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The Central Molecular Zone (CMZ) is the largest reservoir of dense molecular gas in the Galaxy and is heavily obscured in the optical and near-IR. We present an overview of the far-IR dust continuum, where the molecular clouds are revealed, provided by Herschel in the inner 40\deg($|l| <$ 20\deg) of the Milky Way with a particular focus on the CMZ. We report a total dense gas ($N$(H$_2$) $> 10^{23}$ cm$^{-2}$) CMZ mass of M=$2\substack{+2 \\ -1} \times 10^7$ M$_{\odot}$ and confirm that there is a highly asymmetric distribution of dense gas, with about 70-75% at positive longitudes. We create and publicly release complete fore/background-subtracted column density and dust temperature maps in the inner 40\deg ($|l| <$ 20\deg) of the Galaxy. We find that the CMZ clearly stands out as a distinct structure, with an average mass per longitude that is at least $3\times$ higher than the rest of the inner Galaxy contiguously from 1.8\deg $> \ell >$ -1.3\deg. This CMZ extent is larger than previously assumed, but is consistent with constraints from velocity information. The inner Galaxy's column density peaks towards the SgrB2 complex with a value of about 2 $\times$ 10$^{24}$ cm$^{-2}$, and typical CMZ molecular clouds are about N(H$_2$)=10$^{23}$ cm$^{-2}$. Typical CMZ dust temperatures range from about $12-35$ K with relatively little variation. We identify a ridge of warm dust in the inner CMZ that potentially traces the base of the northern Galactic outflow seen with MEERKAT., Comment: Submitted to ApJ, 16 pages, project website: https://centralmolecularzone.github.io/3D_CMZ/

The Central Molecular Zone (CMZ) is the way station at the heart of our Milky Way Galaxy, connecting gas flowing in from Galactic scales with the central nucleus. Key open questions remain about its 3-D structure, star formation properties, and role in regulating this gas inflow. In this work, we identify a hierarchy of discrete structures in the CMZ using column density and dust temperature maps from Paper I (Battersby et al., submitted). We calculate the physical ($N$(H$_2$), $T_{\rm{dust}}$, mass, radius) and kinematic (HNCO, HCN, and HC$_3$N moments) properties of each structure as well as their bolometric luminosities and star formation rates (SFRs). We compare these properties with regions in the Milky Way disk and external galaxies. We perform power-law fits to the column density probability distribution functions (N-PDFs) of the inner 100 pc, SgrB2, and the outer 100 pc of the CMZ as well as several individual molecular cloud structures and find generally steeper power-law slopes ($-9<\alpha<-2$) compared with the literature ($-6 < \alpha < -1$). We find that individual CMZ structures require a large external pressure ($P_e$/k$_B$ $> 10^{7-9}$ K cm$^{-3}$) to be considered bound. Despite the fact that the CMZ overall is well below the Gao-Solomon dense gas star-formation relation (and in modest agreement with the Schmidt-Kennicutt relation), individual structures on the scale of molecular clouds generally follow these star-formation relations and agree well with other Milky Way and extragalactic regions., Comment: Submitted to ApJ, 22 pages, project website: https://centralmolecularzone.github.io/3D_CMZ/

A comprehensive 3-D model of the central 300 pc of the Milky Way, the Central Molecular Zone (CMZ) is of fundamental importance in understanding energy cycles in galactic nuclei, since the 3-D structure influences the location and intensity of star formation, feedback, and black hole accretion. Current observational constraints are insufficient to distinguish between existing 3-D models. Dust extinction is one diagnostic tool that can help determine the location of dark molecular clouds relative to the bright Galactic Center emission. By combining Herschel and Spitzer observations, we developed three new dust extinction techniques to estimate the likely near/far locations for each cloud in the CMZ. We compare our results to four geometric CMZ orbital models. Our extinction methods show good agreement with each other, and with results from spectral line absorption analysis from Walker et al. (submitted). Our near/far results for CMZ clouds are inconsistent with a projected version of the Sofue (1995) two spiral arms model, and show disagreement in position-velocity space with the Molinari et al. (2011) closed elliptical orbit. Our results are in reasonable agreement with the Kruijssen et al. (2015) open streams. We find that a simplified toy-model elliptical orbit which conserves angular momentum shows promising fits in both position-position and position-velocity space. We conclude that all current CMZ orbital models lack the complexity needed to describe the motion of gas in the CMZ, and further work is needed to construct a complex orbital model to accurately describe gas flows in the CMZ., Comment: Submitted to ApJ; 36 pages; Project series website with relevant code, data, and results: https://centralmolecularzone.github.io/3D_CMZ/

