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A discrete view on fold space
2008
Bioinformatics
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Here we introduce the new concept of a Fold Space Navigator, a user interface enabling the efficient navigation through fold space and the instantaneous visualization of pairwise structure similarities ...
Availability: The Fold Space Navigator is accessible as a public web service at http://services. ...
SCOP and CATH are built on the concept of discrete families and similarly the hierarchical tree of qCOPS emphasizes the discrete view. ...
doi:10.1093/bioinformatics/btn020
pmid:18218654
fatcat:6mm7uygeinehlfz3364prvbcpa
Discrete–continuous duality of protein structure space
2009
Current Opinion in Structural Biology
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The traditional discrete view of protein universe as a set of separate folds has been criticized in the light of growing evidence that almost any arrangement of secondary structures is possible and the ...
whole protein space can be traversed through a path of similar structures. ...
Protein folds as discrete entities An essential point lacking in most discussions about the discreteness of the structure space is the actual space definition. ...
doi:10.1016/j.sbi.2009.04.009
pmid:19482467
pmcid:PMC3688466
fatcat:hoerjrns4zhatpepsznyz2c5ym
Global view of the protein universe
2014
Proceedings of the National Academy of Sciences of the United States of America
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each generally corresponding to a fold. ...
A global view of the protein universe may shed light on these fundamental questions. It could also suggest new strategies for protein search and design (1-3). ...
One could argue that all of fold space is discrete; only each SCOP class requires different thresholds to disintegrate. Our data show that this is not the case. ...
doi:10.1073/pnas.1403395111
pmid:25071170
pmcid:PMC4136566
fatcat:i4qtxupzhbepxochbkrfau5xsq
Discrete gauge groups in certain F-theory models in six dimensions
2019
Journal of High Energy Physics
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We argue that the constructions of the aforementioned models are applicable to Calabi-Yau genus-one fibrations over any base space, except models with a discrete Z 5 gauge group. ...
We demonstrate that a special family of "Fano 3-folds" is a useful tool for constructing the aforementioned models. ...
As explained in section 3.1, 6D Ftheory models on genus-one fibered Calabi-Yau 3-folds are obtained over any base space for a discrete Z 4 gauge group. ...
doi:10.1007/jhep07(2019)027
fatcat:jmdwe4avarbw5bb4vkiv55otiu
Discrete gauge groups in certain F-theory models in six dimensions
[article]
2019
arXiv
pre-print
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We argue that the constructions of the aforementioned models are applicable to Calabi-Yau genus-one fibrations over any base space, except models with a discrete Z_5 gauge group. ...
We demonstrate that a special family of 'Fano 3-folds' is a useful tool for constructing the aforementioned models. ...
As explained in Section 3.1, 6D Ftheory models on genus-one fibered Calabi-Yau 3-folds are obtained over any base space for a discrete Z 4 gauge group. ...
arXiv:1905.03775v1
fatcat:zgvhv7emxraotdffbfgdjw4zcy
Protein structure comparison: implications for the nature of 'fold space', and structure and function prediction
2006
Current Opinion in Structural Biology
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Recently, an alternative view has emerged in which protein fold space is seen as continuous and multidimensional. ...
A number of schemes for the classification of protein structure have found widespread use and these implicitly assume the organization of protein structure space into discrete categories. ...
Acknowledgements We are grateful to Michael Levitt, Chris Tang, Mickey Kosloff and Burkhard Rost for many helpful discussions on the topics covered in this review. ...
doi:10.1016/j.sbi.2006.04.007
pmid:16678402
fatcat:2roxotc6pvfgroowe5u3tzj5ju
Touring protein fold space with Dali/FSSP
1998
Nucleic Acids Research
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From the resulting enumeration of structural neighbours (which form a surprisingly continuous distribution in fold space) we derive a discrete fold classification in three steps: (i) sequence-related families ...
of domains in fold space. ...
In this example, clicking in the lower right corner of the 2D map (top left) leads to a table view (middle) of folds occupying this region of fold space. ...
doi:10.1093/nar/26.1.316
pmid:9399863
pmcid:PMC147193
fatcat:tn2ja25gujbszchyu4b2bym62y
Flexible Developable Surfaces
2012
Computer graphics forum (Print)
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With methods for navigation of this highly nonlinear constraint space in place, we show how to formulate a discrete mean curvature bending energy measuring how far a given discrete developable surface ...
We introduce a discrete paradigm for developable surface modeling. ...
