147 research outputs found
Counting the changes of random Δ20 sets
We study the number of changes of the initial segment Zs ↾n for computable approximations of a Martin-Löf random Δ02Δ20 set Z. We establish connections between this number of changes and various notions of computability theoretic lowness, as well as the fundamental thesis that, among random sets, randomness is antithetical to computational power. We introduce a new randomness notion, called balanced randomness, which implies that for each computable approximation and each constant c, there are infinitely many n such that Zs ↾n changes more than c2n times. We establish various connections with ω-c.e. tracing and omega;-c.e. jump domination, a new lowness property. We also examine some relationships to randomness theoretic notions of highness, and give applications to the study of (weak) Demuth cuppability.Fil: Figueira, Santiago. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones CientÃficas y Técnicas; ArgentinaFil: Hirschfeldt, Denis R.. University of Chicago; Estados UnidosFil: Miller, Joseph S.. University of Wisconsin; Estados UnidosFil: Ng, Keng Meng. Nanyang Technological University; SingapurFil: Nies, André. The University Of Auckland; Nueva Zeland
Bias deconstructed: Unravelling the scale dependence of halo bias using real space measurements
We explore the scale dependence of halo bias using real space
cross-correlation measurements in N-body simulations and in Pinocchio, an
algorithm based on Lagrangian Perturbation Theory. Recent work has shown how to
interpret such real space measurements in terms of k-dependent bias in Fourier
space, and how to remove the k-dependence to reconstruct the k-independent
peak-background split halo bias parameters. We compare our reconstruction of
the linear bias, which requires no free parameters, with previous estimates
from N-body simulations which were obtained directly in Fourier space at large
scales, and find very good agreement. Our reconstruction of the quadratic bias
is similarly parameter-free, although in this case there are no previous
Fourier space measurements to compare with. Our analysis of N-body simulations
explicitly tests the predictions of the excursion set peaks (ESP) formalism of
Paranjape et al. (2013) for the scale dependence of bias; we find that the ESP
predictions accurately describe our measurements. In addition, our measurements
in Pinocchio serve as a useful, successful consistency check between Pinocchio
and N-body simulations that is not accessible to traditional measurements.Comment: 13 pages, 9 figures; v3 -- Matches published versio
Dynamical decoupling of quantum two-level systems by coherent multiple Landau–Zener transitions
Increasing and stabilizing the coherence of superconducting quantum circuits and resonators is of utmost importance for various technologies, ranging from quantum information processors to highly sensitive detectors of low-temperature radiation in astrophysics. A major source of noise in such devices is a bath of quantum two-level systems (TLSs) with broad distribution of energies, existing in disordered dielectrics and on surfaces. Here we study the dielectric loss of superconducting resonators in the presence of a periodic electric bias field, which sweeps near-resonant TLSs in and out of resonance with the resonator, resulting in a periodic pattern of Landau–Zener transitions. We show that at high sweep rates compared to the TLS relaxation rate, the coherent evolution of the TLS over multiple transitions yields a significant reduction in the dielectric loss relative to the intrinsic value. This behavior is observed both in the classical high-power regime and in the quantum single-photon regime, possibly suggesting a viable technique to dynamically decouple TLSs from a qubit
An improved model of HII bubbles during the epoch of reionization
The size distribution of ionized regions during the epoch of reionization --
a key ingredient in understanding the HI power spectrum observable by 21cm
experiments -- can be modelled analytically using the excursion set formalism
of random walks in the smoothed initial density field. To date, such
calculations have been based on simplifying assumptions carried forward from
the earliest excursion set models of two decades ago. In particular, these
models assume that the random walks have uncorrelated steps and that haloes can
form at arbitrary locations in the initial density field. We extend these
calculations by incorporating recent technical developments that allow us to
(a) include the effect of correlations in the steps of the walks induced by a
realistic smoothing filter and (b) more importantly, account for the fact that
dark matter haloes preferentially form near peaks in the initial density. A
comparison with previous calculations shows that including these features,
particularly the peaks constraint on halo locations, has large effects on the
size distribution of the HII bubbles surrounding these haloes. For example,
when comparing models at the same value of the globally averaged ionized volume
fraction, the typical bubble sizes predicted by our model are more than a
factor 2 larger than earlier calculations. Our results can potentially have a
significant impact on estimates of the observable HI power spectrum.Comment: 13 pages, 6 figures; v2 - added clarifications and fixed typos.
Accepted in MNRA
Variants of SGD for Lipschitz Continuous Loss Functions in Low-Precision Environments
Motivated by neural network training in low-bit floating and fixed-point
environments, this work studies the convergence of variants of SGD with
computational error. Considering a general stochastic Lipschitz continuous loss
function, a novel convergence result to a Clarke stationary point is presented
assuming that only an approximation of its stochastic gradient can be computed
as well as error in computing the SGD step itself. Different variants of SGD
are then tested empirically in a variety of low-precision arithmetic
environments, with improved test set accuracy achieved compared to SGD for two
image recognition tasks
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