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This paper presents the training methodology of Arctic-Embed 2.0, a set of open-source text embedding models built for accurate and efficient multilingual retrieval. While prior works have suffered from degraded English retrieval quality, Arctic-Embed 2.0 delivers competitive retrieval quality on multilingual and English-only benchmarks, and supports Matryoshka Representation Learning (MRL) for efficient embedding storage with significantly lower compressed quality degradation compared to alternatives. We detail the design and implementation, presenting several important open research questions that arose during model development. We conduct experiments exploring these research questions and include extensive discussion aimed at fostering further discussion in this field., Comment: 10 pages, 5 figures, 3 tables

The eXTP mission is a major project of the Chinese Academy of Sciences (CAS), with a large involvement of Europe. Its scientific payload includes four instruments: SFA, PFA, LAD and WFM. They offer an unprecedented simultaneous wide-band Xray timing and polarimetry sensitivity. A large European consortium is contributing to the eXTP study, both for the science and the instrumentation. Europe is expected to provide two of the four instruments: LAD and WFM; the LAD is led by Italy and the WFM by Spain. The WFM for eXTP is based on the design originally proposed for the LOFT ESA M3 mission, that underwent a Phase A feasibility study. It will be a wide field of view X-ray monitor instrument working in the 2-50 keV energy range, achieved with large-area Silicon Drift Detectors (SDDs), similar to the ones used for the LAD but with better spatial resolution. The WFM will consist of 3 pairs of coded mask cameras with a total combined field of view (FoV) of 90x180 degrees at zero response and a source localisation accuracy of ~1 arc min. The main goal of the WFM is to provide triggers for the target of opportunity observations of the SFA, PFA and LAD, in order to perform the core science programme, dedicated to the study of matter under extreme conditions of density, gravity and magnetism. In addition, the unprecedented combination of large field of view and imaging capability, down to 2 keV, of the WFM will allow eXTP to make important discoveries of the variable and transient X-ray sky, and provide X-ray coverage of a broad range of astrophysical objects covered under 'observatory science', such as gamma-ray bursts, fast radio bursts, gravitational wave electromagnetic counterparts. In this paper we provide an overview of the WFM instrument, explaining its design, configuration, and anticipated performance., Comment: 15 pages, 13 figures, Proceedings of SPIE 13093, Space Telescopes and Instrumentation 2024: Ultraviolet to Gamma Ray; Proceedings Volume 13093, Space Telescopes and Instrumentation 2024: Ultraviolet to Gamma Ray; 130931Y (2024); doi: 10.1117/12.3020020

The High Energy Modular Array (HEMA) is one of three instruments that compose the STROBE-X mission concept. The HEMA is a large-area, high-throughput non-imaging pointed instrument based on the Large Area Detector developed as part of the LOFT mission concept. It is designed for spectral timing measurements of a broad range of sources and provides a transformative increase in sensitivity to X-rays in the energy range of 2--30 keV compared to previous instruments, with an effective area of 3.4 m$^{2}$ at 8.5 keV and an energy resolution of better than 300 eV at 6 keV in its nominal field of regard., Comment: 16 pages, 10 figures

HERMES-Pathfinder is a space-borne mission based on a constellation of six nano-satellites flying in a low-Earth orbit. The 3U CubeSats, to be launched in early 2025, host miniaturized instruments with a hybrid Silicon Drift Detector/scintillator photodetector system, sensitive to both X-rays and gamma-rays. A seventh payload unit is installed onboard SpIRIT, an Australian-Italian nano-satellite developed by a consortium led by the University of Melbourne and launched in December 2023. The project aims at demonstrating the feasibility of Gamma-Ray Burst detection and localization using miniaturized instruments onboard nano-satellites. The HERMES flight model payloads were exposed to multiple well-known radioactive sources for spectroscopic calibration under controlled laboratory conditions. The analysis of the calibration data allows both to determine the detector parameters, necessary to map instrumental units to accurate energy measurements, and to assess the performance of the instruments. We report on these efforts and quantify features such as spectroscopic resolution and energy thresholds, at different temperatures and for all payloads of the constellation. Finally we review the performance of the HERMES payload as a photon counter, and discuss the strengths and the limitations of the architecture.

