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Single-stranded RNA viruses co-assemble their capsid with the genome and variations in capsid structures can have significant functional relevance. In particular, viruses need to respond to a dehydrating environment to prevent genomic degradation and remain active upon rehydration. Theoretical work has predicted low-energy buckling transitions in icosahedral capsids which could protect the virus from further dehydration. However, there has been no direct experimental evidence, nor molecular mechanism, for such behaviour. Here we observe this transition using X-ray single particle imaging of MS2 bacteriophages after aerosolization. Using a combination of machine learning tools, we classify hundreds of thousands of single particle diffraction patterns to learn the structural landscape of the capsid morphology as a function of time spent in the aerosol phase. We found a previously unreported compact conformation as well as intermediate structures which suggest an incoherent buckling transition which does not preserve icosahedral symmetry. Finally, we propose a mechanism of this buckling, where a single 19-residue loop is destabilised, leading to the large observed morphology change. Our results provide experimental evidence for a mechanism by which viral capsids protect themselves from dehydration. In the process, these findings also demonstrate the power of single particle X-ray imaging and machine learning methods in studying biomolecular structural dynamics., Comment: 10 pages, 4 figures plus 9 pages supplementary information

X-ray Multi-Projection Imaging (XMPI) is an emerging technology that allows for the acquisition of millions of 3D images per second in samples opaque to visible light. This breakthrough capability enables volumetric observation of fast stochastic phenomena, which were inaccessible due to the lack of a volumetric X-ray imaging probe with kHz to MHz repetition rate. These include phenomena of industrial and societal relevance such as fractures in solids, propagation of shock waves, laser-based 3D printing, or even fast processes in the biological domain. Indeed, the speed of traditional tomography is limited by the shear forces caused by rotation, to a maximum of 1000 Hz in state-of-the-art tomography. Moreover, the shear forces can disturb the phenomena in observation, in particular with soft samples or sensitive phenomena such as fluid dynamics. XMPI is based on splitting an X-ray beam to generate multiple simultaneous views of the sample, therefore eliminating the need for rotation. The achievable performances depend on the characteristics of the X-ray source, the detection system, and the X-ray optics used to generate the multiple views. The increase in power density of the X-ray sources around the world now enables 3D imaging with sampling speeds in the kilohertz range at synchrotrons and megahertz range at X-ray Free-Electron Lasers (XFELs). Fast detection systems are already available, and 2D MHz imaging was already demonstrated at synchrotron and XFEL. In this work, we explore the properties of X-ray splitter optics and XMPI schemes that are compatible with synchrotron insertion devices and XFEL X-ray beams. We describe two possible schemes designed to permit large samples and complex sample environments. Then, we present experimental proof of the feasibility of MHz-rate XMPI at the European XFEL., Comment: 47 pages, 17 figures

Nanoparticles, exhibiting functionally relevant structural heterogeneity, are at the forefront of cutting-edge research. Now, high-throughput single-particle imaging (SPI) with x-ray free-electron lasers (XFELs) creates unprecedented opportunities for recovering the shape distributions of millions of particles that exhibit functionally relevant structural heterogeneity. To realize this potential, three challenges have to be overcome: (1) simultaneous parametrization of structural variability in real and reciprocal spaces; (2) efficiently inferring the latent parameters of each SPI measurement; (3) scaling up comparisons between $10^5$ structural models and $10^6$ XFEL-SPI measurements. Here, we describe how we overcame these three challenges to resolve the non-equilibrium shape distributions within millions of gold nanoparticles imaged at the European XFEL. These shape distributions allowed us to quantify the degree of asymmetry in these particles, discover a relatively stable `shape envelope' amongst nanoparticles, discern finite-size effects related to shape-controlling surfactants, and extrapolate nanoparticles' shapes to their idealized thermodynamic limit. Ultimately, these demonstrations show that XFEL SPI can help transform nanoparticle shape characterization from anecdotally interesting to statistically meaningful.

