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Open educational resources (OER) are teaching, learning, or research resources that are offered freely to users in at least one form and that either reside in the public domain or have been released under an open copyright license that allows for its free use, reuse, modification, and sharing with attribution. Course marking (also called attributes, designations, tags, flags, labels) are specific, searchable attributes or designations that are applied to courses, allowing students to quickly identify important information to aid in their decision making and allow them to efficiently plan their academic careers. In 2022, the report, "Toward Convergence: Creating Clarity to Drive More Consistency in Understanding the Benefits and Costs of OER," introduced a set of principles and frameworks that provide guidance for states, systems, and institutions wanting to better understand the benefits of open educational resources (OER). MHEC led the national effort to produce the report, which details recommendations for consistently estimating the cost savings realized by students when a course uses OER compared to traditional course material. Realizing such analyses are not possible without accurate data on course materials, MHEC then led a national effort to create this report to highlight five steps critical for the development of an effective course marking process, providing committed stakeholders with a roadmap and set of recommendations to improve consistency and reliability for marking courses in college registration materials, so students know the costs and nature of such materials at the time they choose their classes. Consistency of course marking efforts across the United States contributes to the ability to aggregate data from many institutions and conduct studies of how OER saves students money and contributes to enhanced student outcomes.

Student records, and specifically academic transcripts, are the traditional record of a student's completed coursework and their earned credential at an educational institution. Transcripts can serve as proof and a signal to potential employers and other educational institutions that a student has engaged in certain learning activities and obtained knowledge in given areas. Early in 2021, staff members from the Higher Learning Commission (HLC), the U.S. Department of Education and the regional compacts -- the Midwestern Higher Education Compact (MHEC), the New England Board of Higher Education (NEBHE), and the Western Interstate Commission for Higher Education (WICHE) -- met to discuss students' access to their records as a matter of student success. Three concerns were identified: student access to transcripts when there are financial or administrative holds placed on student accounts at institutions; access to student records when an institution closes; and the future of student records access. HLC and the regional compacts have continued to discuss and study the topic of transcript holds and closed school records. The issues surrounding transcript holds and closed school records have received ever greater attention in light of supporting student success since the pandemic. Because of the many ways the pandemic caused a re-thinking of business as usual, changes to transcript holds became a policy and process initiative at the federal, state, and institutional levels. The definition of student success for this paper includes enrolling in and completing a postsecondary education, transferring between institutions, earning licensure, securing employment, qualifying for military service, and other scenarios that vary by student. This paper provides an overview of student records issues, from an accreditor and regional compacts perspective. It includes recent legislative and policy actions at the federal and state levels as well as practitioner solutions and tools for institutions created by regional compacts, institutions, and other organizations. Resources are provided for those working at the institutional level as well as at the state or federal policy level to help students succeed.

We consider cylindrical algebraic decomposition (CAD) and the key concept of delineability which underpins CAD theory. We introduce the novel concept of projective delineability which is easier to guarantee computationally. We prove results about this which can allow reduced CAD computations., Comment: Accepted for publication in the Proceedings of the 26th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC 2024)

We compare methods for signal classification applied to voltage traces from transition edge sensors (TES) which are photon-number resolving detectors fundamental for accessing quantum advantages in information processing, communication and metrology. We quantify the impact of numerical analysis on the distinction of such signals. Furthermore, we explore dimensionality reduction techniques to create interpretable and precise photon number embeddings. We demonstrate that the preservation of local data structures of some nonlinear methods is an accurate way to achieve unsupervised classification of TES traces. We do so by considering a confidence metric that quantifies the overlap of the photon number clusters inside a latent space. Furthermore, we demonstrate that for our dataset previous methods such as the signal's area and principal component analysis can resolve up to 16 photons with confidence above $90\%$ while nonlinear techniques can resolve up to 21 with the same confidence threshold. Also, we showcase implementations of neural networks to leverage information within local structures, aiming to increase confidence in assigning photon numbers. Finally, we demonstrate the advantage of some nonlinear methods to detect and remove outlier signals., Comment: Code is publicly available at https://github.com/polyquantique/Photon-Number-Classification. Data is publicly available at https://doi.org/10.5281/zenodo.14042152 and https://doi.org/10.5281/zenodo.14101974

