R on ne be rg er , K a t hr yn T un ya su vu na ko ol,

We describe the operation and improvement of AlphaFold, the system that was entered by the team AlphaFold2 to the "human" category in the 14th Critical Assessment of Protein Structure Prediction (CASP14). The AlphaFold system entered in CASP14 is entirely different to the one entered in CASP13. It used a novel end-toend deep neural network trained to produce protein structures from amino acid sequence, multiple sequence alignments, and homologous proteins. In the assessors' ranking by summed z scores (>2.0), AlphaFold scored 244.0 compared to 90.8 by the next best group. The predictions made by AlphaFold had a median domain GDT_TS of 92.4; this is the first time that this level of average accuracy has been achieved during CASP, especially on the more difficult Free Modeling targets, and represents a significant improvement in the state of the art in protein structure prediction. We reported how AlphaFold was run as a human team during CASP14 and improved such that it now achieves an equivalent level of performance without intervention, opening the door to highly accurate large-scale structure prediction.

From uncovering the structure of the atom to the nature of the universe, spectral measurements have helped some of science’s greatest discoveries. While pointwise spectral measurements date back to Newton, it is commonly thought that hyperspectral images originated in the 1970s. However, the first hyperspectral images are over a century old and are locked in the safes of a handful of museums. These hidden treasures are examples of the first color photographs and earned their inventor, Gabriel Lippmann, the 1908 Nobel Prize in Physics. Since the original work of Lippmann, the process has been predominately understood from the monochromatic perspective, with analogies drawn to Bragg gratings, and the polychromatic case treated as a simple extension. As a consequence, there are misconceptions about the invertibility of the Lippmann process. We show that the multispectral image reflected from a Lippmann plate contains distortions that are not explained by current models. We describe these distortions by directly modeling the process for general spectra and devise an algorithm to recover the original spectra. This results in a complete analysis of the Lippmann process. Finally, we demonstrate the accuracy of our recovery algorithm on self-made Lippmann plates, for which the acquisition setup is fully understood. However, we show that, in the case of historical plates, there are too many unknowns to reliably recover 19th century spectra of natural scenes.

We consider the problem of sampling at unknown locations. We prove that, in this setting, if we take arbitrarily many samples of a polynomial or real bandlimited signal, it is possible to find another function in the same class, arbitrarily far away from the original, that could have generated the same samples. In other words, the error can be arbitrarily large. Motivated by this, we prove that, for polynomials, if the sample positions are constrained such that they can be described by an unknown rational function, uniqueness can be achieved.In addition to our theoretical results, we show that, in 1-D, the problem of recovering a painted surface from a single image exactly fits this framework. Furthermore, we propose a simple iterative algorithm for recovering both the surface and the texture and test it with simple simulations.

Range-only localization has applications as diverse as underwater navigation, drone tracking and indoor localization. While the theoretical foundations of lateration-range-only localization for static points-are well understood, there is a lack of understanding when it comes to localizing a moving device. As most interesting applications in robotics involve moving objects, we study the theory of trajectory recovery. This problem has received a lot of attention; however, state-of-the-art methods are of a probabilistic or heuristic nature and not well suited for guaranteeing trajectory recovery. In this letter, we pose trajectory recovery as a quadratic problem and show that we can relax it to a linear form, which admits a closed-form solution. We provide necessary and sufficient recovery conditions and in particular show that trajectory recovery can be guaranteed when the number of measurements is proportional to the trajectory complexity. Finally, we apply our reconstruction algorithm to simulated and real-world data.