Search Results for « Structured Dynamic Covariance Recovery »

Ransomware recovery in critical manufacturing infrastructure is not only a backup-restoration problem. Production capability depends on coupled information-technology, operational-technology, physical-process, quality, logistics, identity, and supplier systems. After ransomware, a plant may rebuild servers yet remain unable to schedule work, authenticate operators, trust engineering workstations, release product, reconnect OT assets, or coordinate suppliers. This paper reframes manufacturing ransomware recovery as a critical-infrastructure continuity and interdependency problem. We conduct a PRISMA-guided multivocal review of academic literature, standards and government guidance, threat frameworks, public incident material, and verified full-text/source-page evidence anchors. The review identifies nine evidence-backed recovery failure modes: dependency blindness, untrusted restore point and backup over-trust, identity trust collapse, lack of proof-of-recovery, unsafe OT reconnection, segmentation assumption failure, capability mismatch, unmanaged degraded operation, and supplier dependency failure. We then introduce Minimum Viable Factory Recovery (MVF Recovery): the smallest safe, trusted, and operationally meaningful production capability that can be resumed under current dependency, evidence, identity, data, network, OT, and supplier constraints. MVF Recovery is an analytical objective rather than a claim of full recovery, implementation, or safety certification. The paper derives a recovery lifecycle and benchmarking directions as secondary outputs. The contribution is an evidence-calibrated foundation for capability-centric ransomware recovery in critical manufacturing infrastructure.

We propose a flexible yet interpretable model for high-dimensional data with time-varying second order statistics, motivated and applied to functional neuroimaging data. Motivated by the neuroscience literature, we factorize the covariances into sparse spatial and smooth temporal components. While this factorization results in both parsimony and domain interpretability, the resulting estimation problem is nonconvex. To this end, we design a two-stage optimization scheme with a carefully tailored spectral initialization, combined with iteratively refined alternating projected gradient descent. We prove a linear convergence rate up to a nontrivial statistical error for the proposed descent scheme and establish sample complexity guarantees for the estimator. We further quantify the statistical error for the multivariate Gaussian case. Empirical results using simulated and real brain imaging data illustrate that our approach outperforms existing baselines.

A recovery map effectively cancels the action of a quantum operation to a partial or full extent. We study the Petz recovery map in the case where the quantum channel and input states are fermionic and Gaussian. Gaussian states are convenient because they are totally determined by their covariance matrix and because they form a closed set under so-called Gaussian channels. Using a Grassmann representation of fermionic Gaussian maps, we show that the Petz recovery map is also Gaussian and determine it explicitly in terms of the covariance matrix of the reference state and the data of the channel. As a by-product, we obtain a formula for the fidelity between two fermionic Gaussian states. We also discuss subtleties arising from the singularities of the involved matrices.

Protein design is moving beyond structural correctness toward function-aware design, yet existing generative models typically treat dynamics as a downstream property estimated through simulation or prediction after structure generation. Using MD trajectories as a generative target is also undesirable because stochastic, path-dependent trajectories over-specify the underlying equilibrium ensemble. We introduce PhiFold, a framework for jointly generating protein backbones and their second-order dynamics, represented by residue-displacement covariance. Rather than predicting the quadratically sized full covariance, PhiFold decomposes dynamics into three interpretable components: local flexibility, a low-rank collective-motion representation, and residue-wise collective participation. These components are assembled into a positive-definite covariance matrix with exact marginal consistency, yielding a compact and physically constrained representation of equilibrium dynamics. Across generated proteins, PhiFold improves recovery of local fluctuations and long-range residue coupling while remaining competitive on dominant collective-motion subspaces. It further enables bidirectional control of residue flexibility while preserving backbone designability. By unifying structure generation with an explicit representation of equilibrium dynamics, PhiFold lays a foundation for designing proteins not only by how they look, but also by how they move.

We study the problem of determining the configuration of $n$ points by using their distances to $m$ nodes, referred to as anchor nodes. One sampling scheme is Nystrom sampling, which assumes known distances between the anchors and between the anchors and the $n$ points, while the distances among the $n$ points are unknown. For this scheme, a simple adaptation of the Nystrom method, which is often used for kernel approximation, is a viable technique to estimate the configuration of the anchors and the $n$ points. In this manuscript, we propose a modified version of Nystrom sampling, where the distances from every node to one central node are known, but all other distances are incomplete. In this setting, the standard Nystrom approach is not applicable, necessitating an alternative technique to estimate the configuration of the anchors and the $n$ points. We show that this problem can be framed as the recovery of a low-rank submatrix of a Gram matrix. Using synthetic and real data, we demonstrate that the proposed approach can exactly recover configurations of points given sufficient distance samples. This underscores that, in contrast to methods that rely on global sampling of distance matrices, the task of estimating the configuration of points can be done efficiently via structured sampling with well-chosen reliable anchors. Finally, our main analysis is grounded in a specific centering of the points. With this in mind, we extend previous work in Euclidean distance geometry by providing a general dual basis approach for points centered anywhere.