Symbolic integration is a fundamental problem in mathematics: we consider how machine learning may be used to optimise this task in a Computer Algebra System (CAS). We train transformers that predict whether a particular integration method will be successful, and compare against the existing human-made heuristics (called guards) that perform this task in a leading CAS. We find the transformer can outperform these guards, gaining up to 30% accuracy and 70% precision. We further show that the inference time of the transformer is inconsequential which shows that it is well-suited to include as a guard in a CAS. Furthermore, we use Layer Integrated Gradients to interpret the decisions that the transformer is making. If guided by a subject-matter expert, the technique can explain some of the predictions based on the input tokens, which can lead to further optimisations., Comment: 10 pages, 5 figures, to be published in NeurIPS 2024 MATH-AI Workshop

Multiphoton interference is crucial to many photonic quantum technologies. In particular, interference forms the basis of optical quantum information processing platforms and can lead to significant computational advantages. It is therefore interesting to study the interference arising from various states of light in large interferometric networks. Here, we implement a quantum walk in a highly stable, low-loss, multiport interferometer with up to 24 ultrafast time bins. This time-bin interferometer comprises a sequence of birefringent crystals which produce pulses separated by 4.3\,ps, all along a single optical axis. Ultrafast Kerr gating in an optical fiber is employed to time-demultiplex the output from the quantum walk. We measure one-, two-, and three-photon interference arising from various input state combinations, including a heralded single-photon state, a thermal state, and an attenuated coherent state at one or more input ports. Our results demonstrate that ultrafast time bins are a promising platform to observe large-scale multiphoton interference.

Every year, 2 million first-time, full-time undergraduate students enter a degree-granting postsecondary institution in the United States, but more than one-third leave college before obtaining a college degree. This report's analysis shows that job loss has an adverse effect on college persistence for 18- to 24-year-old US working students, that is, whether those students remain in college. Although the effect was minimal during the 2000-08 period, it became significantly magnified after 2008. It is estimated that from the 2009-10 through 2019-20 academic years, involuntary job loss led to a 17 percentage point increase in a working student's probability of dropping out of college in the next academic year. The authors find supporting evidence that the stronger effect in the later period reflects college students' more restricted access to credit card loans after the passage of the Credit Card Accountability Responsibility and Disclosure (CARD) Act of 2009, which imposed tight restrictions on credit extension to individuals who are younger than 21 or older but enrolled in college. For many working students who have difficulty acquiring alternative forms of credit, credit card loans serve as a crucial means of smoothing consumption when income fluctuates. Tightening of the credit card market has a direct impact on these students. This report's findings suggest that employment stability plays a pivotal role in the retention of young working students, and a small contingency fund goes a long way in preventing college dropout due to temporary employment disruptions. While the underlying analysis was conducted using national data, the findings are relevant to New England, where higher education employs 4 percent of the region's workforce, more than twice the national average. Student retention therefore carries implications not only for the individual students seeking a college education, but also for the vitality of the region's labor market. An important caveat is that the report's findings do not imply that credit card loans improve college students' net welfare. While access to credit card loans improves persistence in the short run for unemployed college students, a large credit card debt leads to other adverse consequences and is unlikely the optimal solution to liquidity issues. Instead, the significance of credit card loans in the personal finance of working students reflects a dearth of alternative income assistance to compensate for short-term earnings loss. Extending timely unemployment assistance to college students through either unemployment insurance or student financial aid programs could potentially insure these students against unforeseen job-loss risks and yield retention benefits. Policymakers concerned with the retention of working college students should consider these options and explore them to a greater degree.

