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Building on results of Medvedev, we construct a $\mathsf{ZFC}$ example of a non-Polish topological group that is countable dense homogeneous. Our example is a dense subgroup of $\mathbb{Z}^\omega$ of size $\mathfrak{b}$ that is a $\lambda$-set. We also conjecture that every countable dense homogenous Baire topological group with no isolated points contains a copy of the Cantor set, and give a proof in a very special case., Comment: 7 pages

The landscape of digital servitization in the manufacturing sector is evolving, marked by a strategic shift from traditional product-centric to platform business models (BMs). Manufacturing firms often employ a blend of approaches to develop business-to-business (B2B) platforms, leading to significant reconfigurations in their BMs. However, they frequently encounter failures in their B2B platform development initiatives, leading them to abandon initial efforts and pivot to alternative platform strategies. Therefore, this study, through an in-depth case study of a manufacturer in the energy sector, articulates a three-phase pivoting framework for B2B platform BMs, including platform development and platform strategy. Initially, the manufacturer focused on asset-based product sales supplemented by asset maintenance services and followed an emergent platformization strategy characterized by the rise of multiple, independent B2B platforms catering to diverse functions. Next, focusing on the imposed customer journey strategy, the firm shifted towards a strategic multi-platform integration into an all-encompassing platform supported by artificial intelligence (AI), signaling a maturation of the platform BM to combine a wide range of services into an energy-performance-based contract. Finally, the last step of the firm's platform BM evolution consisted of a deliberate platform strategy open to external stakeholders and enveloping its data-driven offerings within a broader platform ecosystem. This article advances B2B platform BMs and digital servitization literature, highlighting the efficacy of a progressive approach and strategic pivoting.

The ABCT variety is defined as the closure of the image of $G(2,n)$ under the Veronese map. We realize the ABCT variety $V(3,n)$ as the determinantal variety of a vector bundle morphism. We use this to give a recursive formula for the fundamental class of $V(3,n)$. As an application, we show that special Schubert coefficients of this class are given by Eulerian numbers, matching a formula by Cachazo-He-Yuan. On the way to this, we prove that the variety of configuration of points on a common divisor on a smooth variety is reduced and irreducible, generalizing a result of Caminata-Moon-Schaffler., Comment: 20 pages

We address the issues of decoherence, frustrated hops and internal consistency in surface hopping. We demonstrate that moving away from an independent-trajectory picture is the strategy which allows us to propose a robust surface hopping scheme overcoming all these issues at once. Based on the exact factorization and on the idea of coupled trajectories, we consider the swarm of trajectories, that mimic the nuclear dynamics in nonadiabatic processes, as a unique entity. In this way, imposing energy conservation of the swarm and allowing the trajectories to share energy when hops occur clearly indicates the route towards a new surface hopping scheme. Encouraging results are reported, in terms of electronic and vibrational time-dependent properties on the photodynamics of fulvene, modeled with a full-dimensional linear vibronic coupling Hamiltonian.

Multimodal data integration and label scarcity pose significant challenges for machine learning in medical settings. To address these issues, we conduct an in-depth evaluation of the newly proposed Multimodal Variational Mixture-of-Experts (MMVM) VAE on the challenging MIMIC-CXR dataset. Our analysis demonstrates that the MMVM VAE consistently outperforms other multimodal VAEs and fully supervised approaches, highlighting its strong potential for real-world medical applications., Comment: Findings paper presented at Machine Learning for Health (ML4H) symposium 2024, December 15-16, 2024, Vancouver, Canada, 13 pages. arXiv admin note: text overlap with arXiv:2403.05300

In this paper, we first show that current learning-based video codecs, specifically the SSF codec, are not suitable for real-world applications due to the mismatch between the encoder and decoder caused by floating-point round-off errors. To address this issue, we propose the static quantization of the hyper prior decoding path. The quantization parameters are determined through an exhaustive search of all possible combinations of observers and quantization schemes from PyTorch. For the SSF codec, when encoding and decoding on different machines, the proposed solution effectively mitigates the mismatch issue and enhances compression efficiency results by preventing severe image quality degradation. When encoding and decoding are performed on the same machine, it constrains the average BD-rate increase to 9.93% and 9.02% for UVG and HEVC-B sequences, respectively., Comment: 4 pages, submitted to ISCAS2025

