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The superiorization methodology (SM) is an optimization heuristic in which an iterative algorithm, which aims to solve a particular problem, is ``superiorized'' to promote solutions that are improved with respect to some secondary criterion. This superiorization is achieved by perturbing iterates of the algorithm in nonascending directions of a prescribed function that penalizes undesirable characteristics in the solution; the solution produced by the superiorized algorithm should therefore be improved with respect to the value of this function. In this paper, we broaden the SM to allow for the perturbations to be introduced by an arbitrary procedure instead, using a plug-and-play approach. This allows for operations such as image denoisers or deep neural networks, which have applications to a broad class of problems, to be incorporated within the superiorization methodology. As proof of concept, we perform numerical simulations involving low-dose and sparse-view computed tomography image reconstruction, comparing the plug-and-play approach to a conventionally superiorized algorithm, as well as a post-processing approach. The plug-and-play approach provides comparable or better image quality in most cases, while also providing advantages in terms of computing time, and data fidelity of the solutions., Comment: 20 pages, 6 figures

We present a detailed study of a scalar differential equation with threshold state-dependent delayed feedback. This equation arises as a simplification of a gene regulatory model. There are two monotone nonlinearities in the model: one describes the dependence of delay on state, and the other is the feedback nonlinearity. Both increasing and decreasing nonlinearities are considered. Our analysis is exhaustive both analytically and numerically as we examine the bifurcations of the system for various combinations of increasing and decreasing nonlinearities. We identify rich bifurcation patterns including Bautin, Bogdanov-Takens, cusp, fold, homoclinic, and Hopf bifurcations whose existence depend on the derivative signs of nonlinearities. Our analysis confirms many of these patterns in the limit where the nonlinearities are switch-like and change their value abruptly at a threshold. Perhaps one of the most surprising findings is the existence of a Hopf bifurcation to a periodic solution when the nonlinearity is monotone increasing and the time delay is a decreasing function of the state variable--something that is impossible in the case of a constant delay.

The application of Shapley values to high-dimensional, time-series-like data is computationally challenging - and sometimes impossible. For $N$ inputs the problem is $2^N$ hard. In image processing, clusters of pixels, referred to as superpixels, are used to streamline computations. This research presents an efficient solution for time-seres-like data that adapts the idea of superpixels for Shapley value computation. Motivated by a forensic DNA classification example, the method is applied to multivariate time-series-like data whose features have been classified by a convolutional neural network (CNN). In DNA processing, it is important to identify alleles from the background noise created by DNA extraction and processing. A single DNA profile has $31,200$ scan points to classify, and the classification decisions must be defensible in a court of law. This means that classification is routinely performed by human readers - a monumental and time consuming process. The application of a CNN with fast computation of meaningful Shapley values provides a potential alternative to the classification. This research demonstrates the realistic, accurate and fast computation of Shapley values for this massive task, Comment: 16 pages, 5 figures

Terwilliger algebras are a subalgebra of a matrix algebra that are constructed from association schemes over finite sets. In 2010, Rie Tanaka defined what it means for a Terwilliger algebra to be almost commutative. In that paper she gave five equivalent conditions for a Terwilliger algebra to be almost commutative. In this paper, we provide a classification of which groups result in an almost commutative Terwilliger algebra when looking at the group association scheme (the Schur ring generated by the conjugacy classes of the group). In particular, we show that all such groups are either abelian, or Camina groups. Following this classification, we then compute the dimension and non-primary primitive idempotents for each Terwilliger algebra of this form for the first three types of groups whose group association scheme gives an almost commutative Terwilliger algebra. The final case will be considered in a second paper., Comment: Submitted to Discrete Mathematics

The end of Moore's Law is driving cloud providers to offload virtualization and the network data plane to SmartNICs to improve compute efficiency. Even though individual OS control plane tasks consume up to 5% of cycles across the fleet, they remain on the host CPU because they are tightly intertwined with OS mechanisms. Moreover, offloading puts the slow PCIe interconnect in the critical path of OS decisions. We propose Tide, a new split OS architecture that separates OS control plane policies from mechanisms and offloads the control plane policies onto a SmartNIC. Tide has a new host-SmartNIC communication API, state synchronization mechanism, and communication mechanisms that overcome the PCIe bottleneck, even for $\mu$s-scale workloads. Tide frees up host compute for applications and unlocks new optimization opportunities, including machine learning-driven policies, scheduling on the network I/O path, and reducing on-host interference. We demonstrate that Tide enables OS control planes that are competitive with on-host performance for the most difficult $\mu$s-scale workloads. Tide outperforms on-host control planes for memory management (saving 16 host cores), Stubby network RPCs (saving 8 cores), and GCE virtual machine management (11.2% performance improvement)., Comment: About 11 pages