A significant contribution to the temporal resolution of an ultrafast electron diffraction (UED) instrument is arrival time jitter caused by amplitude and phase variation of radio frequency (RF) cavities. In this paper, we present a semi-analytical approach for calculating RF-induced temporal jitter from klystron and RF cavity parameters. Our approach allows fast estimation of temporal jitter for MeV-UED beamlines and can serve as a virtual timing tool when shot-to-shot measurements of RF amplitude and phase jitters are available. A simulation study for the SLAC MeV-UED instrument is presented and the temporal resolution for several beamline configurations are compared., Comment: 8 pages, 5 figures

Magnetic compressors offer an attractive path toward jitter-free bunch compression in MeV-UED. Compared with RF bunchers, magnetic compressors do not introduce additional timing jitter and can be configured to minimize timing jitter due to upstream energy fluctuation. In this work we discuss the principles of designing magnetic compressors for MeV-UED. Start-to-end simulation of a dogleg compressor is presented. Results show a bunch length of 11 fs and arrival time jitter of 8 fs can be achieved at 100 fC charge with small emittance growth.

This extended abstract accompanies an invited talk at CASC 2024, which surveys recent developments in Real Quantifier Elimination (QE) and Cylindrical Algebraic Decomposition (CAD). After introducing these concepts we will first consider adaptations of CAD inspired by computational logic, in particular the algorithms which underpin modern SAT solvers. CAD theory has found use in collaboration with these via the Satisfiability Modulo Theory (SMT) paradigm; while the ideas behind SAT/SMT have led to new algorithms for Real QE. Second we will consider the optimisation of CAD through the use of Machine Learning (ML). The choice of CAD variable ordering has become a key case study for the use of ML to tune algorithms in computer algebra. We will also consider how explainable AI techniques might give insight for improved computer algebra software without any reliance on ML in the final code., Comment: Extended Abstract to accompany Invited Talk at CASC 2024

Let $p$ be prime and $e,k$ be positive integers, and let $R = {\mathbb Z}_p[\sqrt[e]{p}]$. We calculate the Waring numbers $g_R(k)$ for many values of $p, e$, and $k$, and investigate how the Waring numbers for $p=2$ change as $e$ and $k$ vary., Comment: 18 pages, 3 figures

1 ps timing resolution is the entry point to signature based searches relying on secondary/tertiary vertices and particle identification. We describe a preliminary design for PSEC5, an 8-channel 40 GS/s waveform-sampling ASIC in the TSMC 65 nm process targetting 1 ps resolution at 20 mW power per channel. Each channel consists of four fast and one slow switched capacitor arrays (SCA), allowing ps time resolution combined with a long effective buffer. Each fast SCA is 1.6 ns long and has a nominal sampling rate of 40 GS/s. The slow SCA is 204.8 ns long and samples at 5 GS/s. Recording of the analog data for each channel is triggered by a fast discriminator capable of multiple triggering during the window of the slow SCA. To achieve a large dynamic range, low leakage, and high bandwidth, the SCA sampling switches are implemented as 2.5 V nMOSFETs controlled by 1.2 V shift registers. Stored analog data are digitized by an external ADC at 10 bits or better. Specifications on operational parameters include a 4 GHz analog bandwidth and a dead time of 20 microseconds, corresponding to a 50 kHz readout rate, determined by the choice of the external ADC., Comment: 16th Pisa Meeting on Advanced Detectors

We present the first use of machine learning tools to predict multistationarity of reaction networks. Chemical Reaction Networks (CRNs) are the mathematical formulation of how the quantities associated to a set of species (molecules, proteins, cells, or animals) vary as time passes with respect to their interactions with each other. Their mathematics does not describe just chemical reactions but many other areas of the life sciences such as ecology, epidemiology, and population dynamics. We say a CRN is at a steady state when the concentration (or number) of species do not vary anymore. Some CRNs do not attain a steady state while some others may have more than one possible steady state. The CRNs in the later group are called multistationary. Multistationarity is an important property, e.g. switch-like behaviour in cells needs multistationarity to occur. Existing algorithms to detect whether a CRN is multistationary or not are either extremely expensive or restricted in the type of CRNs they can be used on, motivating a new machine learning approach. We address the problem of representing variable-length CRN data to machine learning models by developing a new graph representation of CRNs for use with graph learning algorithms. We contribute a large dataset of labelled fully open CRNs whose production necessitated the development of new CRN theory. Then we present experimental results on the training and testing of a graph attention network model on this dataset, showing excellent levels of performance. We finish by testing the model predictions on validation data produced independently, demonstrating generalisability of the model to different types of CRN., Comment: 39 pages, 10 Figures, the dataset and code related to this manuscript is available at the Zenodo link given inside the paper

