36,254 research outputs found
Evidence for non-Gaussianity in the CMB
In a recent Letter we have shown how COBE-DMR maps may be used to disprove
Gaussianity at a high confidence level. In this report we digress on a few
issues closely related to this Letter. We present the general formalism for
surveying non-Gaussianity employed. We present a few more tests for
systematics. We wonder about the theoretical implications of our result.Comment: Proceedings of the Planck meeting, Santender 9
Exact treatment of dispersion relations in pp and p\=p elastic scattering
Based on a study of the properties of the Lerch's transcendent, exact closed
forms of dispersion relations for amplitudes and for derivatives of amplitudes
in pp and p\=p scattering are introduced. Exact and complete expressions are
written for the real parts and for their derivatives at based on given
inputs for the energy dependence of the total cross sections and of the slopes
of the imaginary parts. The results are prepared for application in the
analysis of forward scattering data of the pp and p\=p systems at all energies,
where exact and precise representations can be written.Comment: 23 pages, 1 figur
The 4 Year COBE DMR data is non-Gaussian
I review our recent claim that there is evidence of non-Gaussianity in the 4
Year COBE DMR data. I describe the statistic we apply, the result we obtain and
make a detailed list of the systematics we have analysed. I finish with a
qualitative understanding of what it might be and its implications.Comment: Proceedings of Rome 3K conference, 5 pages, 3 figure
Efficient Enumeration of Induced Subtrees in a K-Degenerate Graph
In this paper, we address the problem of enumerating all induced subtrees in
an input k-degenerate graph, where an induced subtree is an acyclic and
connected induced subgraph. A graph G = (V, E) is a k-degenerate graph if for
any its induced subgraph has a vertex whose degree is less than or equal to k,
and many real-world graphs have small degeneracies, or very close to small
degeneracies. Although, the studies are on subgraphs enumeration, such as
trees, paths, and matchings, but the problem addresses the subgraph
enumeration, such as enumeration of subgraphs that are trees. Their induced
subgraph versions have not been studied well. One of few example is for
chordless paths and cycles. Our motivation is to reduce the time complexity
close to O(1) for each solution. This type of optimal algorithms are proposed
many subgraph classes such as trees, and spanning trees. Induced subtrees are
fundamental object thus it should be studied deeply and there possibly exist
some efficient algorithms. Our algorithm utilizes nice properties of
k-degeneracy to state an effective amortized analysis. As a result, the time
complexity is reduced to O(k) time per induced subtree. The problem is solved
in constant time for each in planar graphs, as a corollary
Elastic amplitudes studied with the LHC measurements at 7 and 8 TeV
Recent measurements of the differential cross sections in the forward region
of pp elastic scattering at 7 and 8 TeV show precise form of the
dependence. We propose a detailed analysis of these measurements including the
structures of the real and imaginary parts of the scattering amplitude. A good
description is achieved, confirming in all experiments the existence of a zero
in the real part in the forward region close to the origin, in agreement with
the prediction of a theorem by A. Martin, with important role in the observed
form of . Universal value for the position of this zero and
regularity in other features of the amplitudes are found, leading to
quantitative predictions for the forward elastic scattering at 13 TeV.Comment: 22 pages, 17 figures and 4 table
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