DNA profiles are made up from multiple series of electrophoretic signal measuring fluorescence over time. Typically, human DNA analysts 'read' DNA profiles using their experience to distinguish instrument noise, artefactual signal, and signal corresponding to DNA fragments of interest. Recent work has developed an artificial neural network, ANN, to carry out the task of classifying fluorescence types into categories in DNA profile electrophoretic signal. But the creation of the necessarily large amount of labelled training data for the ANN is time consuming and expensive, and a limiting factor in the ability to robustly train the ANN. If realistic, prelabelled, training data could be simulated then this would remove the barrier to training an ANN with high efficacy. Here we develop a generative adversarial network, GAN, modified from the pix2pix GAN to achieve this task. With 1078 DNA profiles we train the GAN and achieve the ability to simulate DNA profile information, and then use the generator from the GAN as a 'realism filter' that applies the noise and artefact elements exhibited in typical electrophoretic signal., Comment: 29 pages, 9 Figures

We prove strong hybrid subconvex bounds simultaneously in the $q$ and $t$ aspects for $L$-functions of selfdual $\mathrm{GL}_3$ cusp forms twisted by primitive Dirichlet characters. We additionally prove analogous hybrid subconvex bounds for central values of certain $\mathrm{GL}_3 \times \mathrm{GL}_2$ Rankin-Selberg $L$-functions. The subconvex bounds that we obtain are strong in the sense that, modulo current knowledge on estimates for the second moment of $\mathrm{GL}_3$ $L$-functions, they are the natural limit of the first moment method pioneered by Li and by Blomer. The method of proof relies on an explicit $\mathrm{GL}_3 \times \mathrm{GL}_2 \leftrightsquigarrow \mathrm{GL}_4 \times \mathrm{GL}_1$ spectral reciprocity formula, which relates a $\mathrm{GL}_2$ moment of $\mathrm{GL}_3 \times \mathrm{GL}_2$ Rankin-Selberg $L$-functions to a $\mathrm{GL}_1$ moment of $\mathrm{GL}_4 \times \mathrm{GL}_1$ Rankin-Selberg $L$-functions. A key additional input is a Lindel\"of-on-average upper bound for the second moment of Dirichlet $L$-functions restricted to a coset, which is of independent interest., Comment: 46 pages

The choice of coordinate system in a bearings-only (BO) tracking problem influences the methods used to observe and predict the state of a moving target. Modified Polar Coordinates (MPC) and Log-Polar Coordinates (LPC) have some advantages over Cartesian coordinates. In this paper, we derive closed-form expressions for the target state prior distribution after ownship manoeuvre: the mean, covariance, and higher-order moments in LPC. We explore the use of these closed-form expressions in simulation by modifying an existing BO tracker that uses the UKF. Rather than propagating sigma points, we directly substitute current values of the mean and covariance into the time update equations at the ownship turn. This modified UKF, the CFE-UKF, performs similarly to the pure UKF, verifying the closed-form expressions. The closed-form third and fourth central moments indicate non-Gaussianity of the target state when the ownship turns. By monitoring these metrics and appropriately initialising relative range error, we can achieve a desired output mean estimated range error (MRE). The availability of these higher-order moments facilitates other extensions of the tracker not possible with a standard UKF., Comment: 11 pages, 6 figures. This work has been submitted to the IEEE for possible publication

Dense plasma environment affects the electronic structure of ions via variations of the microscopic electrical fields, also known as plasma screening. This effect can be either estimated by simplified analytical models, or by computationally expensive and to date unverified numerical calculations. We have experimentally quantified plasma screening from the energy shifts of the bound-bound transitions in matter driven by the x-ray free electron laser (XFEL). This was enabled by identification of detailed electronic configurations of the observed K{\alpha}, K\b{eta} and K{\gamma} lines. This work paves the way for improving plasma screening models including connected effects like ionization potential depression and continuum lowering, which will advance the understanding of atomic physics in Warm Dense Matter regime.

