31,251 research outputs found

### Experience enrichment based task independent reward model

For most reinforcement learning approaches, the learning is performed by
maximizing an accumulative reward that is expectedly and manually defined for
specific tasks. However, in real world, rewards are emergent phenomena from the
complex interactions between agents and environments. In this paper, we propose
an implicit generic reward model for reinforcement learning. Unlike those
rewards that are manually defined for specific tasks, such implicit reward is
task independent. It only comes from the deviation from the agents' previous
experiences.Comment: 4 pages, 1 figur

### Identifying codes of lexicographic product of graphs

Gravier et al. investigated the identifying codes of Cartesian product of two
graphs. In this paper we consider the identifying codes of lexicographic
product G[H] of a connected graph G and an arbitrary graph H, and obtain the
minimum cardinality of identifying codes of G[H] in terms of some parameters of
G and H

### On the metric dimension of line graphs

Let $G$ be a (di)graph. A set $W$ of vertices in $G$ is a \emph{resolving
set} of $G$ if every vertex $u$ of $G$ is uniquely determined by its vector of
distances to all the vertices in $W$. The \emph{metric dimension} $\mu (G)$ of
$G$ is the minimum cardinality of all the resolving sets of $G$. C\'aceres et
al. \cite{Ca2} computed the metric dimension of the line graphs of complete
bipartite graphs. Recently, Bailey and Cameron \cite{Ba} computed the metric
dimension of the line graphs of complete graphs. In this paper we study the
metric dimension of the line graph $L(G)$ of $G$. In particular, we show that
$\mu(L(G))=|E(G)|-|V(G)|$ for a strongly connected digraph $G$ except for
directed cycles, where $V(G)$ is the vertex set and $E(G)$ is the edge set of
$G$. As a corollary, the metric dimension of de Brujin digraphs and Kautz
digraphs is given. Moreover, we prove that
$\lceil\log_2\Delta(G)\rceil\leq\mu(L(G))\leq |V(G)|-2$ for a simple connected
graph $G$ with at least five vertices, where $\Delta(G)$ is the maximum degree
of $G$. Finally, we obtain the metric dimension of the line graph of a tree in
terms of its parameters.Comment: 7 page

### The super spanning connectivity of arrangement graph

A $k$-container $C(u, v)$ of a graph $G$ is a set of $k$ internally disjoint
paths between $u$ and $v$. A $k$-container $C(u, v)$ of $G$ is a
$k^*$-container if it is a spanning subgraph of $G$. A graph $G$ is
$k^*$-connected if there exists a $k^*$-container between any two different
vertices of G. A $k$-regular graph $G$ is super spanning connected if $G$ is
$i^*$-container for all $1\le i\le k$. In this paper, we prove that the
arrangement graph $A_{n, k}$ is super spanning connected if $n\ge 4$ and
$n-k\ge 2$

### Modelling Temporal Information Using Discrete Fourier Transform for Recognizing Emotions in User-generated Videos

With the widespread of user-generated Internet videos, emotion recognition in
those videos attracts increasing research efforts. However, most existing works
are based on framelevel visual features and/or audio features, which might fail
to model the temporal information, e.g. characteristics accumulated along time.
In order to capture video temporal information, in this paper, we propose to
analyse features in frequency domain transformed by discrete Fourier transform
(DFT features). Frame-level features are firstly extract by a pre-trained deep
convolutional neural network (CNN). Then, time domain features are transferred
and interpolated into DFT features. CNN and DFT features are further encoded
and fused for emotion classification. By this way, static image features
extracted from a pre-trained deep CNN and temporal information represented by
DFT features are jointly considered for video emotion recognition. Experimental
results demonstrate that combining DFT features can effectively capture
temporal information and therefore improve emotion recognition performance. Our
approach has achieved a state-of-the-art performance on the largest video
emotion dataset (VideoEmotion-8 dataset), improving accuracy from 51.1% to
62.6%.Comment: 5 pages. arXiv admin note: substantial text overlap with
arXiv:1603.0618

