14,857 research outputs found
Matching under Preferences
Matching theory studies how agents and/or objects from different sets can be matched with each other while taking agents\u2019 preferences into account. The theory originated in 1962 with a celebrated paper by David Gale and Lloyd Shapley (1962), in which they proposed the Stable Marriage Algorithm as a solution to the problem of two-sided matching. Since then, this theory has been successfully applied to many real-world problems such as matching students to universities, doctors to hospitals, kidney transplant patients to donors, and tenants to houses. This chapter will focus on algorithmic as well as strategic issues of matching theory.
Many large-scale centralized allocation processes can be modelled by matching problems where agents have preferences over one another. For example, in China, over 10 million students apply for admission to higher education annually through a centralized process. The inputs to the matching scheme include the students\u2019 preferences over universities, and vice versa, and the capacities of each university. The task is to construct a matching that is in some sense optimal with respect to these inputs.
Economists have long understood the problems with decentralized matching markets, which can suffer from such undesirable properties as unravelling, congestion and exploding offers (see Roth and Xing, 1994, for details). For centralized markets, constructing allocations by hand for large problem instances is clearly infeasible. Thus centralized mechanisms are required for automating the allocation process.
Given the large number of agents typically involved, the computational efficiency of a mechanism's underlying algorithm is of paramount importance. Thus we seek polynomial-time algorithms for the underlying matching problems. Equally important are considerations of strategy: an agent (or a coalition of agents) may manipulate their input to the matching scheme (e.g., by misrepresenting their true preferences or underreporting their capacity) in order to try to improve their outcome. A desirable property of a mechanism is strategyproofness, which ensures that it is in the best interests of an agent to behave truthfully
How to remove the spurious resonances from ring polymer molecular dynamics
Two of the most successful methods that are presently available for
simulating the quantum dynamics of condensed phase systems are centroid
molecular dynamics (CMD) and ring polymer molecular dynamics (RPMD). Despite
their conceptual differences, practical implementations of these methods differ
in just two respects: the choice of the Parrinello-Rahman mass matrix and
whether or not a thermostat is applied to the internal modes of the ring
polymer during the dynamics. Here we explore a method which is halfway between
the two approximations: we keep the path integral bead masses equal to the
physical particle masses but attach a Langevin thermostat to the internal modes
of the ring polymer during the dynamics. We justify this by showing
analytically that the inclusion of an internal mode thermostat does not affect
any of the desirable features of RPMD: thermostatted RPMD (TRPMD) is equally
valid with respect to everything that has actually been proven about the method
as RPMD itself. In particular, because of the choice of bead masses, the
resulting method is still optimum in the short-time limit, and the transition
state approximation to its reaction rate theory remains closely related to the
semiclassical instanton approximation in the deep quantum tunneling regime. In
effect, there is a continuous family of methods with these properties,
parameterised by the strength of the Langevin friction. Here we explore
numerically how the approximation to quantum dynamics depends on this friction,
with a particular emphasis on vibrational spectroscopy. We find that a broad
range of frictions approaching optimal damping give similar results, and that
these results are immune to both the resonance problem of RPMD and the
curvature problem of CMD
Observing and Verifying the Quantum Trajectory of a Mechanical Resonator
Continuous weak measurement allows localizing open quantum systems in state
space, and tracing out their quantum trajectory as they evolve in time.
Efficient quantum measurement schemes have previously enabled recording quantum
trajectories of microwave photon and qubit states. We apply these concepts to a
macroscopic mechanical resonator, and follow the quantum trajectory of its
motional state conditioned on a continuous optical measurement record. Starting
with a thermal mixture, we eventually obtain coherent states of 78%
purity--comparable to a displaced thermal state of occupation 0.14. We
introduce a retrodictive measurement protocol to directly verify state purity
along the trajectory, and furthermore observe state collapse and decoherence.
This opens the door to measurement-based creation of advanced quantum states,
and potential tests of gravitational decoherence models.Comment: 20 pages, 4 figure
Modelling loans to non-financial corporations in the euro area
We model the determinants of loans to non-financial corporations in the euro area. Using the Johansen (1992) methodology, we identify three cointegrating relationships. These relationships are interpreted as the long-run loan demand, investment and loan supply equations. The short-run dynamics of loan demand for the euro area are subsequently modelled by means of a Vector Error Correction Model (VECM). We perform a number of specification tests, which suggest that developments in loans to non-financial corporations in the euro area can be reasonably explained by the model. We then use the estimated model to analyse the impact of permanent and temporary shocks to the policy rate on bank lending to nonfinancial corporations. JEL Classification: C32, C51bank credit, cointegration, error-correction model, euro area, non-financial corporations
Measurement-based quantum control of mechanical motion
Controlling a quantum system based on the observation of its dynamics is
inevitably complicated by the backaction of the measurement process. Efficient
measurements, however, maximize the amount of information gained per
disturbance incurred. Real-time feedback then enables both canceling the
measurement's backaction and controlling the evolution of the quantum state.
