilloscope as the RF receiver that has an analogue-to-digital converter (ADC) chip of 256 billion samples per second. In 1 $\mathsf{\mu }$s, then, 256 thousand voltage samples are taken. We want to determine if a signal is present using the 256 thousand voltage samples using random matrix theory (RMT). The answer for this particular ADC is that we can detect any signals with SNR >−20 dB, a thousand-fold increase from SNR > 10. This paper gives the physics bound of signal detection. Full article

This paper investigates time-varying output formation (TVOF) tracking for heterogeneous small fixed-wing unmanned aerial vehicles (UAVs) and nonholonomic unmanned ground vehicles (UGVs). The small fixed-wing UAVs operate in three-dimensional space, and the UGVs move on a two-dimensional plane, leading to heterogeneous dynamics with nonholonomic constraints, asymmetric velocity constraints, and input saturation. To address these challenges, distributed adaptive control protocols are developed under switching directed communication topologies. Unlike existing TVOF tracking methods that require global information, the proposed protocols do not rely on the upper bound of the leader’s unknown input or the eigenvalues of the Laplacian matrix. A constructive parameter-selection algorithm is provided, and the closed-loop stability is established using Lyapunov theory. Numerical simulations involving heterogeneous UAV-UGV formations verify that the proposed method achieves TVOF tracking under random disturbance while satisfying the prescribed motion constraints. Full article

This paper explores the relationship between random matrix theory (RMT) and the use of weight conditioning for training deep neural networks by employing an integrated framework. It has been shown that trained neural networks produce singular value distributions that follow universal distributions prescribed by RMT; however, the presence of non-universal outliers in the distribution can contain significant information particular to the task being performed. In addition, this research investigates how the application of diagonal row equilibration as a form of conditioning affects spectral behavior and optimization stability within deep neural networks. The results show that through conditioning, the random bulk of the singular value decomposition (SVD) spectrum is effectively compressed into a narrow band about the value 1, significantly reducing the Marchenko–Pastur bounds. The results also support the claim that weight conditioning retains the informative nature of the spectral outliers. The experimental results show that weight condition numbers (κ(W)) decreased from extremely ill-conditioned regimes of approximately 10³ to 10⁴ to almost 1.0, producing smoother training landscapes, a quicker convergence rate, and an improved ability for gradients to propagate. These results suggest that conditioning weights can be thought of as an implicit spectral regularize linking RMT evidence and concepts to the practical optimization of deep learning methods. Full article

Tensor completion is an extension of matrix completion aimed at recovering a multiway data tensor by leveraging a given subset of its entries (observations) and the pattern of observation. The low-rank assumption is key in establishing a relationship between the observed and unobserved entries of the tensor. The low-rank tensor completion problem is typically solved using numerical optimization techniques, where the rank information is used either implicitly (in the rank minimization approach) or explicitly (in the error minimization approach). Current theories concerning these techniques often study probabilistic recovery guarantees under conditions such as random uniform observations and incoherence requirements. However, if an observation pattern exhibits some low-rank structure that can be exploited, more efficient algorithms with deterministic recovery guarantees can be designed by leveraging this structure. This work shows how to use only standard linear algebra operations to compute the tensor train decomposition of a specific type of “fiber-wise” observed tensor, where some of the fibers of a tensor (along a single specific mode) are either fully observed or entirely missing, unlike the usual entry-wise observations. From an application viewpoint, this setting is relevant when it is easier to sample or collect a multiway data tensor along a specific mode (e.g., temporal). The proposed completion method is fast and is guaranteed to work under reasonable deterministic conditions on the observation pattern. Through numerical experiments, we showcase interesting applications and use cases that illustrate the effectiveness of the proposed approach. Full article