Mosaic crystals, with their high integrated reflectivities, are widely-employed in spectrometers used to diagnose high energy density systems. X-ray Thomson scattering (XRTS) has emerged as a powerful diagnostic tool of these systems, providing in principle direct access to important properties such as the temperature via detailed balance. However, the measured XRTS spectrum is broadened by the spectrometer instrument function (IF), and without careful consideration of the IF one risks misdiagnosing system conditions. Here, we consider in detail the IF of 40 $\mu$m and 100 $\mu$m mosaic HAPG crystals, and how the broadening varies across the spectrometer in an energy range of 6.7-8.6 keV. Notably, we find a strong asymmetry in the shape of the IF towards higher energies. As an example, we consider the effect of the asymmetry in the IF on the temperature inferred via XRTS for simulated 80 eV CH plasmas, and find that the temperature can be overestimated if an approximate symmetric IF is used. We therefore expect a detailed consideration of the full IF will have an important impact on system properties inferred via XRTS in both forward modelling and model-free approaches., Comment: 19 pages, 13 figures

Quantum field theory predicts a nonlinear response of the vacuum to strong electromagnetic fields of macroscopic extent. This fundamental tenet has remained experimentally challenging and is yet to be tested in the laboratory. A particularly distinct signature of the resulting optical activity of the quantum vacuum is vacuum birefringence. This offers an excellent opportunity for a precision test of nonlinear quantum electrodynamics in an uncharted parameter regime. Recently, the operation of the high-intensity laser ReLaX provided by the Helmholtz International Beamline for Extreme Fields (HIBEF) has been inaugurated at the High Energy Density (HED) scientific instrument of the European XFEL. We make the case that this worldwide unique combination of an x-ray free-electron laser and an ultra-intense near-infrared laser together with recent advances in high-precision x-ray polarimetry, refinements of prospective discovery scenarios, and progress in their accurate theoretical modelling have set the stage for performing an actual discovery experiment of quantum vacuum nonlinearity., Comment: 34 pages, 21 figures

We study the problem of privacy-preserving $k$-means clustering in the horizontally federated setting. Existing federated approaches using secure computation, suffer from substantial overheads and do not offer output privacy. At the same time, differentially private (DP) $k$-means algorithms assume a trusted central curator and do not extend to federated settings. Naively combining the secure and DP solutions results in a protocol with impractical overhead. Instead, our work provides enhancements to both the DP and secure computation components, resulting in a design that is faster, more private, and more accurate than previous work. By utilizing the computational DP model, we design a lightweight, secure aggregation-based approach that achieves four orders of magnitude speed-up over state-of-the-art related work. Furthermore, we not only maintain the utility of the state-of-the-art in the central model of DP, but we improve the utility further by taking advantage of constrained clustering techniques.

We present new exclusion bounds obtained at the European X-ray Free Electron Laser facility (EuXFEL) on axion-like particles (ALPs) in the mass range 10^{-3} eV < m_a < 10^{4} eV. Our experiment exploits the Primakoff effect via which photons can, in the presence of a strong external electric field, decay into axions, which then convert back into photons after passing through an opaque wall. While similar searches have been performed previously at a 3^rd generation synchrotron [1], our work demonstrates improved sensitivity, exploiting the higher brightness of X-rays at EuXFEL., Comment: 7 pages, 6 figures

We study commutative Schur rings over the symplectic groups Sp$(n,2)$ containing the class $\mathcal C$ of symplectic transvections. We find the possible partitions of $\mathcal C$ determined by the Schur ring. We show how this restricts the possibilities for multiplicity one subgroups of Sp$(n,2)$., Comment: 28 pages; one figure

We establish two new variants of arithmetic quantum ergodicity. The first is for self-dual $\mathrm{GL}_2$ Hecke-Maass newforms over $\mathbb{Q}$ as the level and Laplace eigenvalue vary jointly. The second is a nonsplit analogue wherein almost all restrictions of Hilbert (respectively Bianchi) Hecke-Maass cusp forms to the modular surface dissipate as their Laplace eigenvalues grow., Comment: 28 pages. arXiv admin note: substantial text overlap with arXiv:2103.05634

Using a novel ultrahigh resolution ($\Delta E \sim 0.1\,$eV) setup to measure electronic features in x-ray Thomson scattering (XRTS) experiments at the European XFEL in Germany, we have studied the collective plasmon excitation in aluminium at ambient conditions, which we can measure very accurately even at low momentum transfers. As a result, we can resolve previously reported discrepancies between ab initio time-dependent density functional theory simulations and experimental observations. The demonstrated capability for high-resolution XRTS measurements will be a game changer for the diagnosis of experiments with matter under extreme densities, temperatures, and pressures, and unlock the full potential of state-of-the-art x-ray free electron laser (XFEL) facilities to study planetary interior conditions, to understand inertial confinement fusion applications, and for material science and discovery.

