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This work explores the relationship between state space methods and Koopman operator-based methods for predicting the time-evolution of nonlinear dynamical systems. We demonstrate that extended dynamic mode decomposition with dictionary learning (EDMD-DL), when combined with a state space projection, is equivalent to a neural network representation of the nonlinear discrete-time flow map on the state space. We highlight how this projection step introduces nonlinearity into the evolution equations, enabling significantly improved EDMD-DL predictions. With this projection, EDMD-DL leads to a nonlinear dynamical system on the state space, which can be represented in either discrete or continuous time. This system has a natural structure for neural networks, where the state is first expanded into a high dimensional feature space followed by a linear mapping which represents the discrete-time map or the vector field as a linear combination of these features. Inspired by these observations, we implement several variations of neural ordinary differential equations (ODEs) and EDMD-DL, developed by combining different aspects of their respective model structures and training procedures. We evaluate these methods using numerical experiments on chaotic dynamics in the Lorenz system and a nine-mode model of turbulent shear flow, showing comparable performance across methods in terms of short-time trajectory prediction, reconstruction of long-time statistics, and prediction of rare events. We also show that these methods provide comparable performance to a non-Markovian approach in terms of prediction of extreme events.

Behind the scenes of maintaining the safety of technology products from harmful and illegal digital content lies unrecognized human labor. The recent rise in the use of generative AI technologies and the accelerating demands to meet responsible AI (RAI) aims necessitates an increased focus on the labor behind such efforts in the age of AI. This study investigates the nature and challenges of content work that supports RAI efforts, or "RAI content work," that span content moderation, data labeling, and red teaming -- through the lived experiences of content workers. We conduct a formative survey and semi-structured interview studies to develop a conceptualization of RAI content work and a subsequent framework of recommendations for providing holistic support for content workers. We validate our recommendations through a series of workshops with content workers and derive considerations for and examples of implementing such recommendations. We discuss how our framework may guide future innovation to support the well-being and professional development of the RAI content workforce., Comment: To be presented at CSCW 2025

Elastoinertial turbulence (EIT) is a chaotic state that emerges in the flows of dilute polymer solutions. Direct numerical simulation (DNS) of EIT is highly computationally expensive due to the need to resolve the multi-scale nature of the system. While DNS of 2D EIT typically requires $O(10^6)$ degrees of freedom, we demonstrate here that a data-driven modeling framework allows for the construction of an accurate model with 50 degrees of freedom. We achieve a low-dimensional representation of the full state by first applying a viscoelastic variant of proper orthogonal decomposition to DNS results, and then using an autoencoder. The dynamics of this low-dimensional representation are learned using the neural ODE method, which approximates the vector field for the reduced dynamics as a neural network. The resulting low-dimensional data-driven model effectively captures short-time dynamics over the span of one correlation time, as well as long-time dynamics, particularly the self-similar, nested traveling wave structure of 2D EIT in the parameter range considered.

Complex chaotic dynamics, seen in natural and industrial systems like turbulent flows and weather patterns, often span vast spatial domains with interactions across scales. Accurately capturing these features requires a high-dimensional state space to resolve all the time and spatial scales. For dissipative systems the dynamics lie on a finite-dimensional manifold with fewer degrees of freedom. Thus, by building reduced-order data-driven models in manifold coordinates, we can capture the essential behavior of chaotic systems. Unfortunately, these tend to be formulated globally rendering them less effective for large spatial systems. In this context, we present a data-driven low-dimensional modeling approach to tackle the complexities of chaotic motion, Markovian dynamics, multi-scale behavior, and high numbers of degrees of freedom within large spatial domains. Our methodology involves a parallel scheme of decomposing a spatially extended system into a sequence of local `patches', and constructing a set of coupled, local low-dimensional dynamical models for each patch. Here, we choose to construct the set of local models using autoencoders (for constructing the low-dimensional representation) and neural ordinary differential equations, NODE, for learning the evolution equation. Each patch, or local model, shares the same underlying functions (e.g., autoencoders and NODEs) due to the spatial homogeneity of the underlying systems we consider. We apply this method to the Kuramoto-Sivashinsky equation and 2D Kolmogorov flow, and reduce state dimension by up to two orders of magnitude while accurately capturing both short-term dynamics and long-term statistics.

