We develop a stochastic model of cache stampede in distributed systems with a time-to-live (TTL) caching layer. Requests for a cache key form a Poisson process of rate λ, and the backend recomputation time ξ has a general distribution F with finite first two moments μ and μ2. We formally introduce "the vulnerability window"—the interval during which a missing entry exposes the backend to redundant computation—and derive the exact stampede probability P=1−Lξ(λ), where Lξ(λ)=E[e−λξ] is the Laplace–Stieltjes transform of ξ, together with the expected backend load of 1+λμ calls per miss episode. The naive, mutex-lock, and request-deduplication (coalescing) strategies are compared within a common miss-episode model; probabilistic early expiration (XFetch), scoped to an implementation with a single-flight guard on the refresh path, is analyzed separately at the TTL-cycle level, since early refresh changes the renewal cycle itself. We prove that deduplication attains the minimum backend load among strategies that regenerate a fresh value after expiration—exactly one backend computation per miss episode, for every λ. The expected latency of a typical request in a deduplication window is (μ+λμ2/2)/(1+λμ), while the mean waiting time pooled over the non-initiating (coalesced) requests equals the mean residual computation time R=μ2/(2μ) for every λ—a manifestation of the inspection paradox. By contrast, a transient single-server FIFO backend under the naive strategy yields a mean window latency μ+λμ2/2 that grows linearly in λ. We further formulate an optimal-TTL problem balancing expected latency against a data-staleness cost over the exact renewal cycle (idle gap included) and obtain, under a mild explicit condition, the unique interior optimum τ∗=−d+d2+(2μ/λ+μ2−2cd)/γ−−−−−−−−−−−−−−−−−−−−√, d=μ+1/λ, in closed form, without relying on high-popularity approximations (here c is the cache-read latency and γ the staleness cost per unit of age). Monte Carlo simulation (N=2×105 runs for probabilities and 6×104 for latency) numerically verifies the analytical miss-episode and TTL results within the stated model: at the reference point λ=50 req/s the stampede probability for a lognormal backend, evaluated independently by numerical integration, agrees with simulation to 0.02%, and all verification metrics agree with theory to within 0.5%.
Robust 6DoF camera relocalization is critical for autonomous robotics, yet the performance of modern local feature matchers under real-world sensor degradation remains poorly quantified. This paper presents a systematic empirical evaluation of visual localization pipelines under progressive JPEG compression, additive Gaussian noise, and motion blur. By decomposing global runtime, we expose two critical anomalies: the Sinkhorn Computational Collapse in dense transformer matchers (SuperGlue), where normalization latency increases exponentially up to 3354.9 ms, and the RANSAC Paradox in context-free matching (NN-mutual), which pollutes spatial solvers with over 87% outliers, extending verification time up to 2099.6 ms. Additionally, we discover a JPEG Low-Pass Regularization Effect that generates localized accuracy peaks. Pareto frontier analysis demonstrates that LightGlue eliminates these bottlenecks, maintaining a predictable execution profile (1013.6–1273.2 ms) and stable 10–15 cm precision, providing a foundational paradigm for resource-constrained embedded systems.
A physical-mathematical model is proposed for studying Joule heat and temperature in an electrically conductive, non-ferromagnetic hollow cylinder under induction treatment. The model comprises two stages. The first stage involves formulating an electrodynamic problem for the long hollow cylinder to determine the induced electromagnetic field and the Joule heat density. The second stage addresses the resulting heat conduction problem, from which the temperature distribution caused by Joule heating is obtained. The solutions to both the electrodynamic and heat conduction problems are constructed using a cubic approximation of the axial component of the magnetic field intensity vector and the temperature with respect to the radial coordinate. The coefficients of these approximating polynomials are expressed as linear combinations of the radial integral characteristics of the governing functions together with their values at the inner and outer surfaces of the cylinder. This approach reduces the original boundary-value problems to systems of equations for the integral characteristics, for which general solutions under transient electromagnetic excitation are derived. Explicit expressions are then presented for the axial component of the magnetic field intensity, the Joule heat, and the temperature arising from the transient electromagnetic action. A numerical analysis of these quantities is carried out for a long hollow aluminum cylinder, examining their dependence on the amplitude-frequency characteristics of the applied field and on the duration of its action.
This paper provides a comprehensive review of the state-of-the-art in Automated Machine Learning (AutoML) and Symbolic Regression (SR), focusing on the integration of Large Language Models (LLMs) and intelligent agents. We systematically analyze classical AutoML frameworks, End-to-End multi-agent systems, data-centric AI approaches, and hybrid methods combining LLMs with Bayesian Optimization. Each approach is evaluated based on its autonomy, computational efficiency, reliability, and suitability for highly regulated domains. The study highlights that while LLM agents offer high flexibility, they suffer from hallucinations and deployment complexities. Conversely, data-centric and hybrid methods provide better reliability and mathematical convergence. We conclude that no single universal solution exists and propose a pragmatic hybrid modular pipeline: utilizing data-centric agents for semantic data preparation, followed by robust classical or hybrid optimizers for mathematically guaranteed model selection.
The paper studies the numerical stability of branched continued fractions that represent expansions of triple hypergeometric functions FK with real parameters in special cases. Using a new method for estimating the relative errors of computing approximants via a backward recurrence algorithm, we establish the domain of numerical stability for these branched continued fractions. Additionally, the behavior of the relative errors in computing the approximants of the branched continued fractions using this algorithm was experimentally investigated. Numerical experiments confirm the obtained theoretical results.
