相关论文: Types of signature analysis in reliability based o…
A certain type of integer grid, called here an echelon grid, is an object found both in coherent systems whose components have a finite or countable number of levels and in algebraic geometry. If \alpha=(\alpha_1,...,\alpha_d) is an integer…
Let $ R=k[x_1...x_r]$ and $M$ a multigraded $R-$module. In this work we interpret $M$ as a multipersistent homology module and give a multigraded resolution of it. The construction involves cellular resolutions of monomial ideals and…
Strongly stable monomial ideals are important in algebraic geometry, commutative algebra, and combinatorics. Prompted, for example, by combinatorial approaches for studying Hilbert schemes and the existence of maximal total Betti numbers…
This study introduces a framework for evaluating consistency in large language model (LLM) binary text classification, addressing the lack of established reliability assessment methods. Adapting psychometric principles, we determine sample…
The concept of signature is a useful tool in the analysis of semicoherent systems with continuous and i.i.d. component lifetimes, especially for the comparison of different system designs and the computation of the system reliability. For…
We present the design and implementation of a \texttt{C++} class for reliability analysis of multi-state systems using an algebraic approach based on monomial ideals. The class is implemented within the open-source \verb|CoCoALib| library…
We introduce the lcm-filtration and stepwise filtration, comparing their performance across various scenarios in terms of computational complexity, efficiency, and redundancy. The lcm-filtration often involves identical steps or ideals,…
The reliability of a system of components depends on reliability of each component. Thus, the initial statistical work should be the estimation of the reliability of each component of the system. This is not an easy task because when the…
Usually, methods evaluating system reliability require engineers to quantify the reliability of each of the system components. For series and parallel systems, there are some options to handle the estimation of each component's reliability.…
In this paper we review different definitions that multi-state $k$-out-of-$n$ systems have received along the literature and study them in a unified way using the algebra of monomial ideals. We thus obtain formulas and algorithms to compute…
We suggest a purely combinatorial approach to a general problem in system reliability. We show how to determine if a given vector can be the signature of a system, and in the affirmative case exhibit such a system in terms on its structure…
Large language models are increasingly deployed as protocols: structured multi-call procedures that spend additional computation to transform a baseline answer into a final one. These protocols are evaluated only by end-to-end accuracy,…
Large Language Models (LLMs) demonstrate impressive mathematical reasoning abilities, but their solutions frequently contain errors that cannot be automatically checked. Formal theorem proving systems such as Lean 4 offer automated…
The growing reliance on computer systems, particularly personal computers (PCs), necessitates heightened reliability to uphold user satisfaction. This research paper presents an in-depth analysis of extensive system telemetry data,…
A short proof of the "Rigidity theorem" using the sheaf theoretic model for Hilbert modules over polynomial rings is given. The joint kernel for a large class of submodules is described. The completion $[\mathcal I]$ of a homogeneous…
This paper addresses the consensus problem in homonymous distributed systems where processes are prone to crash failures and have no initial knowledge of the system membership ("homonymous" means that several processes may have the same…
Software testing and verification are critical for ensuring the reliability and security of modern software systems. Traditionally, formal verification techniques, such as model checking and theorem proving, have provided rigorous…
Complex systems typically have many different parts and facets, with different characteristics. In a multi-paradigm approach to modeling, formalisms with different natures are used in combination to describe complementary parts and aspects…
We consider the stability and the input-output analysis problems of a class of large-scale hybrid systems composed of continuous dynamics coupled with discrete dynamics defined over finite alphabets, e.g., deterministic finite state…
Recent works have investigated the sample complexity necessary for fair machine learning. The most advanced of such sample complexity bounds are developed by analyzing multicalibration uniform convergence for a given predictor class. We…