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The Alder-Andrews Theorem, a partition inequality generalizing Euler's partition identity, the first Rogers-Ramanujan identity, and a theorem of Schur to $d$-distinct partitions of $n$, was proved successively by Andrews in 1971, Yee in 2008, and Alfes, Jameson, and Lemke Oliver in 2010. While Andrews and Yee utilized $q$-series and combinatorial methods, Alfes et al. proved the finite number of remaining cases using asymptotics originating with Meinardus together with high-performance computing. In 2020, Kang and Park conjectured a "level $2$" Alder-Andrews type partition inequality which relates to the second Rogers-Ramanujan identity. Duncan, Khunger, the second author, and Tamura proved Kang and Park's conjecture for all but finitely many cases using a combinatorial shift identity. Here, we generalize the methods of Alfes et al. to resolve nearly all of the remaining cases of Kang and Park's conjecture.

In the quest for enhanced HIV prevention methods, the advent of antiretroviral drugs as pre-exposure prophylaxis (PrEP) has marked a significant stride forward. However, the ethical challenges in conducting placebo-controlled trials for new PrEP agents against a backdrop of highly effective existing PrEP options necessitates innovative approaches. This manuscript delves into the design and implementation of active-controlled trials that incorporate a counterfactual placebo estimate - a theoretical estimate of what HIV incidence would have been without effective prevention. We introduce a novel statistical framework for regulatory approval of new PrEP agents, predicated on the assumption of an available and consistent counterfactual placebo estimate. Our approach aims to assess the absolute efficacy (i.e., against placebo) of the new PrEP agent relative to the absolute efficacy of the active control. We propose a two-step procedure for hypothesis testing and further develop an approach that addresses potential biases inherent in non-randomized comparison to counterfactual placebos. By exploring different scenarios with moderately and highly effective active controls and counterfactual placebo estimates from various sources, we demonstrate how our design can significantly reduce sample sizes compared to traditional non-inferiority trials and offer a robust framework for evaluating new PrEP agents. This work contributes to the methodological repertoire for HIV prevention trials and underscores the importance of adaptability in the face of ethical and practical challenges.

In recent decades, computer science (CS) has undergone remarkable growth and diversification. Creating attractive, social, or hands-on games has already been identified as a possible approach to get teenagers and young adults interested in CS. However, overcoming the global gap between the interest and participation of men and women in CS is still a worldwide problem. To address this challenge, we present a multiplayer game that is used in a workshop setting to motivate girls to program through a 3D game environment. The paper aims to expand the educational landscape within computer science education by offering a motivating and engaging platform for young women to explore programming quests in a collaborative environment. The study involved 235 girls and 50 coaches for the workshop evaluation and a subset of 20 participants for an in-game analysis. In this paper, we explore the engagement in programming and assess the cognitive workload while playing and solving programming quests within the game, as well as the learning experience and the outcome. The results show that the positive outcomes of the workshop underscore the effectiveness of a game-based collaborative learning approach to get girls interested in computer science activities. The variety of solutions found for the different tasks demonstrates the creativity and problem-solving skills of the participants and underlines the effectiveness of the workshop in promoting critical thinking and computational skills.

Computer Science (CS) has experienced significant growth and diversification in recent decades. However, there is a lack of diversity in CS learning approaches. Traditional teaching methods and hands-on learning dominate this field, with limited use of playful and interactive learning methods such as educational games. This gap is particularly evident in game development as a subfield of CS. To address this problem, we present a game-based learning approach to teach foundational concepts for game development. The paper aims to expand the educational landscape within CSE, offering a unique and engaging platform for learners to explore the intricacies of game creation by integrating gamified learning strategies. In this paper, we investigate the user's learning experience and motivation, and the differences between traditional learning and game-based learning methods for teaching game development concepts. The study involves 57 participants in an AB test to assess learners' motivation, user experience, and learning outcomes. The results indicate a significantly increased learning outcome for the game-based learning approach, as well as higher motivation in learning game development concepts.

