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Ferguson's 1973 introduction of the Dirichlet process marked a breakthrough in Bayesian nonparametric statistics. For the first time, a prior on the space of probability measures fulfilled two key desiderata: large support and analytical tractability. In this paper, we review three complementary constructions of the Dirichlet process, whose roots can be traced back to Ferguson: through finite-dimensional distributions, via normalization of a gamma process, and through predictive distributions. Each perspective not only deepens the understanding of the Dirichlet process but also provides a template for generalizations, from normalized random measures with independent increments to Gibbs--type priors and beyond. Over the past fifty years, the Dirichlet process has become the cornerstone of Bayesian nonparametric methodology and applications, while simultaneously inspiring the expansion of the landscape of nonparametric priors. Since de Finetti laid out the Bayesian nonparametric framework in the 1930s, the key obstacle had been the absence of a tractable nonparametric prior. Ferguson's contribution overcame this challenge, providing a solution to a decades-long open problem. In recog

The seminal 2009 paper by Bernard, Krauth, and Wilson marked a paradigm shift in Monte Carlo sampling. By abandoning the restrictive condition of detailed balance in favor of the more fundamental principle of global balance, they introduced the Event-Chain Monte Carlo (ECMC) algorithm, which achieves rejection-free, deterministic sampling for hard spheres. This breakthrough demonstrated that persistent, directional dynamics could dramatically accelerate equilibration in dense particle systems. In this commentary, we review this foundational work and elucidate its underlying mechanism using the broader Event-Driven Monte Carlo (EDMC) framework developed in subsequent years. We show how the original hard-sphere concept naturally generalizes to continuous potentials and modern lifted Markov chain formalisms, transforming a surprising specific result into a powerful general class of sampling algorithms.

Loss curves are smooth during most of model training, so visible discontinuities stand out as possible conceptual breakthroughs. Studying these breakthroughs enables a deeper understanding of learning dynamics, but only when they are properly identified. This paper argues that similar breakthroughs occur frequently throughout training but they are obscured by a loss metric that collapses all variation into a single scalar. To find these hidden transitions, we introduce POLCA, a method for decomposing changes in loss along arbitrary bases of the low-rank training subspace. We use our method to identify clusters of samples that share similar changes in loss during training, disaggregating the overall loss into that of smaller groups of conceptually similar data. We validate our method on synthetic arithmetic and natural language tasks, showing that POLCA recovers clusters that represent interpretable breakthroughs in the model's capabilities. We demonstrate the promise of these hidden phase transitions as a tool for unsupervised interpretability.

Progress in science and technology is punctuated by disruptive innovation and breakthroughs. Researchers have characterized these disruptions to explore the factors that spark such innovations and to assess their long-term trends. However, although understanding disruptive breakthroughs and their drivers hinges upon accurately quantifying disruptiveness, the core metric used in previous studies -- the disruption index -- remains insufficiently understood and tested. Here, after demonstrating the critical shortcomings of the disruption index, including its conflicting evaluations for simultaneous discoveries, we propose a new, continuous measure of disruptiveness based on a neural embedding framework that addresses these limitations. Our measure not only better distinguishes disruptive works, such as Nobel Prize-winning papers, from others, but also reveals simultaneous disruptions by allowing us to identify the "twins" that have the most similar future context. By offering a more robust and precise lens for identifying disruptive innovations and simultaneous discoveries, our study provides a foundation for deepening insights into the mechanisms driving scientific breakthroughs whil

The article provides a brief description of the MathPartner service. This freely available cloud-based Mathematics is a universal system for symbolic-numeric calculations. Its Mathpar language is a subset of the LaTeX language, but allows you to create mathematical texts that contain "computable" mathematical operators. This opens up completely new opportunities for improving the educational process for all natural science disciplines, for the use of mathematics in scientific and engineering calculations. To save and freely exchange educational and other texts in the Mathpar language, a GitHub repository has been created. It is concluded that cloud mathematics MathPartner is a new breakthrough technology for school and university natural science education, for scientific and engineering applications.

