Machine Learning Optimization of the Collocation Point Set for Solving the Kohn–Sham Equation

Jonas Ku; Aditya Kamath; Tucker Carrington; Sergei Manzhos

doi:10.1021/acs.jpca.9b09732

Machine Learning Optimization of the Collocation Point Set for Solving the Kohn–Sham Equation

The Journal of Physical Chemistry A ◽

10.1021/acs.jpca.9b09732 ◽

2019 ◽

Vol 123 (49) ◽

pp. 10631-10642 ◽

Cited By ~ 4

Author(s):

Jonas Ku ◽

Aditya Kamath ◽

Tucker Carrington ◽

Sergei Manzhos

Keyword(s):

Machine Learning ◽

Collocation Point ◽

Sham Equation ◽

Point Set

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The Parallel Seeding Algorithm for k-Means Problem with Penalties

Asia Pacific Journal of Operational Research ◽

10.1142/s0217595920400059 ◽

2020 ◽

Vol 37 (04) ◽

pp. 2040005

Author(s):

Min Li ◽

Dachuan Xu ◽

Jun Yue ◽

Dongmei Zhang

Keyword(s):

Machine Learning ◽

Computational Geometry ◽

Theoretical Analysis ◽

Hard Problem ◽

Np Hard ◽

Np Hard Problem ◽

Point Set ◽

Data Point

As a classic NP-hard problem in machine learning and computational geometry, the [Formula: see text]-means problem aims to partition a data point set into [Formula: see text] clusters such that the sum of the squared distance from each point to its nearest center is minimized. The [Formula: see text]-means problem with penalties, denoted by [Formula: see text]-MPWP, generalizing the [Formula: see text]-means problem, allows that some points can be paid some penalties instead of being clustered. In this paper, we study the seeding algorithm of [Formula: see text]-MPWP and propose a parallel seeding algorithm for [Formula: see text]-MPWP along with the corresponding theoretical analysis.

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Mind wandering as data augmentation: How mental travel supports abstraction

Behavioral and Brain Sciences ◽

10.1017/s0140525x1900311x ◽

2020 ◽

Vol 43 ◽

Author(s):

Myrthe Faber

Keyword(s):

Machine Learning ◽

Data Augmentation ◽

Mental Content ◽

Mind Wandering ◽

Theoretical Framework ◽

Important Addition

Abstract Gilead et al. state that abstraction supports mental travel, and that mental travel critically relies on abstraction. I propose an important addition to this theoretical framework, namely that mental travel might also support abstraction. Specifically, I argue that spontaneous mental travel (mind wandering), much like data augmentation in machine learning, provides variability in mental content and context necessary for abstraction.

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Computational Micrograph Registration with Sieve Processes

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100164660 ◽

1996 ◽

Vol 54 ◽

pp. 440-441

Author(s):

P.J. Phillips ◽

J. Huang ◽

S. M. Dunn

Keyword(s):

Planar Graph ◽

Efficient Algorithm ◽

Spatial Organization ◽

Spatial Arrangement ◽

Stereo Image ◽

Image Model ◽

Geometric Invariants ◽

Point Set

In this paper we present an efficient algorithm for automatically finding the correspondence between pairs of stereo micrographs, the key step in forming a stereo image. The computation burden in this problem is solving for the optimal mapping and transformation between the two micrographs. In this paper, we present a sieve algorithm for efficiently estimating the transformation and correspondence.In a sieve algorithm, a sequence of stages gradually reduce the number of transformations and correspondences that need to be examined, i.e., the analogy of sieving through the set of mappings with gradually finer meshes until the answer is found. The set of sieves is derived from an image model, here a planar graph that encodes the spatial organization of the features. In the sieve algorithm, the graph represents the spatial arrangement of objects in the image. The algorithm for finding the correspondence restricts its attention to the graph, with the correspondence being found by a combination of graph matchings, point set matching and geometric invariants.

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