This document presents the outcomes of a comprehensive survey conducted among early career researchers (ECRs) in academic particle physics. Running from September 24, 2022, to March 3, 2023, the survey gathered responses from 759 ECRs employed in 39 countries. The study aimed to gain insights into the career prospects and experiences of ECRs while also delving into diversity and sociological aspects within particle physics research. The survey results are presented in a manner consistent with the survey choices. The document offers insights for the particle physics community, and provides a set of recommendations for enhancing career prospects, fostering diversity, and addressing sociological dimensions within this field., Comment: Editors: Julia Allen, Kate\v{r}ina Jarkovsk\'a, Aleksandra Lelek, Holly Pacey, Guillaume Pietrzyk and G\'eraldine R\"auber

The next generation of space-based networks will contain optical clocks embedded within satellites. To fully realize the capabilities of such clocks, high-precision clock synchronization across the networks will be necessary. Current experiments have shown the potential for classical frequency combs to synchronize remote optical clocks over free-space. However, these classical combs are restricted in precision to the standard quantum limit. Quantum frequency combs, however, which exhibit quantum properties such as squeezing and entanglement, provide pathways for going beyond the standard quantum limit. Here, we present our perspective on the prospects for practical clock synchronization in space using both classical and quantum frequency combs. We detail the current outcomes achievable with a classical frequency comb approach to synchronization, before quantifying the potential outcomes offered by quantum frequency combs. Challenges to be overcome in deploying frequency combs in space are presented, and the implications of almost-perfect synchronization for future space-based applications and experiments discussed., Comment: 23 pages, 11 figures, perspective, comments welcome

Projecting sea-level change in various climate-change scenarios typically involves running forward simulations of the Earth's gravitational, rotational and deformational (GRD) response to ice mass change, which requires high computational cost and time. Here we build neural-network emulators of sea-level change at 27 coastal locations, due to the GRD effects associated with future Antarctic Ice Sheet mass change over the 21st century. The emulators are based on datasets produced using a numerical solver for the static sea-level equation and published ISMIP6-2100 ice-sheet model simulations referenced in the IPCC AR6 report. We show that the neural-network emulators have an accuracy that is competitive with baseline machine learning emulators. In order to quantify uncertainty, we derive well-calibrated prediction intervals for simulated sea-level change via a linear regression postprocessing technique that uses (nonlinear) machine learning model outputs, a technique that has previously been applied to numerical climate models. We also demonstrate substantial gains in computational efficiency: a feedforward neural-network emulator exhibits on the order of 100 times speedup in comparison to the numerical sea-level equation solver that is used for training.

In this effort, we demonstrate the performance of a highly stable time reference for the proposed Black Hole Explorer (BHEX) mission, a space-based extension to the Event Horizon Telescope (EHT) Very Long Baseline Interferometry (VLBI) project. This precision timing system is based on the use of a space-qualified, ultra-low noise laser developed as part of the Laser Interferometer Space Antenna (LISA) mission as the timing reference, and an optical frequency comb to transfer the stability of this laser to the microwave regime for instrumentation use. We describe the implementation of this system and experimental setup to characterize the stability performance. We present the results of this experiment that demonstrate the performance of this system meets requirements for the BHEX mission., Comment: To be published in the proceedings of SPIE Astronomical Telescopes + Instrumentation 2024

In a 2016 paper, Straub proved an analogue to Euler's partition identity for partitions with fixed perimeter. Later, Fu and Tang provided a refinement and generalization of Straub's analogue to $d$-distinct partitions as well as a result related to the first Rogers-Ramanujan identity. Motivated by Alder-type partition identities and their generalizations, we build on work of Fu and Tang to establish generalized Alder-type partition inequalities in a fixed perimeter setting, and notably, a reverse Alder-type inequality., Comment: 13 pages

Skills in the field of computer science (CS) are increasingly in demand. Often traditional teaching approaches are not sufficient to teach complex computational concepts. Interactive and digital learning experiences have been shown as valuable tools to support learners in understanding. However, the missing social interaction affects the quality of the learning experience. Adding collaborative and competitive elements can make the virtual learning environment even more social, engaging, and motivating for learners. In this paper, we explore the potential of collaborative and competitive elements in an interactive virtual laboratory environment with a focus on computer science education. In an AB study with 35 CS students, we investigated the effectiveness of collaborative and competitive elements in a virtual laboratory using interactive visualizations of sorting algorithms.

