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

In this paper, the first algorithm for learning hybrid Bayesian Networks with Gaussian mixture and Dirac mixture conditional densities from data given their structure is presented. The mixture densities to be learned allow for nonlinear dependencies between the variables and exact closed-form inference. For learning the network's parameters, an incremental gradient ascent algorithm is derived. Analytic expressions for the partial derivatives and their combination with messages are presented. This hybrid approach subsumes the existing approach for purely discrete-valued networks and is applicable to partially observable networks, too. Its practicability is demonstrated by a reference example.

/pdf/parameter-learning-for-hybrid-bayesian-networks-with-352fwiftur.pdf

Parameter learning for hybrid Bayesian Networks with Gaussian mixture and Dirac mixture conditional densities

Prior to its technological realization or the scientific reflection on it, sensor data fusion is an omnipresent capability. In fact, all living creatures by nature or intuitively perform sensor data fusion. Each in their own way, they combine or sensations provided by different and mutually complementary sense organs with knowledge learned from previous experiences and communications from other creatures. The result is a mental model of their individual environment, the basis of behaving appropriately. As a sophisticated technology with significant economic implications, sensor data fusion aims at automating this capability in various areas.

Sensor Data Fusion: Trends, Solutions, Applications

Robotic beating heart surgery requires accurate information about the current state of the heart For this purpose, it is of great importance to have a good estimate of the heart's current phase, which in essence corresponds to the percentage of the current heart cycle that has already passed Estimation of the heart phase is a highly nontrivial problem as the heart motion is not exactly periodic On the contrary, it varies slightly from beat to beat and changes in frequency over time In order to derive a robust phase estimation algorithm, we rely on directional statistics, a subfield of statistics that deals with quantities that are inherently periodic, such as the phase of the beating heart The proposed methods are evaluated on a real data set and shown to be superior to the state of the art

Heart phase estimation using directional statistics for robotic beating heart surgery

In this work, we propose a novel way to approximating mixtures of Gaussian distributions by a set of deter-ministically chosen Dirac delta components. This approximation is performed by adapting a method for approximating single Gaussian distributions to the considered case. The proposed method turns the approximation problem into an optimization problem by minimizing a distance measure between the Gaussian mixture and its Dirac mixture approximation. Compared to the simple Gaussian case, the minimization criterion is much more complex as multiple, non-standard Gaussian distributions have to be considered.

Uwe D. Hanebeck

Papers

Parameter learning for hybrid Bayesian Networks with Gaussian mixture and Dirac mixture conditional densities

Sensor Data Fusion: Trends, Solutions, Applications

Heart phase estimation using directional statistics for robotic beating heart surgery

Deterministic Dirac mixture approximation of Gaussian mixtures

Absolute Localization of Fast Mobile Robots Based on an Angle Measurement Technique