We introduce a new method that extracts knowledge from a large language model (LLM) to produce object-level plans, which describe high-level changes to object state, and uses them to bootstrap task and motion planning (TAMP) in a hierarchical manner. Existing works use LLMs to either directly output task plans or to generate goals in representations like PDDL. However, these methods fall short because they either rely on the LLM to do the actual planning or output a hard-to-satisfy goal. Our approach instead extracts knowledge from a LLM in the form of plan schemas as an object level representation called functional object-oriented networks (FOON), from which we automatically generate PDDL subgoals. Our experiments demonstrate how our method's performance markedly exceeds alternative planning strategies across several tasks in simulation., Comment: 11 pages (6 pages + 1 page references + 4 pages appendix)

Every polygon with n vertices in the complex projective plane is naturally associated with its adjoint curve of degree n-3. Hence the adjoint of a heptagon is a plane quartic. We prove that a general plane quartic is the adjoint of exactly 864 distinct complex heptagons. This number had been numerically computed by Kohn et al. We use intersection theory and the Scorza correspondence for quartics to show that 864 is an upper bound, complemented by a lower bound obtained through explicit analysis of the famous Klein quartic., Comment: 18 pages, 1 figure

We model the Hartree-exchange-correlation potential of Kohn-Sham density-functional theory adopting a novel strategy inspired by the strictly-correlated-electrons limit and relying on the exact decomposition of the potential based on the exact factorization formalism. Starting with accurate density and conditional potential for a one-dimensional model of a stretched heteronuclear molecule, we provide a proof-of-principle example of an approximation that accurately reproduces the step of the exact Kohn-Sham potential without resorting to the Kohn-Sham orbitals, virtual or occupied. We also test our strategy using the approximate conditional potentials corresponding to the strictly-correlated-electron and the exact-exchange functionals. The results are encouraging in that the initial approximations are modified in the qualitatively correct way: decreasing correlation in the former and increasing it in the latter.

Answer Sentence Selection (AS2) is a critical task for designing effective retrieval-based Question Answering (QA) systems. Most advancements in AS2 focus on English due to the scarcity of annotated datasets for other languages. This lack of resources prevents the training of effective AS2 models in different languages, creating a performance gap between QA systems in English and other locales. In this paper, we introduce new high-quality datasets for AS2 in five European languages (French, German, Italian, Portuguese, and Spanish), obtained through supervised Automatic Machine Translation (AMT) of existing English AS2 datasets such as ASNQ, WikiQA, and TREC-QA using a Large Language Model (LLM). We evaluated our approach and the quality of the translated datasets through multiple experiments with different Transformer architectures. The results indicate that our datasets are pivotal in producing robust and powerful multilingual AS2 models, significantly contributing to closing the performance gap between English and other languages.

A search for full energy depositions from bosonic keV-scale dark matter candidates of masses between 65 keV and 1021 keV has been performed with data collected during Phase II of the GERmanium Detector Array (GERDA) experiment. Our analysis includes direct dark matter absorption as well as dark Compton scattering. With a total exposure of 105.5 kg yr, no evidence for a signal above the background has been observed. The resulting exclusion limits deduced with either Bayesian or Frequentist statistics are the most stringent direct constraints in the major part of the 140-1021 keV mass range. As an example, at a mass of 150 keV the dimensionless coupling of dark photons and axion-like particles to electrons has been constrained to $\alpha$'/$\alpha$ < 8.7x10$^{-24}$ and g$_{ae}$ < 3.3x10$^{-12}$ at 90% credible interval (CI), respectively. Additionally, a search for peak-like signals from beyond the Standard Model decays of nucleons and electrons is performed. We find for the inclusive decay of a single neutron in $^{76}$Ge a lower lifetime limit of $\tau_n$ > 1.5x10$^{24}$ yr and for a proton $\tau_p$ > 1.3x10$^{24}$ yr at 90% CI. For the electron decay e$^-\rightarrow\nu_e\gamma$ a lower limit of $\tau_e$ > 5.4x10$^{25}$ yr at 90% CI has been determined., Comment: 20 pages, 12 figures, 7 tables

This report summarizes some considerations on possible evolutions of grant-free random access in the next generation of the 3GPP wireless cellular standard. The analysis is carried out by mapping the problem to the recently-introduced unsourced multiple access channel (UMAC) setup. By doing so, the performance of existing solutions can be benchmarked with information-theoretic bounds, assessing the potential gains that can be achieved over legacy 3GPP schemes. The study focuses on the two-step random access (2SRA) protocol introduced by Release 16 of the 5G New Radio standard, investigating its applicability to support large MTC / IoT terminal populations in a grant-free fashion. The analysis shows that the existing 2SRA scheme may not succeed in providing energy-efficient support to large user populations. Modifications to the protocol are proposed that enable remarkable gains in both energy and spectral efficiency while retaining a strong resemblance to the legacy protocol., Comment: Version 1.0 of the report

