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A discrete view on fold space

M. J. Sippl, S. J. Suhrer, M. Gruber, M. Wiederstein
2008 Bioinformatics  
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

Ruslan I Sadreyev, Bong-Hyun Kim, Nick V Grishin
2009 Current Opinion in Structural Biology  
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/ pmid:19482467 pmcid:PMC3688466 fatcat:hoerjrns4zhatpepsznyz2c5ym

Global view of the protein universe

S. Nepomnyachiy, N. Ben-Tal, R. Kolodny
2014 Proceedings of the National Academy of Sciences of the United States of America  
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

Yusuke Kimura
2019 Journal of High Energy Physics  
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]

Yusuke Kimura
2019 arXiv   pre-print
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

Rachel Kolodny, Donald Petrey, Barry Honig
2006 Current Opinion in Structural Biology  
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/ pmid:16678402 fatcat:2roxotc6pvfgroowe5u3tzj5ju

Touring protein fold space with Dali/FSSP

L Holm
1998 Nucleic Acids Research  
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

Justin Solomon, Etienne Vouga, Max Wardetzky, Eitan Grinspun
2012 Computer graphics forum (Print)  
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]

Robert Lee, Daniel Ward, Akansel Cosgun, Vibhavari Dasagi, Peter Corke, Jurgen Leitner
2020 arXiv   pre-print
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:  ...  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

Alexander Zaslavsky
2014 International Frontier Science Letters  
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/ fatcat:2levrls33ncz3nqfohlle5qfxq

Uncovering Distant Protein Relationships with Deep Generative Models

Draizen, Eli J,
2020 Zenodo  
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?

M. Uecker, T. J. Sumpf, J. Frahm
2011 Magnetic Resonance in Medicine  
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

Nicolas Brener, Faiz Ben Amar, Philippe Bidaud
2008 2008 IEEE International Conference on Robotics and Automation  
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

Ofer Aharony, Yuji Tachikawa
2016 Journal of High Energy Physics  
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

C I Lazaroiu, C S Shahbazi
2017 Journal of Physics A: Mathematical and Theoretical  
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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