Generative artificial intelligence has shown promise in prompting virtual worlds into existence, yet little attention has been given to understanding how this process unfolds as social interaction. We present Social Conjurer, a framework for AI-augmented dynamic 3D scene co-creation, where multiple users collaboratively build and modify virtual worlds in real-time. Through an expanded set of interactions, including social and tool-based engagements as well as spatial reasoning, our framework facilitates the creation of rich, diverse virtual environments. Findings from a preliminary user study (N=12) provide insight into the user experience of this approach, how social contexts shape the prompting of spatial environments, and perspective on social applications of prompt-based 3D co-creation. In addition to highlighting the potential of AI-supported multi-user world creation and offering new pathways for AI-augmented creative processes in VR, this article presents a set of implications for designing human-centered interfaces that incorporate AI models into 3D content generation., Comment: 27 pages + Appendix, 16 figures; fixed some minor UTF-8 encoding issues in arXiv compilation

Could belief in AI predictions be just another form of superstition? This study investigates psychological factors that influence belief in AI predictions about personal behavior, comparing it to belief in astrology- and personality-based predictions. Through an experiment with 238 participants, we examined how cognitive style, paranormal beliefs, AI attitudes, personality traits, and other factors affect perceived validity, reliability, usefulness, and personalization of predictions from different sources. Our findings reveal that belief in AI predictions is positively correlated with belief in predictions based on astrology and personality psychology. Notably, paranormal beliefs and positive attitudes about AI significantly increased perceived validity, reliability, usefulness, and personalization of AI predictions. Conscientiousness was negatively correlated with belief in predictions across all sources, and interest in the prediction topic increased believability across predictions. Surprisingly, we found no evidence that cognitive style has an impact on belief in fictitious AI-generated predictions. These results highlight the "rational superstition" phenomenon in AI, where belief is driven more by mental heuristics and intuition than critical evaluation. This research advances our understanding of the psychology of human-AI interaction, offering insights into designing and promoting AI systems that foster appropriate trust and skepticism, critical for responsible integration in an increasingly AI-driven world.

The simulation of turbulent flow requires many degrees of freedom to resolve all the relevant times and length scales. However, due to the dissipative nature of the Navier-Stokes equations, the long-term dynamics are expected to lie on a finite-dimensional invariant manifold with fewer degrees of freedom. In this study, we build low-dimensional data-driven models of pressure-driven flow through a circular pipe. We impose the `shift-and-reflect' symmetry to study the system in a minimal computational cell (e.g., smallest domain size that sustains turbulence) at a Reynolds number of 2500. We build these models by using autoencoders to parametrize the manifold coordinates and neural ODEs to describe their time evolution. Direct numerical simulations (DNS) typically require on the order of O(105) degrees of freedom, while our data-driven framework enables the construction of models with fewer than 20 degrees of freedom. Remarkably, these reduced order models effectively capture crucial features of the flow, including the streak breakdown. In short-time tracking, these models accurately track the true trajectory for one Lyapunov time, while at long-times, they successfully capture key aspects of the dynamics such as Reynolds stresses and energy balance. Additionally, we report a library of exact coherent states (ECS) found in the DNS with the aid of these low-dimensional models. This approach leads to the discovery of seventeen previously unknown solutions within the turbulent pipe flow system, notably featuring relative periodic orbits characterized by the longest reported periods for such flow conditions.

We explore the application of large language models (LLMs), pre-trained models with massive textual data for detecting and improving these altered states. We investigate the use of LLMs to estimate attention states, sleep stages, and sleep quality and generate sleep improvement suggestions and adaptive guided imagery scripts based on electroencephalogram (EEG) and physical activity data (e.g. waveforms, power spectrogram images, numerical features). Our results show that LLMs can estimate sleep quality based on human textual behavioral features and provide personalized sleep improvement suggestions and guided imagery scripts; however detecting attention, sleep stages, and sleep quality based on EEG and activity data requires further training data and domain-specific knowledge.

