3,752 research outputs found
Computing Equilibrium in Matching Markets
Market equilibria of matching markets offer an intuitive and fair solution
for matching problems without money with agents who have preferences over the
items. Such a matching market can be viewed as a variation of Fisher market,
albeit with rather peculiar preferences of agents. These preferences can be
described by piece-wise linear concave (PLC) functions, which however, are not
separable (due to each agent only asking for one item), are not monotone, and
do not satisfy the gross substitute property-- increase in price of an item can
result in increased demand for the item. Devanur and Kannan in FOCS 08 showed
that market clearing prices can be found in polynomial time in markets with
fixed number of items and general PLC preferences. They also consider Fischer
markets with fixed number of agents (instead of fixed number of items), and
give a polynomial time algorithm for this case if preferences are separable
functions of the items, in addition to being PLC functions.
Our main result is a polynomial time algorithm for finding market clearing
prices in matching markets with fixed number of different agent preferences,
despite that the utility corresponding to matching markets is not separable. We
also give a simpler algorithm for the case of matching markets with fixed
number of different items
Key polynomials for simple extensions of valued fields
Let be a simple transcendental extension
of valued fields, where is equipped with a valuation of rank 1. That
is, we assume given a rank 1 valuation of and its extension to
. Let denote the valuation ring of . The purpose
of this paper is to present a refined version of MacLane's theory of key
polynomials, similar to those considered by M. Vaqui\'e, and reminiscent of
related objects studied by Abhyankar and Moh (approximate roots) and T.C. Kuo.
Namely, we associate to a countable well ordered set the are called {\bf key
polynomials}. Key polynomials which have no immediate predecessor are
called {\bf limit key polynomials}. Let .
We give an explicit description of the limit key polynomials (which may be
viewed as a generalization of the Artin--Schreier polynomials). We also give an
upper bound on the order type of the set of key polynomials. Namely, we show
that if then the set of key polynomials has
order type at most , while in the case
this order type is bounded above by , where stands
for the first infinite ordinal.Comment: arXiv admin note: substantial text overlap with arXiv:math/060519
12th International Workshop on Termination (WST 2012) : WST 2012, February 19–23, 2012, Obergurgl, Austria / ed. by Georg Moser
This volume contains the proceedings of the 12th International Workshop on Termination (WST 2012), to be held February 19–23, 2012 in Obergurgl, Austria. The goal of the Workshop on Termination is to be a venue for presentation and discussion of all topics in and around termination. In this way, the workshop tries to bridge the gaps between different communities interested and active in research in and around termination. The 12th International Workshop on Termination in Obergurgl continues the successful workshops held in St. Andrews (1993), La Bresse (1995), Ede (1997), Dagstuhl (1999), Utrecht (2001), Valencia (2003), Aachen (2004), Seattle (2006), Paris (2007), Leipzig (2009), and Edinburgh (2010). The 12th International Workshop on Termination did welcome contributions on all aspects of termination and complexity analysis. Contributions from the imperative, constraint, functional, and logic programming communities, and papers investigating applications of complexity or termination (for example in program transformation or theorem proving) were particularly welcome. We did receive 18 submissions which all were accepted. Each paper was assigned two reviewers. In addition to these 18 contributed talks, WST 2012, hosts three invited talks by Alexander Krauss, Martin Hofmann, and Fausto Spoto
Encrypted statistical machine learning: new privacy preserving methods
We present two new statistical machine learning methods designed to learn on
fully homomorphic encrypted (FHE) data. The introduction of FHE schemes
following Gentry (2009) opens up the prospect of privacy preserving statistical
machine learning analysis and modelling of encrypted data without compromising
security constraints. We propose tailored algorithms for applying extremely
random forests, involving a new cryptographic stochastic fraction estimator,
and na\"{i}ve Bayes, involving a semi-parametric model for the class decision
boundary, and show how they can be used to learn and predict from encrypted
data. We demonstrate that these techniques perform competitively on a variety
of classification data sets and provide detailed information about the
computational practicalities of these and other FHE methods.Comment: 39 page
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