Welfare Maximization with Limited Interaction

We continue the study of welfare maximization in unit-demand (matching) markets, in a distributed information model where agent's valuations are unknown to the central planner, and therefore communication is required to determine an efficient allocation. Dobzinski, Nisan and Oren (STOC'14) showed that if the market size is $n$, then $r$ rounds of interaction (with logarithmic bandwidth) suffice to obtain an $n^{1/(r+1)}$-approximation to the optimal social welfare. In particular, this implies that such markets converge to a stable state (constant approximation) in time logarithmic in the market size. We obtain the first multi-round lower bound for this setup. We show that even if the allowable per-round bandwidth of each agent is $n^{\epsilon(r)}$, the approximation ratio of any $r$-round (randomized) protocol is no better than $\Omega(n^{1/5^{r+1}})$, implying an $\Omega(\log \log n)$ lower bound on the rate of convergence of the market to equilibrium. Our construction and technique may be of interest to round-communication tradeoffs in the more general setting of combinatorial auctions, for which the only known lower bound is for simultaneous ($r=1$) protocols [DNO14]

Resolution over Linear Equations and Multilinear Proofs

We develop and study the complexity of propositional proof systems of varying strength extending resolution by allowing it to operate with disjunctions of linear equations instead of clauses. We demonstrate polynomial-size refutations for hard tautologies like the pigeonhole principle, Tseitin graph tautologies and the clique-coloring tautologies in these proof systems. Using the (monotone) interpolation by a communication game technique we establish an exponential-size lower bound on refutations in a certain, considerably strong, fragment of resolution over linear equations, as well as a general polynomial upper bound on (non-monotone) interpolants in this fragment. We then apply these results to extend and improve previous results on multilinear proofs (over fields of characteristic 0), as studied in [RazTzameret06]. Specifically, we show the following: 1. Proofs operating with depth-3 multilinear formulas polynomially simulate a certain, considerably strong, fragment of resolution over linear equations. 2. Proofs operating with depth-3 multilinear formulas admit polynomial-size refutations of the pigeonhole principle and Tseitin graph tautologies. The former improve over a previous result that established small multilinear proofs only for the \emph{functional} pigeonhole principle. The latter are different than previous proofs, and apply to multilinear proofs of Tseitin mod p graph tautologies over any field of characteristic 0. We conclude by connecting resolution over linear equations with extensions of the cutting planes proof system.Comment: 44 page

Ontology-based data access with databases: a short course

Ontology-based data access (OBDA) is regarded as a key ingredient of the new generation of information systems. In the OBDA paradigm, an ontology defines a high-level global schema of (already existing) data sources and provides a vocabulary for user queries. An OBDA system rewrites such queries and ontologies into the vocabulary of the data sources and then delegates the actual query evaluation to a suitable query answering system such as a relational database management system or a datalog engine. In this chapter, we mainly focus on OBDA with the ontology language OWL 2QL, one of the three profiles of the W3C standard Web Ontology Language OWL 2, and relational databases, although other possible languages will also be discussed. We consider different types of conjunctive query rewriting and their succinctness, different architectures of OBDA systems, and give an overview of the OBDA system Ontop

Structure of Fat Jets at the Tevatron and Beyond

Boosted resonances is a highly probable and enthusiastic scenario in any process probing the electroweak scale. Such objects when decaying into jets can easily blend with the cornucopia of jets from hard relative light QCD states. We review jet observables and algorithms that can contribute to the identification of highly boosted heavy jets and the possible searches that can make use of such substructure information. We also review previous studies by CDF on boosted jets and its measurements on specific jet shapes.Comment: invited review for a special "Top and flavour physics in the LHC era" issue of The European Physical Journal C, we invite comments regarding contents of the review; v2 added references and institutional preprint number

A data-driven method of pile-up correction for the substructure of massive jets

We describe a method to measure and subtract the incoherent component of energy flow arising from multiple interactions from jet shape/substructure observables of ultra-massive jets. The amount subtracted is a function of the jet shape variable of interest and not a universal property. Such a correction is expected to significantly reduce any bias in the corresponding distributions generated by the presence of multiple interactions, and to improve measurement resolution. Since in our method the correction is obtained from the data, it is not subject to uncertainties coming from the use of theoretical calculations and/or Monte Carlo event generators. We derive our correction method for the jet mass, angularity and planar flow. We find these corrections to be in good agreement with data on massive jets observed by the CDF collaboration. Finally, we comment on the linkage with the concept of jet area and jet mass area.Comment: 7 pages and 3 figures, minor correction

Genetic Manipulation of Iron Biomineralization Enhances MR Relaxivity in a Ferritin-M6A Chimeric Complex

Ferritin has gained significant attention as a potential reporter gene for in vivo imaging by magnetic resonance imaging (MRI). However, due to the ferritin ferrihydrite core, the relaxivity and sensitivity for detection of native ferritin is relatively low. We report here on a novel chimeric magneto-ferritin reporter gene – ferritin-M6A – in which the magnetite binding peptide from the magnetotactic bacteria magnetosome-associated Mms6 protein was fused to the C-terminal of murine h-ferritin. Biophysical experiments showed that purified ferritin-M6A assembled into a stable protein cage with the M6A protruding into the cage core, enabling magnetite biomineralisation. Ferritin-M6A-expressing C6-glioma cells showed enhanced (per iron) r2 relaxivity. MRI in vivo studies of ferritin-M6A-expressing tumour xenografts showed enhanced R2 relaxation rate in the central hypoxic region of the tumours. Such enhanced relaxivity would increase the sensitivity of ferritin as a reporter gene for non-invasive in vivo MRI-monitoring of cell delivery and differentiation in cellular or gene-based therapies

Fast Sparse Matrix Multiplication

Let A and B two n n matrices over a ring R (e.g., the reals or the integers) each containing at most m non-zero elements. We present a new algorithm that multiplies A and B using O(m ) algebraic operations (i.e., multiplications, additions and subtractions) over R. The naive matrix multiplication algorithm, on the other hand, may need to perform #(mn) operations to accomplish the same task. For , the new algorithm performs an almost optimal number of only n operations. For m the new algorithm is also faster than the best known matrix multiplication algorithm for dense matrices which uses O(n ) algebraic operations. The new algorithm is obtained using a surprisingly straightforward combination of a simple combinatorial idea and existing fast rectangular matrix multiplication algorithms. We also obtain improved algorithms for the multiplication of more than two sparse matrices