The Koopman operator enables the analysis of nonlinear dynamical systems through a linear perspective by describing time evolution in the infinite-dimensional space of observables. Here this formalism is applied to shear flows, specifically the minimal flow unit plane Couette flow and a nine-dimensional model of turbulent shear flow between infinite parallel free-slip walls under a sinusoidal body force (Moehlis et al., New J. Phys. 6, 56 (2004)). We identify a finite set of observables and approximate the Koopman operator using neural networks, following the method developed by Constante-Amores et al., Chaos, 34(4), 043119 (2024). Then the time evolution is determined with a method here denoted as "Projected Koopman Dynamics". Using a high-dimensional approximate Koopman operator directly for the plane Couette system is computationally infeasible due to the high state space dimension of direct numerical simulations (DNS). However, the long-term dynamics of the dissipative Navier-Stokes equations are expected to live on a lower-dimensional invariant manifold. Motivated by this fact, we perform dimension reduction on the DNS data with a variant of the IRMAE-WD (implicit rank-minimizing autoencoder-weight decay) autoencoder (Zeng et al., MLST 5(2), 025053 (2024)) before applying the Koopman approach. We compare the performance of data-driven state space (neural ordinary differential equation) and Projected Koopman Dynamics approaches in manifold coordinates for plane Couette flow. Projected Koopman Dynamics effectively captures the chaotic behavior of Couette flow and the nine-dimensional model, excelling in both short-term tracking and long-term statistical analysis, outperforming other frameworks applied to these shear flows.

The ESO public survey VISTA Variables in the V\'ia L\'actea (VVV) surveyed the inner Galactic bulge and the adjacent southern Galactic disk from $2009-2015$. Upon its conclusion, the complementary VVV eXtended (VVVX) survey has expanded both the temporal as well as spatial coverage of the original VVV area, widening it from $562$ to $1700$ sq. deg., as well as providing additional epochs in $JHK_{\rm s}$ filters from $2016-2023$. With the completion of VVVX observations during the first semester of 2023, we present here the observing strategy, a description of data quality and access, and the legacy of VVVX. VVVX took $\sim 2000$ hours, covering about 4% of the sky in the bulge and southern disk. VVVX covered most of the gaps left between the VVV and the VISTA Hemisphere Survey (VHS) areas and extended the VVV time baseline in the obscured regions affected by high extinction and hence hidden from optical observations. VVVX provides a deep $JHK_{\rm s}$ catalogue of $\gtrsim 1.5\times10^9$ point sources, as well as a $K_{\rm s}$ band catalogue of $\sim 10^7$ variable sources. Within the existing VVV area, we produced a $5D$ map of the surveyed region by combining positions, distances, and proper motions of well-understood distance indicators such as red clump stars, RR Lyrae, and Cepheid variables. In March 2023 we successfully finished the VVVX survey observations that started in 2016, an accomplishment for ESO Paranal Observatory upon 4200 hours of observations for VVV+VVVX. The VVV+VVVX catalogues complement those from the Gaia mission at low Galactic latitudes and provide spectroscopic targets for the forthcoming ESO high-multiplex spectrographs MOONS and 4MOST., Comment: 17 pages, 11 figures (+ appendix). Accepted for publication in Astronomy and Astrophysics in section 14: Catalogs and data

