69,401 research outputs found
Stepwise Thinking in Strategic Games with Incomplete Information
This paper proposes a general incomplete information framework for studying behavior in strategic games with stepwise (viz. `level-k' or `cognitive hierarchy') thinking, which has been found to describe strategic behavior well in experiments involving players' initial responses to games. It is shown that there exist coherent stepwise beliefs, implied by step types, that have the potential to encode all relevant information. In the structure of stepwise beliefs, players are unaware of opponents doing at least as much thinking as themselves. As a result, there exists a Bayesian Nash equilibrium strategy profile in which any player at some step fixes the best responses of opponents at lower steps and then best responds herself.game theory; interactive epistemology; unawareness; Bayesian Nash equilibrium; bounded rationality; level-k; cognitive hierarchy
Classical simulation of commuting quantum computations implies collapse of the polynomial hierarchy
We consider quantum computations comprising only commuting gates, known as
IQP computations, and provide compelling evidence that the task of sampling
their output probability distributions is unlikely to be achievable by any
efficient classical means. More specifically we introduce the class post-IQP of
languages decided with bounded error by uniform families of IQP circuits with
post-selection, and prove first that post-IQP equals the classical class PP.
Using this result we show that if the output distributions of uniform IQP
circuit families could be classically efficiently sampled, even up to 41%
multiplicative error in the probabilities, then the infinite tower of classical
complexity classes known as the polynomial hierarchy, would collapse to its
third level. We mention some further results on the classical simulation
properties of IQP circuit families, in particular showing that if the output
distribution results from measurements on only O(log n) lines then it may in
fact be classically efficiently sampled.Comment: 13 page
A model for - kaon cross section
We calculate the cross section for the dissociation of by kaons
within the framework of a meson exchange model. We find that, depending on the
values of the coupling constants used, the cross section can vary from 5 mb to
30 mb at GeV.Comment: 4 pages, 3 eps figure
The (11112) model on a 1+1 dimensional lattice
We study the chiral gauge model (11112) of four left-movers and one
right-mover with strong interactions in the 1+1 dimensional lattice. Exact
computations of relevant -matrix elements demonstrate a loophole that so
constructed model and its dynamics can possibly evade the ``no-go'' theorem of
Nielsen and Ninomiya.Comment: 15 pages, 1 fig. to appear in Phys. Rev.
High purity bright single photon source
Using cavity-enhanced non-degenerate parametric downconversion, we have built
a frequency tunable source of heralded single photons with a narrow bandwidth
of 8 MHz, making it compatible with atomic quantum memories. The photon state
is 70% pure single photon as characterized by a tomographic measurement and
reconstruction of the quantum state, revealing a clearly negative Wigner
function. Furthermore, it has a spectral brightness of ~1,500 photons/s per MHz
bandwidth, making it one of the brightest single photon sources available. We
also investigate the correlation function of the down-converted fields using a
combination of two very distinct detection methods; photon counting and
homodyne measurement.Comment: 9 pages, 4 figures; minor changes, added referenc
Local polynomial Whittle estimation of perturbed fractional processes
We propose a semiparametric local polynomial Whittle with noise estimator of the memory parameter in long memory time series perturbed by a noise term which may be serially correlated. The estimator approximates the log-spectrum of the short-memory component of the signal as well as that of the perturbation by two separate polynomials. Including these polynomials we obtain a reduction in the order of magnitude of the bias, but also inflate the asymptotic variance of the long memory estimator by a multiplicative constant. We show that the estimator is consistent for d in (0,1), asymptotically normal for d in (0,3/4), and if the spectral density is sufficiently smooth near frequency zero, the rate of convergence can become arbitrarily close to the parametric rate, sqrt(n). A Monte Carlo study reveals that the proposed estimator performs well in the presence of a serially correlated perturbation term. Furthermore, an empirical investigation of the 30 DJIA stocks shows that this estimator indicates stronger persistence in volatility than the standard local Whittle (with noise) estimator.Bias reduction, local Whittle, long memory, perturbed fractional process, semiparametric estimation, stochastic volatility
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