There has been a growing need to devise processes that can create comprehensive datasets in the world of Computer Algebra, both for accurate benchmarking and for new intersections with machine learning technology. We present here a method to generate integrands that are guaranteed to be integrable, dubbed the LIOUVILLE method. It is based on Liouville's theorem and the Parallel Risch Algorithm for symbolic integration. We show that this data generation method retains the best qualities of previous data generation methods, while overcoming some of the issues built into that prior work. The LIOUVILLE generator is able to generate sufficiently complex and realistic integrands, and could be used for benchmarking or machine learning training tasks related to symbolic integration., Comment: To appear in proc. CASC (2024)

In this work, we introduce a quantum-based quantitative phase microscopy technique using a phase gradient approach that is inherently background resistant and does not rely on interferometry or scanning. Here, a transparent sample is illuminated by both photons of a position-momentum entangled pair with one photon setup for position measurement in the near-field (NF) of the sample and its partner for momentum measurement in the far-field (FF). By virtue of the spatial correlation property inherent to the entanglement, both the position and momentum information of the photons can thus be obtained simultaneously. The phase profile of the sample is then deduced through a phase gradient measurement obtained by measuring the centroid shift of the photons' in the FF momentum plane for each NF position. We show that the technique, while achieving an imaging resolution of 2.76\,$\mu$m, is phase accurate to at least $\lambda/30$ and phase sensitive to $\lambda/100$ at a wavelength of 810\,nm. In addition, through the temporal correlation between the photon pairs, our technique shows resilience to strong dynamic background lights, which can prove difficult to account for in classical phase imaging techniques. We believe this work marks a significant advancement in the capabilities of quantum phase microscopy and quantum imaging in general, it showcases imaging and phase resolutions approaching those attainable with classical phase microscopes. This advancement brings quantum imaging closer to practical real-world applications, heralding new possibilities in the field.

Strongly-driven nonlinear optical processes such as spontaneous parametric down-conversion and spontaneous four-wave mixing can produce multiphoton nonclassical beams of light which have applications in quantum information processing and sensing. In contrast to the low-gain regime, new physical effects arise in a high-gain regime due to the interactions between the nonclassical light and the strong pump driving the nonlinear process. Here, we describe and experimentally observe a gain-induced group delay between the multiphoton pulses generated in a high-gain type-II spontaneous parametric down-conversion source. Since the group delay introduces distinguishability between the generated photons, it will be important to compensate for it when designing quantum interference devices in which strong optical nonlinearities are required., Comment: 18 pages, 9 figures (including supplemental material)

We propose a quantum information processing platform that utilizes the ultrafast time-bin encoding of photons. This approach offers a pathway to scalability by leveraging the inherent phase stability of collinear temporal interferometric networks at the femtosecond-to-picosecond timescale. The proposed architecture encodes information in ultrafast temporal bins processed using optically induced nonlinearities and birefringent materials while keeping photons in a single spatial mode. We demonstrate the potential for scalable photonic quantum information processing through two independent experiments that showcase the platform's programmability and scalability, respectively. The scheme's programmability is demonstrated in the first experiment, where we successfully program 362 different unitary transformations in up to 8 dimensions in a temporal circuit. In the second experiment, we show the scalability of ultrafast time-bin encoding by building a passive optical network, with increasing circuit depth, of up to 36 optical modes. In each experiment, fidelities exceed 97\%, while the interferometric phase remains passively stable for several days., Comment: 7 pages, 3 figures

We present a new methodology for utilising machine learning technology in symbolic computation research. We explain how a well known human-designed heuristic to make the choice of variable ordering in cylindrical algebraic decomposition may be represented as a constrained neural network. This allows us to then use machine learning methods to further optimise the heuristic, leading to new networks of similar size, representing new heuristics of similar complexity as the original human-designed one. We present this as a form of ante-hoc explainability for use in computer algebra development., Comment: Accepted for presentation at ICMS 2024

