742 research outputs found
Limits of Structures and the Example of Tree-Semilattices
The notion of left convergent sequences of graphs introduced by Lov\' asz et
al. (in relation with homomorphism densities for fixed patterns and
Szemer\'edi's regularity lemma) got increasingly studied over the past
years. Recently, Ne\v set\v ril and Ossona de Mendez introduced a general
framework for convergence of sequences of structures. In particular, the
authors introduced the notion of -convergence, which is a natural
generalization of left-convergence. In this paper, we initiate study of
-convergence for structures with functional symbols by focusing on the
particular case of tree semi-lattices. We fully characterize the limit objects
and give an application to the study of left convergence of -partite
cographs, a generalization of cographs
Conservative constraint satisfaction re-revisited
Conservative constraint satisfaction problems (CSPs) constitute an important
particular case of the general CSP, in which the allowed values of each
variable can be restricted in an arbitrary way. Problems of this type are well
studied for graph homomorphisms. A dichotomy theorem characterizing
conservative CSPs solvable in polynomial time and proving that the remaining
ones are NP-complete was proved by Bulatov in 2003. Its proof, however, is
quite long and technical. A shorter proof of this result based on the absorbing
subuniverses technique was suggested by Barto in 2011. In this paper we give a
short elementary prove of the dichotomy theorem for the conservative CSP
On lattices and their ideal lattices, and posets and their ideal posets
For P a poset or lattice, let Id(P) denote the poset, respectively, lattice,
of upward directed downsets in P, including the empty set, and let
id(P)=Id(P)-\{\emptyset\}. This note obtains various results to the effect that
Id(P) is always, and id(P) often, "essentially larger" than P. In the first
vein, we find that a poset P admits no "<"-respecting map (and so in
particular, no one-to-one isotone map) from Id(P) into P, and, going the other
way, that an upper semilattice S admits no semilattice homomorphism from any
subsemilattice of itself onto Id(S).
The slightly smaller object id(P) is known to be isomorphic to P if and only
if P has ascending chain condition. This result is strengthened to say that the
only posets P_0 such that for every natural number n there exists a poset P_n
with id^n(P_n)\cong P_0 are those having ascending chain condition. On the
other hand, a wide class of cases is noted here where id(P) is embeddable in P.
Counterexamples are given to many variants of the results proved.Comment: 8 pages. Copy at http://math.berkeley.edu/~gbergman/papers may be
updated more frequently than arXiv copy. After publication, updates, errata,
etc. may be noted at that pag
The Design of Arbitrage-Free Data Pricing Schemes
Motivated by a growing market that involves buying and selling data over the
web, we study pricing schemes that assign value to queries issued over a
database. Previous work studied pricing mechanisms that compute the price of a
query by extending a data seller's explicit prices on certain queries, or
investigated the properties that a pricing function should exhibit without
detailing a generic construction. In this work, we present a formal framework
for pricing queries over data that allows the construction of general families
of pricing functions, with the main goal of avoiding arbitrage. We consider two
types of pricing schemes: instance-independent schemes, where the price depends
only on the structure of the query, and answer-dependent schemes, where the
price also depends on the query output. Our main result is a complete
characterization of the structure of pricing functions in both settings, by
relating it to properties of a function over a lattice. We use our
characterization, together with information-theoretic methods, to construct a
variety of arbitrage-free pricing functions. Finally, we discuss various
tradeoffs in the design space and present techniques for efficient computation
of the proposed pricing functions.Comment: full pape
Stability and Index of the Meet Game on a Lattice
We study the stability and the stability index of the meet game form defined on a meet semilattice. Given any active coalition structure, we show that the stability index relative to the equilibrium, to the beta core and to the exact core is a function of the Nakamura number, the depth of the semilattice and its gap function.Effectivity Function, Lattice, Stability Index, Equilibrium, Nakamura Number
Closed subgroups of the infinite symmetric group
Let S=Sym(\Omega) be the group of all permutations of a countably infinite
set \Omega, and for subgroups G_1, G_2\leq S let us write G_1\approx G_2 if
there exists a finite set U\subseteq S such that = .
It is shown that the subgroups closed in the function topology on S lie in
precisely four equivalence classes under this relation. Which of these classes
a closed subgroup G belongs to depends on which of the following statements
about pointwise stabilizer subgroups G_{(\Gamma)} of finite subsets
\Gamma\subseteq\Omega holds:
(i) For every finite set \Gamma, the subgroup G_{(\Gamma)} has at least one
infinite orbit in \Omega.
(ii) There exist finite sets \Gamma such that all orbits of G_{(\Gamma)} are
finite, but none such that the cardinalities of these orbits have a common
finite bound.
(iii) There exist finite sets \Gamma such that the cardinalities of the
orbits of G_{(\Gamma)} have a common finite bound, but none such that
G_{(\Gamma)}=\{1\}.
(iv) There exist finite sets \Gamma such that G_{(\Gamma)}=\{1\}.
Some questions for further investigation are discussed.Comment: 33 pages. See also http://math.berkeley.edu/~gbergman/papers and
http://shelah.logic.at (pub. 823). To appear, Alg.Univ., issue honoring
W.Taylor. Main results as before (greater length due to AU formatting), but
some new results in \S\S11-12. Errors in subscripts between displays (12) and
(13) fixed. Error in title of orig. posting fixed. 1 ref. adde
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