X-ray Free Electron Lasers (XFELs) can probe chemical and biological reactions as they unfold with unprecedented spatial and temporal resolution. A principal challenge in this pursuit is the delivery of samples to the X-ray interaction point in a way that produces data of the highest possible quality and efficiency. This is hampered by constraints posed by the light source and operation within a beamline environment. For liquid samples, the solution typically involves a high-speed liquid jet, capable of keeping up with the rate of X-ray pulses. However, conventional jets are not ideal because of radiation-induced explosions of the jet, as well as their cylindrical geometry combined with the X-ray pointing instability of many beamlines causes the interaction volume to differ for every pulse. This complicates data analysis and contributes to measurement errors. An alternative geometry is a liquid sheet jet which, with its constant thickness over large areas, eliminates the X-ray pointing related problems. Since liquid sheets can be made very thin, the radiation-induced explosion is reduced, boosting their stability. They are especially attractive for experiments which benefit from small interaction volumes such as fluctuation X-ray scattering and several types of spectroscopy. Although they have seen increasing use for soft X-ray applications in recent years, there has not yet been wide-scale adoption at XFELs. Here, we demonstrate liquid sheet jet sample injection at the European XFEL. We evaluate several aspects of its performance relative to a conventional liquid jet including thickness profile, stability, and radiation-induced explosion dynamics at high repetition rates. The sheet jet exhibits superior performance across these critical experimental parameters. Its minute thickness also suggests ultrafast single-particle solution scattering is a possibility.

X-ray time-resolved tomography is one of the most popular X-ray techniques to probe dynamics in three dimensions (3D). Recent developments in time-resolved tomography opened the possibility of recording kilohertz-rate 3D movies. However, tomography requires rotating the sample with respect to the X-ray beam, which prevents characterization of faster structural dynamics. Here, we present megahertz (MHz) X-ray multi-projection imaging (MHz-XMPI), a technique capable of recording volumetric information at MHz rates and micrometer resolution without scanning the sample. We achieved this by harnessing the unique megahertz pulse structure and intensity of the European X-ray Free-electron Laser with a combination of novel detection and reconstruction approaches that do not require sample rotations. Our approach enables generating multiple X-ray probes that simultaneously record several angular projections for each pulse in the megahertz pulse burst. We provide a proof-of-concept demonstration of the MHz-XMPI technique's capability to probe 4D (3D+time) information on stochastic phenomena and non-reproducible processes three orders of magnitude faster than state-of-the-art time-resolved X-ray tomography, by generating 3D movies of binary droplet collisions. We anticipate that MHz-XMPI will enable in-situ and operando studies that were impossible before, either due to the lack of temporal resolution or because the systems were opaque (such as for MHz imaging based on optical microscopy).

Ultrasonic liquid phase exfoliation is a promising method for the production of two-dimensional (2D) layered materials. A large number of studies have been made in investigating the underlying ultrasound exfoliation mechanisms. However, due to the experimental challenges for capturing the highly transient and dynamic phenomena in real-time at sub-microsecond time and micrometer length scales simultaneously, most theories reported to date still remain elusive. Here, using the ultra-short X-ray Free Electron Laser pulses (~25ps) with a unique pulse train structure, we applied MHz X-ray Microscopy and machine-learning technique to reveal unambiguously the full cycles of the ultrasound cavitation and graphite layer exfoliation dynamics with sub-microsecond and micrometer resolution. Cyclic fatigue shock wave impacts produced by ultrasound cloud implosion were identified as the dominant mechanism to deflect and exfoliate graphite layers mechanically. For the graphite flakes, exfoliation rate as high as ~5 angstroms per shock wave impact was observed. For the HOPG graphite, the highest exfoliation rate was ~0.15 angstroms per impact. These new findings are scientifically and technologically important for developing industrial upscaling strategies for ultrasonic exfoliation of 2D materials.

