Dynamic Mode Decomposition ( <scp>DMD</scp> ) for Low‐Latency Real‐Time Cardiac <scp>MRI</scp>

Magnetic Resonance in Medicine · 2026-03-30

PURPOSE: To demonstrate dynamic mode decomposition (DMD) for high spatiotemporal low-latency online reconstruction in 2D real-time cardiac MRI. METHODS: DMD was applied to 2D spiral balanced steady state free precession (bSSFP) real-time adult and fetal cardiac MRI at 0.55 T, with data from 10 healthy adult volunteers (3F/7M; age: 21-49; BMI: 20-34) and 6 pregnant females (maternal age: 30-41; maternal BMI: 22-47; gestational age: 23 weeks 6 days-37 weeks 5 days). DMD model appropriateness was assessed against off-line spatiotemporally constrained reconstruction (STCR) as the reference. We retrospectively evaluated DMD-based low-latency online reconstruction at two temporal resolutions (21 and 42 ms/frame). DMD modes were estimated from the most recently acquired frames and used to remove aliasing while preserving underlying physiological motion. RESULTS: DMD represented cardiac dynamics with normalized root-mean-square error (NRMSE) less than 7% when all modes retained. Low-latency DMD-based online reconstruction performed de-aliasing while preserving the physiological motion, supporting framerates (21 and 42 ms/frame). CONCLUSION: We have demonstrated that the DMD framework is applicable to 2D real-time cardiac MRI and for low-latency de-aliasing for better online reconstruction.

Patterns of Human Injuries and Fatalities in Fire Incidents in Serbia: A Comprehensive Statistical and Data Mining Analysis

Fire · 2026-04-02

This manuscript is a continuation of the research published in Fire 2025, 8(8), 302, i.e., it deals with the examination of the cause-and-effect relationships of fires in the Republic of Serbia from the aspect of human safety. Among others, variables related to gender, age, and severity of injuries caused by fires are introduced, on which various methods of statistical analysis and stochastic modeling are first applied. Continuous age variables are modelled using the flexible Generalized Additive Models for Location, Scale, and Shape (GAMLSS) framework, where the Generalized Normal Distribution (GND) is identified as the optimal generative model for injuries, while a Reflected Log-Normal Distribution with positive support (RefLOGND+) provides the best fit for fatalities. The quality of such modeling is formally verified, and the probabilities of injury and death of individuals in certain age categories are predicted, revealing a pronounced concentration of injuries in the working-age population and a markedly higher relative risk of fatal outcomes among elderly individuals. Thereafter, by applying certain Data Mining (DM) techniques, primarily the Apriori algorithm, the most frequently occurring association rules are found, which indicate typical patterns and demographic structure of injuries and deaths in fires in Serbia. Finally, using the CART (Classification and Regression Trees) algorithm, several decision trees are formed that describe the impact and relationship of different causes of fires on injury and death in fires. In this way, some important and frequent patterns are observed that indicate key fire risk factors that significantly affect the demographic structure of human casualties. The results thus obtained provide a basis for developing targeted strategies for fire prevention and improving emergency response planning.

Tannenbaum's gain-margin optimization meets Polyak's heavy-ball algorithm

IEEE Transactions on Automatic Control · 2026-01-01

This paper highlights an apparent, yet relatively unknown link between algorithm design in optimization theory and controller synthesis in robust control. Specifically, quadratic optimization can be recast as a regulation problem within the framework of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_\infty$</tex-math></inline-formula> control. From this vantage point, the optimality of Polyak's fastest heavy-ball algorithm can be ascertained as a solution to a gain margin optimization problem. The approach is independent of Polyak's original and brilliant argument, and relies on foundational work by Tannenbaum, who introduced and solved gain margin optimization via Nevanlinna–Pick interpolation theory. The link between first-order optimization methods and robust control sheds new light on the limits of algorithmic performance of such methods, and suggests a framework where similar computational tasks can be systematically studied and algorithms optimized. In particular, it raises the question as to whether periodically scheduled algorithms can achieve faster rates for quadratic optimization, in a manner analogous to periodic control that extends the gain margin beyond that of time-invariant control. This turns out not to be the case, due to the analytic obstruction of a transmission zero that is inherent in causal schemes. Interestingly, this obstruction can be removed with implicit algorithms, cast as feedback regulation problems with causal, but not strictly causal dynamics, thereby devoid of the transmission zero at infinity and able to achieve superior convergence rates.