The Milky Way's Central Molecular Zone (CMZ) is the largest concentration of dense molecular gas in the Galaxy, the structure of which is shaped by the complex interplay between Galactic-scale dynamics and extreme physical conditions. Understanding the 3-D geometry of this gas is crucial as it determines the locations of star formation and subsequent feedback. We present a catalogue of clouds in the CMZ using Herschel data. Using archival data from the APEX and MOPRA CMZ surveys, we measure averaged kinematic properties of the clouds at 1mm and 3mm. We use archival ATCA data of the H$_{2}$CO (1$_{1,0}$ - 1$_{1,1}$) 4.8 GHz line to search for absorption towards the clouds, and 4.85 GHz GBT C-band data to measure the radio continuum emission. We measure the absorption against the continuum to provide new constraints for the line-of-sight positions of the clouds relative to the Galactic centre, and find a highly asymmetric distribution, with most clouds residing in front of the Galactic centre. The results are compared with different orbital models, and we introduce a revised toy model of a vertically-oscillating closed elliptical orbit. We find that most models describe the PPV structure of the gas reasonably well, but find significant inconsistencies in all cases regarding the near vs. far placement of individual clouds. Our results highlight that the CMZ is likely more complex than can be captured by these simple geometric models, along with the need for new data to provide further constraints on the true 3-D structure of the CMZ., Comment: Submitted to ApJ, 30 pages, project website: https://centralmolecularzone.github.io/3D_CMZ/

Microwave-optical quantum transduction is a key enabling technology in quantum networking, but has been plagued by a formidable technical challenge. As most microwave-optical-transduction techniques rely on three-wave mixing processes, the processes consume photons from a driving telecom-band (pump) laser to convert input microwave photons into telecom-band photons detuned from the laser by this microwave frequency. However, cleanly separating out single photons detuned only a few GHz away from a classically bright laser in the same spatial mode requires frequency filters of unprecedented extinction over a very narrow transition band, straining the capabilities of today's technology. Instead of confronting this challenge directly, we show how one may achieve the same transduction objective with comparable efficiency using a four-wave mixing process in which $pairs$ of pump photons are consumed to produce transduced optical photons widely separated in frequency from the pump. We develop this process by considering higher-order analogues of photoelasticity and electrostriction than those used in conventional optomechanics, and examine how the efficiency of this process can be made to exceed conventional optomechanical couplings., Comment: 5 pages + 2 more for appendices, and 1 figure

Replicating causal estimates across different cohorts is crucial for increasing the integrity of epidemiological studies. However, strong assumptions regarding unmeasured confounding and effect modification often hinder this goal. By employing an instrumental variable (IV) approach and targeting the local average treatment effect (LATE), these assumptions can be relaxed to some degree; however, little work has addressed the replicability of IV estimates. In this paper, we propose a novel survey weighted LATE (SWLATE) estimator that incorporates unknown sampling weights and leverages machine learning for flexible modeling of nuisance functions, including the weights. Our approach, based on influence function theory and cross-fitting, provides a doubly-robust and efficient framework for valid inference, aligned with the growing "double machine learning" literature. We further extend our method to provide bounds on a target population ATE. The effectiveness of our approach, particularly in non-linear settings, is demonstrated through simulations and applied to a Mendelian randomization analysis of the relationship between triglycerides and cognitive decline.