### Inference on the History of a Randomly Growing Tree

The spread of infectious disease in a human community or the proliferation of
fake news on social media can be modeled as a randomly growing tree-shaped
graph. The history of the random growth process is often unobserved but
contains important information such as the source of the infection. We consider
the problem of statistical inference on aspects of the latent history using
only a single snapshot of the final tree. Our approach is to apply random
labels to the observed unlabeled tree and analyze the resulting distribution of
the growth process, conditional on the final outcome. We show that this
conditional distribution is tractable under a shape-exchangeability condition,
which we introduce here, and that this condition is satisfied for many popular
models for randomly growing trees such as uniform attachment, linear
preferential attachment and uniform attachment on a $D$-regular tree. For
inference of the root under shape-exchangeability, we propose O(n log n) time
algorithms for constructing confidence sets with valid frequentist coverage as
well as bounds on the expected size of the confidence sets. We also provide
efficient sampling algorithms that extend our methods to a wide class of
inference problems.Comment: 36 pages; 7 figures; 5 table

### Unifying quantum heat transfer and superradiant signature in a nonequilibrium collective-qubit system: a polaron-transformed Redfield approach

We investigate full counting statistics of quantum heat transfer in a
collective-qubit system, constructed by multi-qubits interacting with two
thermal baths. The nonequilibrium polaron-transformed Redfield approach
embedded with an auxiliary counting field is applied to obtain the steady state
heat current and fluctuations, which enables us to study the impact of the
qubit-bath interaction in a wide regime. The heat current, current noise and
skewness are all found to clearly unify the limiting results in the weak and
strong couplings, respectively. Moreover, the superradiant heat transfer is
clarified as a system-size-dependent effect, and large number of qubits
dramatically suppresses the nonequilibrium superradiant signature.Comment: 12pages, 3figs, accepted by Chin. Phys.

### A Rigidity Theorem for Affine K\"ahler-Ricci Flat Graph

It is shown that any smooth strictly convex global solution of
$\det(\frac{\partial^{2}u}{\partial \xi_{i}\partial \xi_{j}}) = \exp
\left\{-\sum_{i=1}^n d_i \frac{\partial u}{\partial \xi_{i}} - d_0\right\},$
where $d_0$, $d_1$,...,$d_n$ are constants, must be a quadratic polynomial.
This extends a well-known theorem of J\"{o}rgens-Calabi-Pogorelov.Comment: 24 page

### Rational Solitons in the Parity-Time-Symmetric Nonlocal Nonlinear Schr\"{o}dinger Model

In this paper, via the generalized Darboux transformation, rational soliton
solutions are derived for the parity-time-symmetric nonlocal nonlinear
Schr\"{o}dinger (NLS) model with the defocusing-type nonlinearity. We find that
the first-order solution can exhibit the elastic interactions of rational
antidark-antidark, dark-antidark, and antidark-dark soliton pairs on a
continuous wave background, but there is no phase shift for the interacting
solitons. Also, we discuss the degenerate case in which only one rational dark
or antidark soliton survives. Moreover, we reveal that the second-order
rational solution displays the interactions between two solitons with
combined-peak-valley structures in the near-field regions, but each interacting
soliton vanishes or evolves into a rational dark or antidark soliton as |z|\ra
\infty. In addition, we numerically examine the stability of the first- and
second-order rational soliton solutions.Comment: 18 pages, 9 figures, 1 tabl

### Automatic Detection and Diagnosis of Biased Online Experiments

We have seen a massive growth of online experiments at LinkedIn, and in
industry at large. It is now more important than ever to create an intelligent
A/B platform that can truly democratize A/B testing by allowing everyone to
make quality decisions, regardless of their skillset. With the tremendous
knowledge base created around experimentation, we are able to mine through
historical data, and discover the most common causes for biased experiments. In
this paper, we share four of such common causes, and how we build into our A/B
testing platform the automatic detection and diagnosis of such root causes.
These root causes range from design-imposed bias, self-selection bias, novelty
effect and trigger-day effect. We will discuss in detail what each bias is and
the scalable algorithm we developed to detect the bias. Surfacing up the
existence and root cause of bias automatically for every experiment is an
important milestone towards intelligent A/B testing

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