16,193 research outputs found
A Tur\'an-type problem on degree sequence
Given and a graph whose degree sequence is
, let . Caro and Yuster
introduced a Tur\'an-type problem for : given , how large can
be if has no subgraph of a particular type. Denote by
the maximum value of taken over all graphs with vertices that do
not contain as a subgraph. Clearly, , where
denotes the classical Tur\'an number, i.e., the maximum number of edges among
all -free graphs with vertices. Pikhurko and Taraz generalize this
Tur\'an-type problem: let be a non-negative increasing real function and
, and then define as the maximum value
of taken over all graphs with vertices that do not contain as
a subgraph. Observe that if ,
if . Bollob\'as and Nikiforov mentioned that it
is important to study concrete functions. They gave an example
, since counts the
-vertex subgraphs of with a dominating vertex.
Denote by the -partite Tur\'an graph of order . In this paper,
using the Bollob\'as--Nikiforov's methods, we give some results on
as follows: for ,
; for each , there exists a constant
such that for every and sufficiently large ,
; for a fixed -chromatic graph
and every , when is sufficiently large, we have
.Comment: 9 page
Two-Particle Correlations and Meson-Antimeson Mixing Effects
We discuss 2-particle correlations which arise in the time evolution of C-odd
and C-even meson--antimeson states of flavoured neutral mesons. In order to
keep our discussion general, we do not use the Weisskopf -- Wigner
approximation. Possible deviations from quantum-mechanical coherence effects
are parameterized by a so-called decoherence parameter . In particular,
we study the -dependence of the asymmetry of unlike and like-flavoured
events which was recently observed experimentally in the
system. In this -dependence, we point out some important general
features which do not rely on the Weisskopf -- Wigner approximation. Some other
related results are derived more generally than in the literature.Comment: 12 pages, revtex, no figure
Making Triangles Colorful
We prove that for any point set P in the plane, a triangle T, and a positive
integer k, there exists a coloring of P with k colors such that any homothetic
copy of T containing at least ck^8 points of P, for some constant c, contains
at least one of each color. This is the first polynomial bound for range spaces
induced by homothetic polygons. The only previously known bound for this
problem applies to the more general case of octants in R^3, but is doubly
exponential.Comment: 6 page
The Spend-It-All Region and Small Time Results for the Continuous Bomber Problem
A problem of optimally allocating partially effective ammunition to be
used on randomly arriving enemies in order to maximize an aircraft's
probability of surviving for time~, known as the Bomber Problem, was first
posed by \citet{Klinger68}. They conjectured a set of apparently obvious
monotonicity properties of the optimal allocation function . Although
some of these conjectures, and versions thereof, have been proved or disproved
by other authors since then, the remaining central question, that is
nondecreasing in~, remains unsettled. After reviewing the problem and
summarizing the state of these conjectures, in the setting where is
continuous we prove the existence of a ``spend-it-all'' region in which
and find its boundary, inside of which the long-standing, unproven
conjecture of monotonicity of~ holds. A new approach is then taken
of directly estimating~ for small~, providing a complete small-
asymptotic description of~ and the optimal probability of survival
RED: Reinforced Encoder-Decoder Networks for Action Anticipation
Action anticipation aims to detect an action before it happens. Many real
world applications in robotics and surveillance are related to this predictive
capability. Current methods address this problem by first anticipating visual
representations of future frames and then categorizing the anticipated
representations to actions. However, anticipation is based on a single past
frame's representation, which ignores the history trend. Besides, it can only
anticipate a fixed future time. We propose a Reinforced Encoder-Decoder (RED)
network for action anticipation. RED takes multiple history representations as
input and learns to anticipate a sequence of future representations. One
salient aspect of RED is that a reinforcement module is adopted to provide
sequence-level supervision; the reward function is designed to encourage the
system to make correct predictions as early as possible. We test RED on
TVSeries, THUMOS-14 and TV-Human-Interaction datasets for action anticipation
and achieve state-of-the-art performance on all datasets
Multiple Instance Curriculum Learning for Weakly Supervised Object Detection
When supervising an object detector with weakly labeled data, most existing
approaches are prone to trapping in the discriminative object parts, e.g.,
finding the face of a cat instead of the full body, due to lacking the
supervision on the extent of full objects. To address this challenge, we
incorporate object segmentation into the detector training, which guides the
model to correctly localize the full objects. We propose the multiple instance
curriculum learning (MICL) method, which injects curriculum learning (CL) into
the multiple instance learning (MIL) framework. The MICL method starts by
automatically picking the easy training examples, where the extent of the
segmentation masks agree with detection bounding boxes. The training set is
gradually expanded to include harder examples to train strong detectors that
handle complex images. The proposed MICL method with segmentation in the loop
outperforms the state-of-the-art weakly supervised object detectors by a
substantial margin on the PASCAL VOC datasets.Comment: Published in BMVC 201
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