scholarly journals The Profinite Dimensional Manifold Structure of Formal Solution Spaces of Formally Integrable PDEs

2017 ◽  
Author(s):  
Batu Güneysu ◽  
◽  
Markus J. Pflaum ◽  
◽  
◽  
...  
Keyword(s):  
Formal Solution ◽  
Dimensional Manifold ◽  
Manifold Structure ◽  
Integrable Pdes

scholarly journals Neural Excursions from Low-Dimensional Manifold Structure Explain Intersubject Variation in Human Motor Learning

2021 ◽  
Author(s):  
Corson N Areshenkoff ◽  
Daniel J Gale ◽  
Joe Y Nashed ◽  
Dominic Standage ◽  
John Randall Flanagan ◽  
...  
Keyword(s):  
Motor Learning ◽  
Large Scale ◽  
Brain Activity ◽  
Dimensional Subspace ◽  
Learning Performance ◽  
Dimensional Manifold ◽  
Learning Abilities ◽  
Manifold Structure ◽  
Electrophysiological Studies ◽  
Low Dimensional

Humans vary greatly in their motor learning abilities, yet little is known about the neural mechanisms that underlie this variability. Recent neuroimaging and electrophysiological studies demonstrate that large-scale neural dynamics inhabit a low-dimensional subspace or manifold, and that learning is constrained by this intrinsic manifold architecture. Here we asked, using functional MRI, whether subject-level differences in neural excursion from manifold structure can explain differences in learning across participants. We had subjects perform a sensorimotor adaptation task in the MRI scanner on two consecutive days, allowing us to assess their learning performance across days, as well as continuously measure brain activity. We find that the overall neural excursion from manifold activity in both cognitive and sensorimotor brain networks is associated with differences in subjects' patterns of learning and relearning across days. These findings suggest that off-manifold activity provides an index of the relative engagement of different neural systems during learning, and that intersubject differences in patterns of learning and relearning across days are related to reconfiguration processes in cognitive and sensorimotor networks during learning.

scholarly journals Online Subspace Tracking of Sensors Data for Damage Propagation Modeling and Predictive Analytics

2019 ◽  
Author(s):  
Farhan Khan
Keyword(s):  
Remaining Useful Life ◽  
Propagation Model ◽  
Dimensional Manifold ◽  
Subspace Tracking ◽  
Static Behavior ◽  
Damage Propagation ◽  
Propagation Modeling ◽  
Manifold Structure ◽  
Low Dimensional ◽  
Low Dimensional Manifold

We analyze damage propagation modeling of turbo-engines in a data-driven approach. We investigate subspace tracking assuming a low dimensional manifold structure and a static behavior during the healthy state of the machines. Our damage propagation model is based on the deviation of the data from the static behavior and uses the notion of health index as a measure of the condition. Hence, we incorporate condition-based maintenance and estimate the remaining useful life based on the current and previous health indexes. This paper proposes an algorithm that adapts well to the dynamics of the data and underlying system, and reduces the computational complexity by utilizing the low dimensional manifold structure of the data. A significant performance improvement is demonstrated over existing methods by using the proposed algorithm on CMAPSS Turbo-engine datasets.

Nonnegative matrix factorization with manifold structure for face recognition

2019 ◽  
Vol 17 (02) ◽  
pp. 1940006
Author(s):  
Wen-Sheng Chen ◽  
Qian Wang ◽  
Binbin Pan ◽  
Bo Chen
Keyword(s):  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Low Rank ◽  
Function Technique ◽  
Dimensional Euclidean Space ◽  
Gradient Descent Method ◽  
Dimensional Manifold ◽  
Manifold Structure ◽  
Facial Images

Nonnegative matrix factorization (NMF) is a promising method to represent facial images using nonnegative features under a low-rank nonnegative basis-image matrix. The facial images usually reside on a low-dimensional manifold due to the variations of illumination, pose and facial expression. However, NMF has no ability to uncover the manifold structure of data embedded in a high-dimensional Euclidean space, while the manifold structure contains both local and nonlocal intrinsic features. These two kinds of features are of benefit to class discrimination. To enhance the discriminative power of NMF, this paper proposes a novel NMF algorithm with manifold structure (Mani-NMF). Two quantities related to adjacent graph and non-adjacent graph are incorporated into the objective function, which will be minimized by solving two convex suboptimization problems. Based on the gradient descent method and auxiliary function technique, we acquire the update rules of Mani-NMF and theoretically prove the convergence of the proposed Mani-NMF algorithm. Three publicly available face databases, Yale, pain expression and CMU databases, are selected for evaluations. Experiments results show that our algorithm achieves a better performance than some state-of-the-art algorithms.

