60 research outputs found
Public Goods in Networks with Constraints on Sharing
This paper considers incentives to provide goods that are partially
excludable along social links. We introduce a model in which each individual in
a networked society makes a two-pronged decision: (i) decide how much of the
good to provide, and (ii) decide which subset of neighbours to nominate as
co-beneficiaries. An outcome specifies an endogenous subnetwork generated by
nominations and a public goods game occurring over the realised subnetwork. We
show the existence of specialised pure strategy Nash equilibria: those in which
some individuals (the Drivers) contribute while the remaining individuals (the
Passengers) free ride. We then consider how the set of efficient specialised
equilibria vary as the constraints on sharing are relaxed and we show a
monotonicity result. Finally, we introduce dynamics and show that only
specialised equilibria can be stable against individuals unilaterally changing
their provision level
The asymptotic number of prefix normal words
We show that the number of prefix normal binary words of length is
. We also show that the maximum number of binary
words of length with a given fixed prefix normal form is
.Comment: 9 page
Connectivity of the Uniform Random Intersection Graph
A \emph{uniform random intersection graph} is a random graph
constructed as follows. Label each of nodes by a randomly chosen set of
distinct colours taken from some finite set of possible colours of size .
Nodes are joined by an edge if and only if some colour appears in both their
labels. These graphs arise in the study of the security of wireless sensor
networks. Such graphs arise in particular when modelling the network graph of
the well known key predistribution technique due to Eschenauer and Gligor.
The paper determines the threshold for connectivity of the graph
when with a function of such that and
for some fixed positive real number . In
this situation, is almost surely connected when and is almost surely disconnected when Comment: 19 pages New version with rewritten intro, and a discussion section
added. The results and proofs are unchanged from the previous versio
Die zeitgenössische Ruine.
Stefanie Gerke untersucht in der vorliegenden Dissertation die Frage, in welcher Weise sich Künstler*innen mit verfallender Architektur der 1960er und 1970er Jahre beschäftigen. Sie analysiert Fotografie-, Film- und Videoarbeiten seit 1990, die gezielt ikonografische Traditionen des Topos Ruine erweitern, aktualisieren und unter den Bedingungen ihres Mediums neu orientieren. War die Ruinenikonografie bislang durch die Ästhetik der Romantik sowie Georg Simmels geprägt, der den Reiz verfallender Bauten in der Rückeroberung durch die Natur sah, bestehen die modernen Ruinen aus industriellen, schwer vergänglichen Baustoffen und sind häufig die Folge menschlicher statt natürlicher Zerstörung. Die Analyse der Werke zeitgenössischer Künstler*innen, die sich maßgeblich mit dem Verfall von Nachkriegsbauten beschäftigt haben, führt in der Dissertation daher zu einer Aktualisierung der für den Ruinenbegriff prägenden ästhetischen Kategorien des Pittoresken und des Erhabenen für das 21. Jahrhundert. Einige der analysierten Arbeiten nutzen Nachkriegsarchitektur als zeitgemäßes Symbol der Vergänglichkeit und widmen sich in pittoresker Tradition vor allem Wahrnehmungsfragen, um die Konstruktionsmechanismen ihrer eigenen Medien zu reflektieren, wie etwa die 16-mm-Filme Tacita Deans (*1965), die Polaroid-Serie Cyprien Gaillards (*1980) und die Fotomontagen Beate Gütschows (*1970). Andere Künstler gewinnen den radikalen Bildern abgerissener oder dem Abbruch geweihter, gescheiterter Nachkriegsarchitektur und den damit einhergehenden sozialen Folgen eine ästhetische Komponente ab, die in der Tradition des Erhabenen Lust und Schrecken miteinander verbindet, wie etwa Julian Rosefeldt (*1965), Clemens von Wedemeyer (*1974) und Tobias Zielony (*1973).