While such a discrete structure is piecewise flat, we do not view our surface as a collection of planar segments bordered by sharp folds. ...
doi:10.1111/j.1467-8659.2012.03162.x
fatcat:dzaxplzv3fhhpmyme5njyhnjxm
Learning Arbitrary-Goal Fabric Folding with One Hour of Real Robot Experience
[article]
2020
arXiv
pre-print
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We demonstrate our method on a set of towel-folding tasks, and show that our approach is able to discover sequential folding strategies, purely from trial-and-error. ...
Videos available at: https://sites.google.com/view/learningtofold ...
We use a discrete action space that consists of pixel grasp locations and predefined sets of fold angles and fold distances. ...
arXiv:2010.03209v1
fatcat:wzajwisuizhbzla6wbohudqm7u
Time Discreteness & Wave Function Aliasing
2014
International Frontier Science Letters
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In view of the fact the discreteness of particle states at a time is a prerequisite for aliasing, the effect under consideration, in case of its experimental verification, may serve a proof of this discreteness ...
When the repetition frequency of a particle discrete state proves to be commensurable with its own frequency (energy), the aliasing effect of its wave function may take place. ...
The discrete space positions of a particle correspond to the discrete instants of time. ...
doi:10.18052/www.scipress.com/ifsl.1.28
fatcat:2levrls33ncz3nqfohlle5qfxq
Uncovering Distant Protein Relationships with Deep Generative Models
2020
Zenodo
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structure or 'fold' space. ...
Identifying patterns with these distances with Stochastic Block Models provides a new view of protein interrelationships—a view that extends beyond simple structural/geometric similarity, towards the realm ...
Hierarchical clustering might not be the the best view of fold space • Our van der Waals representation of each Sparse Sparse Question 3.2: Z 1x1024 Latent space Sparse Sparse Encoder 3D-CNN q(z|x) Decoder ...
doi:10.5281/zenodo.6321396
fatcat:5vziuau3xbfzvkphv4fijau53e
Reply to: MRI resolution enhancement: How useful are shifted images obtained by changing the demodulation frequency?
2011
Magnetic Resonance in Medicine
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In a recent article, Tieng et al. studied a super-resolution MRI technique, which relies on the combination of several low-quality images (same field-of-view and resolution) that are shifted against each ...
other by a fraction of a pixel (1). ...
A well-known and widely used procedure to resolve the image on a finer grid is to expand the k-space with zeros before applying a discrete Fourier transform. ...
doi:10.1002/mrm.22989
pmid:22086731
fatcat:ovspkpwbu5acxf3swfjp5q4d5y
From crystals to lattice robots
2008
2008 IEEE International Conference on Robotics and Automation
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We present a framework for the design of lattice robots by assembling compatible joints and connectors into a space group and give a 3D example. Point group Order Chiral space groups 1 1 P1 2 2 ...
described by space groups. ...
For example a connector having a 4-fold symmetry axis must be on a 4-fold rotation axis of the space group. ...
doi:10.1109/robot.2008.4543748
dblp:conf/icra/BrenerAB08
fatcat:augk3td4zjgtnkvndgyio3wtsi
S-folds and 4d N $$ \mathcal{N} $$ = 3 superconformal field theories
2016
Journal of High Energy Physics
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In this note, we classify the different variants of these N=3 preserving S-folds, distinguished by an analog of discrete torsion, using both a direct analysis of the different torsion classes and the compactification ...
of the S-folds to three dimensional M-theory backgrounds. ...
Again let us limit ourselves to the points on the moduli space corresponding to a Coulomb branch from the point of view of an N = 2 description of our SCFTs. ...
doi:10.1007/jhep06(2016)044
fatcat:ur3urw27lrcdvmffgpxsu3nwku
Geometric U-folds in four dimensions
2017
Journal of Physics A: Mathematical and Theoretical
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2016 pre-print arXiv:1603.03095v1 fatcat:6laj75zsbrczvg2skc5lm3nwhqOther Versions
We also discuss the relation between geometric U-folds and a moduli space of flat connections defined on the scalar manifold, which involves certain character varieties not studied in the literature. ...
We describe a construction of geometric U-folds compatible with a non-trivial extension of the global formulation of four-dimensional extended supergravity on a differentiable spin manifold. ...
Thus every fiber bundle on M 0 is topologically trivial and the standard theory does not admit non-trivial geometric U-folds. Let Γ be a discrete subgroup of E 7 (7) . ...
doi:10.1088/1751-8121/aa9665
fatcat:varuoy4adzhtjcgtrstuqvzvpy
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