Minimal Envy and Popular Matchings

We study ex-post fairness in the object allocation problem where objects are valuable and commonly owned. A matching is fair from individual perspective if it has only inevitable envy towards agents who received most preferred objects -- minimal envy matching. A matching is fair from social perspective if it is supported by majority against any other matching -- popular matching. Surprisingly, the two perspectives give the same outcome: when a popular matching exists it is equivalent to a minimal envy matching. We show the equivalence between global and local popularity: a matching is popular if and only if there does not exist a group of size up to 3 agents that decides to exchange their objects by majority, keeping the remaining matching fixed. We algorithmically show that an arbitrary matching is path-connected to a popular matching where along the path groups of up to 3 agents exchange their objects by majority. A market where random groups exchange objects by majority converges to a popular matching given such matching exists. When popular matching might not exist we define most popular matching as a matching that is popular among the largest subset of agents. We show that each minimal envy matching is a most popular matching and propose a polynomial-time algorithm to find them

Quantum search using non-Hermitian adiabatic evolution

We propose a non-Hermitian quantum annealing algorithm which can be useful for solving complex optimization problems. We demonstrate our approach on Grover's problem of finding a marked item inside of unsorted database. We show that the energy gap between the ground and excited states depends on the relaxation parameters, and is not exponentially small. This allows a significant reduction of the searching time. We discuss the relations between the probabilities of finding the ground state and the survival of a quantum computer in a dissipative environment.Comment: 5 pages, 3 figure

Smooth Loops and Fiber Bundles: Theory of Principal Q-bundles

A nonassociative generalization of the principal fiber bundles with a smooth loop mapping on the fiber is presented. Our approach allows us to construct a new kind of gauge theories that involve higher ''nonassociative'' symmetries.Comment: 20 page

Smooth Loops, Generalized Coherent States and Geometric Phases

A description of generalized coherent states and geometric phases in the light of the general theory of smooth loops is given.Comment: LATeX file, 11 page

Selective Functionalization of Microstructured Surfaces by Laser-Assisted Particle Transfer

Microcavity arrays represent millions of different reaction compartments to screen for e.g. molecular interactions, exogenous factors for cells or enzymatic activity. We present a novel method to selectively synthesize different compounds in arrays of microcavities with up to 1,000,000 cavities per cm2. In our approach, polymer microparticles with embedded pre-activated monomers are selectively transferred into microcavities with laser radiation. After particle patterning, heating of the particle matrix simultaneously leads to diffusion and coupling of the monomers inside each microcavity separately. This method exhibits flexibility, not only in the choice of compounds, but also in the choice of particle matrix material, which determines the chemical reaction environment. The laser-assisted selective functionalization of microcavities can be easily combined with the intensively growing number of laser applications for patterning of molecules and cells, which is useful for the development of novel biological assays

Standalone vertex finding in the ATLAS muon spectrometer

A dedicated reconstruction algorithm to find decay vertices in the ATLAS muon spectrometer is presented. The algorithm searches the region just upstream of or inside the muon spectrometer volume for multi-particle vertices that originate from the decay of particles with long decay paths. The performance of the algorithm is evaluated using both a sample of simulated Higgs boson events, in which the Higgs boson decays to long-lived neutral particles that in turn decay to bbar b final states, and pp collision data at √s = 7 TeV collected with the ATLAS detector at the LHC during 2011

Measurements of Higgs boson production and couplings in diboson final states with the ATLAS detector at the LHC

Measurements are presented of production properties and couplings of the recently discovered Higgs boson using the decays into boson pairs, H →γ γ, H → Z Z∗ →4l and H →W W∗ →lνlν. The results are based on the complete pp collision data sample recorded by the ATLAS experiment at the CERN Large Hadron Collider at centre-of-mass energies of √s = 7 TeV and √s = 8 TeV, corresponding to an integrated luminosity of about 25 fb−1. Evidence for Higgs boson production through vector-boson fusion is reported. Results of combined fits probing Higgs boson couplings to fermions and bosons, as well as anomalous contributions to loop-induced production and decay modes, are presented. All measurements are consistent with expectations for the Standard Model Higgs boson