Approximate Multiplication of Sparse Matrices with Limited Space

Approximate matrix multiplication with limited space has received ever-increasing attention due to the emergence of large-scale applications. Recently, based on a popular matrix sketching algorithm---frequent directions, previous work has introduced co-occuring directions (COD) to reduce the approximation error for this problem. Although it enjoys the space complexity of $O((m_x+m_y)\ell)$ for two input matrices $X\in\mathbb{R}^{m_x\times n}$ and $Y\in\mathbb{R}^{m_y\times n}$ where $\ell$ is the sketch size, its time complexity is $O\left(n(m_x+m_y+\ell)\ell\right)$, which is still very high for large input matrices. In this paper, we propose to reduce the time complexity by exploiting the sparsity of the input matrices. The key idea is to employ an approximate singular value decomposition (SVD) method which can utilize the sparsity, to reduce the number of QR decompositions required by COD. In this way, we develop sparse co-occuring directions, which reduces the time complexity to \widetilde{O}\left((\nnz(X)+\nnz(Y))\ell+n\ell^2\right) in expectation while keeps the same space complexity as $O((m_x+m_y)\ell)$, where \nnz(X) denotes the number of non-zero entries in $X$. Theoretical analysis reveals that the approximation error of our algorithm is almost the same as that of COD. Furthermore, we empirically verify the efficiency and effectiveness of our algorithm

Efficient Algorithms for Generalized Linear Bandits with Heavy-tailed Rewards

This paper investigates the problem of generalized linear bandits with heavy-tailed rewards, whose $(1+\epsilon)$-th moment is bounded for some $\epsilon\in (0,1]$. Although there exist methods for generalized linear bandits, most of them focus on bounded or sub-Gaussian rewards and are not well-suited for many real-world scenarios, such as financial markets and web-advertising. To address this issue, we propose two novel algorithms based on truncation and mean of medians. These algorithms achieve an almost optimal regret bound of $\widetilde{O}(dT^{\frac{1}{1+\epsilon}})$, where $d$ is the dimension of contextual information and $T$ is the time horizon. Our truncation-based algorithm supports online learning, distinguishing it from existing truncation-based approaches. Additionally, our mean-of-medians-based algorithm requires only $O(\log T)$ rewards and one estimator per epoch, making it more practical. Moreover, our algorithms improve the regret bounds by a logarithmic factor compared to existing algorithms when $\epsilon=1$. Numerical experimental results confirm the merits of our algorithms

The isolation and characterization of twelve novel microsatellite loci from Haliotis ovina

Twelve (12) microsatellite loci were developed from Haliotis ovina by magnetic bead hybridization method. Genetic variability was assessed using 30 individuals from three wild populations. The number of alleles per locus was from 2 to 5 and polymorphism information content was from 0.1228 to 0.6542. The observed and expected heterozygosities ranged from 0.0000 to 0.7778 and 0.1288 to 0.6310, respectively. These loci should provide useful information for genetic studies such as genetic diversity, pedigree analysis, construction of genetic linkage maps and marker-assisted selection breeding in H. ovina.Key words: Genetic markers, Haliotis ovina, microsatellites

Opportunistic Wiretapping/Jamming: A New Attack Model in Millimeter-Wave Wireless Networks

While the millimeter-wave (mmWave) communication is robust against the conventional wiretapping attack due to its short transmission range and directivity, this paper proposes a new opportunistic wiretapping and jamming (OWJ) attack model in mmWave wireless networks. With OWJ, an eavesdropper can opportunistically conduct wiretapping or jamming to initiate a more hazardous attack based on the instantaneous costs of wiretapping and jamming. We also provide three realizations of the OWJ attack, which are mainly determined by the cost models relevant to distance, path loss and received power, respectively. To understand the impact of the new attack on mmWave network security, we first develop novel approximation techniques to characterize the irregular distributions of wiretappers, jammers and interferers under three OWJ realizations. With the help of the results of node distributions, we then derive analytical expressions for the secrecy transmission capacity to depict the network security performance under OWJ. Finally, we provide extensive numerical results to illustrate the effect of OWJ and to demonstrate that the new attack can more significantly degrade the network security performance than the pure wiretapping or jamming attack