On some universal sums of generalized polygonal numbers

For $m=3,4,\ldots$ those $p_m(x)=(m-2)x(x-1)/2+x$ with $x\in\mathbb Z$ are called generalized $m$-gonal numbers. Sun [13] studied for what values of positive integers $a,b,c$ the sum $ap_5+bp_5+cp_5$ is universal over $\mathbb Z$ (i.e., any $n\in\mathbb N=\{0,1,2,\ldots\}$ has the form $ap_5(x)+bp_5(y)+cp_5(z)$ with $x,y,z\in\mathbb Z$). We prove that $p_5+bp_5+3p_5\,(b=1,2,3,4,9)$ and $p_5+2p_5+6p_5$ are universal over $\mathbb Z$, as conjectured by Sun. Sun also conjectured that any $n\in\mathbb N$ can be written as $p_3(x)+p_5(y)+p_{11}(z)$ and $3p_3(x)+p_5(y)+p_7(z)$ with $x,y,z\in\mathbb N$; in contrast, we show that $p_3+p_5+p_{11}$ and $3p_3+p_5+p_7$ are universal over $\mathbb Z$. Our proofs are essentially elementary and hence suitable for general readers.Comment: Final published versio

Thermoelectric DC conductivities with momentum dissipation from higher derivative gravity

We present a mechanism of momentum relaxation in higher derivative gravity by adding linear scalar fields to the Gauss-Bonnet theory. We analytically computed all of the DC thermoelectric conductivities in this theory by adopting the method given by Donos and Gauntlett in [arXiv:1406.4742]. The results show that the DC electric conductivity is not a monotonic function of the effective impurity parameter $\beta$: in the small $\beta$ limit, the DC conductivity is dominated by the coherent phase, while for larger $\beta$, pair creation contribution to the conductivity becomes dominant, signaling an incoherent phase. In addition, the DC heat conductivity is found independent of the Gauss-Bonnet coupling constant.Comment: 1+19 pages, 2 figures,typos in Eq.(40) correcte

3E: Energy-Efficient Elastic Scheduling for Independent Tasks in Heterogeneous Computing Systems

Reducing energy consumption is a major design constraint for modern heterogeneous computing systems to minimize electricity cost, improve system reliability and protect environment. Conventional energy-efficient scheduling strategies developed on these systems do not sufficiently exploit the system elasticity and adaptability for maximum energy savings, and do not simultaneously take account of user expected finish time. In this paper, we develop a novel scheduling strategy named energy-efficient elastic (3E) scheduling for aperiodic, independent and non-real-time tasks with user expected finish times on DVFS-enabled heterogeneous computing systems. The 3E strategy adjusts processors’ supply voltages and frequencies according to the system workload, and makes trade-offs between energy consumption and user expected finish times. Compared with other energy-efficient strategies, 3E significantly improves the scheduling quality and effectively enhances the system elasticity

Authorship Attribution Using a Neural Network Language Model

In practice, training language models for individual authors is often expensive because of limited data resources. In such cases, Neural Network Language Models (NNLMs), generally outperform the traditional non-parametric N-gram models. Here we investigate the performance of a feed-forward NNLM on an authorship attribution problem, with moderate author set size and relatively limited data. We also consider how the text topics impact performance. Compared with a well-constructed N-gram baseline method with Kneser-Ney smoothing, the proposed method achieves nearly 2:5% reduction in perplexity and increases author classification accuracy by 3:43% on average, given as few as 5 test sentences. The performance is very competitive with the state of the art in terms of accuracy and demand on test data. The source code, preprocessed datasets, a detailed description of the methodology and results are available at https://github.com/zge/authorship-attribution.Comment: Proceedings of the 30th AAAI Conference on Artificial Intelligence (AAAI'16