Matching structure and bargaining outcomes in buyer–seller networks

We examine the relationship between the matching structure of a bipartite (buyer-seller) network and the (expected) shares of the unit surplus that each connected pair in this network can create. We show that in different bargaining environments, these shares are closely related to the Gallai-Edmonds Structure Theorem. This theorem characterizes the structure of maximum matchings in an undirected graph. We show that the relationship between the (expected) shares and the tructure Theorem is not an artefact of a particular bargaining mechanism or trade centralization. However, this relationship does not necessarily generalize to non-bipartite networks or to networks with heterogeneous link values

Group Strategyproof Pareto-Stable Marriage with Indifferences via the Generalized Assignment Game

We study the variant of the stable marriage problem in which the preferences of the agents are allowed to include indifferences. We present a mechanism for producing Pareto-stable matchings in stable marriage markets with indifferences that is group strategyproof for one side of the market. Our key technique involves modeling the stable marriage market as a generalized assignment game. We also show that our mechanism can be implemented efficiently. These results can be extended to the college admissions problem with indifferences

Biorthogonal quantum mechanics

The Hermiticity condition in quantum mechanics required for the characterization of (a) physical observables and (b) generators of unitary motions can be relaxed into a wider class of operators whose eigenvalues are real and whose eigenstates are complete. In this case, the orthogonality of eigenstates is replaced by the notion of biorthogonality that defines the relation between the Hilbert space of states and its dual space. The resulting quantum theory, which might appropriately be called 'biorthogonal quantum mechanics', is developed here in some detail in the case for which the Hilbert-space dimensionality is finite. Specifically, characterizations of probability assignment rules, observable properties, pure and mixed states, spin particles, measurements, combined systems and entanglements, perturbations, and dynamical aspects of the theory are developed. The paper concludes with a brief discussion on infinite-dimensional systems. © 2014 IOP Publishing Ltd

Orthonormal sequences in L2(Rd)L^2(R^d) and time frequency localization

We study uncertainty principles for orthonormal bases and sequences in $L^2(\R^d)$. As in the classical Heisenberg inequality we focus on the product of the dispersions of a function and its Fourier transform. In particular we prove that there is no orthonormal basis for $L^2(\R)$ for which the time and frequency means as well as the product of dispersions are uniformly bounded. The problem is related to recent results of J. Benedetto, A. Powell, and Ph. Jaming. Our main tool is a time frequency localization inequality for orthonormal sequences in $L^2(\R^d)$. It has various other applications.Comment: 18 page

Temperature activated absorption during laser-induced damage: the evolution of laser-supported solid-state absorption fronts

Previously we have shown that the size of laser induced damage sites in both KDP and SiO{sub 2} is largely governed by the duration of the laser pulse which creates them. Here we present a model based on experiment and simulation that accounts for this behavior. Specifically, we show that solid-state laser-supported absorption fronts are generated during a damage event and that these fronts propagate at constant velocities for laser intensities up to 4 GW/cm{sup 2}. It is the constant absorption front velocity that leads to the dependence of laser damage site size on pulse duration. We show that these absorption fronts are driven principally by the temperature-activated deep sub band-gap optical absorptivity, free electron transport, and thermal diffusion in defect-free silica for temperatures up to 15,000K and pressures < 15GPa. In addition to the practical application of selecting an optimal laser for pre-initiation of large aperture optics, this work serves as a platform for understanding general laser-matter interactions in dielectrics under a variety of conditions

Pump and probe damage testing for investigation of transient material modifications associated with laser damage in optical materials

Laser-induced breakdown in the bulk of transparent dielectric materials is associated with the generation of extreme localized conditions of temperatures and pressures. In this work, we perform pump and probe damage testing experiments to investigate the evolution of transient absorption by the host material arising from modifications following confined laser energy deposition in fused silica and DKDP materials. Specifically, we measure the size of the damage sites observed in the region of spatial overlap between the pump and probe pulses versus probe time delay and energy. Results of this proof-of-principle experimental work confirm that material modifications under extreme conditions created during a damage event include transient optical absorption. In addition, we found that the relaxation times of the induced absorption are very distinct for DKDP and SiO{sub 2} even under identical excitation conditions, on the order of 100 ns and 100 {micro}s, respectively