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Trimmed Moebius Inversion and Graphs of Bounded Degree [article]

Andreas Björklund, Thore Husfeldt, Petteri Kaski, Mikko Koivisto
2008 arXiv   pre-print
For an n-element universe U and a family F of its subsets, trimmed Moebius inversion allows us to compute the number of packings, coverings, and partitions of U with k sets from F in time within a polynomial  ...  Relying on an intersection theorem of Chung et al. (1986) to bound the sizes of set families, we apply these ideas to well-studied combinatorial optimisation problems on graphs of maximum degree Δ.  ...  We use the trimmed algorithms for zeta and Moebius transforms to expedite Moebius inversion, a generalisation of the principle of inclusion-exclusion, which allows us to compute the cover, packing, and  ... 
arXiv:0802.2834v1 fatcat:sy3xys7v4rdzrcgbb2dpsrua2u

Trimmed Moebius Inversion and Graphs of Bounded Degree

Andreas Björklund, Thore Husfeldt, Petteri Kaski, Mikko Koivisto
2009 Theory of Computing Systems  
For an n-element universe U and a family F of its subsets, trimmed Moebius inversion allows us to compute the number of packings, coverings, and partitions of U with k sets from F in time within a polynomial  ...  Relying on an intersection theorem of Chung et al. (1986) to bound the sizes of set families, we apply these ideas to well-studied combinatorial optimisation problems on graphs of maximum degree ∆.  ...  We use the trimmed algorithms for zeta and Moebius transforms to expedite Moebius inversion, a generalisation of the principle of inclusion-exclusion, which allows us to compute the cover, packing, and  ... 
doi:10.1007/s00224-009-9185-7 fatcat:rtmnxlf3cjagjajtzchszzhkou

The fast intersection transform with applications to counting paths [article]

Andreas Björklund, Thore Husfeldt, Petteri Kaski, Mikko Koivisto
2008 arXiv   pre-print
As an application, we develop an algorithm that, given as input a digraph with n vertices and bounded integer weights at the edges, counts paths by weight and given length 0≤ℓ≤ n-1 in time O^*((n· H(ℓ/  ...  We present an algorithm for evaluating a linear "intersection transform" of a function defined on the lattice of subsets of an n-element set.  ...  the trimmed up-zeta transform of f and g, take pointwise product of transforms, take the trimmed up-Moebius transform, and sum over all j-subsets in ↓F ∪ ↓G).  ... 
arXiv:0809.2489v1 fatcat:3lsv37dauzavdjej2k72yob4gy

There are 1,132,835,421,602,062,347 nonisomorphic one-factorizations ofK14

Petteri Kaski, Patric R. J. Östergård
2009 Journal of combinatorial designs (Print)  
Koivisto, Trimmed Moebius inversion and graphs of bounded degree, Proceedings of the 25th Annual Symposium on Theoretical Aspects of Computer Science (Bordeaux, February 21-23, 2008) (S.  ...  For α < 1/4 a positive answer is obtained by combining a trimmed fast subset convolution of f 1 , f 2 with the fast intersection transform of f 3 , where f 1 , f 2 , f 3 are indicator functions of F 1  ... 
doi:10.1002/jcd.20188 fatcat:gqreaywcwnacjhodu5oebzzn64

Quadratic maps with a periodic critical point of period 2

Jung Kyu Canci, Solomon Vishkautsan
2017 International Journal of Number Theory  
We provide data related to the analogous classification of graphs of endomorphisms of degree 2 with a rational periodic critical point of period 3 or 4.  ...  We provide a complete classification of possible graphs of rational preperiodic points of endomorphisms of the projective line of degree 2 defined over the rationals with a rational periodic critical point  ...  We also thank Fabrizio Barroero, Laura Capuano, Xander Faber, Patrick Ingram, Vincenzo Mantova, Olaf Merkert, Michael Stoll and Umberto Zannier for their comments and suggestions.  ... 
doi:10.1142/s1793042117500786 fatcat:js44pk6rzranxjjrf6pclykdnu

Quadratic maps with a periodic critical point of period 2 [article]

J.K. Canci, Solomon Vishkautsan
2015 arXiv   pre-print
We provide data related to the analogous classification of graphs of endomorphisms of degree 2 with a rational periodic critical point of period 3 or 4.  ...  We provide a complete classification of possible graphs of rational preperiodic points of endomorphisms of the projective line of degree 2 defined over the rationals with a rational periodic critical point  ...  We also thank Fabrizio Barroero, Laura Capuano, Xander Faber, Patrick Ingram, Vincenzo Mantova, Olaf Merkert, Michael Stoll and Umberto Zannier for their comments and suggestions.  ... 
arXiv:1510.04726v2 fatcat:juuha7fcxra57bpxo6iodu2afe

Analysis of boundary representation model rectification

Guoling Shen, Takis Sakkalis, Nicholas Patrikalakis
2001 Proceedings of the sixth ACM symposium on Solid modeling and applications - SMA '01  
Finally, longer term research on realizing exact B-rep models bounded by general arbitrary degree curves and surfaces with rational, algebraic and transcendental coefficients is also recommended.  ...  We say that g is continuous, if for every point b E A 2 and r > 0, the inverse image of B(b, r) n A 2 is equal to C n A 1 , where C is an open set in Rn.  ...  In the following, we study the location and size of such boxes. For detailed description of interval arithmetic and interval B-splines, see [49, 57, 58 ].  ... 
doi:10.1145/376957.376975 dblp:conf/sma/ShenSP01 fatcat:jcza2adddnhldkmq7tpmvucmke

