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Friedrich Wilhelm Tobias Hunger (1874–1952). Biograaf van botanische helden en 'anti-vaderlander'
2013
Studium: Tijdschrift voor Wetenschaps- en Universiteitsgeschiedenis
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Daniel Tobias Bauer: Das Bildungsverständnis des Theologen Friedrich Schleiermacher (= Praktische Theologie in Geschichte und Gegenwart, Bd. 16). 2015
2016
Zeitschrift für Pädagogik und Theologie
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Disrupted Arts and Marginalized Humans: A Commentary on Friedrich Kittler's "Signal-to-Noise Ratio"
[chapter]
2018
Disruption in the Arts
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The geodynamo for non-geophysicists
[article]
2019
arXiv
pre-print
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The geodynamo usually appears as a somewhat intimidating subject. Its understanding seems to require the intricate theory of magnetohydrodynamics. The solution of the corresponding equations can only be achieved numerically. It seems to be a subject for the specialist. We show that one can understand the basics of the functioning of the geodynamo solely by using the well-known laws of electrodynamics. The topic is not only important for geophysicists. The same physics is the cause for the
arXiv:1912.13158v1
fatcat:brdrpg72tfer5itk7qepbbcklm
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... ic fields of sun-like stars, of the very strong fields of neutron stars, and also of the cosmic magnetic fields.
Smoothed Analysis of Balancing Networks
[article]
2010
arXiv
pre-print
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In a balancing network each processor has an initial collection of unit-size jobs (tokens) and in each round, pairs of processors connected by balancers split their load as evenly as possible. An excess token (if any) is placed according to some predefined rule. As it turns out, this rule crucially affects the performance of the network. In this work we propose a model that studies this effect. We suggest a model bridging the uniformly-random assignment rule, and the arbitrary one (in the
arXiv:1006.1443v1
fatcat:5g5ynfd45vf35nx52337x723lm
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... of smoothed-analysis). We start with an arbitrary assignment of balancer directions and then flip each assignment with probability α independently. For a large class of balancing networks our result implies that after ( n) rounds the discrepancy is ( (1/2-α) n + n) with high probability. This matches and generalizes known upper bounds for α=0 and α=1/2. We also show that a natural network matches the upper bound for any α.
Quasirandom Rumor Spreading
[article]
2013
arXiv
pre-print
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We propose and analyze a quasirandom analogue of the classical push model for disseminating information in networks ("randomized rumor spreading"). In the classical model, in each round each informed vertex chooses a neighbor at random and informs it, if it was not informed before. It is known that this simple protocol succeeds in spreading a rumor from one vertex to all others within O(log n) rounds on complete graphs, hypercubes, random regular graphs, Erdos-Renyi random graph and Ramanujan
arXiv:1012.5351v2
fatcat:66oaunhlt5hz3ogyqxe6kugq4i
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... aphs with probability 1-o(1). In the quasirandom model, we assume that each vertex has a (cyclic) list of its neighbors. Once informed, it starts at a random position on the list, but from then on informs its neighbors in the order of the list. Surprisingly, irrespective of the orders of the lists, the above-mentioned bounds still hold. In some cases, even better bounds than for the classical model can be shown.
Flow-Based Network Creation Games
[article]
2020
arXiv
pre-print
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Network Creation Games(NCGs) model the creation of decentralized communication networks like the Internet. In such games strategic agents corresponding to network nodes selfishly decide with whom to connect to optimize some objective function. Past research intensively analyzed models where the agents strive for a central position in the network. This models agents optimizing the network for low-latency applications like VoIP. However, with today's abundance of streaming services it is
arXiv:2006.14964v1
fatcat:oiens3vbtzgyhdixpeg6y2oyb4
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... to ensure that the created network can satisfy the increased bandwidth demand. To the best of our knowledge, this natural problem of the decentralized strategic creation of networks with sufficient bandwidth has not yet been studied. We introduce Flow-Based NCGs where the selfish agents focus on bandwidth instead of latency. In essence, budget-constrained agents create network links to maximize their minimum or average network flow value to all other network nodes. Equivalently, this can also be understood as agents who create links to increase their connectivity and thus also the robustness of the network. For this novel type of NCG we prove that pure Nash equilibria exist, we give a simple algorithm for computing optimal networks, we show that the Price of Stability is 1 and we prove an (almost) tight bound of 2 on the Price of Anarchy. Last but not least, we show that our models do not admit a potential function.
The Cover Time of Deterministic Random Walks
[article]
2010
arXiv
pre-print
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The rotor router model is a popular deterministic analogue of a random walk on a graph. Instead of moving to a random neighbor, the neighbors are served in a fixed order. We examine how fast this "deterministic random walk" covers all vertices (or all edges). We present general techniques to derive upper bounds for the vertex and edge cover time and derive matching lower bounds for several important graph classes. Depending on the topology, the deterministic random walk can be asymptotically
arXiv:1006.3430v1
fatcat:37gronuukzaqlo4ugjyrdtrlpa
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... ter, slower or equally fast as the classic random walk. We also examine the short term behavior of deterministic random walks, that is, the time to visit a fixed small number of vertices or edges.
