584 research outputs found
Coreness of Cooperative Games with Truncated Submodular Profit Functions
Coreness represents solution concepts related to core in cooperative games,
which captures the stability of players. Motivated by the scale effect in
social networks, economics and other scenario, we study the coreness of
cooperative game with truncated submodular profit functions. Specifically, the
profit function is defined by a truncation of a submodular function
: if and
otherwise, where is a given threshold. In this paper, we
study the core and three core-related concepts of truncated submodular profit
cooperative game. We first prove that whether core is empty can be decided in
polynomial time and an allocation in core also can be found in polynomial time
when core is not empty. When core is empty, we show hardness results and
approximation algorithms for computing other core-related concepts including
relative least-core value, absolute least-core value and least average
dissatisfaction value
Budget feasible mechanisms on matroids
Motivated by many practical applications, in this paper we study budget feasible mechanisms where the goal is to procure independent sets from matroids. More specifically, we are given a matroid =(,) where each ground (indivisible) element is a selfish agent. The cost of each element (i.e., for selling the item or performing a service) is only known to the element itself. There is a buyer with a budget having additive valuations over the set of elements E. The goal is to design an incentive compatible (truthful) budget feasible mechanism which procures an independent set of the matroid under the given budget that yields the largest value possible to the buyer. Our result is a deterministic, polynomial-time, individually rational, truthful and budget feasible mechanism with 4-approximation to the optimal independent set. Then, we extend our mechanism to the setting of matroid intersections in which the goal is to procure common independent sets from multiple matroids. We show that, given a polynomial time deterministic blackbox that returns -approximation solutions to the matroid intersection problem, there exists a deterministic, polynomial time, individually rational, truthful and budget feasible mechanism with (3+1) -approximation to the optimal common independent set
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
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
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
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Different precursor populations revealed by microscopic studies of bulk damage in KDP and DKDP crystals
We present experimental results aiming to reveal the relationship between damage initiating defect populations in KDP and DKDP crystals under irradiation at different wavelengths. Our results indicate that there is more than one type of defects leading to damage initiation, each defect acting as damage initiators over a different wavelength range. Results showing disparities in the morphology of damage sites from exposure at different wavelengths provides additional evidence for the presence of multiple types of defects responsible for damage initiation
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Time-Resolved Imaging of Material Response Following Laser-Induced Breakdown in the Bulk and Surface of Fused Silica
Optical components within high energy laser systems are susceptible to laser-induced material modification when the breakdown threshold is exceeded or damage is initiated by pre-existing impurities or defects. These modifications are the result of exposure to extreme conditions involving the generation of high temperatures and pressures and occur on a volumetric scale of the order of a few cubic microns. The response of the material following localized energy deposition, including the timeline of events and the individual processes involved during this timeline, is still largely unknown. In this work, we investigate the events taking place during the entire timeline in both bulk and surface damage in fused silica using a set of time-resolved microscopy systems. These microscope systems offer up to 1 micron spatial resolution when imaging static or dynamic effects, allowing for imaging of the entire process with adequate temporal and spatial resolution. These systems incorporate various pump-probe geometries designed to optimize the sensitivity for detecting individual aspects of the process such as the propagation of shock waves, near-surface material motion, the speed of ejecta, and material transformations. The experimental results indicate that the material response can be separated into distinct phases, some terminating within a few tens of nanoseconds but some extending up to about 100 microseconds. Overall the results demonstrate that the final characteristics of the modified region depend on the material response to the energy deposition and not on the laser parameters
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A new expedited approach to evaluate the importance of different crystal growth parameters on laser damage performance in KDP and DKDP
In this work, we investigate the laser-induced damage resistance at 355 nm in DKDP crystals grown with varying growth parameters, including temperature, speed of growth and impurity concentration. In order to perform this work, a DKDP crystal was grown over 34 days by the rapid-growth technique with varied growth conditions. By using the same crystal, we are able to isolate growth-related parameters affecting LID from raw material or other variations that are encountered when testing in different crystals. The objective is to find correlations of damage performance to growth conditions and reveal the key parameters for achieving DKDP material in which the number of damage initiating defects is reduced. This approach can lead to reliable and expedite information regarding the importance of different crystal growth parameters on the laser damage characteristics of these crystals
Quantum catastrophes: a case study
The bound-state spectrum of a Hamiltonian H is assumed real in a non-empty
domain D of physical values of parameters. This means that for these
parameters, H may be called crypto-Hermitian, i.e., made Hermitian via an {\it
ad hoc} choice of the inner product in the physical Hilbert space of quantum
bound states (i.e., via an {\it ad hoc} construction of the so called metric).
The name of quantum catastrophe is then assigned to the
N-tuple-exceptional-point crossing, i.e., to the scenario in which we leave
domain D along such a path that at the boundary of D, an N-plet of bound state
energies degenerates and, subsequently, complexifies. At any fixed ,
this process is simulated via an N by N benchmark effective matrix Hamiltonian
H. Finally, it is being assigned such a closed-form metric which is made unique
via an N-extrapolation-friendliness requirement.Comment: 23 p
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