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Expander graphs and their applications

Shlomo Hoory, Nathan Linial, Avi Wigderson
2006 Bulletin of the American Mathematical Society  
In mathematics, we will encounter e.g. their role in the study of metric embeddings, and in particular in work around the Baum-Connes Conjecture.  ...  These are extremely important for applications. There are algorithmic problems -given a graph, test if it is an expander with given parameters.  ...  He is mostly interested in the interplay between mathematics, computer science, and other fields of science. Avi Wigderson is a professor at the Institute for Advanced Study in Princeton.  ... 
doi:10.1090/s0273-0979-06-01126-8 fatcat:5u65bvautndzhnkhxurqrudqfy

Rank-Metric Codes and Their Applications [article]

Hannes Bartz, Lukas Holzbaur, Hedongliang Liu, Sven Puchinger, Julian Renner, Antonia Wachter-Zeh
2022 arXiv   pre-print
This survey gives a general introduction to rank-metric codes, explains their most important applications, and highlights their relevance to these areas of research.  ...  Codes designed for the rank metric have attracted considerable attention in recent years, reinforced by network coding and further motivated by a variety of applications.  ...  Holzbaur and A. Wachter  ... 
arXiv:2203.12384v1 fatcat:brysqya7ynem5i25adxfwf5vl4

Siegel Modular Forms and Their Applications [chapter]

Gerard van der Geer
2008 The 1-2-3 of Modular Forms  
These are the lecture notes of the lectures on Siegel modular forms at the Nordfjordeid Summer School on Modular Forms and their Applications.  ...  We give a survey of Siegel modular forms and explain the joint work with Carel Faber on vector-valued Siegel modular forms of genus 2 and present evidence for a conjecture of Harder on congruences between  ...  Such a hermitian metric can always be found and is unique up to a scalar for irreducible representations. Definition 3.1.  ... 
doi:10.1007/978-3-540-74119-0_3 fatcat:fgrl4yexp5fiteme6tg5gmrpum

Invariant connections with torsion on group manifolds and their application in Kaluza–Klein theories

Yu. A. Kubyshin, V. O. Malyshenko, D. Marín Ricoy
1994 Journal of Mathematical Physics  
We calculate the potential of scalar fields, emerging from extra components of the metric and torsion, and analyze the role of the torsion for the stability of spontaneous compactification.  ...  This result is used for the dimensional reduction in a theory of multidimensional gravity with curvature squared terms on M^4× S.  ...  Acknowledgements It is a pleasure for us to thank A.P. Demichev A.P., J.I. Pérez Cadenas, G. Rudolph G. and I.P. Volobujev I.P. for their useful comments and critical remarks and J.  ... 
doi:10.1063/1.530877 fatcat:ygty3azinrhble5hig2j3umx3a

General Schwarz Lemmata and their applications [article]

Lei Ni
2019 arXiv   pre-print
We prove estimates interpolating the Schwarz Lemmata of Royden-Yau and the ones recently established by the author.  ...  Acknowledgments We would like to thank James McKernan (particularly bringing my attention to the work [11] ) and Fangyang Zheng for conversations regarding holomorphic maps from P m .  ...  We are also grateful to Yanyan Niu for informing [15] .  ... 
arXiv:1907.11337v2 fatcat:hklqhvfptjdz7fjgdkgf2d3pm4

Incidence Theorems and Their Applications

Zeev Dvir
2012 Foundations and Trends® in Theoretical Computer Science  
We survey recent (and not so recent) results concerning arrangements of lines, points and other geometric objects and the applications these results have in theoretical computer science and combinatorics  ...  Suppose we want a two-source extractor for min-entropy k that outputs a single bit (with some fixed small ). A probabilistic argument shows that this can be done with k ∼ log(n).  ...  Fix > 0 to be sufficiently small and let N = G (K).  ... 
doi:10.1561/0400000056 fatcat:oko74dgd7jgpjizkhcdykpqpzm

Incidence Theorems and Their Applications [article]

Zeev Dvir
2013 arXiv   pre-print
We will see several results of this type, such as the Szemeredi-Trotter theorem, over the reals and over finite fields and discuss their applications in combinatorics (e.g., in the recent solution of Guth  ...  We survey recent (and not so recent) results concerning arrangements of lines, points and other geometric objects and the applications these results have in theoretical computer science and combinatorics  ...  Picking c(α, β) small enough we get that for all λ ∈ F, |A + λA| ≤ K ′ |A| ≪ min{|A| 2 , p}. This contradicts Lemma 3.2.1.  ... 
arXiv:1208.5073v2 fatcat:lcnezuwqubbf3jxjgdykt3glea

Lipschitz free spaces isomorphic to their infinite sums and geometric applications [article]

