Related papers: Asymptotic Mean Time To Failure and Higher Moments…
We study the reliability of phase oscillator networks in response to fluctuating inputs. Reliability means that an input elicits essentially identical responses upon repeated presentations, regardless of the network's initial condition. In…
Exponential averages that appear in integral fluctuation theorems can be recast as a sum over moments of thermodynamic observables. We use two examples to show that such moment series can exhibit non-uniform convergence in certain singular…
Incipient fault detection in power distribution systems is crucial to improve the reliability of the grid. However, the non-stationary nature and the inadequacy of the training dataset due to the self-recovery of the incipient fault signal,…
We obtain exponential moment asymptotics for the Bessel point process. As a direct consequence, we improve on the asymptotics for the expectation and variance of the associated counting function, and establish several central limit…
This paper considers multi-dimensional affine processes with continuous sample paths. By analyzing the Riccati system, which is associated with affine processes via the transform formula, we fully characterize the regions of exponents in…
By application of the theory for second-order linear differential equations with two turning points developed in [Olver F.W.J., Philos. Trans. Roy. Soc. London Ser. A 278 (1975), 137-174], uniform asymptotic approximations are obtained in…
Self-powered intermittent systems typically adopt runtime checkpointing as a means to accumulate computation progress across power cycles and recover system status from power failures. However, existing approaches based on the checkpointing…
Although it is widely accepted that every system should be robust, in the sense that "small" violations of environment assumptions should lead to "small" violations of system guarantees, it is less clear how to make this intuitive notion of…
We studied metastability and extinction time of a finite system with a large number of interacting components in discrete time by means of analytical and numerical investigation. The system is markovian with respect to the potential profile…
We found that a reliability model commonly used to estimate Mean-Time-To-Data-Loss (MTTDL), while suitable for modeling RAID 0 and RAID 5, fails to accurately model systems having a fault-tolerance greater than 1. Therefore, to model the…
Recursive learning -- where models are trained on data generated by previous versions of themselves -- is increasingly common in large language models, autonomous agents, and self-supervised systems. However, standard performance metrics…
Large Language Models (LLMs) have revolutionized conversational AI, yet their robustness in extended multi-turn dialogues remains poorly understood. Existing evaluation frameworks focus on static benchmarks and single-turn assessments,…
The first passage time (FPT) distribution for random walk in complex networks is calculated through an asymptotic analysis. For network with size $N$ and short relaxation time $\tau\ll N$, the computed mean first passage time (MFPT), which…
Large Language Model (LLM) serving systems remain fundamentally fragile, where frequent hardware faults in hyperscale clusters trigger disproportionate service outages in the software stack. Current recovery mechanisms are prohibitively…
Affine point processes are a class of simple point processes with self- and mutually-exciting properties, and they have found useful applications in several areas. In this paper, we obtain large-time asymptotic expansions in large…
In this paper, we study large multi-server loss models under power-of-$d$ routing scheme when service time distributions are general with finite mean. Previous works have addressed the exponential service time case when the number of…
This paper considers inference for conditional moment inequality models using a multiscale statistic. We derive the asymptotic distribution of this test statistic and use the result to propose feasible critical values that have a simple…
This paper develops the asymptotic theory for parametric and nonparametric regression models when the errors have a fractional local to unity root (FLUR) model structure. FLUR models are stationary time series with semi-long range…
Large Language Models (LLMs), despite their impressive capabilities, often fail to accurately repeat a single word when prompted to, and instead output unrelated text. This unexplained failure mode represents a vulnerability, allowing even…
While statement autoformalization has advanced rapidly, full-theorem autoformalization remains largely unexplored. Existing iterative refinement methods in statement autoformalization typically improve isolated aspects of formalization,…