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