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On Δ-Modular Integer Linear Problems In The Canonical Form And Equivalent Problems [article]

D.V. Gribanov, I.A. Shumilov, D.S. Malyshev, P.M. Pardalos
2022 arXiv   pre-print
We show that any ILP problem in the standard form can be polynomially reduced to some ILP problem in the canonical form, preserving m and Δ(A), but the reverse reduction is not always possible.  ...  Many papers in the field of integer linear programming (ILP, for short) are devoted to problems of the type max{c^⊤ x A x = b, x ∈ℤ^n_≥ 0}, where all the entries of A,b,c are integer, parameterized by  ...  Paat for useful discussions during preparation of this article. Additionally, the authors would like to thank anonymous reviewers for their useful comments and remarks.  ... 
arXiv:2002.01307v6 fatcat:ps4zs63kxbbpheavasyutx5z5i

Gromov's theorem on groups of polynomial growth and elementary logic

L van den Dries, A.J Wilkie
1984 Journal of Algebra  
Define f E S' by f (i,) = uj, wherej is maximal such that aj E Ai,, if j exists, a,,j otherwise, where j is minimal such that a, +j E A in ; since f (i) E Ai for all i E Z, we have f/D EA.  ...  (See [8, Chap. 71 for the notion of Hausdorff dimension and its connections with topological dimension.)  ... 
doi:10.1016/0021-8693(84)90223-0 fatcat:7ke4eipwt5fjlofzehjhukohxa

Orientation Dynamics And Microscope Imaging Of Colloidal Suspensions

Brian Leahy
Morexi xii xv 4.1 (a) ρ(φ) for particles with aspect ratio p = 5.0 under continuous shear is sharply peaked and constant in time.  ...  These particles are large enough to be easily imaged with a microscope, allowing for detailed, mechanistic testing of statistical theories, yet small enough to still feel the effects of Brownian motion  ...  Sethna for useful discussions.  ... 
doi:10.7298/x4x63jvp fatcat:uuwfageysbf7ndoc2kfts7gn54

Polyhedral and combinatorial aspects in optimization [article]

Dirk Theis, Universitäts- Und Landesbibliothek Sachsen-Anhalt, Martin-Luther Universität, Volker Kaibel
Note added in preparation: Following the results in this manuscript, an alternative proof of the fact that the tree routing property holds for csVPN has been given [GOS08a] .  ...  Cops & Robber The game of Cops and Robber is played on a connected graph by two players -the cops and the robber.  ...  latter is a full-dimensional unbounded polyhedron in R E [CFN85] , the former is a polytope of dimension n 2 − n [Nor55] , and the inequality e∈E x e ≥ n is valid for P and satisfied with equality only  ... 
doi:10.25673/3869 fatcat:lnnb3uceujdufb7gghvybgazdy

Position Papers of the 2014 Federated Conference on Computer Science and Information Systems

Maria Ganzha, Leszek Maciaszek, Marcin Paprzycki, Maria Ganzha, Leszek Maciaszek, Marcin Paprzycki, Wil Van Der Aalst, Marco Aiello, Barrett Bryant, Ana Fred, Janusz Górski, Mike Hinchey (+13 others)
2014 Polskie Towarzystwo Informatyczne Annals of Computer Science and Information Systems   unpublished
A significant advantage of the SMCVB algorithm is that it is not restricted to fixed-dimensional space.  ...  Considering the discrete and ordinal nature of the above parameters, there is a possibility to create mathematical model of security S in a form of a discrete function: S = f(A, V, E, I, O) Evidently,  ...  /convic) II.  ...