Absence of Singular Continuous Diffraction for Discrete Multi-Component Particle Models

Absence of singular continuous diffraction for discrete multi-component particle models

Particle models with finitely many types of particles are considered, both on Z and on discrete point sets of finite local complexity. Such sets include many standard examples of aperiodic order such as model sets or certain substitution systems. The particle gas is defined by an interaction potential and a corresponding Gibbs measure. Under some reasonable conditions on the underlying point se...

Discrete Multi Objective Particle Swarm Optimization Algorithm for FPGA Placement (RESEARCH NOTE)

Placement process is one of the vital stages in physical design. In this stage, modules and elements of circuit are placed in distinct locations according to optimization basis. So that, each placement process tries to influence on one or more optimization factor. In the other hand, it can be told unequivocally that FPGA is one of the most important and applicable devices in our electronic worl...

The singular continuous diffraction measure of the Thue-Morse chain

The paradigm for singular continuous spectra in symbolic dynamics and in mathematical diffraction is provided by the Thue-Morse chain, in its realisation as a binary sequence with values in {±1}. We revisit this example and derive a functional equation together with an explicit form of the corresponding singular continuous diffraction measure, which is related to the known representation as a R...

Improved Continuous Models for Discrete Media

Rates for Branching Particle Approximations of Continuous - Discrete Filters

Herein, we analyze an efficient branching particle method for asymptotic solutions to a class of continuous-discrete filtering problems. Suppose that t→Xt is a Markov process and we wish to calculate the measure-valued process t→ μt(·) . = P{Xt ∈ ·|σ{Ytk , tk ≤ t}}, where tk = kε and Ytk is a distorted, corrupted, partial observation of Xtk . Then, one constructs a particle system with observat...