Computer Algebra Systems (e.g. Maple) are used in research, education, and industrial settings. One of their key functionalities is symbolic integration, where there are many sub-algorithms to choose from that can affect the form of the output integral, and the runtime. Choosing the right sub-algorithm for a given problem is challenging: we hypothesise that Machine Learning can guide this sub-algorithm choice. A key consideration of our methodology is how to represent the mathematics to the ML model: we hypothesise that a representation which encodes the tree structure of mathematical expressions would be well suited. We trained both an LSTM and a TreeLSTM model for sub-algorithm prediction and compared them to Maple's existing approach. Our TreeLSTM performs much better than the LSTM, highlighting the benefit of using an informed representation of mathematical expressions. It is able to produce better outputs than Maple's current state-of-the-art meta-algorithm, giving a strong basis for further research.

Ultrafast electron diffraction using MeV energy beams(MeV-UED) has enabled unprecedented scientific opportunities in the study of ultrafast structural dynamics in a variety of gas, liquid and solid state systems. Broad scientific applications usually pose different requirements for electron probe properties. Due to the complex, nonlinear and correlated nature of accelerator systems, electron beam property optimization is a time-taking process and often relies on extensive hand-tuning by experienced human operators. Algorithm based efficient online tuning strategies are highly desired. Here, we demonstrate multi-objective Bayesian active learning for speeding up online beam tuning at the SLAC MeV-UED facility. The multi-objective Bayesian optimization algorithm was used for efficiently searching the parameter space and mapping out the Pareto Fronts which give the trade-offs between key beam properties. Such scheme enables an unprecedented overview of the global behavior of the experimental system and takes a significantly smaller number of measurements compared with traditional methods such as a grid scan. This methodology can be applied in other experimental scenarios that require simultaneously optimizing multiple objectives by explorations in high dimensional, nonlinear and correlated systems.

The quantum walk (QW) has proven to be a valuable testbed for fundamental inquiries in quantum technology applications such as quantum simulation and quantum search algorithms. Many benefits have been found by exploring implementations of QWs in various physical systems, including photonic platforms. Here, we propose a novel platform to perform quantum walks using an ultrafast time-bin encoding (UTBE) scheme. This platform supports the scalability of quantum walks to a large number of steps while retaining a significant degree of programmability. More importantly, ultrafast time bins are encoded at the picosecond time scale, far away from mechanical fluctuations. This enables the scalability of our platform to many modes while preserving excellent interferometric phase stability over extremely long periods of time without requiring active phase stabilization. Our 18-step QW is shown to preserve interferometric phase stability over a period of 50 hours, with an overall walk fidelity maintained above $95\%$, Comment: 13 pages, 8 figures

Coupled climate model simulations designed to isolate the effects of Arctic sea-ice loss often apply artificial heating, either directly to the ice or through modification of the surface albedo, to constrain sea-ice in the absence of other forcings. Recent work has shown that this approach may lead to an overestimation of the climate response to sea-ice loss. In this study, we assess the spurious impacts of ice-constraining methods on the climate of an idealised aquaplanet general circulation model (GCM) with thermodynamic sea-ice. The true effect of sea-ice loss in this model is isolated by inducing ice loss through reduction of the freezing point of water, which does not require additional energy input. We compare results from freezing point modification experiments with experiments where sea-ice loss is induced using traditional ice-constraining methods, and confirm the result of previous work that traditional methods induce spurious additional warming. Furthermore, additional warming leads to an overestimation of the circulation response to sea-ice loss, which involves a weakening of the zonal wind and storm track activity in midlatitudes. Our results suggest that coupled model simulations with constrained sea-ice should be treated with caution, especially in boreal summer, where the true effect of sea-ice loss is weakest but we find the largest spurious response. Given that our results may be sensitive to the simplicity of the model we use, we suggest that devising methods to quantify the spurious effects of ice-constraining methods in more sophisticated models should be an urgent priority for future work., Comment: Submitted to Journal of Climate

