16,540 research outputs found
Single Parameter Combinatorial Auctions with Partially Public Valuations
We consider the problem of designing truthful auctions, when the bidders'
valuations have a public and a private component. In particular, we consider
combinatorial auctions where the valuation of an agent for a set of
items can be expressed as , where is a private single parameter
of the agent, and the function is publicly known. Our motivation behind
studying this problem is two-fold: (a) Such valuation functions arise naturally
in the case of ad-slots in broadcast media such as Television and Radio. For an
ad shown in a set of ad-slots, is, say, the number of {\em unique}
viewers reached by the ad, and is the valuation per-unique-viewer. (b)
From a theoretical point of view, this factorization of the valuation function
simplifies the bidding language, and renders the combinatorial auction more
amenable to better approximation factors. We present a general technique, based
on maximal-in-range mechanisms, that converts any -approximation
non-truthful algorithm () for this problem into
and -approximate truthful
mechanisms which run in polynomial time and quasi-polynomial time,
respectively
Fibrational induction meets effects
This paper provides several induction rules that can be used to prove properties of effectful data types. Our results are semantic in nature and build upon Hermida and Jacobsâ fibrational formulation of induction for polynomial data types and its extension to all inductive data types by Ghani, Johann, and Fumex. An effectful data type ÎŒ(TF) is built from a functor F that describes data, and a monad T that computes effects. Our main contribution is to derive induction rules that are generic over all functors F and monads T such that ÎŒ(TF) exists. Along the way, we also derive a principle of definition by structural recursion for effectful data types that is similarly generic. Our induction rule is also generic over the kinds of properties to be proved: like the work on which we build, we work in a general fibrational setting and so can accommodate very general notions of properties, rather than just those of particular syntactic forms. We give examples exploiting the generality of our results, and show how our results specialize to those in the literature, particularly those of Filinski and StĂžvring
Live and Dead Nodes
In this paper, we explore the consequences of a distinction between `live'
and `dead' network nodes; `live' nodes are able to acquire new links whereas
`dead' nodes are static. We develop an analytically soluble growing network
model incorporating this distinction and show that it can provide a
quantitative description of the empirical network composed of citations and
references (in- and out-links) between papers (nodes) in the SPIRES database of
scientific papers in high energy physics. We also demonstrate that the death
mechanism alone can result in power law degree distributions for the resulting
network.Comment: 12 pages, 3 figures. To be published in Computational and
Mathematical Organization Theor
Gibrat's law for cities: uniformly most powerful unbiased test of the Pareto against the lognormal
We address the general problem of testing a power law distribution versus a
log-normal distribution in statistical data. This general problem is
illustrated on the distribution of the 2000 US census of city sizes. We provide
definitive results to close the debate between Eeckhout (2004, 2009) and Levy
(2009) on the validity of Zipf's law, which is the special Pareto law with tail
exponent 1, to describe the tail of the distribution of U.S. city sizes.
Because the origin of the disagreement between Eeckhout and Levy stems from the
limited power of their tests, we perform the {\em uniformly most powerful
unbiased test} for the null hypothesis of the Pareto distribution against the
lognormal. The -value and Hill's estimator as a function of city size lower
threshold confirm indubitably that the size distribution of the 1000 largest
cities or so, which include more than half of the total U.S. population, is
Pareto, but we rule out that the tail exponent, estimated to be ,
is equal to 1. For larger ranks, the -value becomes very small and Hill's
estimator decays systematically with decreasing ranks, qualifying the lognormal
distribution as the better model for the set of smaller cities. These two
results reconcile the opposite views of Eeckhout (2004, 2009) and Levy (2009).
We explain how Gibrat's law of proportional growth underpins both the Pareto
and lognormal distributions and stress the key ingredient at the origin of
their difference in standard stochastic growth models of cities
\cite{Gabaix99,Eeckhout2004}.Comment: 7 pages + 2 figure
Encroachment diminishes herbaceous plant diversity in grassy ecosystems worldwide
Woody encroachment is ubiquitous in grassy ecosystems worldwide, but its global impacts on the diversity of herbaceous plants that characterise and define these ecosystems remain unquantified. The pervasiveness of encroachment is relatively easily observed via remote sensing, but its impacts on plant diversity and richness below the canopy can only be observed via fieldâbased studies. Via a metaâanalysis of 42 field studies across tropical to temperate grassy ecosystems, we quantified how encroachment altered herbaceous species richness, and the richness of forbs, C(3) graminoids and C(4) graminoids. Across studies, the natural logarithm of the response ratio (lnRR) of herbaceous species richness ranged from â3.33 to 0.34 with 87% of encroached ecosystems negatively impacted. Assessment of the extent of encroachment, duration of encroachment, mean annual rainfall, latitude, and continent demonstrated that only extent of encroachment had relevance in the data (univariate model including a random effect of study explained 45.4% of variance). The global weighted mean lnRR of species richness decreased from â0.245 at 66%. Continued encroachment results in substantial loss of herbaceous diversity at medium and high extents, with a loss of richness that is not replaced. Although all functional groups are significantly negatively impacted by encroachment, forb richness is relatively more sensitive than graminoid richness, and C(4) graminoid richness relatively more than C(3) graminoid richness. Although no geographic or climatic correlates had relevance in the data, encroachment as an emergent product of global change coalesces to decrease ground layer light availability, lead to loss of fire and grazers, and alter hydrology and soils. Encroachment is accelerating and grassy ecosystems require urgent attention to determine critical woody cover thresholds that facilitate diverse and resilient grassy ecosystems
A quantitative analysis of measures of quality in science
Condensing the work of any academic scientist into a one-dimensional measure
of scientific quality is a difficult problem. Here, we employ Bayesian
statistics to analyze several different measures of quality. Specifically, we
determine each measure's ability to discriminate between scientific authors.
Using scaling arguments, we demonstrate that the best of these measures require
approximately 50 papers to draw conclusions regarding long term scientific
performance with usefully small statistical uncertainties. Further, the
approach described here permits the value-free (i.e., statistical) comparison
of scientists working in distinct areas of science.Comment: 11 pages, 8 figures, 4 table
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