We consider rank-$1$ lattices for integration and reconstruction of functions with series expansion supported on a finite index set. explore the connection between periodic Fourier space non-periodic cosine Chebyshev space, via tent transform then transform, to transfer known results from setting into new insights settings. Fast discrete can be applied phase. To reduce size auxiliary set in ass...

If R(ω,q) denotes Dyson’s partition rank generating function, due to work of Bringmann and Ono, it is known that for roots of unity ω = 1, R(ω,q) is the “holomorphic part” of a harmonic weak Maass form. Dating back to Ramanujan, it is also known that ̂ R(ω,q) := R(ω,q−1) is given by Eichler integrals and modular forms. In analogy to these results, more recently Monks and Ono have shown that modu...

The Routing Protocol for Low-Power and Lossy Networks (RPL) constructs routes by using Objective Functions that optimize or constrain the routes it selects and uses. This specification describes the Minimum Rank with Hysteresis Objective Function (MRHOF), an Objective Function that selects routes that minimize a metric, while using hysteresis to reduce churn in response to small metric changes....

Compressive sensing (CS) theory asserts that we can reconstruct signals and images with only a small number of samples or measurements. Recent works exploiting the nonlocal similarity have led to better results in various CS studies. To better exploit the nonlocal similarity, in this paper, we propose a non-convex smoothed rank function based model for CS image reconstruction. We also propose a...

We propose a novel value function approximation technique for Markov decision processes. We consider the problem of compactly representing the state-action value function using a low-rank and sparse matrix model. The problem is to decompose a matrix that encodes the true value function into low-rank and sparse components, and we achieve this using Robust Principal Component Analysis (PCA). Unde...