Though larger vessels may be well-equipped to deal with wavy conditions, smaller vessels are often more susceptible to disturbances. This paper explores the development of a nonlinear model predictive control (NMPC) system for Uncrewed Surface Vessels (USVs) in wavy conditions to minimize average roll. The NMPC is based on a prediction method that uses information about the vessel's dynamics and an assumed wave model. This method is able to mitigate the roll of an under-actuated USV in a variety of conditions by adjusting the weights of the cost function. The results show a reduction of 39% of average roll with a tuned controller in conditions with 1.75-metre sinusoidal waves. A general and intuitive tuning strategy is established. This preliminary work is a proof of concept which sets the stage for the leveraging of wave prediction methodologies to perform planning and control in real time for USVs in real-world scenarios and field trials., Comment: 6 pages, 10 figures. To appear in Proceedings of the 2024 IEEE/RSJ International Conference on Robots and Systems (IROS), October 2024

In a recent class of phase field crystal (PFC) models, the density order parameter is coupled to powers of its mean field. This effectively introduces a phenomenology of higher-order direct correlation functions acting on long wavelengths, which is required for modelling solid-liquid-vapor systems. The present work generalizes these models by incorporating, into a single-field theory, higher-order direct correlations, systematically constructed in reciprocal space to operate across long {\it and} short wavelengths. The correlation kernels introduced are also readily adaptable to describe distinct crystal structures. We examine the three-phase equilibrium properties and phase diagrams of the proposed model, and reproduce parts of the aluminum phase diagram as an example of its versatile parametrization. We assess the dynamics of the model, showing that it allows robust control of the interface energy between the vapor and condensed phases (liquid and solid). We also examine the dynamics of solid-vapor interfaces over a wide range of parameters and find that dynamical artifacts reported in previous PFC models do not occur in the present formalism. Additionally, we demonstrate the capacity of the proposed formalism for computing complex microstructures and defects such as dislocations, grain boundaries, and voids in solid-liquid-vapor systems, all of which are expected to be crucial for investigating rapid solidification processes.

We obtain an infinite-dimensional cone of singular twisted Hilbert spaces $Z(\varphi)$ which are isomorphic to their duals but not to their conjugate duals. We do that by showing that the subset of all bi-Lipschitz maps from $[0, \infty)$ to $\mathbb{R}$ is coneable. We also provide a characterization of the Kalton-Peck space among all twisted Hilbert spaces of the form $Z(\varphi)$, which gives a partial answer to a conjecture of F. Cabello S\'anchez and J. Castillo.

We present different techniques for applying Combinatorial Nullstellensatz to polynomials over finite fields. For examples, we generalize theorems from Noga Alon's paper on the subject, and present a few of our own.

The central regions of the Milky Way constitute a unique laboratory for a wide swath of astrophysical studies, consequently the inner $\sim$400 pc has been the target of numerous large surveys at all accessible wavelengths. In this paper we present a catalog of sources at 25 and 37 $\mu$m located within all of the regions observed with the SOFIA/FORCAST instrument in the inner $\sim$200 pc of the Galaxy. The majority of the observations were obtained as part of the SOFIA Cycle 7 Galactic Center Legacy program survey, which was designed to complement the Spitzer/MIPS 24 $\mu$m catalog in regions saturated in the MIPS observations. Due to the wide variety of source types captured by our observations at 25 and 37 $\mu$m, we do not limit the FORCAST source catalog to unresolved point sources, or treat all sources as if they are point-like sources. The catalog includes all detectable sources in the regions, resulting in a catalog of 950 sources, including point sources, compact sources, and extended sources. We also provide the user with metrics to discriminate between the source types., Comment: 29 pages, 13 figures, Accepted to ApJ