Science is driven by community endeavors across diverse fields and specializations, forming a complex structure that renders conventional performance evaluation methods inadequate. Using established indicators, the network-based normalized citation score, and the disruptive index, combined with the GENEPY algorithm, we evaluate the complexity rank of countries based on their breakthrough performance across 89 subfields of physical sciences, drawing on nearly 60 million articles (1900-2023). This quality-focused integrated approach reveals pronounced asymmetries: while countries such as the United States, Israel, and several in Europe sustain long-term structural advantages, emerging nations show rapid gains in later decades. A power-law relationship between aggregated breakthrough performance and countries' R&D expenditure underscores the unequal and scale-dependent nature of global science. These results demonstrate that scientific advancement arises not from uniform growth but from asymmetric complexity, offering actionable insights for policymakers and funding agencies aiming to foster sustainable, high-quality research ecosystems.

3I/ATLAS, an interstellar object, made its closest approach to Earth on 2025 December 19. On 2025 December 18, the Breakthrough Listen program conducted a technosignature search toward 3I/ATLAS using the 100 m Robert C. Byrd Green Bank Telescope at 1-12 GHz. We report a nondetection of candidate signals down to the 100 mW level.

We implement a machine learning algorithm to search for extra-terrestrial technosignatures in radio observations of several hundred nearby stars, obtained with the Parkes and Green Bank Telescopes by the Breakthrough Listen collaboration. Advances in detection technology have led to an exponential growth in data, necessitating innovative and efficient analysis methods. This problem is exacerbated by the large variety of possible forms an extraterrestrial signal might take, and the size of the multidimensional parameter space that must be searched. It is then made markedly worse by the fact that our best guess at the properties of such a signal is that it might resemble the signals emitted by human technology and communications, the main (yet diverse) contaminant in radio observations. We address this challenge by using a combination of simulations and machine learning methods for anomaly detection. We rank candidates by how unusual they are in frequency, and how persistent they are in time, by measuring the similarity between consecutive spectrograms of the same star. We validate that our filters significantly improve the quality of the candidates that are selected for human vettin

Despite the usefulness of machine learning approaches for the early screening of potential breakthrough technologies, their practicality is often hindered by opaque models. To address this, we propose an interpretable machine learning approach to predicting future citation counts from patent texts using a patent-specific hierarchical attention network (PatentHAN) model. Central to this approach are (1) a patent-specific pre-trained language model, capturing the meanings of technical words in patent claims, (2) a hierarchical network structure, enabling detailed analysis at the claim level, and (3) a claim-wise self-attention mechanism, revealing pivotal claims during the screening process. A case study of 35,376 pharmaceutical patents demonstrates the effectiveness of our approach in early screening of potential breakthrough technologies while ensuring interpretability. Furthermore, we conduct additional analyses using different language models and claim types to examine the robustness of the approach. It is expected that the proposed approach will enhance expert-machine collaboration in identifying breakthrough technologies, providing new insight derived from text mining into tech

When conflicting images are presented to either eye, binocular fusion is disrupted. Rather than experiencing a blend of both percepts, often only one eye's image is experienced, whilst the other is suppressed from awareness. Importantly, suppression is transient - the two rival images compete for dominance, with stochastic switches between mutually exclusive percepts occurring every few seconds with law-like regularity. From the perspective of dynamical systems theory, visual rivalry offers an experimentally tractable window into the dynamical mechanisms governing perceptual awareness. In a recently developed visual rivalry paradigm - tracking continuous flash suppression (tCFS) - it was shown that the transition between awareness and suppression is hysteretic, with a higher contrast threshold required for a stimulus to breakthrough suppression into awareness than to be suppressed from awareness. Here, we present an analytically-tractable model of visual rivalry that quantitatively explains the hysteretic transition between periods of awareness and suppression in tCFS. Grounded in the theory of neural dynamics, we derive closed-form expressions for the duration of perceptual domina

