23 papers · ranked by Valyu relevance
Loïc Van Hoorebeeck, P. -A. Absil, Anthony Papavasiliou
We address the problem of projecting a point onto a quadratic hypersurface, more specifically a central quadric. We show how this problem reduces to finding a given root of a scalar-valued nonlinear function. We completely characterize one of the optimal solutions of the projection as either the unique root of this…
Thomas F. Kirk, Martin S. Craig, Michael A. Chappell
Projection of volumetric data onto the cortical surface is an important precursor to performing surface-based analysis. Numerous projection methods have been reported in the literature, many of which make assumptions which tie them to use with specific modalities, notably blood oxygenation level dependent (BOLD)…
Loïc Van Hoorebeeck, P. -A. Absil
Quadratic hypersurfaces are a natural generalization of affine subspaces, and projections are elementary blocks of algorithms in optimization and machine learning. It is therefore intriguing that no proper studies and tools have been developed to tackle this nonconvex optimization problem. The quadproj package is a…
Ismail Melik Turker, Isa Yildirim
Using ((150-9)$18$) and ((150-10)$20$), we determine the local coordinates of the projection of the point. Through this approach, we solve the linear equation system in ((150-11)$12$) for a and b individually, without the need for inverse matrix operations in ((150-12)$13$), making it computationally more efficient. It…
Yong-Jin Liu, Weimi Zhou
Solving the distributional worst-case in the distributionally robust optimization problem is equivalent to finding the projection onto the intersection of simplex and singly linear inequality constraint, which is an important ingredient in the design of some first-order efficient algorithms. This paper focuses on…
Yael Harpaz, Yoel Shkolnisky
A common task in cryo-electron microscopy (cryo-EM) data processing is to compare three-dimensional density maps of macromolecules. In this paper, we propose an algorithm for aligning three-dimensional density maps that exploits common lines between projection images of the maps. The algorithm is fully automatic and…
Dimitry Tegunov
Fourier-space projection operations are central to electron microscopy single-particle analysis and electron tomography algorithms. Machine learning methods require differentiable implementations for end-to-end model training, but PyTorch’s built-in operations are too slow for practical use. This paper introduces…
Haseeb Younis, Paul Trust, Rosane Minghim
Data visualisation helps understanding data represented by multiple variables, also called features, stored in a large matrix where individuals are stored in lines and variable values in columns. These data structures are frequently called multidimensional spaces. A large set of mathematical tools, named frequently as…
Haoxiang Su, Zhenghong Dong, Yi Liu, Yao Mu + 2 more
The fitness function value is a kind of important information in the search process, which can be more targeted according to the guidance of the fitness function value. Most existing meta-heuristic algorithms only use the fitness function value as an indicator to compare the current variables as good or bad but do not…
Authors not listed
High-level quantum mechanical (QM) simulations provide accurate electronic information of chemical systems but scale unfavourably with system size, making calculations of applied systems challenging. Hierarchical quantum mechanics in quantum mechanics embedding (QM/QM) addresses this issue by localising the highly…
Emil Dumic, Anamaria Bjelopera, Andreas Nüchter, Steve Vanlanduit
In this paper we will present a new dynamic point cloud compression based on different projection types and bit depth, combined with the surface reconstruction algorithm and video compression for obtained geometry and texture maps. Texture maps have been compressed after creating Voronoi diagrams. Used video…
Sirio Bolaños-Puchet, Aleksandra Teska, Juan B. Hernando, Huanxiang Lu + 3 more
Digital brain atlases define a hierarchy of brain regions and their locations in three-dimensional Cartesian space. They provide a standard coordinate system in which diverse datasets can be integrated for visualization and analysis. Although this coordinate system has well-defined anatomical axes, it does not provide…
Ruochen Zhao, Ruonan Wang, Yang Gao, Xiaolin Ning + 3 more
'Francesco Amato' 'Raissa Schiavoni'] A class of algorithms based on subspace projection is widely used in the denoising of magnetoencephalography (MEG) signals. Setting the dimension of the interference (external) subspace matrix of these algorithms is the key to balancing the denoising effect and the degree of signal…
Václav Skala
Many algorithms used are based on geometrical computation. There are several criteria in selecting appropriate algorithm from already known. Recently, the fastest algorithms have been preferred. Nowadays, algorithms with a high stability are preferred. Also today's technology and computer architecture, like GPU etc.…
Andrew Lee, Harlin Lee, José A. Perea, Nikolas Schonsheck + 1 more
'Madeleine Weinstein'] - Abstract. Many real-world datasets live on high-dimensional Stiefel and Grassmannian manifolds, Vk(R N ) and Gr(k, R N ) respectively, and benefit from projection onto lower-dimensional Stiefel (respectively, Grassmannian) manifolds. In this work, we propose an algorithm called Principal…
Kenneth Lange
The current paper proposes and tests algorithms for finding the diameter of a compact convex set and the farthest point in the set to another point. For these two nonconvex problems, I construct Frank-Wolfe and projected gradient ascent algorithms. Although these algorithms are guaranteed to go uphill, they can become…
Christina Humer, Rachel Nicholls, Henry Heberle, Moritz Heckmann + 7 more
Chemical reaction optimization (RO) is an iterative process that results in large and high-dimensional datasets. Current tools only allow for limited analysis and understanding of parameter spaces, making it hard for scientists to review or follow changes throughout the process. With the recent emergence of using…
Eric Hermes, Khachik Sargsyan, Habib Najm, Judit Zádor
We present a new algorithm for the optimization of molecular structures to saddle points on the potential energy surface using a redundant internal coordinate system. This algorithm automates the procedure of defining the internal coordinate system, including the handling of linear bending angles, e.g. through the…
Alejandro Omar Blenkmann, Sabine Liliana Leske, Anaïs Llorens, Jack J. Lin + 8 more
Precise electrode localization is important for maximizing the utility of intracranial EEG data. Electrodes are typically localized from post-implantation CT artifacts, but algorithms can fail due to low signal-to-noise ratio, unrelated artifacts, or high-density electrode arrays. Minimizing these errors usually…
Andy Jiang, Zachary Glick, David Poole, Justin Turney + 2 more
Here, we present an efficient, open-source formulation for coupled-cluster theory through perturbative triples with domain-based local pair natural orbitals [DLPNO-CCSD(T)]. Similar to the implementation of the DLPNO-CCSD(T) method found in the ORCA package, the most expensive integral generation and contraction steps…
Christoph Jacob, Johannes Neugebauer
The past years since the publication of our review on subsystem density-functional theory (sDFT) [WIREs Comput. Mol. Sci. 2014, 4:325--362] have witnessed a rapid development and diversification of quantum mechanical fragmentation and embedding approaches related to sDFT and frozen-density embedding (FDE). In this…
Alonso Viladomat Jasso, Ark Modi, Roberto Ferrara, Christian Deppe + 4 more
'Janis Nötzel' 'Fred Fung' 'Maximilian Schädler' 'Aleksey Fedorov'] Nearest-neighbour clustering is a simple yet powerful machine learning algorithm that finds natural application in the decoding of signals in classical optical-fibre communication systems. Quantum k-means clustering promises a speed-up over the…
Zilong Li, Jonas Meisner, Anders Albrechtsen
Principal Component Analysis (PCA) is widely utilized in statistics, machine learning, and genomics for dimensionality reduction and uncovering low-dimensional latent structure. To address the challenges posed by ever-growing data size, fast and memory-efficient PCA methods have gained prominence. In this paper, we…