We give further evidence that the matrix-tensor model studied in \cite{belin2023} is dual to AdS$_{3}$ gravity including the sum over topologies. This provides a 3D version of the duality between JT gravity and an ensemble of random Hamiltonians, in which the matrix and tensor provide random CFT$_2$ data subject to a potential that incorporates the bootstrap constraints. We show how the Feynman rules of the ensemble produce a sum over all three-manifolds and how surgery is implemented by the matrix integral. The partition functions of the resulting 3d gravity theory agree with Virasoro TQFT (VTQFT) on a fixed, hyperbolic manifold. However, on non-hyperbolic geometries, our 3d gravity theory differs from VTQFT, leading to a difference in the eigenvalue statistics of the associated ensemble. As explained in \cite{belin2023}, the Schwinger-Dyson (SD) equations of the matrix-tensor integral play a crucial role in understanding how gravity emerges in the limit that the ensemble localizes to exact CFT's. We show how the SD equations can be translated into a combinatorial problem about three-manifolds., Comment: Equations 1.1 and 2.1 corrected. Section 3.1 revised. Typos fixed and references added. 75 pages

Human children far exceed modern machine learning algorithms in their sample efficiency, achieving high performance in key domains with much less data than current models. This ''data gap'' is a key challenge both for building intelligent artificial systems and for understanding human development. Egocentric video capturing children's experience -- their ''training data'' -- is a key ingredient for comparison of humans and models and for the development of algorithmic innovations to bridge this gap. Yet there are few such datasets available, and extant data are low-resolution, have limited metadata, and importantly, represent only a small set of children's experiences. Here, we provide the first release of the largest developmental egocentric video dataset to date -- the BabyView dataset -- recorded using a high-resolution camera with a large vertical field-of-view and gyroscope/accelerometer data. This 493 hour dataset includes egocentric videos from children spanning 6 months - 5 years of age in both longitudinal, at-home contexts and in a preschool environment. We provide gold-standard annotations for the evaluation of speech transcription, speaker diarization, and human pose estimation, and evaluate models in each of these domains. We train self-supervised language and vision models and evaluate their transfer to out-of-distribution tasks including syntactic structure learning, object recognition, depth estimation, and image segmentation. Although performance in each scales with dataset size, overall performance is relatively lower than when models are trained on curated datasets, especially in the visual domain. Our dataset stands as an open challenge for robust, humanlike AI systems: how can such systems achieve human-levels of success on the same scale and distribution of training data as humans?, Comment: 9 pages, 2 figures, 4 tables and SI. Submitted to NeurIPS Datasets and Benchmarks

We investigate the failure of the Stone-Weierstrass theorem focusing on the existence of large dimensional vector spaces within the set $\mathcal{C}(L, \mathbb{K}) \setminus \overline{\mathcal{A}}$, where $L$ is a compact Hausdorff space and $\mathcal{A}$ is a self-adjoint subalgebra of $\mathcal{C}(L, \mathbb{K})$ that vanishes nowhere on $L$ but does not necessarily separate the points of $L$. We address the problem of finding the precise codimension of $\overline{\mathcal{A}}$ in a broad setting, which allows us to describe the lineability of $\mathcal{C}(L, \mathbb{K}) \setminus \overline{\mathcal{A}}$ in detail. Our analysis yields both affirmative and negative results regarding the lineability of this set. Furthermore, we also study the set $(\mathcal{C}(\partial{D}, \mathbb{C}) \setminus \overline{\text{Pol}(\partial{D})}) \cup \{0\}$, where $\text{Pol}(\partial{D})$ is the set of all complex polynomials in one variable restricted to the boundary of the unit disk. Recent lineability properties are also taken into account., Comment: This updated version of the manuscript includes corrections for typos, results and certain inaccuracies

We show how dynamic heterogeneities (DH), a hallmark of glass-forming materials, depend on chain flexibility and chain length in polymers. For highly flexible polymers, a relatively large number of monomers ($N_c\sim500$) undergo correlated motion at the glass transition temperature $T_g$, independent of molecular weight ($M$). In contrast, less flexible polymers show a complex $N_c(M)$ behaviour divided into three regimes, consistent with observation in both $T_g(M)$ and chain conformational structure. For short oligomers ($\lesssim$ 2 Kuhn steps), a transition from mainly $\it{inter}$molecular correlations and $N_c\sim 200$, to strongly $\it{intra}$molecular correlations and $N_c< 50$ (roughly the molecular size) is observed; for longer chains, $N_c$ increases weakly, before saturating. For poly(methyl methacrylate), a remarkable similarity is found between $N_c(M)$ and the $M$-dependent ratio of the activation barriers of the structural ($\alpha$) and secondary ($\beta$) relaxations. Our results suggest a link between the DH length-scale and the number of $\beta$ relaxation events jointly-activated to facilitate the $\alpha$ relaxation., Comment: Main manuscript: 8 pages, 5 figures; Supplementary: 9 pages, 8 figures and 1 table

