Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userWhy and How to Avoid the Flipped Quaternion Multiplication
531
0
0.0
(
0
)
Added by
Hannes Sommer
Publication date
2018
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
Over the last decades quaternions have become a crucial and very successful tool for attitude representation in robotics and aerospace. However, there is a major problem that is continuously causing trouble in practice when it comes to exchanging formulas or implementations: there are two quaternion multiplications in common use, Hamiltons original multiplication and its flipped version, which is often associated with NASAs Jet Propulsion Laboratory. We believe that this particular issue is completely avoidable and only exists today due to a lack of understanding. This paper explains the underlying problem for the popular passive world to body usage of rotation quaternions, and derives an alternative solution compatible with Hamiltons multiplication. Furthermore, it argues for entirely discontinuing the flipped multiplication. Additionally, it provides recipes for efficiently detecting relevant conventions and migrating formulas or algorithms between them.
rate research
Read More
Quaternion symmetry is ubiquitous in the physical sciences. As such, much work has been afforded over the years to the development of efficient schemes to exploit this symmetry using real and complex linear algebra. Recent years have also seen many advances in the formal theoretical development of explicitly quaternion linear algebra with promising applications in image processing and machine learning. Despite these advances, there do not currently exist optimized software implementations of quaternion linear algebra. The leverage of optimized linear algebra software is crucial in the achievement of high levels of performance on modern computing architectures, and thus provides a central tool in the development of high-performance scientific software. In this work, a case will be made for the efficacy of high-performance quaternion linear algebra software for appropriate problems. In this pursuit, an optimized software implementation of quaternion matrix multiplication will be presented and will be shown to outperform a vendor tuned implementation for the analogous complex matrix operation. The results of this work pave the path for further development of high-performance quaternion linear algebra software which will improve the performance of the next generation of applicable scientific applications.
So far the lens J1131-1231 has been studied only at optical and X-ray wavelengths. A detection in the radio was almost missed as a result of an incorrect position and archive problems. A direct analysis of NVSS uv data - in contrast to the catalogue or images alone - provided sufficient evidence of a detection to justify further radio investigations. The system was subsequently observed with MERLIN and the EVN in e-VLBI mode. Even though MERLIN seems to show the lensed star-forming regions and the compact cores, a preliminary analysis of the EVN data only shows an AGN in the lens itself but not the lensed cores. Additional VLA observations will be carried out soon.
Informally, a `spurious correlation is the dependence of a model on some aspect of the input data that an analyst thinks shouldnt matter. In machine learning, these have a know-it-when-you-see-it character; e.g., changing the gender of a sentences subject changes a sentiment predictors output. To check for spurious correlations, we can `stress test models by perturbing irrelevant parts of input data and seeing if model predictions change. In this paper, we study stress testing using the tools of causal inference. We introduce emph{counterfactual invariance} as a formalization of the requirement that changing irrelevant parts of the input shouldnt change model predictions. We connect counterfactual invariance to out-of-domain model performance, and provide practical schemes for learning (approximately) counterfactual invariant predictors (without access to counterfactual examples). It turns out that both the means and implications of counterfactual invariance depend fundamentally on the true underlying causal structure of the data. Distinct causal structures require distinct regularization schemes to induce counterfactual invariance. Similarly, counterfactual invariance implies different domain shift guarantees depending on the underlying causal structure. This theory is supported by empirical results on text classification.
Edge computing is the natural progression from Cloud computing, where, instead of collecting all data and processing it centrally, like in a cloud computing environment, we distribute the computing power and try to do as much processing as possible, close to the source of the data. There are various reasons this model is being adopted quickly, including privacy, and reduced power and bandwidth requirements on the Edge nodes. While it is common to see inference being done on Edge nodes today, it is much less common to do training on the Edge. The reasons for this range from computational limitations, to it not being advantageous in reducing communications between the Edge nodes. In this paper, we explore some scenarios where it is advantageous to do training on the Edge, as well as the use of checkpointing strategies to save memory.
Ever since the inception of mobile telephony, the downlink and uplink of cellular networks have been coupled, i.e. mobile terminals have been constrained to associate with the same base station (BS) in both the downlink and uplink directions. New trends in network densification and mobile data usage increase the drawbacks of this constraint, and suggest that it should be revisited. In this paper we identify and explain five key arguments in favor of Downlink/Uplink Decoupling (DUDe) based on a blend of theoretical, experimental, and logical arguments. We then overview the changes needed in current (LTE-A) mobile systems to enable this decoupling, and then look ahead to fifth generation (5G) cellular standards. We believe the introduced paradigm will lead to significant gains in network throughput, outage and power consumption at a much lower cost compared to other solutions providing comparable or lower gains.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
