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Register a new userWhat we talk about when we talk about fields
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Ewan Cameron
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In astronomical and cosmological studies one often wishes to infer some properties of an infinite-dimensional field indexed within a finite-dimensional metric space given only a finite collection of noisy observational data. Bayesian inference offers an increasingly-popular strategy to overcome the inherent ill-posedness of this signal reconstruction challenge. However, there remains a great deal of confusion within the astronomical community regarding the appropriate mathematical devices for framing such analyses and the diversity of available computational procedures for recovering posterior functionals. In this brief research note I will attempt to clarify both these issues from an applied statistics perpective, with insights garnered from my post-astronomy experiences as a computational Bayesian / epidemiological geostatistician.
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Research in machine learning (ML) has primarily argued that models trained on incomplete or biased datasets can lead to discriminatory outputs. In this commentary, we propose moving the research focus beyond bias-oriented framings by adopting a power-aware perspective to study up ML datasets. This means accounting for historical inequities, labor conditions, and epistemological standpoints inscribed in data. We draw on HCI and CSCW work to support our argument, critically analyze previous research, and point at two co-existing lines of work within our community -- one bias-oriented, the other power-aware. This way, we highlight the need for dialogue and cooperation in three areas: data quality, data work, and data documentation. In the first area, we argue that reducing societal problems to bias misses the context-based nature of data. In the second one, we highlight the corporate forces and market imperatives involved in the labor of data workers that subsequently shape ML datasets. Finally, we propose expanding current transparency-oriented efforts in dataset documentation to reflect the social contexts of data design and production.
In the present paper, we investigate the cosmographic problem using the bias-variance trade-off. We find that both the z-redshift and the $y=z/(1+z)$-redshift can present a small bias estimation. It means that the cosmography can describe the supernova data more accurately. Minimizing risk, it suggests that cosmography up to the second order is the best approximation. Forecasting the constraint from future measurements, we find that future supernova and redshift drift can significantly improve the constraint, thus having the potential to solve the cosmographic problem. We also exploit the values of cosmography on the deceleration parameter and equation of state of dark energy $w(z)$. We find that supernova cosmography cannot give stable estimations on them. However, much useful information was obtained, such as that the cosmography favors a complicated dark energy with varying $w(z)$, and the derivative $dw/dz<0$ for low redshift. The cosmography is helpful to model the dark energy.
We demonstrate that a quasi-uniform cosmological seed field is a much less suitable seed for a galactic dynamo than has often been believed. The age of the Universe is insufficient for a conventional galactic dynamo to generate a contemporary galactic magnetic field starting from such a seed, accepting conventional estimates for physical quantities. We discuss modifications to the scenario for the evolution of galactic magnetic fields implied by this result. We also consider briefly the implications of a dynamo number that is significantly larger than that given by conventional estimates.
String theory has transformed our understanding of geometry, topology and spacetime. Thus, for this special issue of Foundations of Physics commemorating Forty Years of String Theory, it seems appropriate to step back and ask what we do not understand. As I will discuss, time remains the least understood concept in physical theory. While we have made significant progress in understanding space, our understanding of time has not progressed much beyond the level of a century ago when Einstein introduced the idea of space-time as a combined entity. Thus, I will raise a series of open questions about time, and will review some of the progress that has been made as a roadmap for the future.
This document will review the most prominent proposals using multilayer convolutional architectures. Importantly, the various components of a typical convolutional network will be discussed through a review of different approaches that base their design decisions on biological findings and/or sound theoretical bases. In addition, the different attempts at understanding ConvNets via visualizations and empirical studies will be reviewed. The ultimate goal is to shed light on the role of each layer of processing involved in a ConvNet architecture, distill what we currently understand about ConvNets and highlight critical open problems.
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