Polymers are an effective test-bed for studying topological constraints in condensed matter due to a wide array of synthetically-available chain topologies. When linear and ring polymers are blended together, emergent rheological properties are observed as the blend can be more viscous than either of the individual components. This emergent behavior arises since ring-linear blends can form long-lived topological constraints as the linear polymers thread the ring polymers. Here, we demonstrate how the Gauss linking integral can be used to efficiently evaluate the relaxation of topological constraints in ring-linear polymer blends. For majority-linear blends, the relaxation rate of topological constraints depends primarily on reptation of the linear polymers, resulting in the diffusive time $\tau_{d,R}$ for rings of length $N_R$ blended with linear chains of length $N_l$ to scale as $\tau_{d,R}\sim N_R^2N_L^{3.4}$., Comment: 6 pages, 6 figures

Data is growing rapidly in volume and complexity. Proficiency in database query languages is pivotal for crafting effective queries. As coding assistants become more prevalent, there is significant opportunity to enhance database query languages. The Kusto Query Language (KQL) is a widely used query language for large semi-structured data such as logs, telemetries, and time-series for big data analytics platforms. This paper introduces NL2KQL an innovative framework that uses large language models (LLMs) to convert natural language queries (NLQs) to KQL queries. The proposed NL2KQL framework includes several key components: Schema Refiner which narrows down the schema to its most pertinent elements; the Few-shot Selector which dynamically selects relevant examples from a few-shot dataset; and the Query Refiner which repairs syntactic and semantic errors in KQL queries. Additionally, this study outlines a method for generating large datasets of synthetic NLQ-KQL pairs which are valid within a specific database contexts. To validate NL2KQL's performance, we utilize an array of online (based on query execution) and offline (based on query parsing) metrics. Through ablation studies, the significance of each framework component is examined, and the datasets used for benchmarking are made publicly available. This work is the first of its kind and is compared with available baselines to demonstrate its effectiveness.

Many existing benchmarks of large (multimodal) language models (LLMs) focus on measuring LLMs' academic proficiency, often with also an interest in comparing model performance with human test takers. While these benchmarks have proven key to the development of LLMs, they suffer from several limitations, including questionable measurement quality (e.g., Do they measure what they are supposed to in a reliable way?), lack of quality assessment on the item level (e.g., Are some items more important or difficult than others?) and unclear human population reference (e.g., To whom can the model be compared?). In response to these challenges, we propose leveraging knowledge from psychometrics - a field dedicated to the measurement of latent variables like academic proficiency - into LLM benchmarking. We make three primary contributions. First, we introduce PATCH: a novel framework for {P}sychometrics-{A}ssis{T}ed ben{CH}marking of LLMs. PATCH addresses the aforementioned limitations, presenting a new direction for LLM benchmark research. Second, we implement PATCH by measuring GPT-4 and Gemini-Pro-Vision's proficiency in 8th grade mathematics against 56 human populations. We show that adopting a psychometrics-based approach yields evaluation outcomes that diverge from those based on existing benchmarking practices. Third, we release 4 high-quality datasets to support measuring and comparing LLM proficiency in grade school mathematics and science against human populations.

