Multi-peaked localized stationary solutions of the discrete nonlinear Schrödinger (DNLS) equation are presented in one (1D) and two (2D) dimensions. These are excited states of the discrete spectrum and correspond to multi-breather solutions. A simple, very fast, and efficient numerical method, suggested by Aubry, has been used for their calculation. The method involves no diagonalization, but ...

2.1 Differentiability and first order conditions If a function f : R → R has partial derivatives ∂if(x) = limt→0 t−1(f(x + tei) − f(x)) which exist and are continuous on R, it is a C1(R) function, and is differentiable at every x in the sense that f(x + h) − f(x) −∇f(x) · h = o(‖h‖) as h → 0. This means it can be approximated linearly, and the derivative is the linear map on R given by Df(x)(h)...

Given a collection of regions on a map, we seek a method of altering the regions over time so they are still visible when the map is scaled. This is formalized and brought to rigor as well-defined problems in homotopic deformation. We ask the regions to preserve topology, area-ratios and relative position as they change over time. A solution is conjectured, using differential methods, leading t...

We introduce a novel discretization paradigm and specify MAP estimators for linear inverse problems by using the theory of continuous-domain sparse stochastic processes. We characterize the complete class of admissible priors for the discretized version of the signal and show that the said class is restricted to the family of infinitely divisible distributions. We also explain the connections b...

The factor graph approach to discrete-time linear Gaussian state space models is well developed. The paper extends this approach to continuous-time linear systems / filters that are driven by white Gaussian noise. By Gaussian message passing, we then obtain MAP / MMSE / LMMSE estimates of the input signal, or of the state, or of the output signal from noisy observations of the output signal. Th...

Ant colony optimization algorithms (ACOs) have been basically introduced to discrete variable problems and applied to different research domains in several engineering fields. Meanwhile, abundant studies have been already involved to adapt different ant models to continuous search spaces. Assessments indicate competitive performance of ACOs on discrete or continuous domains. Therefore, as poten...

If a spectral numerical method for solving ordinary or partial differential equations is written as a biinfinite linear system b = Za with a map Z : l2 → l2 that has a continuous inverse, this paper shows that one can discretize the biinfinite system in such a way that the resulting finite linear system b̃ = Z̃ã is uniquely solvable and is unconditionally stable, i.e. the stability can be made to...