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 $i$ for a set $S$ of items can be expressed as $v_if(S)$, where $v_i$ is a private single parameter of the agent, and the function $f$ 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 $S$ of ad-slots, $f(S)$ is, say, the number of {\em unique} viewers reached by the ad, and $v_i$ 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 $\alpha$-approximation non-truthful algorithm ($\alpha \leq 1$) for this problem into $\Omega(\frac{\alpha}{\log{n}})$ and $\Omega(\alpha)$-approximate truthful mechanisms which run in polynomial time and quasi-polynomial time, respectively

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

Proton Lifetime and Baryon Number Violating Signatures at the LHC in Gauge Extended Models

There exist a number of models in the literature in which the weak interactions are derived from a chiral gauge theory based on a larger group than SU(2)_L x U(1)_Y. Such theories can be constructed so as to be anomaly-free and consistent with precision electroweak measurements, and may be interpreted as a deconstruction of an extra dimension. They also provide interesting insights into the issues of flavor and dynamical electroweak symmetry breaking, and can help to raise the mass of the Higgs boson in supersymmetric theories. In this work we show that these theories can also give rise to baryon and lepton number violating processes, such as nucleon decay and spectacular multijet events at colliders, via the instanton transitions associated with the extended gauge group. For a particular model based on SU(2)_1 x SU(2)_2, we find that the $B+L$ violating scattering cross sections are too small to be observed at the LHC, but that the lower limit on the lifetime of the proton implies an upper bound on the gauge couplings.Comment: 36 page

An upper bound on the total inelastic cross-section as a function of the total cross-section

Recently Andr\'e Martin has proved a rigorous upper bound on the inelastic cross-section $\sigma_{inel}$ at high energy which is one-fourth of the known Froissart-Martin-Lukaszuk upper bound on $\sigma_{tot}$. Here we obtain an upper bound on $\sigma_{inel}$ in terms of $\sigma_{tot}$ and show that the Martin bound on $\sigma_{inel}$ is improved significantly with this added information.Comment: 4 page

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 Jacobs’ 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 μ(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 μ(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 Støvring

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