Average-Case Analysis of Online Topological Ordering
[article]
2008
arXiv
pre-print
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Ajwani, Friedrich, and Meyer (AFM) [1] proposed a new algorithm with runtime O(n 2.75 ), which asymptotically outperforms KB on dense DAGs. ...
arXiv:0802.1059v1
fatcat:kruzcypnwrd7dnkrqb45y4xeva
Genetic and Evolutionary Computation
2014
Theoretical Computer Science
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Deterministic Random Walks on the Two-Dimensional Grid
[article]
2007
arXiv
pre-print
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Jim Propp's rotor router model is a deterministic analogue of a random walk on a graph. Instead of distributing chips randomly, each vertex serves its neighbors in a fixed order. We analyze the difference between Propp machine and random walk on the infinite two-dimensional grid. It is known that, apart from a technicality, independent of the starting configuration, at each time, the number of chips on each vertex in the Propp model deviates from the expected number of chips in the random walk
arXiv:math/0703453v1
fatcat:5ovebwhvqzatnmngz6gt7dfhfe
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... odel by at most a constant. We show that this constant is approximately 7.8, if all vertices serve their neighbors in clockwise or counterclockwise order and 7.3 otherwise. This result in particular shows that the order in which the neighbors are served makes a difference. Our analysis also reveals a number of further unexpected properties of the two-dimensional Propp machine.
Space-Efficient Fault-Tolerant Diameter Oracles
[article]
2021
arXiv
pre-print
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We design f-edge fault-tolerant diameter oracles (f-FDOs). We preprocess a given graph G on n vertices and m edges, and a positive integer f, to construct a data structure that, when queried with a set F of |F| ≤ f edges, returns the diameter of G-F. For a single failure (f=1) in an unweighted directed graph of diameter D, there exists an approximate FDO by Henzinger et al. [ITCS 2017] with stretch (1+ε), constant query time, space O(m), and a combinatorial preprocessing time of O(mn +
arXiv:2107.03485v1
fatcat:3a2l7rvbifdyzjiu4q23fhf7uu
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... /ε)).We present an FDO for directed graphs with the same stretch, query time, and space. It has a preprocessing time of O(mn + n^2/ε). The preprocessing time nearly matches a conditional lower bound for combinatorial algorithms, also by Henzinger et al. With fast matrix multiplication, we achieve a preprocessing time of O(n^2.5794 + n^2/ε). We further prove an information-theoretic lower bound showing that any FDO with stretch better than 3/2 requires Ω(m) bits of space. For multiple failures (f>1) in undirected graphs with non-negative edge weights, we give an f-FDO with stretch (f+2), query time O(f^2log^2n), O(fn) space, and preprocessing time O(fm). We complement this with a lower bound excluding any finite stretch in o(fn) space. We show that for unweighted graphs with polylogarithmic diameter and up to f = o(log n/ loglog n) failures, one can swap approximation for query time and space. We present an exact combinatorial f-FDO with preprocessing time mn^1+o(1), query time n^o(1), and space n^2+o(1). When using fast matrix multiplication instead, the preprocessing time can be improved to n^ω+o(1), where ω < 2.373 is the matrix multiplication exponent.
Routing in Strongly Hyperbolic Unit Disk Graphs
[article]
2021
arXiv
pre-print
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Greedy routing has been studied successfully on Euclidean unit disk graphs, which we interpret as a special case of hyperbolic unit disk graphs. While sparse Euclidean unit disk graphs exhibit grid-like structure, we introduce strongly hyperbolic unit disk graphs as the natural counterpart containing graphs that have hierarchical network structures. We develop and analyze a routing scheme that utilizes these hierarchies. On arbitrary graphs this scheme guarantees a worst case stretch of max{3,
arXiv:2107.05518v1
fatcat:pq2s6y7h3fd2ljqkqulf27r3am
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... +2b/a} for a > 0 and b > 1. Moreover, it stores 𝒪(k(log^2n + logk)) bits at each vertex and takes 𝒪(k) time for a routing decision, where k = π e (1 + a)/(2(b - 1)) (b^2 diam(G) - 1) R + log_b(diam(G)) + 1, on strongly hyperbolic unit disk graphs with threshold radius R > 0. In particular, for hyperbolic random graphs, which have previously been used to model hierarchical networks like the internet, k = 𝒪(log^2n) holds asymptotically almost surely. Thus, we obtain a worst-case stretch of 3, 𝒪(log^4 n) bits of storage per vertex, and 𝒪(log^2 n) time per routing decision on such networks. This beats existing worst-case lower bounds. Our proof of concept implementation indicates that the obtained results translate well to real-world networks.
On the Average-case Complexity of Parameterized Clique
[article]
2014
arXiv
pre-print
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The k-Clique problem is a fundamental combinatorial problem that plays a prominent role in classical as well as in parameterized complexity theory. It is among the most well-known NP-complete and W[1]-complete problems. Moreover, its average-case complexity analysis has created a long thread of research already since the 1970s. Here, we continue this line of research by studying the dependence of the average-case complexity of the k-Clique problem on the parameter k. To this end, we define two
arXiv:1410.6400v1
fatcat:zp5kw6bbujewxdgsppg77evpny
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... atural parameterized analogs of efficient average-case algorithms. We then show that k-Clique admits both analogues for Erdős-Rényi random graphs of arbitrary density. We also show that k-Clique is unlikely to admit neither of these analogs for some specific computable input distribution.
Quasi-random Agents for Image Transition and Animation
[article]
2017
arXiv
pre-print
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Quasi-random walks show similar features as standard random walks, but with much less randomness. We utilize this established model from discrete mathematics and show how agents carrying out quasi-random walks can be used for image transition and animation. The key idea is to generalize the notion of quasi-random walks and let a set of autonomous agents perform quasi-random walks painting an image. Each agent has one particular target image that they paint when following a sequence of
arXiv:1710.07421v1
fatcat:s2e2ugcz2ncc7cnuo77fp22ioe
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... for their quasi-random walk. The sequence can easily be chosen by an artist and allows them to produce a wide range of different transition patterns and animations.
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