The X-ray microscopy technique at the European X-ray free-electron laser (EuXFEL), operating at a MHz repetition rate, provides superior contrast and spatial-temporal resolution compared to typical microscopy techniques at other X-ray sources. In both online visualization and offline data analysis for microscopy experiments, baseline normalization is essential for further processing steps such as phase retrieval and modal decomposition. In addition, access to normalized projections during data acquisition can play an important role in decision-making and improve the quality of the data. However, the stochastic nature of XFEL sources hinders the use of existing flat-flied normalization methods during MHz X-ray microscopy experiments. Here, we present an online dynamic flat-field correction method based on principal component analysis of dynamically evolving flat-field images. The method is used for the normalization of individual X-ray projections and has been implemented as an online analysis tool at the Single Particles, Clusters, and Biomolecules and Serial Femtosecond Crystallography (SPB/SFX) instrument of EuXFEL., Comment: 14 pages, 7 figures

At modern X-ray sources, such as synchrotrons and X-ray Free-Electron Lasers (XFELs), it is important to measure the absolute value of the photon energy directly. Here, a method for absolute spectral metrology is presented. A photon energy estimation method based on the spectral measurements and rocking of diffracting crystals is presented. The photon energy of SASE1 channel of the European XFEL was measured, and the benefits and applications of the precise photon energy evaluation are discussed.

Algorithms that involve both forecasting and optimization are at the core of solutions to many difficult real-world problems, such as in supply chains (inventory optimization), traffic, and in the transition towards carbon-free energy generation in battery/load/production scheduling in sustainable energy systems. Typically, in these scenarios we want to solve an optimization problem that depends on unknown future values, which therefore need to be forecast. As both forecasting and optimization are difficult problems in their own right, relatively few research has been done in this area. This paper presents the findings of the ``IEEE-CIS Technical Challenge on Predict+Optimize for Renewable Energy Scheduling," held in 2021. We present a comparison and evaluation of the seven highest-ranked solutions in the competition, to provide researchers with a benchmark problem and to establish the state of the art for this benchmark, with the aim to foster and facilitate research in this area. The competition used data from the Monash Microgrid, as well as weather data and energy market data. It then focused on two main challenges: forecasting renewable energy production and demand, and obtaining an optimal schedule for the activities (lectures) and on-site batteries that lead to the lowest cost of energy. The most accurate forecasts were obtained by gradient-boosted tree and random forest models, and optimization was mostly performed using mixed integer linear and quadratic programming. The winning method predicted different scenarios and optimized over all scenarios jointly using a sample average approximation method.

In this paper, we examine the concept of the predict and optimise problem with specific reference to the third Technical Challenge of the IEEE Computational Intelligence Society. In this competition, entrants were asked to forecast building energy use and solar generation at six buildings and six solar installations, and then use their forecast to optimize energy cost while scheduling classes and batteries over a month. We examine the possible effect of underforecasting and overforecasting and asymmetric errors on the optimisation cost. We explore the different nature of loss functions for the prediction and optimisation phase and propose to adjust the final forecasts for a better optimisation cost. We report that while there is a positive correlation between these two, more appropriate loss functions can be used to optimise the costs associated with final decisions.

This report provides a description of the methodology I used in the IEEE-CIS 3rd Technical Challenge. For the forecast, I used a quantile regression forest approach using the solar variables provided by the Bureau of Meterology of Australia (BOM) and many of the weather variables from the European Centre for Medium-Range Weather Forecasting (ECMWF). Groups of buildings and all of the solar instances were trained together as they were observed to be closely correlated over time. Other variables used included Fourier values based on hour of day and day of year, and binary variables for combinations of days of the week. The start dates for the time series were carefully tuned based on phase 1 and cleaning and thresholding was used to reduce the observed error rate for each time series. For the optimization, a four-step approach was used using the forecast developed. First, a mixed-integer program (MIP) was solved for the recurring and recurring plus once-off activities, then each of these was extended using a mixed-integer quadratic program (MIQP). The general strategy was chosen from one of two ("array" from the "array" and "tuples" approaches) while the specific step improvement strategy was chosen from one of five ("no forced discharge")., Comment: 4 pages, 3 figures

