8,997 research outputs found
Conformal Prediction: a Unified Review of Theory and New Challenges
In this work we provide a review of basic ideas and novel developments about
Conformal Prediction -- an innovative distribution-free, non-parametric
forecasting method, based on minimal assumptions -- that is able to yield in a
very straightforward way predictions sets that are valid in a statistical sense
also in in the finite sample case. The in-depth discussion provided in the
paper covers the theoretical underpinnings of Conformal Prediction, and then
proceeds to list the more advanced developments and adaptations of the original
idea.Comment: arXiv admin note: text overlap with arXiv:0706.3188,
arXiv:1604.04173, arXiv:1709.06233, arXiv:1203.5422 by other author
Quasi-matter bounce and inflation in the light of the CSL model
The Continuous Spontaneous Localization (CSL) model has been proposed as a
possible solution to the quantum measurement problem by modifying the
Schr\"{o}dinger equation. In this work, we apply the CSL model to two
cosmological models of the early Universe: the matter bounce scenario and slow
roll inflation. In particular, we focus on the generation of the classical
primordial inhomogeneities and anisotropies that arise from the dynamical
evolution, provided by the CSL mechanism, of the quantum state associated to
the quantum fields. In each case, we obtained a prediction for the shape and
the parameters characterizing the primordial spectra (scalar and tensor), i.e.
the amplitude, the spectral index and the tensor-to-scalar ratio. We found that
there exist CSL parameter values, allowed by other non-cosmological
experiments, for which our predictions for the angular power spectrum of the
CMB temperature anisotropy are consistent with the best fit canonical model to
the latest data released by the Planck Collaboration.Comment: 27 pages, including 6 figures, 2 tables and one Appendix. Final
version. Accepted in EPJ
Determinant and Weyl anomaly of Dirac operator: a holographic derivation
We present a holographic formula relating functional determinants: the
fermion determinant in the one-loop effective action of bulk spinors in an
asymptotically locally AdS background, and the determinant of the two-point
function of the dual operator at the conformal boundary. The formula originates
from AdS/CFT heuristics that map a quantum contribution in the bulk partition
function to a subleading large-N contribution in the boundary partition
function. We use this holographic picture to address questions in spectral
theory and conformal geometry. As an instance, we compute the type-A Weyl
anomaly and the determinant of the iterated Dirac operator on round spheres,
express the latter in terms of Barnes' multiple gamma function and gain insight
into a conjecture by B\"ar and Schopka.Comment: 11 pages; new comments and references added, typos correcte
Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
We use the conformal bootstrap to perform a precision study of the operator
spectrum of the critical 3d Ising model. We conjecture that the 3d Ising
spectrum minimizes the central charge c in the space of unitary solutions to
crossing symmetry. Because extremal solutions to crossing symmetry are uniquely
determined, we are able to precisely reconstruct the first several Z2-even
operator dimensions and their OPE coefficients. We observe that a sharp
transition in the operator spectrum occurs at the 3d Ising dimension
Delta_sigma=0.518154(15), and find strong numerical evidence that operators
decouple from the spectrum as one approaches the 3d Ising point. We compare
this behavior to the analogous situation in 2d, where the disappearance of
operators can be understood in terms of degenerate Virasoro representations.Comment: 55 pages, many figures; v2 - refs and comments added, to appear in a
special issue of J.Stat.Phys. in memory of Kenneth Wilso
Scale-dependent mass anomalous dimension from Dirac eigenmodes
We investigate the eigenmodes of the massless Dirac operator to extract the
scale-dependent fermion mass anomalous dimension gamma_m(mu). By combining
simulations on multiple lattice volumes, and when possible several gauge
couplings, we are able to measure the anomalous dimension across a wide range
of energy scales. The method that we present is universal and can be applied to
any lattice model of interest, including both conformal or chirally broken
systems. We consider SU(3) lattice gauge theories with Nf=4, 8 and 12 light or
massless fermions. The 4-flavor model behaves as expected for a QCD-like system
and demonstrates that systematic effects are manageable in practical lattice
calculations. Our 12-flavor results are consistent with the existence of an
infrared fixed point, at which we predict the scheme-independent mass anomalous
dimension gamma_m^*=0.32(3). For the 8-flavor model we observe a large
anomalous dimension across a wide range of energy scales. Further investigation
is required to determine whether Nf=8 is chirally broken and walking, or if it
possesses a strongly-coupled conformal fixed point.Comment: Version to be published in JHE
- …