The multiplier spectral curve of a conformal torus f : T 2 → S in the 4– sphere is essentially [3] given by all Darboux transforms of f . In the particular case when the conformal immersion is a Hamiltonian stationary torus f : T 2 → R in Euclidean 4–space, the left normal N : M → S of f is harmonic, hence we can associate a second Riemann surface: the eigenline spectral curve of N , as defined...

We propose a fast and e cient algorithm which nds the optimal quad-tree (QT) decomposition with leaf dependencies in the rate distortion sense. The underlying problem is the encoding of an image by a variable block size scheme, where the block size is encoded using a QT, each block is encoded by one of the admissible quantizers and the quantizers are transmitted using a rst order di erential pu...

The purpose of this study is to enhance the stability properties of our recentlydeveloped numerical method [D. Kamensky, M.-C. Hsu, D. Schillinger, J.A. Evans, A. Aggarwal, Y. Bazilevs, M.S. Sacks, T.J.R. Hughes, “An immersogeometric variational framework for fluid–structure interaction: Application to bioprosthetic heart valves”, Comput. Methods Appl. Mech. Engrg., 284 (2015) 1005–1053] for im...

2 ‖z− Fx−Gy‖22 , where ρ ∈ R is the Lagrangian multiplier and φ > 0 is a penalty parameter. ADMM utilizes the separability form of (1) and replaces the joint minimization over x and y with two simpler problems. The ADMM first minimizes L over x, then over y, and then applies a proximal minimization step with respect to the Lagrange multiplier ρ. The entire ADMM procedure is summarized in Algori...

In this thesis structure-preserving time integrators for mechanical systems whose configuration space is a Lie Group are derived from a Hamilton-Pontryagin (HP) variational principle. In addition to its attractive properties for degenerate mechanical systems, the HP viewpoint also affords a practical way to design discrete Lagrangians, which are the cornerstone of variational integration theory...

In this paper we consider the problem of recovering an N-dimensional data from a subset of its observed entries. We provide a generalization for the smooth Shcatten-p rank approximation function in [1] to the N-dimensional space. In addition, we derive an optimization algorithm using the Augmented Lagrangian Multiplier in the N-dimensional space to solve the tensor completion problem. We compar...

We study quantum spin systems described by Heisenberg-like models at finite temperature with a strict site-occupation constraint imposed by a procedure originally proposed by V. N. Popov and S. A. Fedotov [66]. We show that the strict site-occupation constraint modifies quantitatively the behaviour of physical quantities when compared to the case for which this constraint is fixed in the averag...

The information bottleneck (IB) method is a technique for extracting that relevant predicting the target random variable from source variable, which typically implemented by optimizing IB Lagrangian balances compression and prediction terms. However, hard to optimize, multiple trials tuning values of multiplier are required. Moreover, we show performance strictly decreases as gets stronger duri...

Heuristic repair algorithms, a class of local search methods, demonstrate impressive eeciency in solving some large-scale and hard instances of constraint satisfaction problems (CSP's). In this paper, we draw a surprising connection between heuristic repair techniques and the discrete Lagrange multiplier methods by transforming CSP's into zero-one constrained optimization problems. A Lagrangian...