Integrating CAD and numerical analysis: 'Dirty geometry' handling using the Finite Cell Method

Benjamin Wassermann, Stefan Kollmannsberger, Shuohui Yin, László Kudela, Ernst Rank
2019 Computer Methods in Applied Mechanics and Engineering  
The potential and merit for practical applications of the proposed method is demonstrated by several numerical examples.  ...  This paper proposes a computational methodology for the integration of Computer Aided Design (CAD) and the Finite Cell Method (FCM) for models with "dirty geometries".  ...  Ernst Rank and Dr. Stefan Kollmannsberger at Technische Universität München for one-year academic guidance and discussion.  ... 
doi:10.1016/j.cma.2019.04.017 fatcat:hcxqxqc7trgobcexjezv3cspri

Introduction to the JEI Focal Track Presentations

Todor Georgiev, Andrew Lumsdaine, Cees G. M. Snoek, Lyndon S. Kennedy, Reiner Creutzburg, David Akopian, Dietmar Wüller, Kevin J. Matherson, Todor G. Georgiev, Andrew Lumsdaine
2013 Multimedia Content and Mobile Devices  
In their paper "Resolution and sensitivity of wafer-level multi-aperture cameras," Oberdorster and Lensch 1 present an analysis of some of the ensemble optical properties of wafer-level cameras, with particular  ...  Many of these technologies can be leveraged and brought to help provide higher quality (and innovative) photographic capabilities.  ...  Acknowledgments This work was supported in part by the Academy of Sciences of the Czech Republic under Grant M100751201 and by the Grant Agency of the Czech Republic under Project P103/ 11/1552.  ... 
doi:10.1117/12.2004110 fatcat:z2ftysyb7nagzdpwptjzcje2uy

Moderately Exponential Time Algorithms Dagstuhl Seminar

Fedor Fomin, Kazuo Iwama, Dieter Kratsch
unpublished
Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper.  ...  During the seminar, several participants presented their current research, and ongoing work and open problems were discussed.  ...  Koivisto, Trimmed Moebius inversion and graphs of bounded degree, Proceedings of the 25th Annual Symposium on Theoretical Aspects of Computer Science (Bordeaux, February 21-23, 2008) (S.  ... 
fatcat:df3g3wm5pvcu7c2g4br4d3lh5y

Geometric modeling based on triangle meshes

Mario Botsch, Mark Pauly, Christian Rossl, Stephan Bischoff, Leif Kobbelt
2006 ACM SIGGRAPH 2006 Courses on - SIGGRAPH '06  
Given this and the fact that each triangle is bounded by three edges and that each (interior) edge is incident to two triangles, one can derive the following mesh statistics: • The number of triangles  ...  lie either inside, outside, or exactly on the surface S bounding a solid object.  ...  (This defines also degree of the face and the inverse operation for the previous halfedge.  ... 
doi:10.1145/1185657.1185839 dblp:conf/siggraph/BotschPRBK06 fatcat:osmn4jpgcbdf7f6n5zirkunl7q

Phenotype loss is associated with widespread divergence of the gene regulatory landscape in evolution

Juliana G. Roscito, Katrin Sameith, Genis Parra, Bjoern E. Langer, Andreas Petzold, Claudia Moebius, Marc Bickle, Miguel Trefaut Rodrigues, Michael Hiller
2018 Nature Communications  
Detecting the genomic changes underlying phenotypic changes between species is a main goal of evolutionary biology and genomics.  ...  loss of these phenotypes.  ...  of the MPI-CBG and MPI-PKS, and the DNA Sequencing, Microarray and Biomedical service facilities of the MPI-CBG for their support.  ... 
doi:10.1038/s41467-018-07122-z pmid:30413698 pmcid:PMC6226452 fatcat:2nkclui35zenffzzzprr2w7kwy

Line Drawings from 3D Models: A Tutorial

Pierre Bénard, Aaron Hertzmann
2019 Foundations and Trends in Computer Graphics and Vision  
A thorough survey of the field of non-photorealistic 3D rendering is also included, covering other kinds of line drawings and artistic shading.  ...  The geometry of occluding contours on meshes and on smooth surfaces is described in detail, together with algorithms for extracting contours, computing their visibility, and creating stylized renderings  ...  Acknowledgements We thank Doug DeCarlo for comments on a draft of this tutorial, and a reviewer for extremely detailed comments.  ... 
doi:10.1561/0600000075 fatcat:vfuxfjozhbgjrkcburw4geuvrq

Line Drawings from 3D Models [article]

Pierre Bénard, Aaron Hertzmann
2019 arXiv   pre-print
A thorough survey of the field of non-photorealistic 3D rendering is also included, covering other kinds of line drawings and artistic shading.  ...  The geometry of occluding contours on meshes and on smooth surfaces is described in detail, together with algorithms for extracting contours, computing their visibility, and creating stylized renderings  ...  Acknowledgements We thank Doug DeCarlo for comments on a draft of this tutorial, and a reviewer for extremely detailed comments.  ... 
arXiv:1810.01175v2 fatcat:23jyjtvbfjem7eq46mo2rbct4e

Numerical fluid dynamics

1988 Mathematics and Computers in Simulation  
at Sink and trim.  ...  Such a body has six degrees of freedom in space: three of translation, and three of rotation.  ...  Analogies between the continuum mechanics and the 'dynamics of particles and rigid bodies' having a finite number of degrees of freedom are of more than philosophical interest for numerical fluid dynamics  ... 
doi:10.1016/0378-4754(88)90144-9 fatcat:m65zkk4dbrc6zg3epxx3wpzhjy
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