Climate models must simulate hundreds of future scenarios for hundreds of years at coarse resolutions, and a handful of high-resolution decadal simulations to resolve localized extreme events. Using Oceananigans.jl, written from scratch in Julia, we report several achievements: First, a global ocean simulation with breakthrough horizontal resolution -- 488m -- reaching 15 simulated days per day (0.04 simulated years per day; SYPD). Second, Oceananigans simulates the global ocean at 488m with breakthrough memory efficiency on just 768 Nvidia A100 GPUs, a fraction of the resources available on current and upcoming exascale supercomputers. Third, and arguably most significant for climate modeling, Oceananigans achieves breakthrough energy efficiency reaching 0.95 SYPD at 1.7 km on 576 A100s and 9.9 SYPD at 10 km on 68 A100s -- the latter representing the highest horizontal resolutions employed by current IPCC-class ocean models. Routine climate simulations with 10 km ocean components are within reach.

Real world data is an increasingly utilized resource for post-market monitoring of vaccines and provides insight into real world effectiveness. However, outside of the setting of a clinical trial, heterogeneous mechanisms may drive observed breakthrough infection rates among vaccinated individuals; for instance, waning vaccine-induced immunity as time passes and the emergence of a new strain against which the vaccine has reduced protection. Analyses of infection incidence rates are typically predicated on a presumed mechanism in their choice of an "analytic time zero" after which infection rates are modeled. In this work, we propose an explicit test for driving mechanism situated in a standard Cox proportional hazards framework. We explore the test's performance in simulation studies and in an illustrative application to real world data. We additionally introduce subgroup differences in infection incidence and evaluate the impact of time zero misspecification on bias and coverage of model estimates. In this study we observe strong power and controlled type I error of the test to detect the correct infection-driving mechanism under various settings. Similar to previous studies, we f

Reactive flows in porous media play an important role in our life and are crucial for many industrial, environmental and biomedical applications. Very often the concentration of the species at the inlet is known, and the so-called breakthrough curves, measured at the outlet, are the quantities which could be measured or computed numerically. The measurements and the simulations could be time-consuming and expensive, and machine learning and Big Data approaches can help to predict breakthrough curves at lower costs. Machine learning (ML) methods, such as Gaussian processes and fully-connected neural networks, and a tensor method, cross approximation, are well suited for predicting breakthrough curves. In this paper, we demonstrate their performance in the case of pore scale reactive flow in catalytic filters.

The Breakthrough Listen search for intelligent life is, to date, the most extensive technosignature search of nearby celestial objects. We present a radio technosignature search of the centers of 97 nearby galaxies, observed by Breakthrough Listen at the Robert C. Byrd Green Bank Telescope. We performed a narrowband Doppler drift search using the turboSETI pipeline with a minimum signal-to-noise parameter threshold of 10, across a drift rate range of $\pm$ 4 Hz\ $s^{-1}$, with a spectral resolution of 3 Hz and a time resolution of $\sim$ 18.25 s. We removed radio frequency interference by using an on-source/off-source cadence pattern of six observations and discarding signals with Doppler drift rates of 0. We assess factors affecting the sensitivity of the Breakthrough Listen data reduction and search pipeline using signal injection and recovery techniques and apply new methods for the investigation of the RFI environment. We present results in four frequency bands covering 1 -- 11 GHz, and place constraints on the presence of transmitters with equivalent isotropic radiated power on the order of $10^{26}$ W, corresponding to the theoretical power consumption of Kardashev Type II ci

The Breakthrough Listen Initiative is conducting a program using multiple telescopes around the world to search for "technosignatures": artificial transmitters of extraterrestrial origin from beyond our solar system. The VERITAS Collaboration joined this program in 2018, and provides the capability to search for one particular technosignature: optical pulses of a few nanoseconds duration detectable over interstellar distances. We report here on the analysis and results of dedicated VERITAS observations of Breakthrough Listen targets conducted in 2019 and 2020 and of archival VERITAS data collected since 2012. Thirty hours of dedicated observations of 136 targets and 249 archival observations of 140 targets were analyzed and did not reveal any signals consistent with a technosignature. The results are used to place limits on the fraction of stars hosting transmitting civilizations. We also discuss the minimum-pulse sensitivity of our observations and present VERITAS observations of CALIOP: a space-based pulsed laser onboard the CALIPSO satellite. The detection of these pulses with VERITAS, using the analysis techniques developed for our technosignature search, allows a test of our a

