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The parareal in time algorithm allows to efficiently use parallel computing for the simulation of time-dependent problems. It is based on a decomposition of the time interval into subintervals, and on a predictor-corrector strategy, where…

Transformer-based large language model (LLM) inference serving is now the backbone of many cloud services. LLM inference consists of a prefill phase and a decode phase. However, existing LLM deployment practices often overlook the distinct…

Thermodynamic integration (TI) for computing marginal likelihoods is based on an inverse annealing path from the prior to the posterior distribution. In many cases, the resulting estimator suffers from high variability, which particularly…

A stability analysis of the Borel-Laplace series summation technique, used as explicit time integrator, is carried out. Its numerical performance on stiff and non-stiff problems is analyzed. Applications to ordinary and partial differential…

We propose a scheme to realize parity-time (PT) symmetry via electromagnetically induced transparency (EIT). The system we consider is an ensemble of cold four-level atoms with an EIT core. We show that the cross-phase modulation…

We present a framework for learning of modeling uncertainties in Linear Time Invariant (LTI) systems. We propose a methodology to extend the dynamics of an LTI (without uncertainty) with an uncertainty model, based on measured data, to…

Artificial Intelligence for Theorem Proving has given rise to a plethora of benchmarks and methodologies, particularly in Interactive Theorem Proving (ITP). Research in the area is fragmented, with a diverse set of approaches being spread…

The inversion of nabla Laplace transform, corresponding to a causal sequence, is considered. Two classical methods, i.e., residual calculation method and partial fraction method are developed to perform the inverse nabla Laplace transform.…

Recent advances in Large Language Models (LLMs) have demonstrated new possibilities for accurate and efficient time series analysis, but prior work often required heavy fine-tuning and/or ignored inter-series correlations. In this work, we…

We generalize ideas in the recent literature and develop new ones in order to propose a general class of contour integral methods for linear convection-diffusion PDEs and in particular for those arising in finance. These methods aim to…

Sparse Identification of Nonlinear Dynamical Systems (SINDy) is a powerful tool for the data-driven discovery of governing equations. However, it encounters challenges when modeling complex dynamical systems involving high-order derivatives…

This paper proposes a new methodology for subspace identification of linear time-periodic (LTP) systems with periodic inputs. This method overcomes the issues related to the computation of frequency response of LTP systems by utilizing the…

The authors propose a robust semi-parametric empirical likelihood method to integrate all available information from multiple samples with a common center of measurements. Two different sets of estimating equations are used to improve the…

Propositional linear time temporal logic (LTL) is the standard temporal logic for computing applications and many reasoning techniques and tools have been developed for it. Tableaux for deciding satisfiability have existed since the 1980s.…

We introduce a significant improvement for a relatively new machine learning method called Transformation-Based Learning. By applying a Monte Carlo strategy to randomly sample from the space of rules, rather than exhaustively analyzing all…

Quantized tensor trains (QTTs) are a low-rank and multiscale framework that allows for efficient approximation and manipulation of multi-dimensional, high resolution data. One area of active research is their use in numerical simulation of…

Recent Transformer-based large language models (LLMs) demonstrate in-context learning ability to perform various functions based solely on the provided context, without updating model parameters. To fully utilize the in-context capabilities…

In this paper we apply the innovative Laplace transformation method introduced by Sheen, Sloan, and Thom\'ee (IMA J. Numer. Anal., 2003) to solve the Black-Scholes equation. The algorithm is of arbitrary high convergence rate and naturally…

The aim of this work is to prove inverse formulas for Laplace transform on semilattices of open-and-compact sets in a both discrete and non-discrete cases. These are partial answers to a question posed by Yu.~I.~Lyubich.

Temporal Logic (TL) can be used to rigorously specify complex high-level specification for systems in many engineering applications. The translation between natural language (NL) and TL has been under-explored due to the lack of dataset and…