SPECT can enable the quantification of activity uptake in lesions and at-risk organs in {\alpha}-particle-emitting radiopharmaceutical therapies ({\alpha}-RPTs). But this quantification is challenged by the low photon counts, complicated isotope physics, and the image-degrading effects in {\alpha}-RPT SPECT. Thus, strategies to optimize the SPECT system and protocol designs for the task of regional uptake quantification are needed. Objectively performing this task-based optimization requires a reliable (accurate and precise) regional uptake quantification method. Conventional reconstruction-based quantification (RBQ) methods have been observed to be erroneous for {\alpha}-RPT SPECT. Projection-domain quantification methods, which estimate regional uptake directly from SPECT projections, have demonstrated potential in providing reliable regional uptake estimates, but these methods assume constant uptake within the regions, an assumption that may not hold. To address these challenges, we propose WIN-PDQ, a Wiener-estimator-based projection-domain quantitative SPECT method. The method accounts for the heterogeneity within the regions of interest while estimating mean uptake. An early-stage evaluation of the method was conducted using 3D Monte Carlo-simulated SPECT of anthropomorphic phantoms with radium-223 uptake and lumpy-model-based intra-regional uptake heterogeneity. In this evaluation with phantoms of varying mean regional uptake and intra-regional uptake heterogeneity, the WIN-PDQ method yielded ensemble unbiased estimates and significantly outperformed both reconstruction-based and previously proposed projection-domain quantification methods. In conclusion, based on these preliminary findings, the proposed method is showing potential for estimating mean regional uptake in {\alpha}-RPTs and towards enabling the objective task-based optimization of SPECT system and protocol designs., Comment: The work has been accepted for publication in 2024 SPIE Medical Imaging conference proceedings

Radio signals propagating via the solar corona and solar wind are significantly affected by compressive waves, impacting properties of solar bursts as well as sources viewed through the turbulent solar atmosphere. While static fluctuations scatter radio waves elastically, moving, turbulent or oscillating density irregularities act to broaden the frequency of the scattered waves. Using a new anisotropic density fluctuation model from the kinetic scattering theory for solar radio bursts, we deduce the plasma velocities required to explain observations of spacecraft signal frequency broadening. The inferred velocities are consistent with motions that are dominated by the solar wind at distances $\gtrsim 10$ $R_\odot$, but the levels of frequency broadening for $\lesssim 10$ $R_\odot$ require additional radial speeds $\sim (100-300)$ km s$^{-1}$ and/or transverse speeds $\sim (20-70)$ km s$^{-1}$. The inferred radial velocities also appear consistent with the sound or proton thermal speeds, while the speeds perpendicular to the radial direction are consistent with non-thermal motions measured via coronal Doppler-line broadening, interpreted as Alfv\'enic fluctuations. Landau damping of parallel propagating ion-sound (slow MHD) waves allow an estimate of the proton heating rate. The energy deposition rates due to ion-sound wave damping peak at a heliocentric distance of $\sim(1-3)$ $R_\odot$ are comparable to the rates available from a turbulent cascade of Alfv\'enic waves at large scales, suggesting a coherent picture of energy transfer, via the cascade or/and parametric decay of Alfv\'en waves to the small scales where heating takes place., Comment: 27 pages, 5 figures, submitted to The Astrophysical Journal

We explicitly construct the states of the 2d free boson on the infinite line with specified asymptotic charges. The Minkowski CFT states derive from (the analytic continuation of) the shrinking limit of Euclidean angular quantization, wherein the superselection sector for fixed asymptotic charges corresponds to specific endpoint operators for the angular quantization on the sphere. When applied to string theory, we obtain a new class of fundamental strings that are neither open nor closed and which we dub "stretched strings". We describe constant-time snapshots of the worldsheets of the different types of stretched strings, and as a special case we find a heuristic picture of Maldacena's "long strings" in the $c=1$ string theory., Comment: 40 pages, 4 figures

$\alpha'$ corrections to near horizon dynamics of a Schwarzschild black hole in a large number of spacetime dimensions $D$ are governed by the worldsheet theory composed of the cigar CFT and the classical sigma model on the sphere at the horizon, along with a timelike-Liouville theory of central charge $26-D$. At leading order in weak string coupling, blackhole thermodynamics is insensitive to the details of timelike Liouville theory. In this limit, we use Lewkowycz-Maldacena-trick motivated infinitesimally off-shell closed string worldsheet formalism in [arxiv: 2310.02313] to calculate thermal entropy exactly in $\alpha'$. The leading term in $\alpha'\to 0$ limit and the first stingy correction of our result is in precise agreement with the target space Callan-Myers-Perry formula. Also, we point out a remarkable simplification at an ultra-low temperature of order $1/\sqrt{\alpha'D}$ and show that for a certain special set of vertex operators involving modes of the $D$ dimensional spacetime and the time-like Liouville theory, the resulting worldsheet theory is related to Virasoro minimal string., Comment: 29 pages, 2 figures