HERMES (High Energy Rapid Modular Ensemble of Satellites) Pathfinder mission aims to observe and localize Gamma Ray Bursts (GRBs) and other transients using a constellation of nanosatellites in low-Earth orbit (LEO). Scheduled for launch in early 2025, the 3U CubeSats will host miniaturized instruments featuring a hybrid Silicon Drift Detector (SDD) and GAGG:Ce scintillator photodetector system, sensitive to X-rays and gamma-rays across a wide energy range. Each HERMES payload contains 120 SDD cells, each with a sensitive area of 45 mm^2, organized into 12 matrices, reading out 60 12.1x6.94x15.0 mm^3 GAGG:Ce scintillators. Photons interacting with an SDD are identified as X-ray events (2-60 keV), while photons in the 20-2000 keV range absorbed by the crystals produce scintillation light, which is read by two SDDs, allowing event discrimination. The detector system, including front-end and back-end electronics, a power supply unit, a chip-scale atomic clock, and a payload data handling unit, fits within a 10x10x10 cm^3 volume, weighs 1.5 kg, and has a maximum power consumption of about 2 W. This paper outlines the development of the HERMES constellation, the design and selection of the payload detectors, and laboratory testing, presenting the results of detector calibrations and environmental tests to provide a comprehensive status update of the mission., Comment: 8 pages, 6 figures. Proceedings of SPIE 13093, Space Telescopes and Instrumentation 2024: Ultraviolet to Gamma Ray

In this paper, we study $k$-unit single sample prophet inequalities. A seller has $k$ identical, indivisible items to sell. A sequence of buyers arrive one-by-one, with each buyer's private value for the item, $X_i$, revealed to the seller when they arrive. While the seller is unaware of the distribution from which $X_i$ is drawn, they have access to a single sample, $Y_i$ drawn from the same distribution as $X_i$. What strategies can the seller adopt so as to maximize social welfare? Previous work has demonstrated that when $k = 1$, if the seller sets a price equal to the maximum of the samples, they can achieve a competitive ratio of $\frac{1}{2}$ of the social welfare, and recently Pashkovich and Sayutina established an analogous result for $k = 2$. In this paper, we prove that for $k \geq 3$, setting a (static) price equal to the $k^{\text{th}}$ largest sample also obtains a competitive ratio of $\frac{1}{2}$, resolving a conjecture Pashkovich and Sayutina pose. We then consider the situation where $k$ is large. We demonstrate that setting a price equal to the $(k-\sqrt{2k\log k})^{\text{th}}$ largest sample obtains a competitive ratio of $1 - \sqrt{\frac{2\log k}{k}} - o\left(\sqrt{\frac{\log k}{k}}\right)$, and that this is the optimal possible ratio achievable with a static pricing scheme that sets one of the samples as a price.

HERMES (High Energy Rapid Modular Ensemble of Satellites) Pathfinder is a space-borne mission based on a constellation of six nano-satellites flying in a low-Earth orbit (LEO). The 3U CubeSats, to be launched in early 2025, host miniaturized instruments with a hybrid Silicon Drift Detector/GAGG:Ce scintillator photodetector system, sensitive to X-rays and gamma-rays in a large energy band. HERMES will operate in conjunction with Australian Space Industry Responsive Intelligent Thermal (SpIRIT) 6U CubeSat, launched in December 2023. HERMES will probe the temporal emission of bright high-energy transients such as Gamma-Ray Bursts (GRBs), ensuring a fast transient localization in a field of view of several steradians exploiting the triangulation technique. HERMES intrinsically modular transient monitoring experiment represents a keystone capability to complement the next generation of gravitational wave experiments. In this paper we outline the scientific case, development and programmatic status of the mission, Comment: 13 pages, 16 figures. Proceedings of SPIE "Astronomical Telescopes and Instrumentation" 2024. arXiv admin note: text overlap with arXiv:2210.13866

The persistence of the DAMA/LIBRA (DAMA) modulation over the past two decades has been a source of great contention within the dark matter community. The DAMA collaboration reports a persistent, modulating event rate within their setup of NaI(Tl) scintillating crystals at the INFN Laboratori Nazionali del Gran Sasso (LNGS) underground laboratory. A recent work alluded that this signal could have arisen due to an analysis artefact, caused by DAMA not accounting for time variation of decaying background radioisotopes in their analysis procedure. In this work, we examine in detail this 'induced modulation' effect, arguing that a number of aspects of the DAMA signal are incompatible with an induced modulation arising from decays of background isotopes over the lifetime of the experiment. Using a toy model of the DAMA/LIBRA experiment, we explore the induced modulation effect under different variations of the activities of the relevant isotopes - namely, $^3$H and $^{210}$Pb - highlighting the various inconsistencies between the resultant toy datasets and the DAMA signal. We stress the importance of the SABRE experiment, whose goal is to unambiguously test for the presence of such a modulating signal in an experiment using the same target material and comparable levels of background.

