This paper studies a discrete-time major-minor mean field game of stopping where the major player can choose either an optimal control or stopping time. We look for the relaxed equilibrium as a randomized stopping policy, which is formulated as a fixed point of a set-valued mapping, whose existence is challenging by direct arguments. To overcome the difficulties caused by the presence of a major player, we propose to study an auxiliary problem by considering entropy regularization in the major player's problem while formulating the minor players' optimal stopping problems as linear programming over occupation measures. We first show the existence of regularized equilibria as fixed points of some simplified set-valued operator using the Kakutani-Fan-Glicksberg fixed-point theorem. Next, we prove that the regularized equilibrium converges as the regularization parameter $λ$ tends to 0, and the limit corresponds to a fixed point of the original operator, thereby confirming the existence of a relaxed equilibrium in the original mean field game problem. We also extend this entropy regularization method to the mean-field game problem where the minor players choose optimal controls.
We use stellar mass functions to study the properties and the significance of quenching through major galaxy mergers. In addition to SDSS DR7 and Galaxy Zoo 1 data, we use samples of visually selected major galaxy mergers and post merger galaxies. We determine the stellar mass functions of the stages that we would expect major merger quenched galaxies to pass through on their way from the blue cloud to the red sequence: 1: major merger, 2: post merger, 3: blue early type, 4: green early type and 5: red early type. Based on the similar mass function shapes we conclude that major mergers are likely to form an evolutionary sequence from star formation to quiescence via quenching. Relative to all blue galaxies, the major merger fraction increases as a function of stellar mass. Major merger quenching is inconsistent with the mass and environment quenching model. At z~0 major merger quenched galaxies are unlikely to constitute the majority of galaxies that transition the green valley. Furthermore, between z~0-0.5 major merger quenched galaxies account for 1-5% of all quenched galaxies at a given stellar mass. Major galaxy mergers are therefore not a significant quenching pathway, neither
A new study from Northern Arizona University is raising red flags about a widely used global emissions database from Climate TRACE, a consortium co-founded by Al Gore。 Researchers found that the database may be dramatically undercounting carbon dioxide emissions from cars and trucks in cities—by an average of 70% across 260 U。 cities, with some cit
A bold claim that the universe’s accelerating expansion was an illusion has been put to the test—and failed。 Researchers found that the study behind the controversy made key mistakes when analyzing supernova data。 After revisiting the evidence, astronomers concluded that cosmic acceleration remains as strong as ever
The local curvature of the space produced by the Sun causes not only the perihelion precession of Mercury's elliptical orbit, but also the variations of the whole orbit, in comparison with those predicted by the Newtonian theory of gravitation. Calculations show that the gravitational major-axis contraction of the Mercury's elliptical orbit is 1.3 kilometers which can be confirmed by the present astronomical distance measurement technology.
(abridged abstract) We present an analysis of the stellar mass growth over the last 10 Gyrs using a large 3.6$μ$ selected sample. We split our sample into active (blue) and quiescent (red) galaxies. Our measurements of the K-LFs and LD evolution support the idea that a large fraction of galaxies is already assembled at $z\sim 1.2$. Based on the analysis of the evolution of the stellar mass-to-light ratio (in K-band) for the spectroscopic sub-sample, we derive the stellar mass density for the entire sample. We find that the global evolution of the stellar mass density is well reproduced by the star formation rate derived from UV dust corrected measurements. Over the last 8Gyrs, we observe that the stellar mass density of the active population remains approximately constant while it gradually increases for the quiescent population over the same timescale. As a consequence, the growth of the stellar mass in the quiescent population must be due to the shutoff of star formation in active galaxies that migrate into the quiescent population. From $z=2$ to $z=1.2$, we observe a major build-up of the quiescent population with an increase by a factor of 10 in stellar mass, suggesting that we
Black hole entropy is identified with the counting of the dynamical degrees of freedom of trapped gravitational modes continually sourced by the Hawking-Unruh process. In the context of linear perturbations of Schwarzschild spacetime the density of states is derived from the orthogonality of states in the solution space of the Regge-Wheeler-Zerilli equation. The otherwise divergent energy and entropy is cutoff by the Planck scale closest approach of constantly accelerating observers near the horizon. The thermal distribution of the trapped modes, which represent shape fluctuations in the near horizon geometry, store a significant fraction of the spacetime mass as observed from far away. Unlike quasi-normal modes the modes are not directly observable outside of $\sim 3 M$ but, being external to the horizon, they affect the propagation of null rays near the black hole. The characteristic frequencies, around 100 Hz for solar mass black holes, are discussed in relation to possible observations.