In this article, we investigate the existence of closed vector subspaces (i.e.spaceability) in various nonlinear subsets of Orlicz-Lorentz spaces $\Lambda_{\varphi,w}$, equipped with the Luxemburg norm. If a family of Orlicz functions $(\varphi_n)_{n=1}^{\infty}$ satisfies certain order relations with respect to a given Orlicz function $\varphi$, the subset of the order-continuous subspace $(\Lambda_{\varphi,w})_a$ whose elements do not belong to $\bigcup_{n=1}^{\infty}\Lambda_{\varphi_n,w}$ is spaceable, and even maximal-spaceable when $\varphi$ satisfies the $\Delta_2$-condition. We also show that this subset is either residual or empty. In addition, sufficient conditions for this subset not being $(\alpha, \beta)$-spaceable are provided. A similar analysis is also performed on the subset $\Lambda_{\varphi,w} \setminus (\Lambda_{\varphi,w})_a$ when $\varphi$ does not satisfy the $\Delta_2$-condition. The comparison between different Orlicz-Lorentz spaces is characterized via the generating pairs $(\varphi,w)$. For a fixed Orlicz function that satisfies the $\Delta_2^{\infty}$-condition, we provide a characterization of disjointly strictly singular inclusion operators between Orlicz-Lorentz spaces with different weights. As a consequence, there are certain subsets of Orlicz-Lorentz spaces on $[0,1]$ for which lineability problem is not valid. Moreover, various types of $(\alpha,\beta)$-lineability and pointwise lineability properties on other nonlinear subsets of Orlicz-Lorentz spaces are examined. These results extend a number of previously known results in Orlicz and Lorentz spaces., Comment: 38 pages

Learning general-purpose user representations based on user behavioral logs is an increasingly popular user modeling approach. It benefits from easily available, privacy-friendly yet expressive data, and does not require extensive re-tuning of the upstream user model for different downstream tasks. While this approach has shown promise in search engines and e-commerce applications, its fit for instant messaging platforms, a cornerstone of modern digital communication, remains largely uncharted. We explore this research gap using Snapchat data as a case study. Specifically, we implement a Transformer-based user model with customized training objectives and show that the model can produce high-quality user representations across a broad range of evaluation tasks, among which we introduce three new downstream tasks that concern pivotal topics in user research: user safety, engagement and churn. We also tackle the challenge of efficient extrapolation of long sequences at inference time, by applying a novel positional encoding method., Comment: SIGIR 2024

This paper studies ML systems that interactively learn from users across multiple subpopulations with heterogeneous data distributions. The primary objective is to provide specialized services for different user groups while also predicting user preferences. Once the users select a service based on how well the service anticipated their preference, the services subsequently adapt and refine themselves based on the user data they accumulate, resulting in an iterative, alternating minimization process between users and services (learning dynamics). Employing such tailored approaches has two main challenges: (i) Unknown user preferences: Typically, data on user preferences are unavailable without interaction, and uniform data collection across a large and diverse user base can be prohibitively expensive. (ii) Suboptimal Local Solutions: The total loss (sum of loss functions across all users and all services) landscape is not convex even if the individual losses on a single service are convex, making it likely for the learning dynamics to get stuck in local minima. The final outcome of the aforementioned learning dynamics is thus strongly influenced by the initial set of services offered to users, and is not guaranteed to be close to the globally optimal outcome. In this work, we propose a randomized algorithm to adaptively select very few users to collect preference data from, while simultaneously initializing a set of services. We prove that under mild assumptions on the loss functions, the expected total loss achieved by the algorithm right after initialization is within a factor of the globally optimal total loss with complete user preference data, and this factor scales only logarithmically in the number of services. Our theory is complemented by experiments on real as well as semi-synthetic datasets.