We study the performance of sequential contention resolution and matching algorithms on random graphs with vanishing edge probabilities. When the edges of the graph are processed in an adversarially-chosen order, we derive a new OCRS that is $0.382$-selectable, attaining the "independence benchmark" from the literature under the vanishing edge probabilities assumption. Complementary to this positive result, we show that no OCRS can be more than $0.390$-selectable, significantly improving upon the upper bound of $0.428$ from the literature. We also derive negative results that are specialized to bipartite graphs or subfamilies of OCRS's. Meanwhile, when the edges of the graph are processed in a uniformly random order, we show that the simple greedy contention resolution scheme which accepts all active and feasible edges is $1/2$-selectable. This result is tight due to a known upper bound. Finally, when the algorithm can choose the processing order, we show that a slight tweak to the random order -- give each vertex a random priority and process edges in lexicographic order -- results in a strictly better contention resolution scheme that is $1-\ln(2-1/e)\approx0.510$-selectable. Our positive results also apply to online matching on $1$-uniform random graphs with vanishing (non-identical) edge probabilities, extending and unifying some results from the random graphs literature., Comment: Improved the exposition, and corrected typos from the previous version

This report describes the training dataset creation and recipe behind the family of \texttt{arctic-embed} text embedding models (a set of five models ranging from 22 to 334 million parameters with weights open-sourced under an Apache-2 license). At the time of their release, each model achieved state-of-the-art retrieval accuracy for models of their size on the MTEB Retrieval leaderboard, with the largest model, arctic-embed-l outperforming closed source embedding models such as Cohere's embed-v3 and Open AI's text-embed-3-large. In addition to the details of our training recipe, we have provided several informative ablation studies, which we believe are the cause of our model performance., Comment: 17 pages, 11 Figures, 9 tables

Most of the literature on online algorithms and sequential decision-making focuses on settings with "irrevocable decisions" where the algorithm's decision upon arrival of the new input is set in stone and can never change in the future. One canonical example is the classic prophet inequality problem, where realizations of a sequence of independent random variables $X_1, X_2,\ldots$ with known distributions are drawn one by one and a decision maker decides when to stop and accept the arriving random variable, with the goal of maximizing the expected value of their pick. We consider "prophet inequalities with recourse" in the linear buyback cost setting, where after accepting a variable $X_i$, we can still discard $X_i$ later and accept another variable $X_j$, at a \textit{buyback cost} of $f \times X_i$. The goal is to maximize the expected net reward, which is the value of the final accepted variable minus the total buyback cost. Our first main result is an optimal prophet inequality in the regime of $f \geq 1$, where we prove that we can achieve an expected reward $\frac{1+f}{1+2f}$ times the expected offline optimum. The problem is still open for $0

This paper discusses several linear algebra activities designed to help enhance students' skills in collaborating, exploring mathematics, and linking together abstract and visual ways of approaching mathematics. Most of these activities are short, accessible, engaging, and easy to incorporate into any classroom. In addition, we discuss some questions instructors can ask themselves to design novel and engaging activities when constrained to teaching from a particular curriculum., Comment: 22 pages, 3 figures. Accepted for publication in PRIMUS. See https://github.com/sfushidahardy/SSEA-Linear-Algebra-22/blob/main/README.md for supplementary material

In this paper we consider the online Submodular Welfare (SW) problem. In this problem we are given $n$ bidders each equipped with a general (not necessarily monotone) submodular utility and $m$ items that arrive online. The goal is to assign each item, once it arrives, to a bidder or discard it, while maximizing the sum of utilities. When an adversary determines the items' arrival order we present a simple randomized algorithm that achieves a tight competitive ratio of $\nicefrac{1}{4}$. The algorithm is a specialization of an algorithm due to [Harshaw-Kazemi-Feldman-Karbasi MOR`22], who presented the previously best known competitive ratio of $3-2\sqrt{2}\approx 0.171573 $ to the problem. When the items' arrival order is uniformly random, we present a competitive ratio of $\approx 0.27493$, improving the previously known $\nicefrac{1}{4}$ guarantee. Our approach for the latter result is based on a better analysis of the (offline) Residual Random Greedy (RRG) algorithm of [Buchbinder-Feldman-Naor-Schwartz SODA`14], which we believe might be of independent interest.

