15,648 research outputs found
Probing the Top-Higgs Yukawa CP Structure in dileptonic with -Assisted Reconstruction
Constraining the Higgs boson properties is a cornerstone of the LHC program.
We study the potential to directly probe the Higgs-top CP-structure via the
channel at the LHC with the Higgs boson decaying to a bottom pair
and top-quarks in the dileptonic mode. We show that a combination of laboratory
and rest frame observables display large CP-sensitivity, exploring
the spin correlations in the top decays. To efficiently reconstruct our final
state, we present a method based on simple mass minimization and prove its
robustness to shower, hadronization and detector effects. In addition, the mass
reconstruction works as an extra relevant handle for background suppression.
Based on our results, we demonstrate that the Higgs-top CP-phase can
be probed up to at the high luminosity LHC.Comment: 25 pages, 11 figures, 3 table
Near Optimal Bounds for Collision in Pollard Rho for Discrete Log
We analyze a fairly standard idealization of Pollard's Rho algorithm for
finding the discrete logarithm in a cyclic group G. It is found that, with high
probability, a collision occurs in steps,
not far from the widely conjectured value of . This
improves upon a recent result of Miller--Venkatesan which showed an upper bound
of . Our proof is based on analyzing an appropriate
nonreversible, non-lazy random walk on a discrete cycle of (odd) length |G|,
and showing that the mixing time of the corresponding walk is
Two Approaches to Sidorenko's Conjecture
Sidorenko's conjecture states that for every bipartite graph on
, holds, where is the
Lebesgue measure on and is a bounded, non-negative, symmetric,
measurable function on . An equivalent discrete form of the conjecture
is that the number of homomorphisms from a bipartite graph to a graph
is asymptotically at least the expected number of homomorphisms from to the
Erd\H{o}s-R\'{e}nyi random graph with the same expected edge density as . In
this paper, we present two approaches to the conjecture. First, we introduce
the notion of tree-arrangeability, where a bipartite graph with bipartition
is tree-arrangeable if neighborhoods of vertices in have a
certain tree-like structure. We show that Sidorenko's conjecture holds for all
tree-arrangeable bipartite graphs. In particular, this implies that Sidorenko's
conjecture holds if there are two vertices in such that each
vertex satisfies or ,
and also implies a recent result of Conlon, Fox, and Sudakov \cite{CoFoSu}.
Second, if is a tree and is a bipartite graph satisfying Sidorenko's
conjecture, then it is shown that the Cartesian product of and
also satisfies Sidorenko's conjecture. This result implies that, for all , the -dimensional grid with arbitrary side lengths satisfies
Sidorenko's conjecture.Comment: 20 pages, 2 figure
Finding cores of random 2-SAT formulae via Poisson cloning
For the random 2-SAT formula , let be the formula left
after the pure literal algorithm applied to stops. Using the recently
developed Poisson cloning model together with the cut-off line algorithm
(COLA), we completely analyze the structure of . In particular, it
is shown that, for \gl:= p(2n-1) = 1+\gs with \gs\gg n^{-1/3}, the core of
has \thl^2 n +O((\thl n)^{1/2}) variables and \thl^2 \gl n+O((\thl
n))^{1/2} clauses, with high probability, where \thl is the larger solution
of the equation \th- (1-e^{-\thl \gl})=0. We also estimate the probability of
being satisfiable to obtain \pr[ F_2(n, \sfrac{\gl}{2n-1}) is
satisfiable ] = \caseth{1-\frac{1+o(1)}{16\gs^3 n}}{if $\gl= 1-\gs$ with
$\gs\gg n^{-1/3}$}{}{}{e^{-\Theta(\gs^3n)}}{if $\gl=1+\gs$ with $\gs\gg
n^{-1/3}$,} where goes to 0 as \gs goes to 0. This improves the
bounds of Bollob\'as et al. \cite{BBCKW}
Finding Weighted Graphs by Combinatorial Search
We consider the problem of finding edges of a hidden weighted graph using a
certain type of queries. Let be a weighted graph with vertices. In the
most general setting, the vertices are known and no other information about
is given. The problem is finding all edges of and their weights using
additive queries, where, for an additive query, one chooses a set of vertices
and asks the sum of the weights of edges with both ends in the set. This model
has been extensively used in bioinformatics including genom sequencing.
Extending recent results of Bshouty and Mazzawi, and Choi and Kim, we present a
polynomial time randomized algorithm to find the hidden weighted graph when
the number of edges in is known to be at most and the weight
of each edge satisfies \ga \leq |w(e)|\leq \gb for fixed constants
\ga, \gb>0. The query complexity of the algorithm is , which is optimal up to a constant factor
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