404 research outputs found
Surface salinity fields in the Arctic Ocean and statistical approaches to predicting anomalies and patterns
Significant salinity anomalies have been observed in the Arctic Ocean surface
layer during the last decade. Using gridded data of winter salinity in the
upper 50 m layer of the Arctic Ocean for the period 1950-1993 and 2007-2012, we
investigated the inter-annual variability of the salinity fields, attempted to
identify patterns and anomalies, and developed a statistical model for the
prediction of surface layer salinity. The statistical model is based on linear
regression equations linking the principal components with environmental
factors, such as atmospheric circulation, river runoff, ice processes, and
water exchange with neighboring oceans. Using this model, we obtained
prognostic fields of the surface layer salinity for the winter period
2013-2014. The prognostic fields demonstrated the same tendencies of surface
layer freshening that were observed previously. A phase portrait analysis
involving the first two principal components exhibits a dramatic shift in
behavior of the 2007-2012 data in comparison to earlier observations
Jets in Effective Theory: Summing Phase Space Logs
We demonstrate how to resum phase space logarithms in the Sterman-Weinberg
(SW) dijet decay rate within the context of Soft Collinear Effective theory
(SCET). An operator basis corresponding to two and three jet events is defined
in SCET and renormalized. We obtain the RGE of the two and three jet operators
and run the operators from the scale to the phase space scale . This phase space scale, where is the
cone half angle of the jet, defines the angular region of the jet. At we determine the mixing of the three and two jet operators. We
combine these results with the running of the two jet shape function, which we
run down to an energy cut scale . This defines the resumed SW
dijet decay rate in the context of SCET. The approach outlined here
demonstrates how to establish a jet definition in the context of SCET. This
allows a program of systematically improving the theoretical precision of jet
phenomenology to be carried out.Comment: 25 pages, 4 figures, V2: Typos fixed, writing clarified, detail on
PSRG added. Matching onto jet definition changed to taking place at collinear
scal
A simple shower and matching algorithm
We present a simple formalism for parton-shower Markov chains. As a first
step towards more complete uncertainty bands, we incorporate a comprehensive
exploration of the ambiguities inherent in such calculations. To reduce this
uncertainty, we then introduce a matching formalism which allows a generated
event sample to simultaneously reproduce any infrared safe distribution
calculated at leading or next-to-leading order in perturbation theory, up to
sub-leading corrections. To enable a more universal definition of perturbative
calculations, we also propose a more general definition of the hadronization
cutoff. Finally, we present an implementation of some of these ideas for
final-state gluon showers, in a code dubbed VINCIA.Comment: 32 pages, 6 figure
Directed Ramsey number for trees
We call a family F of subsets of [n] s-saturated if it contains no s pairwise disjoint sets, and
moreover no set can be added to F while preserving this property (here [n] = {1, . . . , n}).
More than 40 years ago, Erd˝os and Kleitman conjectured that an s-saturated family of subsets
of [n] has size at least (1 − 2
−(s−1))2n. It is easy to show that every s-saturated family has size
at least 1
2
· 2
n, but, as was mentioned by Frankl and Tokushige, even obtaining a slightly better
bound of (1/2 + ε)2n, for some fixed ε > 0, seems difficult. In this note, we prove such a result,
showing that every s-saturated family of subsets of [n] has size at least (1 − 1/s)2n.
This lower bound is a consequence of a multipartite version of the problem, in which we seek a
lower bound on |F1| + . . . + |Fs| where F1, . . . , Fs are families of subsets of [n], such that there
are no s pairwise disjoint sets, one from each family Fi
, and furthermore no set can be added to
any of the families while preserving this property. We show that |F1| + . . . + |Fs| ≥ (s − 1) · 2
n,
which is tight e.g. by taking F1 to be empty, and letting the remaining families be the families
of all subsets of [n]
Large cliques and independent sets all over the place
We study the following question raised by Erd\H{o}s and Hajnal in the early
90's. Over all -vertex graphs what is the smallest possible value of
for which any vertices of contain both a clique and an independent set
of size ? We construct examples showing that is at most
obtaining a twofold sub-polynomial
improvement over the upper bound of about coming from the natural
guess, the random graph. Our (probabilistic) construction gives rise to new
examples of Ramsey graphs, which while having no very large homogenous subsets
contain both cliques and independent sets of size in any small subset
of vertices. This is very far from being true in random graphs. Our proofs are
based on an interplay between taking lexicographic products and using
randomness.Comment: 12 page
Clique minors in graphs with a forbidden subgraph
The classical Hadwiger conjecture dating back to 1940's states that any graph
of chromatic number at least has the clique of order as a minor.
Hadwiger's conjecture is an example of a well studied class of problems asking
how large a clique minor one can guarantee in a graph with certain
restrictions. One problem of this type asks what is the largest size of a
clique minor in a graph on vertices of independence number at
most . If true Hadwiger's conjecture would imply the existence of a clique
minor of order . Results of Kuhn and Osthus and Krivelevich and
Sudakov imply that if one assumes in addition that is -free for some
bipartite graph then one can find a polynomially larger clique minor. This
has recently been extended to triangle free graphs by Dvo\v{r}\'ak and
Yepremyan, answering a question of Norin. We complete the picture and show that
the same is true for arbitrary graph , answering a question of Dvo\v{r}\'ak
and Yepremyan. In particular, we show that any -free graph has a clique
minor of order , for some constant
depending only on . The exponent in this result is tight up to a
constant factor in front of the term.Comment: 11 pages, 1 figur
3‐Color bipartite Ramsey number of cycles and paths
The k-colour bipartite Ramsey number of a bipartite graph H is the least integer n for which
every k-edge-coloured complete bipartite graph Kn,n contains a monochromatic copy of H. The
study of bipartite Ramsey numbers was initiated, over 40 years ago, by Faudree and Schelp and,
independently, by Gy´arf´as and Lehel, who determined the 2-colour Ramsey number of paths. In
this paper we determine asymptotically the 3-colour bipartite Ramsey number of paths and (even)
cycles
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