There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.

The Ensemble Kalman Filter: Theoretical formulation and practical implementation

The simultaneous localization and map building (SLAM) problem asks if it is possible for an autonomous vehicle to start in an unknown location in an unknown environment and then to incrementally build a map of this environment while simultaneously using this map to compute absolute vehicle location. Starting from estimation-theoretic foundations of this problem, the paper proves that a solution to the SLAM problem is indeed possible. The underlying structure of the SLAM problem is first elucidated. A proof that the estimated map converges monotonically to a relative map with zero uncertainty is then developed. It is then shown that the absolute accuracy of the map and the vehicle location reach a lower bound defined only by the initial vehicle uncertainty. Together, these results show that it is possible for an autonomous vehicle to start in an unknown location in an unknown environment and, using relative observations only, incrementally build a perfect map of the world and to compute simultaneously a bounded estimate of vehicle location. The paper also describes a substantial implementation of the SLAM algorithm on a vehicle operating in an outdoor environment using millimeter-wave radar to provide relative map observations. This implementation is used to demonstrate how some key issues such as map management and data association can be handled in a practical environment. The results obtained are cross-compared with absolute locations of the map landmarks obtained by surveying. In conclusion, the paper discusses a number of key issues raised by the solution to the SLAM problem including suboptimal map-building algorithms and map management.

/pdf/a-solution-to-the-simultaneous-localization-and-map-building-2pp3i7uhdj.pdf

A solution to the simultaneous localization and map building (SLAM) problem

Brief On combining statistical and set-theoretic estimation

A deterministic procedure for optimal approximation of arbitrary probability density functions by means of Dirac mixtures with equal weights is proposed. The optimality of this approximation is guaranteed by minimizing the distance of the approximation from the true density. For this purpose a distance measure is required, which is in general not well defined for Dirac mixtures. Hence, a key contribution is to compare the corresponding cumulative distribution functions. This paper concentrates on the simple and intuitive integral quadratic distance measure. For the special case of a Dirac mixture with equally weighted components, closed-from solutions for special types of densities like uniform and Gaussian densities are obtained. Closed-form solution of the given optimization problem is not possible in general. Hence, another key contribution is an efficient solution procedure for arbitrary true densities based on a homotopy continuation approach. In contrast to standard Monte Carlo techniques like particle filters that are based on random sampling, the proposed approach is deterministic and ensures an optimal approximation with respect to a given distance measure. In addition, the number of required components (particles) can easily be deduced by application of the proposed distance measure. The resulting approximations can be used as basis for recursive nonlinear filtering mechanism alternative to Monte Carlo methods.

/pdf/density-approximation-based-on-dirac-mixtures-with-regard-to-rc1w2pk1gz.pdf

Density Approximation Based on Dirac Mixtures with Regard to Nonlinear Estimation and Filtering

Purpose
Tracking of beating heart motion in a robotic surgery system is required for complex cardiovascular interventions.

/pdf/efficient-physics-based-tracking-of-heart-surface-motion-for-4g4lccbwb8.pdf

Efficient physics-based tracking of heart surface motion for beating heart surgery robotic systems.

In order to assist surgeons during surgery on moving organs, e.g. minimally invasive beating heart bypass surgery, a master-slave system which synchronizes surgical instruments with the organ's motion is desired. This synchronization requires reliable estimation of the organ's motion. In this paper, we present a new approach to motion estimation based on a state motion model for a partition of the heart's surface. Its motion behavior is described by a partial differential equation whose input function is assumed to be periodic. An estimator is used on one hand to predict future model states based on reconstruction of the input function and on the other hand to incorporate noisy spatially discrete measurements in order to improve state estimation. The model-based motion estimation is evaluated using a simple heart simulator. Measurements are obtained by reconstructing 3D position of markers on a pulsating membrane by means of a stereo camera system.

/pdf/model-based-motion-estimation-of-elastic-surfaces-for-4fkdy0mfdg.pdf

Model-based Motion Estimation of Elastic Surfaces for Minimally Invasive Cardiac Surgery

Intention recognition is an important topic in human-robot cooperation that can be tackled using probabilistic model-based methods. A popular instance of such methods are Bayesian networks where the dependencies between random variables are modeled by means of a directed graph. Bayesian networks are very efficient for treating networks with conditionally independent parts. Unfortunately, such independence sometimes has to be constructed by introducing so called hidden variables with an intractably large state space. An example are human actions which depend on human intentions and on other human actions. Our goal in this paper is to find models for intention-action mapping with a reduced state space in order to allow for tractable on-line evaluation. We present a systematic derivation of the reduced model and experimental results of recognizing the intention of a real human in a virtual environment.

/pdf/tractable-probabilistic-models-for-intention-recognition-bsb7jgobvg.pdf

Uwe D. Hanebeck

Papers

Brief On combining statistical and set-theoretic estimation

Density Approximation Based on Dirac Mixtures with Regard to Nonlinear Estimation and Filtering

Efficient physics-based tracking of heart surface motion for beating heart surgery robotic systems.

Model-based Motion Estimation of Elastic Surfaces for Minimally Invasive Cardiac Surgery

Tractable probabilistic models for intention recognition based on expert knowledge