Fernando Albiac, Jose L. Ansorena, Marek Cuth, Michal Doucha
2020 arXiv   pre-print
We find general conditions under which Lipschitz-free spaces over metric spaces are isomorphic to their infinite direct ℓ_1-sum and exhibit several applications.  ...  sum, or that the Lipschitz-free space over any snowflake of a doubling metric space is isomorphic to ℓ_1.  ...  to their ℓ p -sums (Theorem 3.8, Theorem 3.9, and Theorem 3.10).  ... 
arXiv:2005.06555v2 fatcat:gmsyerg56rbwvj276vkwwpraoq

A survey on spectral embeddings and their applications in data analysis [article]

David Tewodrose
2020 arXiv   pre-print
The aim of this survey is to present some aspects of the B\'erard-Besson-Gallot spectral embeddings of a closed Riemannian manifold from their origins in Riemannian geometry to more recent applications  ...  For numerical applications (see Section 3), it is important to know whether truncating the rescaled spectral embeddings Ψ a t keep their nice metric properties.  ...  As so they provide, for t small enough, a faithful representation of the point cloud into a low dimensional Euclidean space. Convergence of the Laplacian Eigenmaps. In [BN07] , M. Belkin and P.  ... 
arXiv:2001.11697v2 fatcat:tidwfd6v6nhe3ca62spddtutoi

Discrete Convex Functions on Graphs and Their Algorithmic Applications [article]

Hiroshi Hirai
2017 arXiv   pre-print
We outline the theory and algorithmic applications in combinatorial optimization problems.  ...  This theory is a spin-off of discrete convex analysis by Murota, and is motivated by combinatorial dualities in multiflow problems and the complexity classification of facility location problems on graphs  ...  Acknowledgments The author thanks Yuni Iwamasa for careful reading, Satoru Fujishige for remarks, and Kazuo Murota for numerous comments improving presentation.  ... 
arXiv:1706.09106v2 fatcat:eqzvcv7cnrguznp4lkdjvz3tfm

Empirical processes indexed by smooth functions

Winfried Stute
1983 Stochastic Processes and their Applications  
As one further application we get the convcrgcnce of the so-called empirical characteristic function process.  ...  In this paper we derive a general invariance principle for empirical processes indexed by smooth functions.  ...  The first sum is easily bounded by ~~~~ar-lexp(_K2~l-~)3h~(~)]dl, which by assumption can be made arbitrarily small by choosing K sufficiently large and a > 0 sufficiently small.  ... 
doi:10.1016/0304-4149(83)90046-7 fatcat:x3tsp4ftj5fkff4pbzxvrc3jke

On k-Path Covers and their applications

Stefan Funke, André Nusser, Sabine Storandt
2015 The VLDB journal  
This paper considers the problem of constructing small k-Path Covers in the context of road networks with millions of nodes and edges.  ...  In many application scenarios, the set C and its induced overlay graph constitute a very compact synopsis of G, which is the basis for the currently fastest data structure for personalized shortest path  ...  Let us look at a few applications for SNDBs which can benefit from small k-Path Covers.  ... 
doi:10.1007/s00778-015-0392-3 fatcat:wzuvcrzrdvdobnte7e5htyxkom

On k-path covers and their applications

Stefan Funke, André Nusser, Sabine Storandt
2014 Proceedings of the VLDB Endowment  
This paper considers the problem of constructing small k-Path Covers in the context of road networks with millions of nodes and edges.  ...  In many application scenarios, the set C and its induced overlay graph constitute a very compact synopsis of G, which is the basis for the currently fastest data structure for personalized shortest path  ...  Let us look at a few applications for SNDBs which can benefit from small k-Path Covers.  ... 
doi:10.14778/2732951.2732963 fatcat:pnmi5wpezvdhxlw6ohyaoqukce

Limits of Ordered Graphs and their Applications [article]

Omri Ben-Eliezer, Eldar Fischer, Amit Levi, Yuichi Yoshida
2019 arXiv   pre-print
We show that the space of orderons is compact with respect to this distance notion, which is key to a successful analysis of combinatorial objects through their limits.  ...  As a special case, this yields limit objects for matrices whose rows and columns are ordered, and for dynamic graphs that expand (via vertex insertions) over time.  ...  Completeness and compactness The space of limit objects must be complete with respect to the metric: Cauchy sequences should converge in this metric space.  ... 
arXiv:1811.02023v2 fatcat:xcxchcjakveyzjaknomde4a4cy

Topological Characteristics of Oil and Gas Reservoirs and Their Applications [chapter]

V. A. Baikov, R. R. Gilmanov, I. A. Taimanov, A. A. Yakovlev
2017 Lecture Notes in Computer Science  
To assess economic efficiency and optimal placement of wells and to predict hydrocarbon production levels, it is important to have some quantitative representation of the object under study.  ...  At present no company develops oil and gas fields without constructing geologic and hydrodynamic models.  ...  topology for geological applications however that was started not long ago (see [1] for oil and gas reservoirs and [12, 13] and references therein for applications to structural geology).  ... 
doi:10.1007/978-3-319-69775-8_11 fatcat:qexd73qaqne5jgkr47q6owr3be
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