3D ab initio modeling in cryo-EM by autocorrelation analysis

Single-Particle Reconstruction (SPR) in Cryo-Electron Microscopy (cryo-EM) is the task of estimating the 3D structure of a molecule from a set of noisy 2D projections, taken from unknown viewing directions. Many algorithms for SPR start from an initial reference molecule, and alternate between refining the estimated viewing angles given the molecule, and refining the molecule given the viewing angles. This scheme is called iterative refinement. Reliance on an initial, user-chosen reference introduces model bias, and poor initialization can lead to slow convergence. Furthermore, since no ground truth is available for an unsolved molecule, it is difficult to validate the obtained results. This creates the need for high quality ab initio models that can be quickly obtained from experimental data with minimal priors, and which can also be used for validation. We propose a procedure to obtain such an ab initio model directly from raw data using Kam's autocorrelation method. Kam's method has been known since 1980, but it leads to an underdetermined system, with missing orthogonal matrices. Until now, this system has been solved only for special cases, such as highly symmetric molecules or molecules for which a homologous structure was already available. In this paper, we show that knowledge of just two clean projections is sufficient to guarantee a unique solution to the system. This system is solved by an optimization-based heuristic. For the first time, we are then able to obtain a low-resolution ab initio model of an asymmetric molecule directly from raw data, without 2D class averaging and without tilting. Numerical results are presented on both synthetic and experimental data

The effect of smooth parametrizations on nonconvex optimization landscapes

We develop new tools to study landscapes in nonconvex optimization. Given one optimization problem, we pair it with another by smoothly parametrizing the domain. This is either for practical purposes (e.g., to use smooth optimization algorithms with good guarantees) or for theoretical purposes (e.g., to reveal that the landscape satisfies a strict saddle property). In both cases, the central question is: how do the landscapes of the two problems relate? More precisely: how do desirable points such as local minima and critical points in one problem relate to those in the other problem? A key finding in this paper is that these relations are often determined by the parametrization itself, and are almost entirely independent of the cost function. Accordingly, we introduce a general framework to study parametrizations by their effect on landscapes. The framework enables us to obtain new guarantees for an array of problems, some of which were previously treated on a case-by-case basis in the literature. Applications include: optimizing low-rank matrices and tensors through factorizations; solving semidefinite programs via the Burer-Monteiro approach; training neural networks by optimizing their weights and biases; and quotienting out symmetries.Comment: Substantially reorganized the paper to make the main results and examples more prominen

P6_4 Tee Off Into Space

Our aim in this paper was explore the possibility of hitting a gold ball into orbit around various objects inthe solar system by using the orbital velocity equation. We found this to be possible around four moons,four dwarf planet candidates and a trojan of Jupiter with masses greater than 10^18kg

P6_5 Matrioshka Brain

The Matrioshka brain is a hypothetical structure originally proposed by Robert Bradbury in 1999[1]. It consists of layers of Dyson spheres around a star, generating energy through solar panels, to power a supercomputer. In this paper we look at the amount of energy and thus computational power that could be obtained from a Matrioshka brain at our current level of technology and then go on to discuss how it would not be feasible to build said structure

Staying on Track from Paris: Advancing the Key Elements of the Paris Agreement

The Paris Agreement adopted in December 2015 provides essential building blocks for universal action to address climate change. Now, much work is needed to breathe life into the provisions and commitments of the Agreement in order to realize the globally agreed vision to limit temperature rise, build the ability to adapt to climate impacts, and align financial flows toward zerocarbon and climate-resilient development. The Parties to the United Nations Framework Convention on Climate Change (UNFCCC) must continue to cooperate effectively to unpack and clarify the key tasks and activities outlined in the Agreement in order to provide a well-defined pathway to implementation. This paper takes an in-depth look at the Paris Agreement, highlighting important outcomes and the tasks and activities that now need to be undertaken to elaborate and develop the critical rules and processes under the Agreement. Ensuring that these rules and processes are strong and effective will be essential to promoting ambitious climate action and accelerating it in the coming years

P6_7 Spider Silk

Spiders silk is often referred to as one of the most amazing materials in nature, with its exceptional strength, able to ensnare insects much greater in size and mass than that of the spider that spun the web. In this paper we explore the idea of using a single piece of spider silk to bring a moving car to a halt. We calculated that a Ford Focus moving at 50 mph could be stopped by a single 10 m long thread with a minimum diameter of 1.88 cm

CDLS: Proving Knowledge of Committed Discrete Logarithms with Soundness

$\Sigma$-protocols, a class of interactive two-party protocols, which are used as a framework to instantiate many other authentication schemes, are automatically a proof of knowledge (PoK) given that they satisfy the special-soundness property. This fact provides a convenient method to compose $\Sigma$-protocols and PoKs for complex relations. However, composing in this manner can be error-prone. While they must satisfy special-soundness, this is unfortunately not the case for many recently proposed composed practical schemes. Here we explore two schemes: ZKAttest from Faz-Hernández et al. and the ones from Agrawal et al., and show that their $\Sigma$-protocol\u27s suffer from several security misdesigns which invalidate their security proofs, and state a practical cheap attack on ZKAttest\u27s implementation. By exploring and resolving their misdesigns, we propose CDLS, a sound and secure variant of their protocols

Two-component Coulomb Glass in Disordered Superconducting Films

Motivated by evidence of local electron-electron attraction in experiments on disordered insulating films, we propose a new two-component Coulomb glass model that combines strong disorder and long-range Coulomb repulsion with the additional possibility of local pockets of a short-range inter-electron attraction. This model hosts a variety of interesting phenomena, in particular a crucial modification of the Coulomb gap previously believed to be universal. Tuning the short-range interaction to be repulsive, we find non-monotonic humps in the density of states within the Coulomb gap. We further study variable-range hopping transport in such systems by extending the standard resistor network approach to include the motion of both single electrons and local pairs. In certain parameter regimes the competition between these two types of carriers results in a distinct peak in resistance as a function of the local attraction strength, which can be tuned by a magnetic field.Comment: 12 pages, 6 figure