889 research outputs found
On colimits and elementary embeddings
We give a sharper version of a theorem of Rosicky, Trnkova and Adamek, and a
new proof of a theorem of Rosicky, both about colimit preservation between
categories of structures. Unlike the original proofs, which use
category-theoretic methods, we use set-theoretic arguments involving elementary
embeddings given by large cardinals such as alpha-strongly compact and
C^(n)-extendible cardinals.Comment: 17 page
Maximizing Utility Among Selfish Users in Social Groups
We consider the problem of a social group of users trying to obtain a
"universe" of files, first from a server and then via exchange amongst
themselves. We consider the selfish file-exchange paradigm of give-and-take,
whereby two users can exchange files only if each has something unique to offer
the other. We are interested in maximizing the number of users who can obtain
the universe through a schedule of file-exchanges. We first present a practical
paradigm of file acquisition. We then present an algorithm which ensures that
at least half the users obtain the universe with high probability for files
and users when , thereby showing an
approximation ratio of 2. Extending these ideas, we show a -
approximation algorithm for , and a - approximation algorithm for , , .
Finally, we show that for any , there exists a schedule of file
exchanges which ensures that at least half the users obtain the universe.Comment: 11 pages, 3 figures; submitted for review to the National Conference
on Communications (NCC) 201
The Online Disjoint Set Cover Problem and its Applications
Given a universe of elements and a collection of subsets
of , the maximum disjoint set cover problem (DSCP) is to
partition into as many set covers as possible, where a set cover
is defined as a collection of subsets whose union is . We consider the
online DSCP, in which the subsets arrive one by one (possibly in an order
chosen by an adversary), and must be irrevocably assigned to some partition on
arrival with the objective of minimizing the competitive ratio. The competitive
ratio of an online DSCP algorithm is defined as the maximum ratio of the
number of disjoint set covers obtained by the optimal offline algorithm to the
number of disjoint set covers obtained by across all inputs. We propose an
online algorithm for solving the DSCP with competitive ratio . We then
show a lower bound of on the competitive ratio for any
online DSCP algorithm. The online disjoint set cover problem has wide ranging
applications in practice, including the online crowd-sourcing problem, the
online coverage lifetime maximization problem in wireless sensor networks, and
in online resource allocation problems.Comment: To appear in IEEE INFOCOM 201
Isolation of organic matter from complex clay matrices
Pòster amb el resum gràfic de la tesi doctoral en curs, que forma part de l'exposició "Doctorat en Recursos Naturals i Medi Ambient de la UPC Manresa. 30 anys formant en recerca a la Catalunya Central 1992-2022".Amphos 21, an SRK company. The authors acknowledge ONDRAS/NIRAS for the financial support of this projectPostprint (published version
Superstrong and other large cardinals are never Laver indestructible
Superstrong cardinals are never Laver indestructible. Similarly, almost huge
cardinals, huge cardinals, superhuge cardinals, rank-into-rank cardinals,
extendible cardinals, 1-extendible cardinals, 0-extendible cardinals, weakly
superstrong cardinals, uplifting cardinals, pseudo-uplifting cardinals,
superstrongly unfoldable cardinals, \Sigma_n-reflecting cardinals,
\Sigma_n-correct cardinals and \Sigma_n-extendible cardinals (all for n>2) are
never Laver indestructible. In fact, all these large cardinal properties are
superdestructible: if \kappa\ exhibits any of them, with corresponding target
\theta, then in any forcing extension arising from nontrivial strategically
<\kappa-closed forcing Q in V_\theta, the cardinal \kappa\ will exhibit none of
the large cardinal properties with target \theta\ or larger.Comment: 19 pages. Commentary concerning this article can be made at
http://jdh.hamkins.org/superstrong-never-indestructible. Minor changes in v
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