We study the streaming model for approximate matrix multiplication (AMM). are interested in scenario that algorithm can only take one pass over data with limited memory. The state-of-the-art deterministic sketching AMM is co-occurring directions (COD), which has much smaller approximation errors than randomized algorithms and outperforms other methods empirically. In this paper, we provide a ti...

Abstract In 1895, Vahlen proved a theorem concerning simultaneous approximation of real number by its two consecutive convergent. this paper, we will provide sharper bound for the theorem.

Musicianship confers enhancements to hearing at nearly all levels of the auditory system from periphery to percept. Musicians' superior psychophysical abilities are particularly evident in spectral discrimination and noise-degraded listening tasks, achieving higher perceptual sensitivity than their nonmusician peers. Greater spectral acuity implies that musicianship may increase auditory filter...

The average effective resistance of a graph can be computed as a function of its eigenvalues. Using this formula and focusing on toroidal d-dimensional graphs, we study the role of the network topology and specifically of the graph dimension in determining the resistance. Considering sequences of graphs of increasing size, we study the asymptotical behavior of the effective resistance, proving ...