One of the outstanding analytical problems in X-ray single particle imaging (SPI) is the classification of structural heterogeneity, which is especially difficult given the low signal-to-noise ratios of individual patterns and that even identical objects can yield patterns that vary greatly when orientation is taken into consideration. We propose two methods which explicitly account for this orientation-induced variation and can robustly determine the structural landscape of a sample ensemble. The first, termed common-line principal component analysis (PCA) provides a rough classification which is essentially parameter-free and can be run automatically on any SPI dataset. The second method, utilizing variation auto-encoders (VAEs) can generate 3D structures of the objects at any point in the structural landscape. We implement both these methods in combination with the noise-tolerant expand-maximize-compress (EMC) algorithm and demonstrate its utility by applying it to an experimental dataset from gold nanoparticles with only a few thousand photons per pattern and recover both discrete structural classes as well as continuous deformations. These developments diverge from previous approaches of extracting reproducible subsets of patterns from a dataset and open up the possibility to move beyond studying homogeneous sample sets and study open questions on topics such as nanocrystal growth and dynamics as well as phase transitions which have not been externally triggered., Comment: 29 pages, 9 figures

We report the 3D structure determination of gold nanoparticles (AuNPs) by X-ray single particle imaging (SPI). Around 10 million diffraction patterns from gold nanoparticles were measured in less than 100 hours of beam time, more than 100 times the amount of data in any single prior SPI experiment, using the new capabilities of the European X-ray free electron laser which allow measurements of 1500 frames per second. A classification and structural sorting method was developed to disentangle the heterogeneity of the particles and to obtain a resolution of better than 3 nm. With these new experimental and analytical developments, we have entered a new era for the SPI method and the path towards close-to-atomic resolution imaging of biomolecules is apparent., Comment: 25 pages, 5 main figures, 6 supplementary figures, 2 supplementary movies (link in document)

This paper studies social cooperation backed peer-to-peer energy trading technique by which prosumers can decide how they can use their batteries opportunistically for participating in the peer-to-peer trading. The objective is to achieve a solution in which the ultimate beneficiaries are the prosumers, i.e., a prosumer-centric solution. To do so, a coalition formation game is designed, which enables a prosumer to compare its benefit of participating in the peer-to-peer trading with and without using its battery and thus, allows the prosumer to form suitable social coalition groups with other similar prosumers in the network for conducting peer-to-peer trading. The properties of the formed coalitions are studied, and it is shown that 1) the coalition structure that stems from the social cooperation between participating prosumers at each time slot is both stable and optimal, and 2) the outcomes of the proposed peer- to-peer trading scheme is prosumer-centric. Case studies are conducted based on real household energy usage and solar generation data to highlight how the proposed scheme can benefit prosumers through exhibiting prosumer-centric properties., Comment: Single column, double space, 24 pages

The emergence of high repetition-rate X-ray free-electron lasers (XFELs) powered by superconducting accelerator technology enables the measurement of significantly more experimental data per day than was previously possible. The European XFEL will soon provide 27,000 pulses per second, more than two orders of magnitude more than any other XFEL. The increased pulse rate is a key enabling factor for single-particle X-ray diffractive imaging, which relies on averaging the weak diffraction signal from single biological particles. Taking full advantage of this new capability requires that all experimental steps, from sample preparation and delivery to the acquisition of diffraction patterns, are compatible with the increased pulse repetition rate. Here, we show that single-particle imaging can be performed using X-ray pulses at megahertz repetition rates. The obtained results pave the way towards exploiting high repetition-rate X-ray free-electron lasers for single-particle imaging at their full repetition rate.