Recent hydrodynamical simulations have shown that circumbinary gas disks drive the orbits of binary black holes to become eccentric, even when general relativistic corrections to the orbit are significant. Here, we study the general relativistic (GR) apsidal precession of eccentric equal-mass binary black holes in circumbinary disks (CBDs) via two-dimensional hydrodynamical simulations. We perform a suite of simulations comparing precessing and non-precessing binaries across a range of eccentricities, semi-major axes, and precession rates. We find that the GR precession of the binary's semi-major axis can introduce a dominant modulation in the binary's accretion rate and the corresponding high-energy electromagnetic light-curves. We discuss the conditions under which this occurs and its detailed characteristics and mechanism. Finally, we discuss the potential to observe these precession signatures in electromagnetic and gravitational wave (GW) observations, as well as the precession signal's unique importance as a potential tool to constrain the mass, eccentricity, and semi-major axis of binary merger events.
We show that, for many choices of finite tuples of generators $X = (x_1, \dots , x_d)$ of a tracial von Neumann algebra $(M, τ)$ satisfying certain decomposition properties (non-primeness, possessing a Cartan subalgebra, or property $Γ$), one can find a diffuse, hyperfinite subalgebra $N \subseteq (W^*(X))^ω$ (often in $W^*(X)$ itself), such that $W^*(N,X+\sqrt{t}S) = W^*(N,X,S)$ for all $t > 0$. (Here $S$ is a free semicircular family, free from $\{X\} \cup N$). This gives a short non-microstates proof of strong 1-boundedness for such algebras.
We develop a theoretical framework to describe how zero-photon detection may be utilized to enhance laser cooling via the anti-Stokes interaction and, somewhat surprisingly, enable cooling via the Stokes interaction commonly associated with heating. Our description includes both pulsed and continuous measurements as well as optical detection efficiency and open-system dynamics. For both cases, we discuss how the cooling depends on the system parameters such as detection efficiency and optomechanical cooperativity, and we study the continuous-measurement-induced dynamics, contrasting to single-photon detection events. For the Stokes case, we explore the interplay between cooling and heating via optomechanical parametric amplification, and we find the efficiency required to cool a mechanical oscillator via zero-photon detection. This work serves as a companion article to the recent experiment [E. A. Cryer-Jenkins, K. D. Major, et al., arXiv:2408.01734 (2024)], which demonstrated enhanced laser cooling of a mechanical oscillator via zero-photon detection on the anti-Stokes signal. The framework developed here provides new approaches for cooling mechanical resonators that can be applie
Soliton-like localised wave solutions in a two-dimensional Fermi superfluid are studied by solving the Bogoliubov-de Gennes equations in the BCS regime of weak pairing interactions. The dispersion relations of these solitons are found to exhibit a peculiar swallow-tail shape, with cusps and multiple branches. The effective mass of the solitons is found to diverge and change sign at the cusp. This behavior is in contrast to the smooth dispersion relations and negative effective masses of solitons in the three-dimensional Fermi superfluid. The swallow-tail dispersion relations are shown to be a consequence of counterflow of the superfluid and sign-changing contributions to the superfluid current from different transverse momenta in the Bogoliubov-de Gennes formalism. The results are relevant for the understanding of solitonic excitations in two-dimensional Fermi superfluids, such as ultracold atomic gases and high-temperature superconductors.
The Burrows-Wheeler Transform (BWT) is a string transformation technique widely used in areas such as bioinformatics and file compression. Many applications combine a run-length encoding (RLE) with the BWT in a way which preserves the ability to query the compressed data efficiently. However, these methods may not take full advantage of the compressibility of the BWT as they do not modify the alphabet ordering for the sorting step embedded in computing the BWT. Indeed, any such alteration of the alphabet ordering can have a considerable impact on the output of the BWT, in particular on the number of runs. For an alphabet $Σ$ containing $σ$ characters, the space of all alphabet orderings is of size $σ!$. While for small alphabets an exhaustive investigation is possible, finding the optimal ordering for larger alphabets is not feasible. Therefore, there is a need for a more informed search strategy than brute-force sampling the entire space, which motivates a new heuristic approach. In this paper, we explore the non-trivial cases for the problem of minimizing the size of a run-length encoded BWT (RLBWT) via selecting a new ordering for the alphabet. We show that random sampling of th
Accessing and understanding contemporary and historical events of global impact such as the US elections and the Olympic Games is a major prerequisite for cross-lingual event analytics that investigate event causes, perception and consequences across country borders. In this paper, we present the Open Event Knowledge Graph (OEKG), a multilingual, event-centric, temporal knowledge graph composed of seven different data sets from multiple application domains, including question answering, entity recommendation and named entity recognition. These data sets are all integrated through an easy-to-use and robust pipeline and by linking to the event-centric knowledge graph EventKG. We describe their common schema and demonstrate the use of the OEKG at the example of three use cases: type-specific image retrieval, hybrid question answering over knowledge graphs and news articles, as well as language-specific event recommendation. The OEKG and its query endpoint are publicly available.