It is a folklore result in arithmetic quantum chaos that quantum unique ergodicity on the modular surface with an effective rate of convergence follows from subconvex bounds for certain triple product $L$-functions. The physical space manifestation of this result, namely the equidistribution of mass of Hecke-Maass cusp forms, was proven to follow from subconvexity by Watson, whereas the phase space manifestation of quantum unique ergodicity has only previously appeared in the literature for Eisenstein series via work of Jakobson. We detail the analogous phase space result for Hecke-Maass cusp forms. The proof relies on the Watson-Ichino triple product formula together with a careful analysis of certain archimedean integrals of Whittaker functions., Comment: 31 pages

Equation of state measurements at Jovian or stellar conditions are currently conducted by dynamic shock compression driven by multi-kilojoule multi-beam nanosecond-duration lasers. These experiments require precise design of the target and specific tailoring of the spatial and temporal laser profiles to reach the highest pressures. At the same time, the studies are limited by the low repetition rate of the lasers. Here, we show that by the irradiation of a thin wire with single beam Joule-class short-pulse laser, a converging cylindrical shock is generated compressing the wire material to conditions relevant for the above applications. The shockwave was observed using Phase Contrast Imaging employing a hard X-ray Free Electron Laser with unprecedented temporal and spatial sensitivity. The data collected for Cu wires is in agreement with hydrodynamic simulations of an ablative shock launched by a highly-impulsive and transient resistive heating of the wire surface. The subsequent cylindrical shockwave travels towards the wire axis and is predicted to reach a compression factor of 9 and pressures above 800 Mbar. Simulations for astrophysical relevant materials underline the potential of this compression technique as a new tool for high energy density studies at high repetition rates.

Resonant inelastic x-ray scattering (RIXS) is a widely used spectroscopic technique, providing access to the electronic structure and dynamics of atoms, molecules, and solids. However, RIXS requires a narrow bandwidth x-ray probe to achieve high spectral resolution. The challenges in delivering an energetic monochromated beam from an x-ray free electron laser (XFEL) thus limit its use in few-shot experiments, including for the study of high energy density systems. Here we demonstrate that by correlating the measurements of the self-amplified spontaneous emission (SASE) spectrum of an XFEL with the RIXS signal, using a dynamic kernel deconvolution with a neural surrogate, we can achieve electronic structure resolutions substantially higher than those normally afforded by the bandwidth of the incoming x-ray beam. We further show how this technique allows us to discriminate between the valence structures of Fe and Fe$_2$O$_3$, and provides access to temperature measurements as well as M-shell binding energies estimates in warm-dense Fe compounds.

Detecting anomalous behaviour of satellites is an important goal within the broader task of space situational awareness. The Two Line Element (TLE) data published by NORAD is the only widely-available, comprehensive source of data for satellite orbits. We present here a filtering approach for detecting anomalies in satellite orbits from TLE data. Optimal proposal particle filters are deployed to track the state of the satellites' orbits. New TLEs that are unlikely given our belief of the current orbital state are designated as anomalies. The change in the orbits over time is modelled using the SGP4 model with some adaptations. A model uncertainty is derived to handle the errors in SGP4 around singularities in the orbital elements. The proposed techniques are evaluated on a set of 15 satellites for which ground truth is available and the particle filters are shown to be superior at detecting the subtle in-track and cross-track manoeuvres in the simulated dataset, as well as providing a measure of uncertainty of detections.

Two parties with private data sets can find shared elements using a Private Set Intersection (PSI) protocol without revealing any information beyond the intersection. Circuit PSI protocols privately compute an arbitrary function of the intersection - such as its cardinality, and are often employed in an unbalanced setting where one party has more data than the other. Existing protocols are either computationally inefficient or require extensive server-client communication on the order of the larger set. We introduce Practically Efficient PSI or PEPSI, a non-interactive solution where only the client sends its encrypted data. PEPSI can process an intersection of 1024 client items with a million server items in under a second, using less than 5 MB of communication. Our work is over 4 orders of magnitude faster than an existing non-interactive circuit PSI protocol and requires only 10% of the communication. It is also up to 20 times faster than the work of Ion et al., which computes a limited set of functions and has communication costs proportional to the larger set. Our work is the first to demonstrate that non-interactive circuit PSI can be practically applied in an unbalanced setting.