Graph Neural Networks (GNNs) are emerging as a formidable tool for processing non-euclidean data across various domains, ranging from social network analysis to bioinformatics. Despite their effectiveness, their adoption has not been pervasive because of scalability challenges associated with large-scale graph datasets, particularly when leveraging message passing. To tackle these challenges, we introduce NeuraChip, a novel GNN spatial accelerator based on Gustavson's algorithm. NeuraChip decouples the multiplication and addition computations in sparse matrix multiplication. This separation allows for independent exploitation of their unique data dependencies, facilitating efficient resource allocation. We introduce a rolling eviction strategy to mitigate data idling in on-chip memory as well as address the prevalent issue of memory bloat in sparse graph computations. Furthermore, the compute resource load balancing is achieved through a dynamic reseeding hash-based mapping, ensuring uniform utilization of computing resources agnostic of sparsity patterns. Finally, we present NeuraSim, an open-source, cycle-accurate, multi-threaded, modular simulator for comprehensive performance analysis. Overall, NeuraChip presents a significant improvement, yielding an average speedup of 22.1x over Intel's MKL, 17.1x over NVIDIA's cuSPARSE, 16.7x over AMD's hipSPARSE, and 1.5x over prior state-of-the-art SpGEMM accelerator and 1.3x over GNN accelerator. The source code for our open-sourced simulator and performance visualizer is publicly accessible on GitHub https://neurachip.us, Comment: Visit https://neurachip.us for WebGUI based simulations

All spaces are assumed to be separable and metrizable. Building on work of van Engelen, Harrington, Michalewski and Ostrovsky, we obtain the following results: (1) Every finite-dimensional analytic space is $\sigma$-homogeneous with analytic witnesses, (2) Every finite-dimensional analytic space is $\sigma$-homogeneous with pairwise disjoint $\mathbf{\Delta}^1_2$ witnesses. Furthermore, the complexity of the witnesses is optimal in both of the above results. This completes the picture regarding $\sigma$-homogeneity in the finite-dimensional realm. It is an open problem whether every analytic space is $\sigma$-homogeneous. We also investigate finite unions of homogeneous spaces., Comment: 10 pages. arXiv admin note: text overlap with arXiv:2107.07747

Variational Autoencoders for multimodal data hold promise for many tasks in data analysis, such as representation learning, conditional generation, and imputation. Current architectures either share the encoder output, decoder input, or both across modalities to learn a shared representation. Such architectures impose hard constraints on the model. In this work, we show that a better latent representation can be obtained by replacing these hard constraints with a soft constraint. We propose a new mixture-of-experts prior, softly guiding each modality's latent representation towards a shared aggregate posterior. This approach results in a superior latent representation and allows each encoding to preserve information better from its uncompressed original features. In extensive experiments on multiple benchmark datasets and two challenging real-world datasets, we show improved learned latent representations and imputation of missing data modalities compared to existing methods., Comment: Accepted at Neurips 2024

We analyze the effects of next-to-eikonal corrections on dijet production in Deep Inelastic Scattering off nuclear targets in the framework of the Color Glass Condensate. They require the knowledge of correlators of fields in the target beyond those computed in the standard McLerran-Venugopalan model, specifically those between transverse and boost-enhanced components, and of the recoil of the fields. We neglect the latter, while for the former we develop a linear model valid for large nuclei. We considered the unpolarized cross sections for dijet production in the approximation of a homogenous dilute nucleus, obtaining simple analytic expressions for the cross sections at nex-to-eikonal accuracy, valid in the limit of total dijet momentum and dijet momentum imbalance larger than the saturation scale of the nucleus. We perform a numerical study of the results at energies of the Electron Ion Collider, finding $\mathcal{O}(10\%)$ effects in the cross sections at large total momentum. We also analyze the azimuthal asymmetries between total momentum and imbalance, finding that non-eikonal corrections induce odd azimuthal harmonics for the situation of jets with equal momentum fractions from the virtual photon, where they are absent in the eikonal approximation. Finally, in the eikonal approximation we have compared the results of our analytic expansion valid in the dilute limit of the target, and the full Color Glass Condensate results in the McLerran-Venugopalan model and their correlation limit. Our analytic expressions match the correlation limit ones in the region where both should be simultaneously valid and reproduce very well the full Color Glass Condensate results in its validity region., Comment: 28 pages, 15 figures

