Exact simulation of coupled Wright–Fisher diffusions

In this paper an exact rejection algorithm for simulating paths of the coupled Wright–Fisher diffusion is introduced. The coupled Wright–Fisher diffusion is a family of multivariate Wright–Fisher diffusions that have drifts depending on each other through a coupling term and that find applications in the study of networks of interacting genes. The proposed rejection algorithm uses independent neutral Wright–Fisher diffusions as candidate proposals, which are only needed at a finite number of points. Once a candidate is accepted, the remainder of the path can be recovered by sampling from neutral multivariate Wright–Fisher bridges, for which an exact sampling strategy is also provided. Finally, the algorithm’s complexity is derived and its performance demonstrated in a simulation study.

Rejection- and importance-sampling-based perfect simulation for Gibbs hard-sphere models

Coupling-from-the-past (CFTP) methods have been used to generate perfect samples from finite Gibbs hard-sphere models, an important class of spatial point processes consisting of a set of spheres with the centers on a bounded region that are distributed as a homogeneous Poisson point process (PPP) conditioned so that spheres do not overlap with each other. We propose an alternative importance-sampling-based rejection methodology for the perfect sampling of these models. We analyze the asymptotic expected running time complexity of the proposed method when the intensity of the reference PPP increases to infinity while the (expected) sphere radius decreases to zero at varying rates. We further compare the performance of the proposed method analytically and numerically with that of a naive rejection algorithm and of popular dominated CFTP algorithms. Our analysis relies upon identifying large deviations decay rates of the non-overlapping probability of spheres whose centers are distributed as a homogeneous PPP.

Ar Color Grab – A Coloring Experience for Autistic Children

Augmented Reality (AR) brings together a hub of technologies together, thus allowing us to visualize computer generated data over reality. AR enhances the view by adding digital components to the view. Computer added elements are placed over a real environment indirectly by the use of AR, which increases the impact on the viewer. Various forms of elements like audio, video, animation or data may be added on the scene. The gap between the real environment and digital enhancements is bridged by Augmented Reality by creating an exciting situation. Therefore, a colouring book app, which leverages the use of Augmented Reality is presented, the app allows children to colour the characters of the colouring book, which can then be verified by a mobile device. The detection and tracking of the drawing are done using the application, and a 3-D view of the character is animated via a video stream. This video stream is developed according to the colouring done by a child. The visible and omitted regions of the 3D character are projected from the 2-D view using a process which is then presented in reality. A new outlier rejection algorithm is implemented to track a deformable surface for coloured drawings. Real time tracking and surface deformation recovery are provided. A pipeline that creates 2-D and 3- D content is effectively presented. The principal idea behind this project is to come up with an enhanced colouring experience for autistic children using AR, and also enable them to learn something out of it via a video option given by the application.

A statistical representation and frequency-domain window-rejection algorithm for single-station HVSR measurements

SUMMARY The horizontal-to-vertical spectral ratio (HVSR) of ambient noise measurement is commonly used to estimate a site's resonance frequency (${f_0}$). For sites with a strong impedance contrast, the HVSR peak frequency (${f_{0,\mathrm{ HVSR}}}$) has been shown to be a good estimate of ${f_0}$. However, the random nature of ambient noise (both in time and space), in conjunction with variable environmental conditions and sensor coupling issues, can lead to uncertainty in ${f_{0,\mathrm{ HVSR}}}$ estimates. Hence, it is important to report ${f_{0,\mathrm{ HVSR}}}$ in a statistical manner (e.g. as a mean or median value with standard deviation). In this paper, we first discuss widely accepted procedures to process HVSR data and estimate the variance in ${f_{0,\mathrm{ HVSR}}}$. Then, we propose modifications to improve these procedures in two specific ways. First, we propose using a lognormal distribution to describe ${f_{0,\mathrm{ HVSR}}}$ rather than the more commonly used normal distribution. The use of a lognormal distribution for ${f_{0,\mathrm{ HVSR}}}$ has several advantages, including consistency with earthquake ground motion processing and allowing for a seamless transition between HVSR statistics in terms of both frequency and its reciprocal, period. Second, we introduce a new frequency-domain window-rejection algorithm to decrease variance and enhance data quality. Finally, we use examples of 114 high-variance HVSR measurements and 77 low-variance HVSR measurements collected at two case study sites to demonstrate the effectiveness of the new rejection algorithm and the proposed statistical approach. To encourage their adoption, and promote standardization, the rejection algorithm and lognormal statistics presented in this paper have been incorporated into hvsrpy, an open-source Python package for HVSR processing.

Disturbances rejection based on sliding mode control

Purpose The purpose of this paper aims to investigate an effective algorithm for different types of disturbances rejection. New dynamics are designed based on disturbance. Observer-based sliding mode control (SMC) technique is used for approximation the disturbances as well as to stabilize the system effectively in presence of uncertainties. Design/methodology/approach This research work investigates the disturbances rejection algorithm for fixed-wing unmanned aerial vehicle. An algorithm based on SMC is introduced for disturbances rejection. Two types of disturbances are considered, the constant disturbance and the sinusoidal disturbance. The comprehensive lateral and longitudinal models of the system are presented. Two types of dynamics, the dynamics without disturbance and the new dynamics with disturbance, are presented. An observer-based algorithm is presented for the estimation of the dynamics with disturbances. Intensive simulations and experiments have been performed; the results not only guarantee the robustness and stability of the system but the effectiveness of the proposed algorithm as well. Findings In previous research work, new dynamics based on disturbances rejection are not investigated in detail; in this research work both the lateral and longitudinal dynamics with different disturbances are investigated. Practical implications As the stability is always important for flight, so the algorithm proposed in this research guarantees the robustness and rejection of disturbances, which plays a vital role in practical life for avoiding any kind of damage. Originality/value In the previous research work, new dynamics based on disturbances rejection are not investigated in detail; in this research work both the lateral and longitudinal dynamics with different disturbances are investigated. An observer-based SMC not only approximates the different disturbances and also these disturbances are rejected in order to guarantee the effectiveness and robustness.

Remote Sampling with Applications to General Entanglement Simulation

We show how to sample exactly discrete probability distributions whose defining parameters are distributed among remote parties. For this purpose, von Neumann’s rejection algorithm is turned into a distributed sampling communication protocol. We study the expected number of bits communicated among the parties and also exhibit a trade-off between the number of rounds of the rejection algorithm and the number of bits transmitted in the initial phase. Finally, we apply remote sampling to the simulation of quantum entanglement in its essentially most general form possible, when an arbitrary finite number m of parties share systems of arbitrary finite dimensions on which they apply arbitrary measurements (not restricted to being projective measurements, but restricted to finitely many possible outcomes). In case the dimension of the systems and the number of possible outcomes per party are bounded by a constant, it suffices to communicate an expected O ( m 2 ) bits in order to simulate exactly the outcomes that these measurements would have produced on those systems.