Compact Expression of Non-manifold Structure for 3D Virtual Plant

2018 ◽  
Vol 30 (10) ◽  
pp. 1810
Author(s):  
Lei Hua ◽  
Chongcheng Chen ◽  
Liyu Tang ◽  
Ying Jiang
Keyword(s):  
Virtual Plant ◽  
Manifold Structure ◽  
Compact Expression

The Nature of Time

2018 ◽  
Author(s):  
Donald C. Williams
Keyword(s):  
Large Scale ◽  
Time Travel ◽  
Dimensional Manifold ◽  
Nature Of Time ◽  
Manifold Theory ◽  
The Universe ◽  
Theoretical Cost ◽  
Do So

This chapter provides a fuller treatment of the pure manifold theory with an expanded discussion of competing doctrines. It is argued that competing doctrines fail to account for the extensive and/or transitory aspect(s) of time, or they do so at great theoretical cost. The pure manifold theory accounts for the extensive aspect of time because it admits a four-dimensional manifold and it accounts for the transitory aspect of time because it hypothesizes that the increase of entropy is the thing that is ‘felt’ in veridical cases of felt passage. A four-dimensionalist theory of time travel is outlined, along with a sketch of large-scale cosmological traits of the universe.

How Reality is Reasonable

2018 ◽  
Author(s):  
Donald C. Williams
Keyword(s):  
A Priori ◽  
A Priori Knowledge ◽  
Dimensional Manifold ◽  
The World ◽  
Being There ◽  
Ways Of Being ◽  
Fundamental Entity ◽  
Spatiotemporal Relations ◽  
Priori Knowledge

This chapter begins with a systematic presentation of the doctrine of actualism. According to actualism, all that exists is actual, determinate, and of one way of being. There are no possible objects, nor is there any indeterminacy in the world. In addition, there are no ways of being. It is proposed that actual entities stand in three fundamental relations: mereological, spatiotemporal, and resemblance relations. These relations govern the fundamental entities. Each fundamental entity stands in parthood relations, spatiotemporal relations, and resemblance relations to other entities. The resulting picture is one that represents the world as a four-dimensional manifold of actual ‘qualitied contents’—upon which all else supervenes. It is then explained how actualism accounts for classes, quantity, number, causation, laws, a priori knowledge, necessity, and induction.

scholarly journals Random Assignment Problems on 2d Manifolds

2021 ◽  
Vol 183 (2) ◽  
Author(s):  
D. Benedetto ◽  
E. Caglioti ◽  
S. Caracciolo ◽  
M. D’Achille ◽  
G. Sicuro ◽  
...  
Keyword(s):  
Assignment Problem ◽  
Unit Area ◽  
Constant Term ◽  
Beltrami Operator ◽  
Explicit Calculation ◽  
Dimensional Manifold ◽  
Two Dimensional ◽  
Random Assignment ◽  
Assignment Problems ◽  
Theoretical Formulation

AbstractWe consider the assignment problem between two sets of N random points on a smooth, two-dimensional manifold $$\Omega $$ Ω of unit area. It is known that the average cost scales as $$E_{\Omega }(N)\sim {1}/{2\pi }\ln N$$ E Ω ( N ) ∼ 1 / 2 π ln N with a correction that is at most of order $$\sqrt{\ln N\ln \ln N}$$ ln N ln ln N . In this paper, we show that, within the linearization approximation of the field-theoretical formulation of the problem, the first $$\Omega $$ Ω -dependent correction is on the constant term, and can be exactly computed from the spectrum of the Laplace–Beltrami operator on $$\Omega $$ Ω . We perform the explicit calculation of this constant for various families of surfaces, and compare our predictions with extensive numerics.

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