We report on experiments where solid-density Mg plasmas are created by heating with the focused output of the Linac Coherent Light Source x-ray free-electron-laser. We study the K-shell emission from the Helium and Lithium-like ions using Bragg crystal spectroscopy. Observation of the dielectronic satellites in Lithium-like ions confirms that the M-shell electrons appear bound for these high charge states. An analysis of the intensity of these satellites indicates that when modelled with an atomic-kinetics code, the ionisation potential depression model employed needs to produce depressions for these ions which lie between those predicted by the well known Stewart-Pyatt and Ecker-Kroll models. These results are largely consistent with recent Density Functional Theory calculations.

A new spectral conjugate subgradient method is presented to solve nonsmooth unconstrained optimization problems. The method combines the spectral conjugate gradient method for smooth problems with the spectral subgradient method for nonsmooth problems. We study the effect of two different choices of line search, as well as three formulas for determining the conjugate directions. In addition to numerical experiments with standard nonsmooth test problems, we also apply the method to several image reconstruction problems in computed tomography, using total variation regularization. Performance profiles are used to compare the performance of the algorithm using different line search strategies and conjugate directions to that of the original spectral subgradient method. Our results show that the spectral conjugate subgradient algorithm outperforms the original spectral subgradient method, and that the use of the Polak-Ribiere formula for conjugate directions provides the best and most robust performance., Comment: 23 pages, 7 figures

For neurological disorders and diseases, functional and anatomical connectomes of the human brain can be used to better inform targeted interventions and treatment strategies. Functional magnetic resonance imaging (fMRI) is a non-invasive neuroimaging technique that captures spatio-temporal brain function through blood flow over time. FMRI can be used to study the functional connectome through the functional connectivity matrix; that is, Pearson's correlation matrix between time series from the regions of interest of an fMRI image. One approach to analysing functional connectivity is using partial least squares (PLS), a multivariate regression technique designed for high-dimensional predictor data. However, analysing functional connectivity with PLS ignores a key property of the functional connectivity matrix; namely, these matrices are positive definite. To account for this, we introduce a generalisation of PLS to Riemannian manifolds, called R-PLS, and apply it to symmetric positive definite matrices with the affine invariant geometry. We apply R-PLS to two functional imaging datasets: COBRE, which investigates functional differences between schizophrenic patients and healthy controls, and; ABIDE, which compares people with autism spectrum disorder and neurotypical controls. Using the variable importance in the projection statistic on the results of R-PLS, we identify key functional connections in each dataset that are well represented in the literature. Given the generality of R-PLS, this method has potential to open up new avenues for multi-model imaging analysis linking structural and functional connectomics., Comment: 15 pages, pre-submission article

Cyber incident response is critical to business continuity -- we describe a new exercise that challenges professionals to play the role of Chief Information Security Officer (CISO) for a major financial organisation. Teams must decide how organisational team and budget resources should be deployed across Enterprise Architecture (EA) upgrades and cyber incidents. Every choice made has an impact -- some prevent whilst others may trigger new or continue current attacks. We explain how the underlying platform supports these interactions through a reactionary event mechanism that introduces events based on the current attack surface of the organisation. We explore how our platform manages to introduce randomness on top of triggered events to ensure that the exercise is not deterministic and better matches incidents in the real world. We conclude by describing next steps for the exercise and how we plan to use it in the future to better understand risk decision making., Comment: DGASP-57

Machine Learning as a Service (MLaaS) is an increasingly popular design where a company with abundant computing resources trains a deep neural network and offers query access for tasks like image classification. The challenge with this design is that MLaaS requires the client to reveal their potentially sensitive queries to the company hosting the model. Multi-party computation (MPC) protects the client's data by allowing encrypted inferences. However, current approaches suffer from prohibitively large inference times. The inference time bottleneck in MPC is the evaluation of non-linear layers such as ReLU activation functions. Motivated by the success of previous work co-designing machine learning and MPC, we develop an activation function co-design. We replace all ReLUs with a polynomial approximation and evaluate them with single-round MPC protocols, which give state-of-the-art inference times in wide-area networks. Furthermore, to address the accuracy issues previously encountered with polynomial activations, we propose a novel training algorithm that gives accuracy competitive with plaintext models. Our evaluation shows between $3$ and $110\times$ speedups in inference time on large models with up to $23$ million parameters while maintaining competitive inference accuracy., Comment: To appear at USENIX Security 2024