The article presents three advanced citation-based methods used to detect potential breakthrough papers among very highly cited papers. We approach the detection of such papers from three different perspectives in order to provide different typologies of breakthrough papers. In all three cases we use the classification of scientific publications developed at CWTS based on direct citation relationships. This classification establishes clusters of papers at three levels of aggregation. Papers are clustered based on their similar citation orientations and it is assumed that they are focused on similar research interests. We use the clustering as the context for detecting potential breakthrough papers. We utilize the Characteristics Scores and Scales (CSS) approach to partition citation distributions and implement a specific filtering algorithm to sort out potential highly-cited followers, papers not considered breakthroughs in themselves. After invoking thresholds and filtering, three methods are explored: A very exclusive one where only the highest cited paper in a micro-cluster is considered as a potential breakthrough paper (M1); as well as two conceptually different methods, one t

Classical law and economics is foundational to the American legal system. Centered at the University of Chicago, its assumptions, most especially that humans act both rationally and selfishly, informs the thinking of legislatures, judges, and government lawyers, and has shaped nearly every aspect of the way commercial transactions are conducted. But what if the Chicago School, as I refer to this line of thinking, is wrong? Alternative approaches such as behavioral law and economics or law and political economy contend that human decisionmaking is based on emotions or should not be regulated as a social geometry of bargains. This Article proposes a different and wholly novel reason that the Chicago School is wrong: a fundamental assumption central to many of its game theory models has been disproven. This Article shows that a 2012 breakthrough from world famous physicist Freeman Dyson shocked the world of game theory. This Article shows that Chicago School game theorists are wrong on their own terms because these 2 x 2 games such as the Prisoner's Dilemma, Chicken, and Snowdrift, ostensibly based on mutual defection and corrective justice, in fact yield to an insight of pure coopera

Axion dark matter (DM) may efficiently convert to photons in the magnetospheres of neutron stars (NSs), producing nearly monochromatic radio emission. This process is resonantly triggered when the plasma frequency induced by the underlying charge distribution approximately matches the axion mass. We search for evidence of this process using archival Green Bank Telescope data collected in a survey of the Galactic Center in the C-Band by the Breakthrough Listen project. While Breakthrough Listen aims to find signatures of extraterrestrial life in the radio band, we show that their high-frequency resolution spectral data of the Galactic Center region is ideal for searching for axion-photon transitions generated by the population of NSs in the inner pc of the Galaxy. We use data-driven models to capture the distributions and properties of NSs in the inner Galaxy and compute the expected radio flux from each NS using state-of-the-art ray tracing simulations. We find no evidence for axion DM and set leading constraints on the axion-photon coupling, excluding values down to the level $g_{a γγ} \sim 10^{-11}$ GeV$^{-1}$ for DM axions for masses between 15 and 35 $μ$eV.

Anomalous behavior is ubiquitous in subsurface solute transport due to the presence of high degrees of heterogeneity at different scales in the media. Although fractional models have been extensively used to describe the anomalous transport in various subsurface applications, their application is hindered by computational challenges. Simpler nonlocal models characterized by integrable kernels and finite interaction length represent a computationally feasible alternative to fractional models; yet, the informed choice of their kernel functions still remains an open problem. We propose a general data-driven framework for the discovery of optimal kernels on the basis of very small and sparse data sets in the context of anomalous subsurface transport. Using spatially sparse breakthrough curves recovered from fine-scale particle-density simulations, we learn the best coarse-scale nonlocal model using a nonlocal operator regression technique. Predictions of the breakthrough curves obtained using the optimal nonlocal model show good agreement with fine-scale simulation results even at locations and time intervals different from the ones used to train the kernel, confirming the excellent ge