Automated algorithm design for convex optimization problems with linear equality constraints

2025-12-09

Synthesis of optimization algorithms typically follows a design-then-analyze approach, which can obscure fundamental performance limits and hinder the systematic development of algorithms that operate near these limits. Recently, a framework grounded in robust control theory has emerged as a powerful tool for automating algorithm synthesis. By integrating design and analysis stages, fundamental performance bounds are revealed and synthesis of algorithms that achieve them is enabled. In this paper, we apply this framework to design algorithms for solving strongly convex optimization problems with linear equality constraints. Our approach yields a single-loop, gradient-based algorithm whose convergence rate is independent of the condition number of the constraint matrix. This improves upon the best known rate within the same algorithm class, which depends on the product of the condition numbers of the objective function and the constraint matrix.

Forensic and Cause-and-Effect Analysis of Fire Safety in the Republic of Serbia: An Approach Based on Data Mining

Fire · 2025-07-31 · 2 citations

The manuscript examines the cause-and-effect relationships of fires in the Republic of Serbia over a fifteen-year period, primarily from the aspect of human safety. For this purpose, numerical variables describing the number of injuries and deaths in fires were introduced, on which various analysis and modeling techniques were implemented, which can be viewed in the context of data mining (DM). First, for both observed variables, stochastic modeling of their temporal dynamics was analyzed, and subsequently, cluster analysis of the values of these variables was performed using two different methods. Finally, by interpreting these variables as outputs (objectives) for the classification problem, several decision trees were formed that describe the influence and relationship of different fire causes on situations in which injuries or human casualties occur or not. In that way, several different types of fires have been identified, including rare but deadly incidents that require urgent preventive measures. Key risk factors such as fire cause, location, season, etc., have been found to significantly influence human casualties. These findings provide practical insights for improving fire protection policies and emergency response. Through such a comprehensive analysis, it is believed that some important results have been obtained that precisely describe the specific relationships between the causes and consequences of fires occurring in the Republic of Serbia.

Application of the GSB Process in Stochastic Modeling the Network Intrusion Detection Threshold

IPSI Transactions on Internet Research · 2025-01-01

This manuscript proposes one possible solution for intrusion detection (IDS) based on stochastic modeling of the threshold value, which is defined as a random variable (RV) obtained using the so-called General Split-BREAK (GSB) stochastic process. Applying such a model to previously recorded traffic values and using this type of stochastic modeling allows for more accurate and real-time threshold adjustment for IDS software. Conducted numerical simulations and application to real data show that alarms obtained by using this method are activated correctly and efficiently, with a potential reduction in the number of incorrect and fraudulent activations.

Reattachment streaks in hypersonic compression ramp flow: an input–output analysis – ERRATUM

Journal of Fluid Mechanics · 2025-10-10

Automated algorithm design for convex optimization problems with linear equality constraints

ArXiv.org · 2025-09-25

Synthesis of optimization algorithms typically follows a {\em design-then-analyze\/} approach, which can obscure fundamental performance limits and hinder the systematic development of algorithms that operate near these limits. Recently, a framework grounded in robust control theory has emerged as a powerful tool for automating algorithm synthesis. By integrating design and analysis stages, fundamental performance bounds are revealed and synthesis of algorithms that achieve them is enabled. In this paper, we apply this framework to design algorithms for solving strongly convex optimization problems with linear equality constraints. Our approach yields a single-loop, gradient-based algorithm whose convergence rate is independent of the condition number of the constraint matrix. This improves upon the best known rate within the same algorithm class, which depends on the product of the condition numbers of the objective function and the constraint matrix.

Accelerated forward–backward and Douglas–Rachford splitting dynamics

Automatica · 2025-02-24 · 1 citations

The Role of Communication Delays in the Optimal Control of Spatially Invariant Systems

IEEE Transactions on Automatic Control · 2025-08-23

We study optimal proportional feedback controllers for spatially invariant systems when the controller has access to delayed state measurements received from different spatial locations. We analyze how delays affect the spatial locality of the optimal feedback gain leveraging the problem decoupling in the spatial frequency domain. For the cases of expensive control and small delay, we provide exact expressions of the optimal controllers in the limit for infinite control weight and vanishing delay, respectively. In the expensive control regime, the optimal feedback control law decomposes into a delay-aware filtering of the delayed state and the optimal controller in the delay-free setting. Under small delays, the optimal controller is a perturbation of the delay-free one which depends linearly on the delay. We illustrate our analytical findings with a reaction-diffusion process over the real line and a multi-agent system coupled through circulant matrices, showing that delays reduce the effectiveness of optimal feedback control and may require each subsystem within a distributed implementation to communicate with farther-away locations.