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A path tracking algorithm that adaptively adjusts precision is presented. By adjusting the level of precision in accordance with the numerical conditioning of the path, the algorithm achieves high reliability with less computational cost…

Numerical Analysis · Mathematics 2007-05-23 Daniel J. Bates , Andrew J. Sommese , Charles W. Wampler

In the realm of robust optimization the k-adaptability approach is one promising method to derive approximate solutions for two-stage robust optimization problems. Instead of allowing all possible second-stage decisions, the k-adaptability…

Optimization and Control · Mathematics 2025-09-04 Jannis Kurtz

We propose a scheme for translating metrological precision bounds into lower bounds on query complexity of quantum search algorithms. Within the scheme the link between quadratic performance enhancement in idealized quantum metrological and…

Quantum Physics · Physics 2016-10-13 Rafal Demkowicz-Dobrzanski , Marcin Markiewicz

Hard thresholding pursuit (HTP) is a recently proposed iterative sparse recovery algorithm which is a result of combination of a support selection step from iterated hard thresholding (IHT) and an estimation step from the orthogonal…

Information Theory · Computer Science 2020-06-03 Samrat Mukhopadhyay , Mrityunjoy Chakraborty

We present the preliminary tests on two modifications of the Hybrid Monte Carlo (HMC) algorithm. Both algorithms are designed to travel much farther in the Hamiltonian phase space for each trajectory and reduce the autocorrelations among…

High Energy Physics - Lattice · Physics 2018-04-18 Guido Cossu , Peter Boyle , Norman Christ , Chulwoo Jung , Andreas Jüttner , Francesco Sanfilippo

Finding the optimal attainable precisions in quantum multiparameter metrology is a non trivial problem. One approach to tackling this problem involves the computation of bounds which impose limits on how accurately we can estimate certain…

Quantum Physics · Physics 2021-07-19 Lorcán Conlon , Jun Suzuki , Ping Koy Lam , Syed M. Assad

Many important cryptographic primitives offer probabilistic guarantees of security that can be specified as quantitative hyperproperties; these are specifications that stipulate the existence of a certain number of traces in the system…

Cryptography and Security · Computer Science 2020-05-18 Shubham Sahai , Rohit Sinha , Pramod Subramanyan

Transient stability assessment of power systems needs to account for increased risk from uncertainties due to the integration of renewables and distributed generators. The uncertain operating condition of the power grid hinders reliable…

Dynamical Systems · Mathematics 2017-05-04 Dongchan Lee , Konstantin Turitsyn

Index tracking is a popular passive investment strategy aimed at optimizing portfolios, but fully replicating an index can lead to high transaction costs. To address this, partial replication have been proposed. However, the cardinality…

Artificial Intelligence · Computer Science 2024-12-24 Wooyeon Jo , Hyunsouk Cho

We present a post-processing certification workflow for nonlinear elliptic boundary value problems that upgrades a standard finite element computation to a rigorous existence and output certificate. For a given approximate discrete state,…

Numerical Analysis · Mathematics 2026-02-03 Hiroki Ishizaka

We solve affirmatively the homotopy limit problem for $K$-theory over fields of finite virtual cohomological dimension. Our solution employs the motivic slice filtration and the first motivic Hopf map.

K-Theory and Homology · Mathematics 2017-01-24 Oliver Röndigs , Markus Spitzweck , Paul Arne Østvær

The paper is concerned with guaranteed a posteriori error estimates for a class of evolutionary problems related to poroelastic media governed by the quasi-static linear Biot equations. The system is decoupled employing the fixed-stress…

Numerical Analysis · Mathematics 2020-01-22 Kundan Kumar , Svetlana Kyas , Jan Nordbotten , Sergey Repin

This article shows several new methods for proofs on Kan complexes while using them to give a compact introduction to the homotopy groups of these complexes. Then more advanced objects are studied starting with homology and the Hurewicz…

Algebraic Topology · Mathematics 2016-08-02 Jan Steinebrunner

We review the methods of constructing confidence intervals that account for a priori information about one-sided constraints on the parameter being estimated. We show that the so-called method of sensitivity limit yields a correct solution…

Data Analysis, Statistics and Probability · Physics 2015-05-20 A. V. Lokhov , F. V. Tkachov

We study the prime pair counting functions $\pi_{2k}(x),$ and their averages over $2k.$ We show that good results can be achieved with relatively little effort by considering averages. We prove an asymptotic relation for longer averages of…

Number Theory · Mathematics 2016-05-17 Jori Merikoski

We propose a new algorithm for numerical path tracking in polynomial homotopy continuation. The algorithm is `robust' in the sense that it is designed to prevent path jumping and in many cases, it can be used in (only) double precision…

Algebraic Geometry · Mathematics 2020-09-11 Simon Telen , Marc Van Barel , Jan Verschelde

This paper generalizes an important result from the PAC-Bayesian literature for binary classification to the case of ensemble methods for structured outputs. We prove a generic version of the \Cbound, an upper bound over the risk of models…

Machine Learning · Statistics 2015-06-16 François Laviolette , Emilie Morvant , Liva Ralaivola , Jean-Francis Roy

We develop a worst-case evaluation complexity bound for trust-region methods in the presence of unbounded Hessian approximations. We use the algorithm of arXiv:2103.15993v3 as a model, which is designed for nonsmooth regularized problems,…

Optimization and Control · Mathematics 2025-10-14 Geoffroy Leconte , Dominique Orban

Determining the number of change-points is a first-step and fundamental task in change-point detection problems, as it lays the groundwork for subsequent change-point position estimation. While the existing literature offers various methods…

Methodology · Statistics 2026-03-31 Ao Sun , Jingyuan Liu

Spectral clustering has become a popular technique due to its high performance in many contexts. It comprises three main steps: create a similarity graph between N objects to cluster, compute the first k eigenvectors of its Laplacian matrix…

Data Structures and Algorithms · Computer Science 2016-05-24 Nicolas Tremblay , Gilles Puy , Remi Gribonval , Pierre Vandergheynst