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- Ultrarigid periodic frameworks

Full text arXiv We give an algebraic characterization of when a dimensional periodic framework has no non trivial symmetry preserving motion for any choice of periodicity lattice Our condition is decidable and we provide a simple algorithm that does not require complicated algebraic computations In dimension we give a combinatorial characterization in the special case when the the number of edge orbits is the minimum possible for ultrarigidity All our

Original URL path: http://theran.lt/papers/p009xx-ur.html (2016-04-26)

Open archived version from archive - Matroid regression

whole signal The method scales only in the sparsity of the system and not in its size and allows to provide error estimates for any solution method At the heart of our approach is the so called regression matroid a combinatorial object associated to sparsity patterns which allows to replace inversion of the large matrix with the inversion of a kernel matrix that is constant size We show that our

Original URL path: http://theran.lt/papers/p009x-matroids.html (2016-04-26)

Open archived version from archive - Dual-to-kernel learning with ideals

we propose a theory which unifies kernel learning and symbolic algebraic methods We show that both worlds are inherently dual to each other and we use this duality to combine the structure awareness of algebraic methods with the efficiency and generality of kernels The main idea lies in relating polynomial rings to feature space and ideals to manifolds then exploiting this generative discriminative duality on kernel matrices We illustrate this

Original URL path: http://theran.lt/papers/p009-avica.html (2016-04-26)

Open archived version from archive - Algebraic matroids with graph symmetry

allows us to introduce for each circuit in an algebraic matroid an invariant called circuit polynomial generalizing the minimal poly nomial in classical Galois theory and studying the matroid structure with multivariate methods For b matroids with symmetries we introduce combinatorial invariants capturing structural properties of the rank function and its limit behavior and obtain proofs which are purely combinatorial and do not assume algebraicity of the matroid these imply

Original URL path: http://theran.lt/papers/p008-graphmatroids.html (2016-04-26)

Open archived version from archive - Coherence and sufficient sampling densities for reconstruction in compressed sensing

features and the set of possibly observable feature combinations forms an analytic variety which models the compression constraints We study the question how many random measurements of the feature components suffice to identify all features We show that the asymptotics of the sufficient number of measurements is determined by the coherence of the signal furthermore if the constraints are algebraic we show that in general the asymptotics depend only on

Original URL path: http://theran.lt/papers/p006-coherence.html (2016-04-26)

Open archived version from archive - Generic rigidity of reflection frameworks

2276 2012 Full text arXiv We give a combinatorial characterization of generic minimally rigid reflection frameworks The main new idea is to study a pair of direction networks on the same graph such that one admits faithful realizations and the other has only collapsed realizations In terms of infinitesimal rigidity realizations of the former produce a framework and the latter certifies that this framework is infinitesimally rigid Note The content

Original URL path: http://theran.lt/papers/p005-reflection.html (2016-04-26)

Open archived version from archive - Henneberg constructions and covers of cone-Laman graphs

text arXiv We give Henneberg type constructions for three families of sparse colored graphs arising in the rigidity theory of periodic and other forced symmetric frameworks The proof method which works with Laman sparse finite covers of colored graphs highlights

Original URL path: http://theran.lt/papers/p004-henneberg.html (2016-04-26)

Open archived version from archive - Lines induced by bichromatic point sets

the Euclidean plane is either nearly general position or nearly collinear there is a constant such that given points in the plane with at most of them collinear the number of lines induced by the points is at least Recent work of Gutkin Rams on billiards orbits requires the following elaboration of Beck s Theorem to bichromatic point sets there is a constant such that given red points and blue

Original URL path: http://theran.lt/papers/p002-bichromatic.html (2016-04-26)

Open archived version from archive