As custom hardware accelerators become more prevalent, it becomes increasingly important to automatically generate efficient host-driver code that can fully leverage the capabilities of these accelerators. This approach saves time and reduces the likelihood of errors that can occur during manual implementation. AXI4MLIR extends the MLIR compiler framework to generate host-driver code for custom accelerators for linear algebra problems. By leveraging specific compiler optimizations, we can further increase accelerator utilization. In this work we offer two key observations through a MatMul accelerator case study. First, the accelerator's compute core utilization is less than 10%, and second, the critical latency bottleneck is caused by copying data between the heap and memory-mapped DMA buffers. We identify a set of missing host code optimizations to improve the under-utilization and the latency bottleneck. Therefore, we propose three key host-code data-movement-related optimizations, extending AXI4MLIR. The optimizations provide DMA-based data allocation, coalescing of DMA transfers, and pipelining of the accelerator's load, compute, and store stages.

Let $\mathcal{L}$ be a first-order two-sorted language and consider a class of $\mathcal{L}$-structures of the form $\langle M, X \rangle$ where $M$ varies among structures of the first sort, while $X$ is fixed in the second sort, and it is assumed to be a compact Hausdorff space. When $X$ is a compact subset of the real line, one way to treat classes of this kind model-theoretically is via continuous-valued logic, as in [Ben Yaacov-Berenstein-Henson-Usvyatsov 2010]. Prior to that, Henson and Iovino proposed an approach based on the notion of positive formulas [Henson-Iovino 2002]. Their work is tailored to the model theory of Banach spaces. Here we show that a similar approach is possible for a more general class of models. We introduce suitable versions of elementarity, compactness, saturation, quantifier elimination and other basic tools, and we develop basic model theory.

We study low-energy dynamics generated by a two-dimensional two-state Jahn-Teller Hamiltonian in the vicinity of a conical intersection using quantum wavepacket and trajectories dynamics. Recently, these dynamics were studied by comparing the adiabatic representation and the exact factorization, with the purpose to highlight the different nature of topological- and geometric-phase effects arising in the two theoretical representation of the same problem. Here, we employ the exact factorization to understand how to model accurately low-energy dynamics in the vicinity of a conical intersection using an approximate description of the nuclear motion that uses trajectories. We find that, since nonadiabatic effects are weak but non-negligible, the trajectory-based description that invokes the classical approximation struggles to capture the correct behavior.

Study Objectives: Polysomnography (PSG) currently serves as the benchmark for evaluating sleep disorders. Its discomfort makes long-term monitoring unfeasible, leading to bias in sleep quality assessment. Hence, less invasive, cost-effective, and portable alternatives need to be explored. One promising contender is the in-ear-EEG sensor. This study aims to establish a methodology to assess the similarity between the single-channel in-ear-EEG and standard PSG derivations. Methods: The study involves four-hour signals recorded from ten healthy subjects aged 18 to 60 years. Recordings are analyzed following two complementary approaches: (i) a hypnogram-based analysis aimed at assessing the agreement between PSG and in-ear-EEG-derived hypnograms; and (ii) a feature-based analysis based on time- and frequency- domain feature extraction, unsupervised feature selection, and definition of Feature-based Similarity Index via Jensen-Shannon Divergence (JSD-FSI). Results: We find large variability between PSG and in-ear-EEG hypnograms scored by the same sleep expert according to Cohen's kappa metric, with significantly greater agreements for PSG scorers than for in-ear-EEG scorers (p < 0.001) based on Fleiss' kappa metric. On average, we demonstrate a high similarity between PSG and in-ear-EEG signals in terms of JSD-FSI (0.79 +/- 0.06 -awake, 0.77 +/- 0.07 -NREM, and 0.67 +/- 0.10 -REM) and in line with the similarity values computed independently on standard PSG-channel-combinations. Conclusions: In-ear-EEG is a valuable solution for home-based sleep monitoring, however further studies with a larger and more heterogeneous dataset are needed., Comment: 20 figures, 6 tables

In task and motion planning (TAMP), the ambiguity and underdetermination of abstract descriptions used by task planning methods make it difficult to characterize physical constraints needed to successfully execute a task. The usual approach is to overlook such constraints at task planning level and to implement expensive sub-symbolic geometric reasoning techniques that perform multiple calls on unfeasible actions, plan corrections, and re-planning until a feasible solution is found. We propose an alternative TAMP approach that unifies task and motion planning into a single heuristic search. Our approach is based on an object-centric abstraction of motion constraints that permits leveraging the computational efficiency of off-the-shelf AI heuristic search to yield physically feasible plans. These plans can be directly transformed into object and motion parameters for task execution without the need of intensive sub-symbolic geometric reasoning.