Despite the popularity of traditional fit index cutoffs like RMSEA ≤ .06 and CFI ≥ .95, several studies have noted issues with overgeneralizing traditional cutoffs. Computational methods have been proposed to avoid overgeneralization by deriving cutoffs specifically tailored to characteristics of the model being evaluated. Simulations show favorable performance of these methods; however, these methods support a narrow set of models and response scales (i.e., only continuous variables) and interpretation of cutoffs is not always standardized, which affects empirical researchers’ ability to confidently and broadly adopt these methods to evaluate model fit. In this paper, we propose an extension to one recently developed computational method—dynamic fit index cutoffs—that (a) permits application to any covariance structure model (e.g., CFA, mediation, bifactor), (b) standardizes interpretation of cutoffs across any covariance structure model, and (c) supports normal, nonnormal, categorical, and missing data. Software is provided to facilitate implementation of the method.

In sparse information recovery, the core problem is to solve the $l_0$-minimization which is NP-hard. On one hand, in order to recover the original sparse solution, there are a lot of papers designing alternative model for $l_0$-minimization. As one of the most popular choice, the logarithmic alternative model is widely used in many applications. In this paper, we present an unified theoretical analysis of this alternative model designed for $l_0$-minimization. By the theoretical analysis, we prove the equivalence relationship between the alternative model and the original $l_0$-minimization. Furthermore, the main contribution of this paper is to give an unified recovery condition and stable result of this model. By presenting the local optimal condition, this paper also designs an unified algorithm and presents the corresponding convergence result. Finally, we use this new algorithm to solve the multiple source location problem.

Covariance is a fundamental measure to describe the dependency structure between two random variables and covariance modelling is significant in a wide range of applications. Existing systems mainly assume the covariance is static even though covariance structure is typically dynamic in real-world settings, which indicates the need of dynamic covariance modelling. Two main approaches are mainly adopted in covariance parameterisation: covariance-function-based methods and matrix-decomposition-based methods. Covariance-function-based approaches describe the covariance structure with parsimonious parameters, thereby effectively solve the the rapid growth in the number of parameters with the increment of covariance dimension but they may fail to guarantee positive definiteness in non-stationary settings. Covariance decomposition methods, on the other hand, offer unconstrained factors that guarantee positive-definite output but suffer from the quadratic increase of estimated parameters and poor statistical interpretability. As a result, methods that simultaneously ensure positive definiteness and maintain parsimonious parameterisations remain largely unexplored. Motivated by these limitations, we propose a flexible estimation framework for covariance functions by adopting positive-definite regularisations of the objective functions. This framework imposes penalties on eigenvalues or the determinant of the estimated covariance matrix, thereby enforcing positive-definiteness with no additional estimated parameters required. This framework effectively addresses the positive-definite issue for covariance functions while maintaining its strengths, which makes it suitable for high-dimensional dynamic covariance modelling. Simulation studies and real-data applications demonstrate that the proposed framework consistently improves estimation accuracy while ensuring positive definite covariance estimates across a range of stationary and non-stationary covariance structures.

Sparse Autoencoders (SAEs) decompose residual-stream activations into interpretable features. Recent latent-space defenses increasingly rely on these decompositions, assuming that identified "unsafe" SAE features serve as actionable handles for monitoring and intervention. In this paradigm, clamping a specific harmful feature is expected to reliably prevent model misbehavior. However, we show that this success may hide a recoverable failure mode: the clamp may block one visible route to a behavior without eliminating the behavior itself. We formulate this vulnerability as post-intervention recovery, a constrained residual-space optimization problem. Starting from the post-intervention residual state, we optimize residual perturbations to recover the pre-intervention behavior while preserving the post-intervention values of the targeted SAE features. Even under a strong threat model where the intervention remains active throughout optimization and generation, recovery remains possible. To rule out that recovery simply undoes the intervention, we use encoder-orthogonal updates for single-layer interventions and the corresponding feature-map Jacobian in the cross-layer setting. Across TPP, unlearning, IOI, and refusal steering experiments, this stress test reveals recoverable behavior despite successful feature-level intervention. Especially in the safety-critical refusal-steering setting, we achieve a 95.8% recovery rate on valid samples while keeping defended-feature relative drift to 0.131, substantially below suffix-based baselines. A recovery-path attribution analysis further localizes this recovery to the SAE reconstruction residual, the component left unexplained by the SAE. These results expose a gap between feature-level control and behavioral completeness: SAE features can support causal intervention, but controlling them does not guarantee control over the underlying behavior.

In this paper, we analyze the relation between the stability of a noisy dynamical system based on linear approximation and the covariance matrix of its stationary distribution. We reformulate the theory of dynamical network biomarkers in terms of the covariance matrix and clarify the limiting behavior of the covariance matrix when a dynamical system approaches a bifurcation point. We also discuss the relation between the Jacobian matrix and principal component analysis. An application to a simple nonlinear network model is also demonstrated.