Die Dissertation verortet sich nicht nur innerhalb der Diskussion um das Erbe der Nachkriegsmoderne, sondern steckt systematisch ein Feld ab, in dem sich zeitgenössische Kunst momentan bewegt.In this dissertation, Stefanie Gerke investigates the question of how artists deal with decaying architecture of the 1960s and 1970s. She analyzes photographic, film, and video works since 1990 that specifically expand the iconographic tradition of the ruin, update it, and rearticulate it within the specific conditions of new media. While the iconography of ruins was previously influenced by the aesthetics of Romanticism as well as Georg Simmel, who saw the appeal of decaying buildings in their reconquest by nature, modern ruins are made of industrial building materials that are difficult to decompose and are often the result of human rather than natural destruction. In the dissertation, the analysis of the works of contemporary artists who are dealing with the decay of post-war buildings therefore leads to an update of two aesthetic categories that characterize the concept of ruins, for the 21st century: the picturesque and the sublime. Some of the works analyzed use postwar architecture as a contemporary symbol of transience and, in the picturesque tradition, devote themselves primarily to questions of perception in order to reflect on the construction mechanisms of their own media, such as Tacita Dean's (*1965) 16mm films, Cyprien Gaillard's (*1980) Polaroid series, and Beate Gütschow's (*1970) photomontages. Other artists extract an aesthetic component from the radical images of demolished or condemned, failed postwar architecture and the accompanying social consequences, which combines pleasure and horror in the tradition of the sublime, such as Julian Rosefeldt and Piero Steinle (*1965/1959), Clemens von Wedemeyer (*1974), and Tobias Zielony (*1973).
The dissertation not only locates itself within the discussion about the legacy of postwar architecture, but also systematically delineates a field in which contemporary art is currently active
Pegging Graphs Yields a Small Diameter
We consider the following process for generating large random cubic graphs. Starting with a given graph, repeatedly add edges that join the midpoints of two randomly chosen edges. We show that the growing graph asymptotically almost surely has logarithmic diameter. This process is motivated by a particular type of peer-to-peer network. Our method extends to similar processes that generate regular graphs of higher degre
Successive shortest paths in complete graphs with random edge weights
Consider a complete graph Kn with edge weights drawn independently from a uniform distribution U(0,1). The weight of the shortest (minimum-weight) path P1 between two given vertices is known to be ln n/n, asymptotically. Define a second-shortest path P2 to be the shortest path edge-disjoint from P1, and consider more generally the shortest path Pk edge-disjoint from all earlier paths. We show that the cost Xk of Pk converges in probability to 2k/n + ln n/n uniformly for all k ≤ n − 1. We show analogous results when the edge weights are drawn from an exponential distribution. The same results characterize the collectively cheapest k edge-disjoint paths, that is, a minimum-cost k-flow. We also obtain the expectation of Xk conditioned on the existence of Pk
Proximity and Remoteness in Directed and Undirected Graphs
Let be a strongly connected digraph. The average distance
of a vertex of is the arithmetic mean of the
distances from to all other vertices of . The remoteness and
proximity of are the maximum and the minimum of the average
distances of the vertices of , respectively. We obtain sharp upper and lower
bounds on and as a function of the order of and
describe the extreme digraphs for all the bounds. We also obtain such bounds
for strong tournaments. We show that for a strong tournament , we have
if and only if is regular. Due to this result, one may
conjecture that every strong digraph with is regular. We
present an infinite family of non-regular strong digraphs such that
We describe such a family for undirected graphs as well
Lower Bounds for Maximum Weight Bisections of Graphs with Bounded Degrees
A bisection in a graph is a cut in which the number of vertices in the two
parts differ by at most 1. In this paper, we give lower bounds for the maximum
weight of bisections of edge-weighted graphs with bounded maximum degree. Our
results improve a bound of Lee, Loh, and Sudakov (J. Comb. Th. Ser. B 103
(2013)) for (unweighted) maximum bisections in graphs whose maximum degree is
either even or equals 3, and for almost all graphs. We show that a tight lower
bound for maximum size of bisections in 3-regular graphs obtained by Bollob\'as
and Scott (J. Graph Th. 46 (2004)) can be extended to weighted subcubic graphs.
We also consider edge-weighted triangle-free subcubic graphs and show that a
much better lower bound (than for edge-weighted subcubic graphs) holds for such
graphs especially if we exclude . We pose three conjectures
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