Many fundamental parameters of biological systems -- eg. productivity, population sizes and biomass -- are most effectively expressed in absolute terms. In contrast to proportional data (eg. percentages), absolute values provide standardised metrics on the functioning of biological entities (eg. organisism, species, ecosystems). These are particularly valuable when comparing assemblages across time and space. Since it is almost always impractical to count entire populations, estimates of population abundances require a sampling method that is both accurate and precise. Such absolute abundance estimates typically entail more "sampling effort" (data collection time) than proportional data. Here we refined a method of absolute abundance estimates -- the "exotic marker technique" -- by producing a variant that is more efficient without losing accuracy. This new method, the "field-of-view subsampling method" (FOVS method) is based on area subsampling, from which large samples can be quickly extrapolated. Two case studies of the exotic marker technique were employed: 1, computer simulations; and 2, an observational "real world" data set of terrestrial organic microfossils from the Permian- and Triassic-aged rock strata of southeastern Australia, spiked with marker grains of known quantity and variance. We compared the FOVS method against the traditional "linear method" method using three metrics: 1, concentration (specimens/gram of sediment); 2, precision and 3, data collection effort. In almost all cases, the FOVS method delivers higher precision than the linear method, with equivalent effort, and our computer simulations suggest that the FOVS method more accurately estimates the true error for large target-to-marker ratios. Since we predict that these conditions are typically common, we recommend the new FOVS method in almost every "real world" case., Comment: 103 pages, of which 67 pages constitutes the main text, and the remaining 36 pages are Supporting Information. 9 figures. The code for the related simulations can be found via a link in the manuscript

PLATO (PLAnetary Transits and Oscillations of stars) is ESA's M3 mission designed to detect and characterise extrasolar planets and perform asteroseismic monitoring of a large number of stars. PLATO will detect small planets (down to <2 R_(Earth)) around bright stars (<11 mag), including terrestrial planets in the habitable zone of solar-like stars. With the complement of radial velocity observations from the ground, planets will be characterised for their radius, mass, and age with high accuracy (5 %, 10 %, 10 % for an Earth-Sun combination respectively). PLATO will provide us with a large-scale catalogue of well-characterised small planets up to intermediate orbital periods, relevant for a meaningful comparison to planet formation theories and to better understand planet evolution. It will make possible comparative exoplanetology to place our Solar System planets in a broader context. In parallel, PLATO will study (host) stars using asteroseismology, allowing us to determine the stellar properties with high accuracy, substantially enhancing our knowledge of stellar structure and evolution. The payload instrument consists of 26 cameras with 12cm aperture each. For at least four years, the mission will perform high-precision photometric measurements. Here we review the science objectives, present PLATO's target samples and fields, provide an overview of expected core science performance as well as a description of the instrument and the mission profile at the beginning of the serial production of the flight cameras. PLATO is scheduled for a launch date end 2026. This overview therefore provides a summary of the mission to the community in preparation of the upcoming operational phases.

A family of leaderless, decentralized consensus protocols, called Snow consensus was introduced in a recent whitepaper by Yin et al. These protocols address limitations of existing consensus methods, such as those using proof-of-work or quorums, by utilizing randomization and maintaining some level of resilience against Byzantine participants. Crucially, Snow consensus underpins the Avalanche blockchain, which provides a popular cryptocurrency and a platform for running smart contracts. Snow consensus algorithms are built on a natural, randomized routine, whereby participants continuously sample subsets of others and adopt an observed majority value until consensus is achieved. Additionally, Snow consensus defines conditions based on participants' local views and security parameters. These conditions indicate when a party can confidently finalize its local value, knowing it will be adopted by honest participants. Although Snow consensus algorithms can be formulated concisely, there is a complex interaction between randomization, adversarial influence, and security parameters, which requires a formal analysis of their security and liveness. Snow protocols form the foundation for Avalanche-type blockchains, and this work aims to increase our understanding of such protocols by providing insights into their liveness and safety characteristics. First, we analyze these Snow protocols in terms of latency and security. Second, we expose a design issue where the trade-off between these two is unfavorable. Third, we propose a modification of the original protocol where this trade-off is much more favorable.

The accurate simulation of complex dynamics in fluid flows demands a substantial number of degrees of freedom, i.e. a high-dimensional state space. Nevertheless, the swift attenuation of small-scale perturbations due to viscous diffusion permits in principle the representation of these flows using a significantly reduced dimensionality. Over time, the dynamics of such flows evolve towards a finite-dimensional invariant manifold. Using only data from direct numerical simulations, in the present work we identify the manifold and determine evolution equations for the dynamics on it. We use an advanced autoencoder framework to automatically estimate the intrinsic dimension of the manifold and provide an orthogonal coordinate system. Then, we learn the dynamics by determining an equation on the manifold by using both a function space approach (approximating the Koopman operator) and a state space approach (approximating the vector field on the manifold). We apply this method to exact coherent states for Kolmogorov flow and minimal flow unit pipe flow. Fully resolved simulations for these cases require O(103) and O(105) degrees of freedom respectively, and we build models with two or three degrees of freedom that faithfully capture the dynamics of these flows. For these examples, both the state space and function space time evaluations provide highly accurate predictions of the long-time dynamics in manifold coordinates., Comment: 10 pages