This paper addresses the need for automatic and efficient generation of host driver code for arbitrary custom AXI-based accelerators targeting linear algebra algorithms, an important workload in various applications, including machine learning and scientific computing. While existing tools have focused on automating accelerator prototyping, little attention has been paid to the host-accelerator interaction. This paper introduces AXI4MLIR, an extension of the MLIR compiler framework designed to facilitate the automated generation of host-accelerator driver code. With new MLIR attributes and transformations, AXI4MLIR empowers users to specify accelerator features (including their instructions) and communication patterns and exploit the host memory hierarchy. We demonstrate AXI4MLIR's versatility across different types of accelerators and problems, showcasing significant CPU cache reference reductions (up to 56%) and up to a 1.65x speedup compared to manually optimized driver code implementations. AXI4MLIR implementation is open-source and available at: https://github.com/AXI4MLIR/axi4mlir., Comment: 13 pages, 17 figures, to appear in CGO2024

This work investigates spanwise wall oscillation (SWO) as a method to preferentially enhance heat transfer over drag in turbulent channel flow. Direct numerical simulations at $Re_\tau=180$ and $\Pr=1$ show set of wall-oscillation parameters reducing drag also decrease heat transfer similarly, maintaining coupled transport. However, large period ($T^+=500$) and amplitude ($W^+=30$) induce substantially greater heat transfer intensification, increasing 15 % versus only 7.7 % drag rise. This Reynolds analogy breaking enables preferential elevation of heat transport over momentum. FIK identity analysis reveals negligible impact of forcing terms on dissimilarity. Instead, differences arise from the solenoidal velocity and linear temperature equations. Both the turbulent shear stress and heat flux are amplified near the wall under oscillation. However, the heat flux intensifies more substantially, especially at its peak. This preferential enhancement of the near-wall heat flux, exceeding the shear stress amplification, facilitates greater thermal transport augmentation relative to the friction increase. Results demonstrate that spanwise wall oscillation can preferentially intensify heat transfer beyond drag, providing a promising technique for improving heat exchanger. Further work should optimize the period and amplitude of the oscillation and elucidate the underlying physics of this dissimilar heat transfer control.

This report introduces a new family of multimodal models, Gemini, that exhibit remarkable capabilities across image, audio, video, and text understanding. The Gemini family consists of Ultra, Pro, and Nano sizes, suitable for applications ranging from complex reasoning tasks to on-device memory-constrained use-cases. Evaluation on a broad range of benchmarks shows that our most-capable Gemini Ultra model advances the state of the art in 30 of 32 of these benchmarks - notably being the first model to achieve human-expert performance on the well-studied exam benchmark MMLU, and improving the state of the art in every one of the 20 multimodal benchmarks we examined. We believe that the new capabilities of the Gemini family in cross-modal reasoning and language understanding will enable a wide variety of use cases. We discuss our approach toward post-training and deploying Gemini models responsibly to users through services including Gemini, Gemini Advanced, Google AI Studio, and Cloud Vertex AI.

Decision-makers often observe the occurrence of events through a reporting process. City governments, for example, rely on resident reports to find and then resolve urban infrastructural problems such as fallen street trees, flooded basements, or rat infestations. Without additional assumptions, there is no way to distinguish events that occur but are not reported from events that truly did not occur--a fundamental problem in settings with positive-unlabeled data. Because disparities in reporting rates correlate with resident demographics, addressing incidents only on the basis of reports leads to systematic neglect in neighborhoods that are less likely to report events. We show how to overcome this challenge by leveraging the fact that events are spatially correlated. Our framework uses a Bayesian spatial latent variable model to infer event occurrence probabilities and applies it to storm-induced flooding reports in New York City, further pooling results across multiple storms. We show that a model accounting for under-reporting and spatial correlation predicts future reports more accurately than other models, and further induces a more equitable set of inspections: its allocations better reflect the population and provide equitable service to non-white, less traditionally educated, and lower-income residents. This finding reflects heterogeneous reporting behavior learned by the model: reporting rates are higher in Census tracts with higher populations, proportions of white residents, and proportions of owner-occupied households. Our work lays the groundwork for more equitable proactive government services, even with disparate reporting behavior., Comment: To appear in the 38th Annual AAAI Conference on Artificial Intelligence (AAAI-24)