Related papers: Fault-Tolerant Modular Reconstruction of Rational …

Tandem duplication is the process of inserting a copy of a segment of DNA adjacent to the original position. Motivated by applications that store data in living organisms, Jain et al. (2017) proposed the study of codes that correct tandem…

Uncertainty estimates must be calibrated (i.e., accurate) and sharp (i.e., informative) in order to be useful. This has motivated a variety of methods for recalibration, which use held-out data to turn an uncalibrated model into a…

Context-sensitive global analysis of large code bases can be expensive, which can make its use impractical during software development. However, there are many situations in which modifications are small and isolated within a few…

In this paper, motivated by diffraction of traveling light waves, a simple mathematical model is proposed, both for the multivariate super-resolution problem and the problem of blind-source separation of real-valued exponential sums. This…

We give a complete characterization of degree two rational maps with potential good reduction over local fields. We show this happens exactly when the map corresponds to an integral point in the moduli space. We detail an algorithm by which…

A reconstruction problem of words from scattered factors asks for the minimal information, like multisets of scattered factors of a given length or the number of occurrences of scattered factors from a given set, necessary to uniquely…

A reconstruction problem is formulated for multisets over commutative groupoids. The cards of a multiset are obtained by replacing a pair of its elements by their sum. Necessary and sufficient conditions for the reconstructibility of…

This paper proposes an algorithm for computing regularized solutions to linear rational expectations models. The algorithm allows for regularization cross-sectionally as well as across frequencies. A variety of numerical examples illustrate…

Generating multi-contrasts/modal MRI of the same anatomy enriches diagnostic information but is limited in practice due to excessive data acquisition time. In this paper, we propose a novel deep-learning model for joint reconstruction and…

We present a simple algorithm for inverting the sweep map on rational $(m,n)$-Dyck paths for a co-prime pair $(m,n)$ of positive integers. This work is inspired by Thomas-Williams work on the modular sweep map. A simple proof of the…

We propose a method to construct a variety of partition identities at once. The main application is an all-moduli generalization of some of Andrews' results in [5]. The novelty is that the method constructs solutions to functional equations…

We derive formulas which connect cumulants of particle numbers observed with efficiency losses with the original ones based on the binomial model. These formulas can describe the case with multiple efficiencies in a compact form. Compared…

The recursive method for computing the generalized LM-inverse of a constant rectangular matrix augmented by a column vector is proposed in Udwadia and Phohomsiri (2007) [16] and [17]. The corresponding algorithm for the sequential…

The Chinese remainder theorem (CRT) provides an efficient way to reconstruct an integer from its remainders modulo several integer moduli, and has been widely applied in signal processing and information theory. Its multidimensional…

In this paper, we develop a method of evaluating general exponential sums with rational amplitude functions for multiple variables which complements works by T. Cochrane and Z. Zheng on the single variable case. As an application, for…

This paper introduces a new series of methods which combine modal decomposition algorithms, such as singular value decomposition and high-order singular value decomposition, and deep learning architectures to repair, enhance, and increase…

We transform the two-matrix model, studied by P.Di Francesco and al., into a normal one-matrix model by identifying a ``formal'' integral used by these authors as a proper integral. We show also, using their method, that the results…

We discuss some examples that illustrate the countability of the positive rational numbers and related sets. Techniques include radix representations, Godel numbering, the fundamental theorem of arithmetic, continued fractions, Egyptian…

Resummation, ie. reorganization of perturbative series, can result in an inconsistent perturbation theory, unless the counterterms are reorganized in an appropriate way. In this paper two methods are presented for resummation of…

Retrieval-augmented generation (RAG) enhances large language models (LLMs) by integrating external knowledge retrieved from a knowledge base. However, its effectiveness is fundamentally constrained by the reliability of both the retriever…