In recent years, neural networks have been used to solve phase retrieval problems in imaging with superior accuracy and speed than traditional techniques, especially in the presence of noise. However, in the context of interferometric imaging, phase noise has been largely unaddressed by existing neural network architectures. Such noise arises naturally in an interferometer due to mechanical instabilities or atmospheric turbulence, limiting measurement acquisition times and posing a challenge in scenarios with limited light intensity, such as remote sensing. Here, we introduce a 3D-2D Phase Retrieval U-Net (PRUNe) that takes noisy and randomly phase-shifted interferograms as inputs, and outputs a single 2D phase image. A 3D downsampling convolutional encoder captures correlations within and between frames to produce a 2D latent space, which is upsampled by a 2D decoder into a phase image. We test our model against a state-of-the-art singular value decomposition algorithm and find PRUNe reconstructions consistently show more accurate and smooth reconstructions, with a x2.5 - 4 lower mean squared error at multiple signal-to-noise ratios for interferograms with low (< 1 photon/pixel) and high (~100 photons/pixel) signal intensity. Our model presents a faster and more accurate approach to perform phase retrieval in extremely low light intensity interferometry in presence of phase noise, and will find application in other multi-frame noisy imaging techniques.

We demonstrate the storage and retrieval of heralded single photons in a fiber-based cavity quantum memory. The photons are stored, and retrieved, from the memory using quantum frequency conversion which switches the photon into, and out of, resonance with the cavity. The photons, generated in the telecom O-band with a bandwidth of 81\,GHz, are retrieved from the memory with a $1/e$ lifetime of 1.64$\mu$s, or 32.8 cavity round trips. We show that non-classical photon statistics remain for 70 round trips. The internal memory efficiency after 0.5$\mu$s of storage is $10.9 \pm 0.5$%; a coupling efficiency of 60% into the memory cavity yields a total efficiency of $6.0\pm0.3$%. These results mark a crucial step forward in the development of fiber-based quantum memories, and high-bandwidth memories operating at telecom wavelengths, with applications to photon source multiplexing and fiber-based quantum networking., Comment: 9 pages, 4 figures

We demonstrate the generation of photons within a fiber-cavity quantum memory, followed by later on-demand readout. Signal photons are generated by spontaneous four-wave mixing in a fiber cavity comprising a birefringent fiber with dichroic reflective end facets. The detection of the partner herald photon indicates the creation of the stored signal photon. After a delay, the signal photon is switched out of resonance with the fiber cavity by intracavity frequency translation using Bragg scattering four-wave mixing, driven by ancillary control pulses. We measure sub-Poissonian statistics in the output signal mode, with $g^{(2)}_{AC}=0.54(1)$ in the first readout bin and a readout frequency translation efficiency of $\approx$80%. The 1/e memory lifetime is $\approx$67 cavity cycles, or 1.68$\mu$s. In an alternate fiber cavity, we show a strategy for noise reduction and measure $g^{(2)}_{AC}=0.068(10)$ after one cavity cycle., Comment: 6 pages, 3 figures

Symbolic Computation algorithms and their implementation in computer algebra systems often contain choices which do not affect the correctness of the output but can significantly impact the resources required: such choices can benefit from having them made separately for each problem via a machine learning model. This study reports lessons on such use of machine learning in symbolic computation, in particular on the importance of analysing datasets prior to machine learning and on the different machine learning paradigms that may be utilised. We present results for a particular case study, the selection of variable ordering for cylindrical algebraic decomposition, but expect that the lessons learned are applicable to other decisions in symbolic computation. We utilise an existing dataset of examples derived from applications which was found to be imbalanced with respect to the variable ordering decision. We introduce an augmentation technique for polynomial systems problems that allows us to balance and further augment the dataset, improving the machine learning results by 28\% and 38\% on average, respectively. We then demonstrate how the existing machine learning methodology used for the problem $-$ classification $-$ might be recast into the regression paradigm. While this does not have a radical change on the performance, it does widen the scope in which the methodology can be applied to make choices.

