相关论文: Rational-Exponent Filters with Applications to Gen…

We present a real-space formulation and higher-order finite-difference implementation of periodic Orbital-free Density Functional Theory (OF-DFT). Specifically, utilizing a local reformulation of the electrostatic and kernel terms, we…

Formal explainability guarantees the rigor of computed explanations, and so it is paramount in domains where rigor is critical, including those deemed high-risk. Unfortunately, since its inception formal explainability has been hampered by…

Lagrangian averaging is a valuable tool for the analysis and modelling of multiscale processes in fluid dynamics. The numerical computation of Lagrangian (time) averages from simulation data is challenging, however. It can be carried out by…

We investigate rational $G$-modules $M$ for a linear algebraic group $G$ over an algebraically closed field $k$ of characteristic $p > 0$ using filtrations by sub-coalgebras of the coordinate algebra $k[G]$ of $G$. Even in the special case…

We combine high-dimensional factor models with fractional integration methods and derive models where nonstationary, potentially cointegrated data of different persistence is modelled as a function of common fractionally integrated factors.…

Parameter-Efficient Fine-Tuning (PEFT) methods achieve performance comparable to Full Fine-Tuning (FFT) while requiring significantly fewer computing resources, making it the go-to choice for researchers. We find that although PEFT can…

Collaborative Filtering (CF) is a pivotal research area in recommender systems that capitalizes on collaborative similarities between users and items to provide personalized recommendations. With the remarkable achievements of node…

The problem of stability of the optimal filter is revisited. The optimal filter (or filtering process) is the conditional probability of the current state of some stochastic process (the signal process), given both present and past values…

First-order logic (FOL) can represent the logical entailment semantics of natural language (NL) sentences, but determining natural language entailment using FOL remains a challenge. To address this, we propose the Entailment-Preserving FOL…

New energy-density functionals (EDFs) inspired by effective-field theories (EFTs) have been recently proposed. The present work focuses on three of such functionals which were developed to produce satisfactory equations of state for nuclear…

We generalize the popular ensemble Kalman filter to an ensemble transform filter where the prior distribution can take the form of a Gaussian mixture or a Gaussian kernel density estimator. The design of the filter is based on a continuous…

This work aims to extend the existing results on the Hausdorff dimension of the classical thick point sets of a Gaussian free field (GFF) to a more general class of exceptional sets. We adopt the circle or sphere averaging regularization to…

This paper deals with the implementation of the extended robust Kalman filter (ERKF) which was developed considering uncertainties in the parameter matrices of the underlying state-space model. A key contribution of this work is the…

Fourier matrices naturally appear in many applications and their stability is closely tied to performance guarantees of algorithms. The starting point of this article is a result that characterizes properties of an exponential system on a…

In this paper the Mittag-Leffler function is given through the exponential functions for any rational derivatives of m/n order, where m<n, n>1 are natural irreducible numbers (if n=1 then m is also equal to unity). Unlike the previous…

We identify the (filter representation of the) logic behind the recent theory of coherent sets of desirable (sets of) things, which generalise coherent sets of desirable (sets of) gambles as well as coherent choice functions, and show that…

As large language models (LLMs) like GPT become increasingly prevalent, it is essential that we assess their capabilities beyond language processing. This paper examines the economic rationality of GPT by instructing it to make budgetary…

A novel wavelet-like function is presented that makes it convenient to create filter banks given mainly two parameters that influence the focus area and the filter count. This is accomplished by computing the inverse Fourier transform of…

A generalization of the Heisenberg algebra has been recently constructed. This generalized algebra has a characteristic function which depends on one of its generators. When this function is linear, $qJ_0+s$, it is possible to construct a…

Counterfactual explanations have been widely studied in explainability, with a range of application dependent methods prominent in fairness, recourse and model understanding. The major shortcoming associated with these methods, however, is…