We report experimental results on the diffractive imaging of three-dimensionally aligned 2,5-diiodothiophene molecules. The molecules were aligned by chirped near-infrared laser pulses, and their structure was probed at a photon energy of 9.5 keV ($\lambda\approx130 \text{pm}$) provided by the Linac Coherent Light Source. Diffracted photons were recorded on the CSPAD detector and a two-dimensional diffraction pattern of the equilibrium structure of 2,5-diiodothiophene was recorded. The retrieved distance between the two iodine atoms agrees with the quantum-chemically calculated molecular structure to within 5 %. The experimental approach allows for the imaging of intrinsic molecular dynamics in the molecular frame, albeit this requires more experimental data which should be readily available at upcoming high-repetition-rate facilities.

This paper proposes a peer-to-peer energy trading scheme that can help the centralized power system to reduce the total electricity demand of its customers at the peak hour. To do so, a cooperative Stackelberg game is formulated, in which the centralized power system acts as the leader that needs to decide on a price at the peak demand period to incentivize prosumers to not seeking any energy from it. The prosumers, on the other hand, act as followers and respond to the leader's decision by forming suitable coalitions with neighboring prosumers in order to participate in P2P energy trading to meet their energy demand. The properties of the proposed Stackelberg game are studied. It is shown that the game has a unique and stable Stackelberg equilibrium, as a result of the stability of prosumers' coalitions. At the equilibrium, the leader chooses its strategy using a derived closed-form expression, while the prosumers choose their equilibrium coalition structure. An algorithm is proposed that enables the centralized power system and the prosumers to reach the equilibrium solution. Numerical case studies demonstrate the beneficial properties of the proposed scheme., Comment: 10 pages, accepted for publication

Smart solar inverters can be used to store, monitor and manage a home's solar energy. We describe a smart solar inverter system with battery which can either operate in an automatic mode or receive commands over a network to charge and discharge at a given rate. In order to make battery storage financially viable and advantageous to the consumers, effective battery scheduling algorithms can be employed. Particularly, when time-of-use tariffs are in effect in the region of the inverter, it is possible in some cases to schedule the battery to save money for the individual customer, compared to the "automatic" mode. Hence, this paper presents and evaluates the performance of a novel battery scheduling algorithm for residential consumers of solar energy. The proposed battery scheduling algorithm optimizes the cost of electricity over next 24 hours for residential consumers. The cost minimization is realized by controlling the charging/discharging of battery storage system based on the predictions for load and solar power generation values. The scheduling problem is formulated as a linear programming problem. We performed computer simulations over 83 inverters using several months of hourly load and PV data. The simulation results indicate that key factors affecting the viability of optimization are the tariffs and the PV to Load ratio at each inverter. Depending on the tariff, savings of between 1% and 10% can be expected over the automatic approach. The prediction approach used in this paper is also shown to out-perform basic "persistence" forecasting approaches. We have also examined the approaches for improving the prediction accuracy and optimization effectiveness., Comment: This paper was presented at the 8th Solar Integration Workshop and published in the workshop's proceedings

This paper explores the feasibility of social cooperation between prosumers within an energy network in establishing their sustainable participation in peer-to-peer (P2P) energy trading. In particular, a canonical coalition game (CCG) is utilized to propose a P2P energy trading scheme, in which a set of participating prosumers form a coalition group to trade their energy, if there is any, with one another. By exploring the concept of the core of the designed CCG framework, the mid-market rate is utilized as a pricing mechanism of the proposed P2P trading to confirm the stability of the coalition as well as to guarantee the benefit to the prosumers for forming the social coalition. The paper further introduces the motivational psychology models that are relevant to the proposed P2P scheme and it is shown that the outcomes of proposed P2P energy trading scheme satisfy the discussed models. Consequently, it is proven that the proposed scheme is consumer-centric that has the potential to corroborate sustainable prosumers participation in P2P energy trading. Finally, some numerical examples are provided to demonstrate the beneficial properties of the proposed scheme., Comment: 11 pages, 3 figures, 1 table