While such measurement-based quantum control has been demonstrated in the clean
settings of cavity and circuit quantum electrodynamics, its application to
motional degrees of freedom has remained elusive. Here we show
measurement-based quantum control of the motion of a millimetre-sized membrane
resonator. An optomechanical transducer resolves the zero-point motion of the
soft-clamped resonator in a fraction of its millisecond coherence time, with an
overall measurement efficiency close to unity. We use this position record to
feedback-cool a resonator mode to its quantum ground state (residual thermal
occupation n = 0.29 +- 0.03), 9 dB below the quantum backaction limit of
sideband cooling, and six orders of magnitude below the equilibrium occupation
of its thermal environment. This realizes a long-standing goal in the field,
and adds position and momentum to the degrees of freedom amenable to
measurement-based quantum control, with potential applications in quantum
information processing and gravitational wave detectors.Comment: New version with corrected detection efficiency as determined with a
NIST-calibrated photodiode, added references and revised structure. Main
conclusions are identical. 41 pages, 18 figure
Continuous Force and Displacement Measurement Below the Standard Quantum Limit
Quantum mechanics dictates that the precision of physical measurements must
be subject to certain constraints. In the case of inteferometric displacement
measurements, these restrictions impose a 'standard quantum limit' (SQL), which
optimally balances the precision of a measurement with its unwanted backaction.
To go beyond this limit, one must devise more sophisticated measurement
techniques, which either 'evade' the backaction of the measurement, or achieve
clever cancellation of the unwanted noise at the detector. In the half-century
since the SQL was established, systems ranging from LIGO to ultracold atoms and
nanomechanical devices have pushed displacement measurements towards this
limit, and a variety of sub-SQL techniques have been tested in
proof-of-principle experiments. However, to-date, no experimental system has
successfully demonstrated an interferometric displacement measurement with
sensitivity (including all relevant noise sources: thermal, backaction, and
imprecision) below the SQL. Here, we exploit strong quantum correlations in an
ultracoherent optomechanical system to demonstrate off-resonant force and
displacement sensitivity reaching 1.5dB below the SQL. This achieves an
outstanding goal in mechanical quantum sensing, and further enhances the
prospects of using such devices for state-of-the-art force sensing
applications.Comment: 18 pages, 7 figure
Transforming Graph Representations for Statistical Relational Learning
Relational data representations have become an increasingly important topic
due to the recent proliferation of network datasets (e.g., social, biological,
information networks) and a corresponding increase in the application of
statistical relational learning (SRL) algorithms to these domains. In this
article, we examine a range of representation issues for graph-based relational
data. Since the choice of relational data representation for the nodes, links,
and features can dramatically affect the capabilities of SRL algorithms, we
survey approaches and opportunities for relational representation
transformation designed to improve the performance of these algorithms. This
leads us to introduce an intuitive taxonomy for data representation
transformations in relational domains that incorporates link transformation and
node transformation as symmetric representation tasks. In particular, the
transformation tasks for both nodes and links include (i) predicting their
existence, (ii) predicting their label or type, (iii) estimating their weight
or importance, and (iv) systematically constructing their relevant features. We
motivate our taxonomy through detailed examples and use it to survey and
compare competing approaches for each of these tasks. We also discuss general
conditions for transforming links, nodes, and features. Finally, we highlight
challenges that remain to be addressed
Heterogeneous chemistry related to Antarctic ozone depletion: Reaction of ClONO2 and N2O5 on ice surfaces
Laboratory studies of heterogeneous reactions of possible importance for Antarctic ozone depletion were performed. In particular, the reactions of chlorine nitrate (ClONO2) and dinitrogen pentoxide (N2O5) were investigated on ice and HCl/ice surfaces. These reactions occur on the surfaces of polar stratospheric clouds (PSCs) over Antarctica. One reaction transforms the stable chlorine reservoir species (ClONO2 and HCl) into photochemically active chlorine in the form of HOCl and Cl2. Condensation of HNO3 in the reactions removes odd nitrogen from the stratosphere, a requirement in nearly all models of Antarctic ozone depletion. Other reactions may also be important for Antarctic ozone depletion. Like the reactions of chlorine nitrate, these reactions deplete odd nitrogen through HNO3 condensation. In addition, one reaction converts a stable chlorine reservior species (HCl) into photochemically active chlorine (ClNO2). These reactions were studied with a modified version of a Knudsen cell flow reactor
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