20,895 research outputs found
Identification of Bright Lenses from the Astrometric Observations of Gravitational Microlensing Events
When a source star is gravitationally microlensed by a dark lens, the
centroid of the source star image is displaced relative to the position of the
unlensed source star with an elliptical trajectory. Recently, routine
astrometric follow-up measurements of these source star image centroid shifts
by using high precision interferometers are proposed to measure the lens proper
motion which can resolve the lens parameter degeneracy in the photometrically
determined Einstein time scale. When an event is caused by a bright lens, on
the other hand, the astrometric shift is affected by the light from the lens,
but one cannot identify the existence of the bright lens from the observed
trajectory because the resulting trajectory of the bright lens event is also an
ellipse. As results, lensing parameters determined from the trajectory differ
from those of a dark lens event, causing wrong identification of lens
population. In this paper, we show that although the shape and size of the
astrometric centroid shift trajectory are changed due to the bright lens, the
angular speed of centroid shifts around the apparent position of the unlensed
source star is not affected by the lens brightness. Then, one can identify the
existence of the bright lens and determine its brightness by comparing the lens
parameters determined from the angular speed curve with those determined from
the trajectory of observed centroid shifts. Once the lens brightness is
determined, one can correct for the lens proper motion. Since the proposed
method provides both information about the lens brightness (dark or bright) and
the corrected values of the physical parameters of the lens, one can
significantly better constrain the nature of MACHOs.Comment: total 5 pages, including 3 Figures and no Table, accepted to MNRA
Brain-Switches for Asynchronous Brain−Computer Interfaces: A Systematic Review
A brain–computer interface (BCI) has been extensively studied to develop a novel communication system for disabled people using their brain activities. An asynchronous BCI system is more realistic and practical than a synchronous BCI system, in that, BCI commands can be generated whenever the user wants. However, the relatively low performance of an asynchronous BCI system is problematic because redundant BCI commands are required to correct false-positive operations. To significantly reduce the number of false-positive operations of an asynchronous BCI system, a two-step approach has been proposed using a brain-switch that first determines whether the user wants to use an asynchronous BCI system before the operation of the asynchronous BCI system. This study presents a systematic review of the state-of-the-art brain-switch techniques and future research directions. To this end, we reviewed brain-switch research articles published from 2000 to 2019 in terms of their (a) neuroimaging modality, (b) paradigm, (c) operation algorithm, and (d) performance
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
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
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