510 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
Superconformal constraints for QCD conformal anomalies
Anomalous superconformal Ward identities and commutator algebra in N = 1
super-Yang-Mills theory give rise to constraints between the QCD special
conformal anomalies of conformal composite operators. We evaluate the
superconformal anomalies that appear in the product of renormalized conformal
operators and the trace anomaly in the supersymmetric spinor current and check
the constraints at one-loop order. In this way we prove the universality of QCD
conformal anomalies, which define the non-diagonal part of the anomalous
dimension matrix responsible for scaling violations of exclusive QCD amplitudes
at the next-to-leading order.Comment: 30 pages, 2 figures, LaTe
Evolution equations beyond one loop from conformal symmetry
We study implications of exact conformal invariance of scalar quantum field
theories at the critical point in non-integer dimensions for the evolution
kernels of the light-ray operators in physical (integer) dimensions. We
demonstrate that all constraints due the conformal symmetry are encoded in the
form of the generators of the collinear sl(2) subgroup. Two of them, S_- and
S_0, can be fixed at all loops in terms of the evolution kernel, while the
generator of special conformal transformations, S_+, receives nontrivial
corrections which can be calculated order by order in perturbation theory.
Provided that the generator S_+ is known at the k-1 loop order, one can fix the
evolution kernel in physical dimension to the k-loop accuracy up to terms that
are invariant with respect to the tree-level generators. The invariant parts
can easily be restored from the anomalous dimensions. The method is illustrated
on two examples: The O(n)-symmetric phi^4 theory in d=4 to the three-loop
accuracy, and the su(n) matrix phi^3 theory in d=6 to the two-loop accuracy. We
expect that the same technique can be used in gauge theories e.g. in QCD.Comment: 19 pages, 3 figure
Two-loop conformal generators for leading-twist operators in QCD
QCD evolution equations in minimal subtraction schemes have a hidden
symmetry: One can construct three operators that commute with the evolution
kernel and form an algebra, i.e. they satisfy (exactly) the
commutation relations. In this paper we find explicit expressions for these
operators to two-loop accuracy going over to QCD in non-integer
space-time dimensions at the intermediate stage. In this way conformal symmetry
of QCD is restored on quantum level at the specially chosen (critical) value of
the coupling, and at the same time the theory is regularized allowing one to
use the standard renormalization procedure for the relevant Feynman diagrams.
Quantum corrections to conformal generators in effectively
correspond to the conformal symmetry breaking in the physical theory in four
dimensions and the commutation relations lead to nontrivial constraints
on the renormalization group equations for composite operators. This approach
is valid to all orders in perturbation theory and the result includes
automatically all terms that can be identified as due to a nonvanishing QCD
-function (in the physical theory in four dimensions). Our result can be
used to derive three-loop evolution equations for flavor-nonsinglet
quark-antiquark operators including mixing with the operators containing total
derivatives. These equations govern, e.g., the scale dependence of generalized
hadron parton distributions and light-cone meson distribution amplitudes.Comment: 36 page
Improved large-scale prediction of growth inhibition patterns using the NCI60 cancer cell line panel
International audienceMotivation: Recent large-scale omics initiatives have catalogued the somatic alterations of cancer cell line panels along with their pharmacological response to hundreds of compounds. In this study, we have explored these data to advance computational approaches that enable more effective and targeted use of current and future anticancer therapeutics.Results: We modelled the 50% growth inhibition bioassay end-point (GI50) of 17 142 compounds screened against 59 cancer cell lines from the NCI60 panel (941 831 data-points, matrix 93.08% complete) by integrating the chemical and biological (cell line) information. We determine that the protein, gene transcript and miRNA abundance provide the highest predictive signal when modelling the GI50 endpoint, which significantly outperformed the DNA copy-number variation or exome sequencing data (Tukey’s Honestly Significant Difference, P <0.05). We demonstrate that, within the limits of the data, our approach exhibits the ability to both interpolate and extrapolate compound bioactivities to new cell lines and tissues and, although to a lesser extent, to dissimilar compounds. Moreover, our approach outperforms previous models generated on the GDSC dataset. Finally, we determine that in the cases investigated in more detail, the predicted drug-pathway associations and growth inhibition patterns are mostly consistent with the experimental data, which also suggests the possibility of identifying genomic markers of drug sensitivity for novel compounds on novel cell lines
Conformal constraints for anomalous dimensions of leading twist operators
Leading-twist operators have a remarkable property that their divergence
vanishes in a free theory. Recently it was suggested that this property can be
used for an alternative technique to calculate anomalous dimensions of
leading-twist operators and allows one to gain one order in perturbation theory
so that, i.e., two-loop anomalous dimensions can be calculated from one-loop
Feynman diagrams, etc. In this work we study feasibility of this program on a
toy-model example of the theory in six dimensions. Our conclusion
is that this approach is valid, although it does not seem to present
considerable technical simplifications as compared to the standard technique.
It does provide one, however, with a very nontrivial check of the calculation
as the structure of the contributions is very different.Comment: 14 pages, 6 figure
Deeply virtual Compton scattering beyond next-to-leading order: the flavor singlet case
We study radiative corrections to deeply virtual Compton scattering in the
kinematics of HERA collider experiments to next--to--leading and
next--to--next--to--leading order. In the latter case the radiative corrections
are evaluated in a special scheme that allows us to employ the predictive power
of conformal symmetry. As observed before, the size of next--to--leading order
corrections strongly depends on the gluonic input, as gluons start to
contribute at this order. Beyond next--to--leading order we find, in contrast,
that the corrections for an input scale of few GeV^2 are small enough to
justify the uses of perturbation theory. For the modification
of the scale dependence is also small. However, with decreasing it
becomes moderate or even large, in particular for the phase.Comment: 17 pages, 2 figure
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