The purpose of this study is to analyse COVID-19 related news published across different geographical places, in order to gain insights in reporting differences. The COVID-19 pandemic had a major outbreak in January 2020 and was followed by different preventive measures, lockdown, and finally by the process of vaccination. To date, more comprehensive analysis of news related to COVID-19 pandemic are missing, especially those which explain what aspects of this pandemic are being reported by newspapers inserted in different economies and belonging to different political alignments. Since LDA is often less coherent when there are news articles published across the world about an event and you look answers for specific queries. It is because of having semantically different content. To address this challenge, we performed pooling of news articles based on information retrieval using TF-IDF score in a data processing step and topic modeling using LDA with combination of 1 to 6 ngrams. We used VADER sentiment analyzer to analyze the differences in sentiments in news articles reported across different geographical places. The novelty of this study is to look at how COVID-19 pandemic was r
Autonomous driving has become real; semi-autonomous driving vehicles in an affordable price range are already on the streets, and major automotive vendors are actively developing full self-driving systems to deploy them in this decade. Before rolling the products out to the end-users, it is critical to test and ensure the safety of the autonomous driving systems, consisting of multiple layers intertwined in a complicated way. However, while safety-critical bugs may exist in any layer and even across layers, relatively little attention has been given to testing the entire driving system across all the layers. Prior work mainly focuses on white-box testing of individual layers and preventing attacks on each layer. In this paper, we aim at holistic testing of autonomous driving systems that have a whole stack of layers integrated in their entirety. Instead of looking into the individual layers, we focus on the vehicle states that the system continuously changes in the driving environment. This allows us to design DriveFuzz, a new systematic fuzzing framework that can uncover potential vulnerabilities regardless of their locations. DriveFuzz automatically generates and mutates driving
In this paper, we introduce and investigate the neighborhood of binary self-dual codes. We prove that there is no better Type I code than the best Type II code of the same length. Further, we give some new necessary conditions for the existence of a singly-even $(56,28,12)$-code and a doubly-even $(72,36,16)$-code.
We consider the stability of the maximally-extended Reissner-Nordström solution in a Minkowski, de Sitter, or anti-de Sitter background. In a broad class of situations, prior work has shown that spherically symmetric perturbations from a massless scalar field cause the inner horizon of an RN black hole to become singular and collapse. Even if this is the case, it may still be possible for an observer to travel through the inner horizon before it fully collapses, thus violating strong cosmic censorship. In this work, we show that the collapse of the inner horizon and the occurrence of a singularity along the inner horizon are sufficient to prevent an observer from accessing the white hole regions and the parallel universe regions of the maximally extended RN space-time. Thus, if an observer passes through the inner horizon, they will inevitably hit the central singularity. Throughout this article, we use natural units where c = G = 4 π ε_0 = 1.
A new study suggests Southern California's major fault system is more stressed than at any point in the last 1,000 years。 Researchers found that the Cajon Pass, where the San Andreas and San Jacinto faults meet, could act as an “earthquake gate” that determines whether a future rupture spreads across both faults。 Current conditions resemble those t
One of the most celebrated claims about Yellowstone’s wolves is facing a major challenge。 Scientists say the study behind the famous trophic cascade story relied on flawed methods that overstated the ecological impact of wolf recovery。 Their reanalysis found no evidence for a dramatic, park-wide surge in willow growth
Researchers have created a new way to reconstruct the evolutionary history of complex plant genomes by analyzing genetic traces left by transposable elements。 The technique revealed that modern strawberries were assembled through multiple ancient genome-merging events, shedding new light on how major crop species evolved