Advances in Large Language Models (LLMs) have led to significant interest in their potential to support human experts across a range of domains, including public health. In this work we present automated evaluations of LLMs for public health tasks involving the classification and extraction of free text. We combine six externally annotated datasets with seven new internally annotated datasets to evaluate LLMs for processing text related to: health burden, epidemiological risk factors, and public health interventions. We initially evaluate five open-weight LLMs (7-70 billion parameters) across all tasks using zero-shot in-context learning. We find that Llama-3-70B-Instruct is the highest performing model, achieving the best results on 15/17 tasks (using micro-F1 scores). We see significant variation across tasks with all open-weight LLMs scoring below 60% micro-F1 on some challenging tasks, such as Contact Classification, while all LLMs achieve greater than 80% micro-F1 on others, such as GI Illness Classification. For a subset of 12 tasks, we also evaluate GPT-4 and find comparable results to Llama-3-70B-Instruct, which scores equally or outperforms GPT-4 on 6 of the 12 tasks. Overall, based on these initial results we find promising signs that LLMs may be useful tools for public health experts to extract information from a wide variety of free text sources, and support public health surveillance, research, and interventions., Comment: 33 pages. Feedback and comments are highly appreciated

Large language models (LLMs) have transformed AI and achieved breakthrough performance on a wide range of tasks that require human intelligence. In science, perhaps the most interesting application of LLMs is for hypothesis formation. A feature of LLMs, which results from their probabilistic structure, is that the output text is not necessarily a valid inference from the training text. These are 'hallucinations', and are a serious problem in many applications. However, in science, hallucinations may be useful: they are novel hypotheses whose validity may be tested by laboratory experiments. Here we experimentally test the use of LLMs as a source of scientific hypotheses using the domain of breast cancer treatment. We applied the LLM GPT4 to hypothesize novel pairs of FDA-approved non-cancer drugs that target the MCF7 breast cancer cell line relative to the non-tumorigenic breast cell line MCF10A. In the first round of laboratory experiments GPT4 succeeded in discovering three drug combinations (out of 12 tested) with synergy scores above the positive controls. These combinations were itraconazole + atenolol, disulfiram + simvastatin and dipyridamole + mebendazole. GPT4 was then asked to generate new combinations after considering its initial results. It then discovered three more combinations with positive synergy scores (out of four tested), these were disulfiram + fulvestrant, mebendazole + quinacrine and disulfiram + quinacrine. A limitation of GPT4 as a generator of hypotheses was that its explanations for them were formulaic and unconvincing. We conclude that LLMs are an exciting novel source of scientific hypotheses., Comment: 13 pages, 6 tables, 1 figure. Supplementary information available

Lepton flavour violation (LFV), and lepton flavour university violation (LFUV), are striking signatures of beyond the Standard Model (BSM) physics. Recent searches for these at the ATLAS and CMS experiments are presented, using proton-proton collisions with a centre of mass energy of 13 TeV. A range of models and signatures are considered, including leptoquarks, heavy neutral leptons, LFV in $\tau$ lepton decays, and new measurements of $R(K)$ and $R(J/\Psi)$., Comment: Contribution to the 2024 QCD session of the 58th Rencontres de Moriond

A growing literature on speech interruptions describes how people interrupt one another with speech, but these behaviours have not yet been implemented in the design of artificial agents which interrupt. Perceptions of a prototype proactive speech agent which adapts its speech to both urgency and to the difficulty of the ongoing task it interrupts are compared against perceptions of a static proactive agent which does not. The study hypothesises that adaptive proactive speech modelled on human speech interruptions will lead to partner models which consider the proactive agent as a stronger conversational partner than a static agent, and that interruptions initiated by an adaptive agent will be judged as better timed and more appropriately asked. These hypotheses are all rejected however, as quantitative analysis reveals that participants view the adaptive agent as a poorer dialogue partner than the static agent and as less appropriate in the style it interrupts. Qualitative analysis sheds light on the source of this surprising finding, as participants see the adaptive agent as less socially appropriate and as less consistent in its interactions than the static agent., Comment: Accepted to CUI 2024 - 6th Conference on Conversational User Interfaces