The covariance matrix performs a vital role for space-time adaptive processing (STAP) in airborne multiple-input multiple-output (MIMO) radar. As is known, the clutter-plus-noise covariance matrix (CPNCM), reflecting the statistical characteristics of radar echo, is a key component for MIMO-STAP. Commonly, an ideal CPNCM is impossible to obtain, and it must be estimated with sufficient snapshots. According to the RMB rule, MIMO-STAP requires many snapshots since MIMO radar has a high degree-of-freedom (DoF) due to its orthogonal transmit waveform. However, this is hard to satisfy in practice. This paper develops a novel covariance matrix estimation method under limited snapshots in airborne MIMO-STAP radar. Motivated by the random matrix theory, the proposed method enhances the CPNCM estimation by noise and clutter sample eigenvalues adjustment (EA). Concretely, the sample eigenvalues of noise are adjusted as noise power, and the ones of clutter are adjusted through minimizing the radar output power. Then, with the sample eigenvectors and adjusted sample eigenvalues, an effective CPNCM is formulated, and EA-MIMO-STAP is implemented reliably. Multiple experiments demonstrate that EA-MIMO-STAP has superior performance and robustness. Full article

In the framework of (fuzzy) Multi-Criteria Decision-Making, we propose a method that allows decision-makers to subjectively approach problems by suitably modifying a decision matrix. We consider a decision problem related to a random quantity X with a set of values $\{x_1,x_2,\dots ,x_n\}$ and a set of properties $\{C_1,C_2,\dots ,C_m\}$ of X. In this setting, the properties $C_j$ are the criteria of the decision problem, the alternatives represent the events $A_i=(X=x_i)$, for $i=1,\dots ,n$, and the criteria’s weights $w_j$, for $j=1,\dots ,m$, are seen as the probabilities for the event that “$C_j$ is relevant with respect to the decision problem”. For each $i=1,\dots ,n$ and $j=1,\dots ,m$, we interpret the scores $a_{ij}$ as membership functions representing “how much alternative $A_i$ satisfies criterion $C_j$”. By adopting an interpretation of membership functions as suitable conditional probabilities together with the theory of logical operations between conditional events, we allow logical operations between criteria and consistently apply this interpretation to the corresponding scores. In particular, when considering the complement, conjunction, and disjunction of criteria, the resulting scores are the (coherent) previsions of the respective compound conditionals within the framework of conditional random quantities. To illustrate our approach, we present an example concerning career choices. Full article

The assessment of reliability in non-repairable subsystems of mining electronic equipment represents a computationally challenging problem, particularly for complex and highly connected structures. This study presents a systematic comparative analysis of several deterministic approaches for reliability estimation, focusing on their computational efficiency, accuracy, and applicability. The investigated methods include classical boundary techniques (minimal paths and cuts), analytical decomposition based on the Bayes theorem, the logic–probabilistic method (LPM) employing triangle–star transformations, and the algorithmic Structure Convolution Method (SCM), which is based on matrix reduction of the system’s connectivity graph. The reliability problem is formally represented using graph theory, where each element is modeled as a binary variable with independent failures, which is a standard and practically justified assumption for power electronic subsystems operating without common-cause coupling. Numerical experiments were carried out on canonical benchmark topologies—bridge, tree, grid, and random connected graphs—representing different levels of structural complexity. The results demonstrate that the SCM achieves exact reliability values with up to six orders of magnitude acceleration compared to the LPM for systems containing more than 20 elements, while maintaining polynomial computational complexity. Qualitatively, the compared approaches differ in the nature of the output and practical applicability: boundary methods provide fast interval estimates suitable for preliminary screening, whereas decomposition may exhibit a systematic bias for highly connected (non-series–parallel) topologies. In contrast, the SCM consistently preserves exactness while remaining computationally tractable for medium and large sparse-to-moderately dense graphs, making it preferable for repeated recalculations in design and optimization workflows. The methods were implemented in Python 3.7 using NumPy and NetworkX, ensuring transparency and reproducibility. The findings confirm that the SCM is an efficient, scalable, and mathematically rigorous tool for reliability assessment and structural optimization of large-scale non-repairable systems. The presented methodology provides practical guidelines for selecting appropriate reliability evaluation techniques based on system complexity and computational resource constraints. Full article