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Related papers: Nested ansatz method for Baker-Akhiezer functions

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We introduce a novel framework for the estimation of the posterior distribution over the weights of a neural network, based on a new probabilistic interpretation of adaptive optimisation algorithms such as AdaGrad and Adam. We demonstrate…

Machine Learning · Statistics 2020-07-21 Samuel Kessler , Arnold Salas , Vincent W. C. Tan , Stefan Zohren , Stephen Roberts

Regularization method and Bayesian inverse method are two dominating ways for solving inverse problems generated from various fields, e.g., seismic exploration and medical imaging. The two methods are related with each other by the MAP…

Numerical Analysis · Mathematics 2019-06-18 Junxiong Jia , Qihang Sun , Bangyu Wu , Jigen Peng

We use twisted sheaves and their moduli spaces to study the Brauer group of a scheme. In particular, we (1) show how twisted methods can be efficiently used to re-prove the basic facts about the Brauer group and cohomological Brauer group…

Algebraic Geometry · Mathematics 2018-06-18 Max Lieblich

Suppose that $F$ is an $\mathbb{A}^{1}$-invariant quasi-stable $\mathbb{Z}F_{\ast}$-presheaf. Then its Zariski sheafification $F_{Zar}$ coincides with its Nisnevich sheafification $F_{Nis}$. Moreover, if $X\in Sm/k$ is $k$-smooth, then for…

K-Theory and Homology · Mathematics 2025-06-10 Ivan Panin , Dimitrii Tyurin

We give a detailed description of the nested algebraic Bethe ansatz. We consider integrable models with a $\mathfrak{gl}_3$-invariant $R$-matrix as the basic example, however, we also describe possible generalizations. We give recursions…

Mathematical Physics · Physics 2020-09-02 N. A. Slavnov

The system of undetermined coefficients of a bifurcation problem G[z]=0 in Banach spaces is investigated for proving the existence of families of solution curves by use of the implicit function theorem. The main theorem represents an…

Algebraic Geometry · Mathematics 2019-07-23 Matthias Stiefenhofer

A brief non-technical review of the recent study of classical integrable structures in quantum integrable systems is given. It is explained how to identify the standard objects of quantum integrable systems (transfer matrices, Baxter's…

High Energy Physics - Theory · Physics 2007-05-23 A. V. Zabrodin

In this paper, we propose a multilevel stochastic framework for the solution of nonconvex unconstrained optimization problems. The proposed approach uses random regularized first-order models that exploit an available hierarchical…

Optimization and Control · Mathematics 2025-11-27 Filippo Marini , Margherita Porcelli , Elisa Riccietti

Accurate reconstruction of piecewise-smooth functions from a finite number of Fourier coefficients is an important problem in various applications. The inherent inaccuracy, in particular the Gibbs phenomenon, is being intensively…

Classical Analysis and ODEs · Mathematics 2012-11-12 Dmitry Batenkov , Yosef Yomdin

A new type of combinations of Bernstein operators is given in [1]. Here, we introduce another one, which can be used to approximate the functions with singularities. The direct and inverse results of the weighted approximation of this new…

Functional Analysis · Mathematics 2011-06-28 Wen-ming Lu , Lin Zhang

Nesterov's accelerated gradient method (NAG) achieves faster convergence than gradient descent for convex optimization but lacks monotonicity in function values. To address this, Beck and Teboulle [2009b] proposed a monotonic variant,…

Optimization and Control · Mathematics 2025-08-06 Mingwei Fu , Bin Shi

This paper presents normalizing flows for incremental smoothing and mapping (NF-iSAM), a novel algorithm for inferring the full posterior distribution in SLAM problems with nonlinear measurement models and non-Gaussian factors. NF-iSAM…

To infer the parameters of mechanistic models with intractable likelihoods, techniques such as approximate Bayesian computation (ABC) are increasingly being adopted. One of the main disadvantages of ABC in practical situations, however, is…

Computation · Statistics 2018-08-03 Jonathan U Harrison , Ruth E Baker

We develop a logic which enables reasoning about single steps of non-deterministic parallel Abstract State Machines (ASMs). Our logic builds upon the unifying logic introduced by Nanchen and St\"ark for reasoning about hierarchical…

Logic in Computer Science · Computer Science 2017-06-01 Flavio Ferrarotti , Klaus-Dieter Schewe , Loredana Tec , Qing Wang

We describe a simple method that produces automatically closed forms for the coefficients of continued fractions expansions of a large number of special functions. The function is specified by a non-linear differential equation and initial…

Symbolic Computation · Computer Science 2015-07-16 Sébastien Maulat , Bruno Salvy

Matrix factorization techniques, especially Nonnegative Matrix Factorization (NMF), have been widely used for dimensionality reduction and interpretable data representation. However, existing NMF-based methods are inherently single-scale…

Machine Learning · Computer Science 2026-02-27 Jichao Zhang , Ran Miao , Limin Li

Various applications such as MRI, solution of PDEs, etc. need to perform an inverse nonequispaced fast Fourier transform (NFFT), i. e., compute $M$ Fourier coefficients from given $N$ nonequispaced data. In the present paper we consider…

Numerical Analysis · Mathematics 2025-06-09 Melanie Kircheis , Daniel Potts

We prove that any function with real-valued coefficients, whose input is 4 binary variables and whose output is a real number, is perfectly equivalent to a quadratic function whose input is 5 binary variables and is minimized over the new…

Discrete Mathematics · Computer Science 2019-10-31 Nike Dattani , Hou Tin Chau

This paper suggests parametrically transformed nested error regression models (TNERM), which transform the data flexibly to follow the normal linear mixed regression. We provide a procedure for estimating consistently the parameters of the…

Methodology · Statistics 2018-03-14 Shonosuke Sugasawa , Tatsuya Kubokawa

The randomized Kaczmarz algorithm has received considerable attention recently because of its simplicity, speed, and the ability to approximately solve large-scale linear systems of equations. In this paper we propose randomized double and…

Numerical Analysis · Mathematics 2020-10-28 Kui Du , Xiao-Hui Sun