DAG-based protocols have been proposed as potential solutions to the latency and throughput limitations of traditional permissionless consensus protocols. However, their adoption has been hindered by security concerns and a lack of a solid foundation to guarantee improvements in both throughput and latency. In this paper, we present a construction that rigorously demonstrates how DAG-based protocols can achieve superior throughput and latency compared to chain-based consensus protocols, all while maintaining the same level of security guarantees.

We introduce a novel method for real-time animation control and generation on rigged models using natural language input. First, we embed a large language model (LLM) in Unity to output structured texts that can be parsed into diverse and realistic animations. Second, we illustrate LLM's potential to enable flexible state transition between existing animations. We showcase the robustness of our approach through qualitative results on various rigged models and motions., Comment: Accepted to NeurIPS Workshop on ML for Creativity and Design 2023

The rise of AI conversational agents has broadened opportunities to enhance human capabilities across various domains. As these agents become more prevalent, it is crucial to investigate the impact of different affective abilities on their performance and user experience. In this study, we surveyed 745 respondents to understand the expectations and preferences regarding affective skills in various applications. Specifically, we assessed preferences concerning AI agents that can perceive, respond to, and simulate emotions across 32 distinct scenarios. Our results indicate a preference for scenarios that involve human interaction, emotional support, and creative tasks, with influences from factors such as emotional reappraisal and personality traits. Overall, the desired affective skills in AI agents depend largely on the application's context and nature, emphasizing the need for adaptability and context-awareness in the design of affective AI conversational agents.

Data-driven approximations of the Koopman operator are promising for predicting the time evolution of systems characterized by complex dynamics. Among these methods, the approach known as extended dynamic mode decomposition with dictionary learning (EDMD-DL) has garnered significant attention. Here we present a modification of EDMD-DL that concurrently determines both the dictionary of observables and the corresponding approximation of the Koopman operator. This innovation leverages automatic differentiation to facilitate gradient descent computations through the pseudoinverse. We also address the performance of several alternative methodologies. We assess a 'pure' Koopman approach, which involves the direct time-integration of a linear, high-dimensional system governing the dynamics within the space of observables. Additionally, we explore a modified approach where the system alternates between spaces of states and observables at each time step -- this approach no longer satisfies the linearity of the true Koopman operator representation. For further comparisons, we also apply a state space approach (neural ODEs). We consider systems encompassing two and three-dimensional ordinary differential equation systems featuring steady, oscillatory, and chaotic attractors, as well as partial differential equations exhibiting increasingly complex and intricate behaviors. Our framework significantly outperforms EDMD-DL. Furthermore, the state space approach offers superior performance compared to the 'pure' Koopman approach where the entire time evolution occurs in the space of observables. When the temporal evolution of the Koopman approach alternates between states and observables at each time step, however, its predictions become comparable to those of the state space approach.

We present Large Language Model for Mixed Reality (LLMR), a framework for the real-time creation and modification of interactive Mixed Reality experiences using LLMs. LLMR leverages novel strategies to tackle difficult cases where ideal training data is scarce, or where the design goal requires the synthesis of internal dynamics, intuitive analysis, or advanced interactivity. Our framework relies on text interaction and the Unity game engine. By incorporating techniques for scene understanding, task planning, self-debugging, and memory management, LLMR outperforms the standard GPT-4 by 4x in average error rate. We demonstrate LLMR's cross-platform interoperability with several example worlds, and evaluate it on a variety of creation and modification tasks to show that it can produce and edit diverse objects, tools, and scenes. Finally, we conducted a usability study (N=11) with a diverse set that revealed participants had positive experiences with the system and would use it again., Comment: 46 pages, 18 figures; Matching version accepted at CHI 2024

Traditional blockchains grant the miner of a block full control not only over which transactions but also their order. This constitutes a major flaw discovered with the introduction of decentralized finance and allows miners to perform MEV attacks. In this paper, we address the issue of sandwich attacks by providing a construction that takes as input a blockchain protocol and outputs a new blockchain protocol with the same security but in which sandwich attacks are not profitable. Furthermore, our protocol is fully decentralized with no trusted third parties or heavy cryptography primitives and carries a linear increase in latency and minimum computation overhead.