This paper builds and extends on the authors previous work related to the algorithmic tool, Cylindrical Algebraic Decomposition (CAD), and one of its core applications, Real Quantifier Elimination (QE). These topics are at the heart of symbolic computation and were first implemented in computer algebra systems decades ago, but have recently received renewed interest as part of the ongoing development of SMT solvers for non-linear real arithmetic. First, we consider the use of iterated univariate resultants in traditional CAD, and how this leads to inefficiencies, especially in the case of an input with multiple equational constraints. We reproduce the workshop paper [Davenport \& England, 2023], adding important clarifications to our suggestions first made there to make use of multivariate resultants in the projection phase of CAD. We then consider an alternative approach to this problem first documented in [McCallum \& Brown, 2009] which redefines the actual object under construction, albeit only in the case of two equational constraints. We correct an important typo and provide a missing proof in that paper. We finish by revising the topic of how to deal with SMT or Real QE problems expressed using rational functions (as opposed to the usual polynomial ones) noting that these are often found in industrial applications. We revisit a proposal made in [Uncu, Davenport and England, 2023] for doing this in the case of satisfiability, explaining why such an approach does not trivially extend to more complicated quantification structure and giving a suitable alternative., Comment: To be submitted to Mathematics in Computer Science

We propose a setup for measuring visible and near-visible internal Smith-Purcell radiation and Cherenkov Diffraction Radiation, based on silica and silicon, and perform quantitative numerical analysis of its radiation efficiency. We calculate the total radiated energy per electron and the spectral distribution of different radiation orders, taking into account material dispersion and absorption. For an optimized silica grating of 200 micrometer length, the total radiated energy reaches 2~eV per electron for 2 MeV electrons. Above the Cherenkov threshold, in most cases the energy of Cherenkov diffraction radiation is several times higher than the energy of internal Smith-Purcell radiation, but for some geometries and frequency ranges first or second order radiation may dominate over Cherenkov radiation (zeroth order). Radiation up to the 4th order is detected in the simulation. The spectrum of Cherenkov radiation is highly resonant, with local minima for frequencies where maxima of the other radiation orders occur. The spectrum of Cherenkov radiation takes a frequency comb-like shape for a uniform layer of Si on SiO2 substrate, due to a Fabry-Perot effect occurring for the evanescent field of the moving electron. The proposed setup could become a prototype of a non-invasive particle beam monitor for both conventional and laser particle accelerators.

The development of long, tunable structures is critical to increasing energy gain in laser-driven dielectric accelerators (DLAs). Here we combine pulse-front-tilt illumination with slab-geometry structures assembled by precisely aligning off-the-shelf 4~mm long transmission gratings to achieve up to 200 keV energy modulation for 6 MeV injected electrons. The effective interaction length is longer than 1~mm, limited by dephasing of the accelerated particles in the structure. The piezo-based independent mounting system for the gratings allows tuning of the gap and field distribution inside the structure., Comment: 6 pages, 5 figures

Holography is an established technique for measuring the wavefront of optical signals through interferometric combination with a reference wave. Conventionally the integration time of a hologram is limited by the interferometer coherence time, thus making it challenging to prepare holograms of remote objects, especially using weak illumination. Here, we circumvent this limitation by using intensity correlation interferometry. Although the exposure time of individual holograms must be shorter than the interferometer coherence time, we show that any number of randomly phase-shifted holograms can be combined into a single intensity-correlation hologram. In a proof-of-principle experiment, we use this technique to perform phase imaging and 3D reconstruction of an object at a ~3m distance using weak illumination and without active phase stabilization., Comment: 10 pages; 3 figures

This paper accompanies a new dataset of non-linear real arithmetic problems for the SMT-LIB benchmark collection. The problems come from an automated proof procedure of Gerhold--Kauers, which is well suited for solution by SMT. The problems of this type have not been tackled by SMT-solvers before. We describe the proof technique and give one new such proof to illustrate it. We then describe the dataset and the results of benchmarking. The benchmarks on the new dataset are quite different to the existing ones. The benchmarking also brings forward some interesting debate on the use/inclusion of rational functions and algebraic numbers in the SMT-LIB., Comment: Presented at the 2022 SC-Square Workshop