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

Diarylethene-Based Photoswitchable Inhibitors of Serine Proteases

A bicyclic peptide scaffold was chemically adapted to generate diarylethene-based photoswitchable inhibitors of serine protease Bos taurus trypsin 1 (T1). Starting from a prototype molecule—sunflower trypsin inhibitor-1 (SFTI-1)—we obtained light-controllable inhibitors of T1 with Ki in the low nanomolar range, whose activity could be modulated over 20-fold by irradiation. The inhibitory potency as well as resistance to proteolytic degradation were systematically studied on a series of 17 SFTI-1 analogues. The hydrogen bond network that stabilizes the structure of inhibitors and possibly the enzyme–inhibitor binding dynamics were affected by isomerization of the photoswitch. The feasibility of manipulating enzyme activity in time and space was demonstrated by controlled digestion of gelatin-based hydrogel and an antimicrobial peptide BP100-RW. Finally, our design principles of diarylethene photoswitches are shown to apply also for the development of other serine protease inhibitor

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

Complex magnetic monopoles, geometric phases and quantum evolution in vicinity of diabolic and exceptional points

We consider the geometric phase and quantum tunneling in vicinity of diabolic and exceptional points. We show that the geometric phase associated with the degeneracy points is defined by the flux of complex magnetic monopole. In weak-coupling limit the leading contribution to the real part of geometric phase is given by the flux of the Dirac monopole plus quadrupole term, and the expansion for its imaginary part starts with the dipolelike field. For a two-level system governed by the generic non-Hermitian Hamiltonian, we derive a formula to compute the non-adiabatic complex geometric phase by integral over the complex Bloch sphere. We apply our results to to study a two-level dissipative system driven by periodic electromagnetic field and show that in the vicinity of the exceptional point the complex geometric phase behaves as step-like function. Studying tunneling process near and at exceptional point, we find two different regimes: coherent and incoherent. The coherent regime is characterized by the Rabi oscillations and one-sheeted hyperbolic monopole emerges in this region of the parameters. In turn with the incoherent regime the two-sheeted hyperbolic monopole is associated. The exceptional point is the critical point of the system where the topological transition occurs and both of the regimes yield the quadratic dependence on time. We show that the dissipation brings into existence of pulses in the complex geometric phase and the pulses are disappeared when dissipation dies out. Such a strong coupling effect of the environment is beyond of the conventional adiabatic treatment of the Berry phase.Comment: 29 pages, 21 figure

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