Diffusion models have achieved remarkable results in image generation, and have similarly been used to learn high-performing policies in sequential decision-making tasks. Decision-making diffusion models can be trained on lower-quality data, and then be steered with a reward function to generate near-optimal trajectories. We consider the problem of extracting a reward function by comparing a decision-making diffusion model that models low-reward behavior and one that models high-reward behavior; a setting related to inverse reinforcement learning. We first define the notion of a relative reward function of two diffusion models and show conditions under which it exists and is unique. We then devise a practical learning algorithm for extracting it by aligning the gradients of a reward function -- parametrized by a neural network -- to the difference in outputs of both diffusion models. Our method finds correct reward functions in navigation environments, and we demonstrate that steering the base model with the learned reward functions results in significantly increased performance in standard locomotion benchmarks. Finally, we demonstrate that our approach generalizes beyond sequential decision-making by learning a reward-like function from two large-scale image generation diffusion models. The extracted reward function successfully assigns lower rewards to harmful images., Comment: NeurIPS 2023

In this paper, we study contention resolution schemes for matchings. Given a fractional matching $x$ and a random set $R(x)$ where each edge $e$ appears independently with probability $x_e$, we want to select a matching $M \subseteq R(x)$ such that $\Pr[e \in M \mid e \in R(x)] \geq c$, for $c$ as large as possible. We call such a selection method a $c$-balanced contention resolution scheme. Our main results are (i) an asymptotically (in the limit as $\|x\|_\infty$ goes to 0) optimal $\simeq 0.544$-balanced contention resolution scheme for general matchings, and (ii) a $0.509$-balanced contention resolution scheme for bipartite matchings. To the best of our knowledge, this result establishes for the first time, in any natural relaxation of a combinatorial optimization problem, a separation between (i) offline and random order online contention resolution schemes, and (ii) monotone and non-monotone contention resolution schemes. We also present an application of our scheme to a combinatorial allocation problem, and discuss some open questions related to van der Waerden's conjecture for the permanent of doubly stochastic matrices., Comment: 33 pages

HERMES (High Energy Rapid Modular Ensemble of Satellites) is a space-borne mission based on a constellation of nano-satellites flying in a low-Earth orbit (LEO). The six 3U CubeSat buses host new miniaturized instruments hosting a hybrid Silicon Drift Detector/GAGG:Ce scintillator photodetector system sensitive to X-rays and gamma-rays. HERMES will probe the temporal emission of bright high-energy transients such as Gamma-Ray Bursts (GRBs), ensuring a fast transient localization (with arcmin-level accuracy) in a field of view of several steradians exploiting the triangulation technique. With a foreseen launch date in late 2023, HERMES transient monitoring represents a keystone capability to complement the next generation of gravitational wave experiments. Moreover, the HERMES constellation will operate in conjunction with the Space Industry Responsive Intelligent Thermal (SpIRIT) 6U CubeSat, to be launched in early 2023. SpIRIT is an Australian-Italian mission for high-energy astrophysics that will carry in a Sun-synchronous orbit (SSO) an actively cooled HERMES detector system payload. On behalf of the HERMES collaboration, in this paper we will illustrate the HERMES and SpIRIT payload design, integration and tests, highlighting the technical solutions adopted to allow a wide-energy-band and sensitive X-ray and gamma-ray detector to be accommodated in a 1U Cubesat volume., Comment: arXiv admin note: substantial text overlap with arXiv:2101.03032

In this paper, we investigate two variants of the secretary problem. In these variants, we are presented with a sequence of numbers $X_i$ that come from distributions $\mathcal{D}_i$, and that arrive in either random or adversarial order. We do not know what the distributions are, but we have access to a single sample $Y_i$ from each distribution $\mathcal{D}_i$. After observing each number, we have to make an irrevocable decision about whether we would like to accept it or not with the goal of maximizing the probability of selecting the largest number. The random order version of this problem was first studied by Correa et al. [SODA 2020] who managed to construct an algorithm that achieves a probability of $0.4529$. In this paper, we improve this probability to $0.5009$, almost matching an upper bound of $\simeq 0.5024$ which we show follows from earlier work. We also show that there is an algorithm which achieves the probability of $\simeq 0.5024$ asymptotically if no particular distribution is especially likely to yield the largest number. For the adversarial order version of the problem, we show that we can select the maximum number with a probability of $1/4$, and that this is best possible. Our work demonstrates that unlike in the case of the expected value objective studied by Rubinstein et al. [ITCS 2020], knowledge of a single sample is not enough to recover the factor of success guaranteed by full knowledge of the distribution., Comment: 16 pages