For the first time, the sulphur abundance relative to hydrogen (S/H) in the Narrow Line Regions of a sample of Seyfert 2 nuclei (Sy 2s) has been derived via direct estimation of the electron temperature. Narrow emission line intensities from the SDSS DR17 [in the wavelength range 3000 < $\lambda$ < 9100] and from the literature for a sample of 45 nearby ($z$ < 0.08) Sy 2s were considered. Our direct estimates indicate that Sy 2s have similar temperatures in the gas region where most of the S+ ions are located in comparison with that of star-forming regions (SFs). However, Sy 2s present higher temperature values ($\sim$10000 K) in the region where most of the S++ ions are located relative to that of SFs. We derive the total sulphur abundance in the range of 6.2 < 12 + log(S/H) < 7.5, corresponding to 0.1-1.8 times the solar value. These sulphur abundance values are lower by $\sim$0.4 dex than those derived in SFs with similar metallicity, indicating a distinct chemical enrichment of the ISM for these object classes. The S/O values for our Sy 2 sample present an abrupt ($\sim$0.5 dex) decrease with increasing O/H for the high metallicity regime [12 + log(O/H) > 8.7)], what is not seen for the SFs. However, when our Sy 2 estimates are combined with those from a large sample of star-forming regions, we did not find any dependence between S/O and O/H., Comment: Accepted for publication in MNRAS. 19 pages, 11 figures, 7 tables

We study the effect of insoluble surfactants on the impact of surfactant-free droplets on surfactant-laden thin liquid films via a fully three-dimensional direct numerical simulations approach that employs a hybrid interface-tracking/level-set method, and by taking into account surfactant-induced Marangoni stresses due to gradients in interfacial surfactant concentration. Our numerical predictions for the temporal evolution of the surfactant-free crown are validated against the experimental work by Che and Matar (2017). We focus on the crown-splash regime, and we observe that the crown dynamics evolves through various stages: from the the growth of linear modes (through a Rayleigh- Plateau instability) to the development of nonlinearities leading to primary and secondary breakup events (through droplet shedding modulated by an end-pinching mechanism). We show that the addition of surfactants does not affect the wave selection via the Rayleigh-Plateau instability. However, the presence of surfactants plays a key role in the late stages of the dynamics as soon as the ligaments are driven out from the rim. Surfactant-induced Marangoni stresses delay the end-pinching mechanisms to result in longer ligaments prior to their capillary singularity, while also promoting the spanwise merging between ligaments. Finally, we show that the addition of surfactants leads to surface rigidification and consequently to the retardation of the flow dynamics.

Avalanche is a blockchain consensus protocol with exceptionally low latency and high throughput. This has swiftly established the corresponding token as a top-tier cryptocurrency. Avalanche achieves such remarkable metrics by substituting proof of work with a random sampling mechanism. The protocol also differs from Bitcoin, Ethereum, and many others by forming a directed acyclic graph (DAG) instead of a chain. It does not totally order all transactions, establishes a partial order among them, and accepts transactions in the DAG that satisfy specific properties. Such parallelism is widely regarded as a technique that increases the efficiency of consensus. Despite its success, Avalanche consensus lacks a complete abstract specification and a matching formal analysis. To address this drawback, this work provides first a detailed formulation of Avalanche through pseudocode. This includes features that are omitted from the original whitepaper or are only vaguely explained in the documentation. Second, the paper gives an analysis of the formal properties fulfilled by Avalanche in the sense of a generic broadcast protocol that only orders related transactions. Last but not least, the analysis reveals a vulnerability that affects the liveness of the protocol. A possible solution that addresses the problem is also proposed.